tag:blogger.com,1999:blog-16896186240187868482024-03-13T09:19:35.705-07:00Math: Challenges and Opportunities in the 21st CenturyThis blog is all about doing the best we possibly can while working within the confines of best practices, the CCSS, and differentiating/engaging content and methods to reach all students. If that is what you are about, by all means join in.Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.comBlogger54125tag:blogger.com,1999:blog-1689618624018786848.post-30187113946283360572021-02-11T18:49:00.004-08:002021-02-11T18:49:38.305-08:00What could be or could have been...<p><span style="font-family: georgia;"> </span></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody><tr><td style="text-align: center;"><a href="https://lh3.googleusercontent.com/-9SdLRxfjY0Q/YCXRrHlbjAI/AAAAAAAADME/NbMK_ozERIQAKni-RIdq5_nUR17YGq8cQCLcBGAsYHQ/image.png" style="margin-left: auto; margin-right: auto;"><span style="font-family: georgia;"><img data-original-height="183" data-original-width="275" height="213" src="https://lh3.googleusercontent.com/-9SdLRxfjY0Q/YCXRrHlbjAI/AAAAAAAADME/NbMK_ozERIQAKni-RIdq5_nUR17YGq8cQCLcBGAsYHQ/w320-h213/image.png" width="320" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"></td></tr></tbody></table><span style="font-family: georgia;"><b></b></span><p></p><div style="text-align: center;"><b><b><span style="font-family: georgia; font-size: large;"> </span></b></b></div><div style="text-align: center;"><b><b><span style="font-family: georgia; font-size: large;"><br /></span></b></b></div><div style="text-align: center;"><b><b><span style="font-family: georgia; font-size: large;">In a Year What are Going to</span></b></b></div><p></p><p></p><div style="text-align: center;"><b><span style="font-family: georgia; font-size: large;"> Remember from COVID?</span></b></div><span style="font-family: georgia;"><br /></span><p></p><p style="text-align: center;"><i><span style="font-family: georgia;">What could be or could have been...</span></i></p><p style="text-align: center;"><i><span style="font-family: georgia;"><br /></span></i></p><p style="text-align: center;"><i><span style="font-family: georgia;"><br /></span></i></p><p><span style="font-family: georgia;">In a field like education it is easy to say change happens quickly because our technology changes, our students change, grading changes, tools change and so much more. However what doesn't seem to change is...us. The people running the classroom, working with the students daily, the ones who have the power to make any change work or not work. Yet in the era of Education during COVID, we have had to throw our fundamental thoughts of education out the window. We had to change everything we do. Finding new ways to meet the needs of children, modifying our content, eliminating topics that were not essential, allowing us to dig deeper not broader. We grabbed onto every technology that could help us. Searched out blogs, Twitter, Facebook, along with every other site or resource available. We have collectively worked harder than we ever had before, and I couldn't be more proud to say I am an educator.</span></p><p><span style="font-family: georgia;">What should come as no surprise to those who have been in the field for a long time is that as announcements came and we could be returning to a 5-day in person schedule, we heard from all aspects of the COVID spectrum. From those who would be nervous to those excited to get back to the normal life of school. However, should it be asked what we are missing? What did we learn? What can we take with us that will lead to changes for the better of our students? Has what we have been through been all bad? Or, is returning to the 5-day schedule just more normal and we all need a breath of normal? </span></p><p><span style="font-family: georgia;">Personally, I feel it's a combination of a lot of things more than any one thing. However more than anything it is the fear of taking the positives of the last 11 months and mixing them with our past theories of instruction. Fear of the work it will take to acknowledge those positives and what it may mean to what has been done in the past. Isn't that what we really do? We are educators but more than anything we are people who are willing to work hard to evolve and make the best learning opportunities possible for our students. Or at least I hope we are.</span></p><p><span style="font-family: georgia;">Let's take a moment and review some of what we have learned:</span></p><p></p><ul><li><span style="font-family: georgia;">Students need more students around to help with social/emotional needs</span></li><li><span style="font-family: georgia;">Having a day for reflection for students, with a proper amount of support can be powerful in retention and creating depth in learning.</span></li><li><span style="font-family: georgia;">Yearly instructional goals can be achieved with a drastically reduced schedule</span></li><li><span style="font-family: georgia;">Students without support, along with those with other needs, can be drastically disadvantaged without daily contact in school.</span></li><li><span style="font-family: georgia;">Teachers have the ability to provide support at very high levels through the use of technology.</span></li><li><span style="font-family: georgia;">The amount of work necessary to co-exist in a synchronous/asynchronous environment may not be sustainable for many educators over long periods of time.</span></li><li><span style="font-family: georgia;">For the majority of students, current academic performance is comparable to the performance in a 5-day face to face environment.</span></li></ul><p></p><span style="font-family: georgia;">I teach in an A/B schedule with Friday's serving as flex days to call in students who needed something additional in support or extensions. I use an LMS at a high-level to assist students in organizing their learning embedded with videos and activities to expose and deepen instruction. On the days I meet with my students in person we try to focus on either content instruction or activities to deepen learning. Some personal reflections from my classroom:</span><p></p><ul><li><span style="font-family: georgia;">It took me a semester to refine my methods and figure out how to make this system work for almost all of my students.</span></li><li><span style="font-family: georgia;">Structure for the students was vital with clear expectations including deadlines.</span></li><li><span style="font-family: georgia;">Students, like always, <u>want to learn</u> but need a connection to the teacher to be successful.</span></li><li><span style="font-family: georgia;">Students, like always, <u>want to feel like they have some ownership</u> of their learning.</span></li><li><span style="font-family: georgia;">We can release content, focusing on depth, with <u>greater results</u> than in previous 5-day schedules. </span></li><li><span style="font-family: georgia;">Students, when they are not in class daily, are excited to come to class.</span></li><li><span style="font-family: georgia;">There are still students who will make choices that prevent them from succeeding.</span></li><li><span style="font-family: georgia;">Meeting with students every day is not necessary to have high achieving students. It shocks me to consider the time spent in previous years to teach the same content as this year. </span></li><li><span style="font-family: georgia;">Students come to class eager because they know that class time is effective and important.</span></li><li><span style="font-family: georgia;">Having a day to work with students in a 1:1 or small group scenario is priceless, especially when they can control when they come in and get support.</span></li></ul><div><span style="font-family: georgia;">What we need to do is take these outcomes and determine what parts we can mix with the successes we have had in the past to make the future better. To do that, we need to communicate openly with each other. What follows are several ideas that may or may not be great but are worth discussing. </span></div><div><ol><li><span style="font-family: georgia;">Keep the flex day. Having one day each week to meet with students in an RTI setting has been the largest win of all changes occurred this year. I question if that is the same for all classrooms. Did some teachers not meet with students or have much need to meet with students? Isn't this more an administrative issue than one that should negatively affect students? Eliminating the flex day <u>would negatively affect all students ability to succeed</u>. An argument could be made that Wednesday would be a better day for the flex day. We could even follow guidelines based on age and offer a later start/end time for school hours to accommodate the high school students preferences.</span></li><li><span style="font-family: georgia;">Given an hour, I wouldn't need to meet with my students daily. It could be said that with time to reflect on the learning students have come to class with better questions, more engagement, and honestly more interest in the topics. There seems to be a more relaxing atmosphere when given a change in a day-to-day schedule. </span></li><li><span style="font-family: georgia;">In math, I still want the ability to have my students do something daily however, like I do now on their off days it should be limited to 10 minutes. Just a touch point to keep them thinking, refine a skill, or expose a topic for future discussion. Eventually, I would love to use these times to pose a "thinker" but I am just not quite there yet - give me a week or two.</span></li><li><span style="font-family: georgia;">I could foresee, with the limited number of quality teachers available, one teacher takes a double schedule. Picture this, instead of having 5 classes of 30 students I have 5 classes of 60 students but only half come on a given day. I see 5 classes of 30 students and repeat that every other day. To do this there would need to be an aide to support record keeping and some day-to-day activities. Scheduling could be interesting but in a school the size I currently teach in, this is possible to do for some classes. One really strong teacher - with support can do this and the affect is your strong teacher reaches twice as many students. That is a win!</span></li><li><span style="font-family: georgia;"> There are so many resources available that a teacher with only a few years of experience no longer needs a textbook. I feel safe saying the web-based resources, with discretion are solid. Especially if a teacher utilizes a mixture of them to meet the needs of all learners.</span></li><li><span style="font-family: georgia;">Some classrooms will want to meet daily. I feel we could make that work alongside those that meet every other day. Giving students the flexibility to leave campus or have an open study area has proven to be effective. Let's treat our students like the young adults they are and not hamper the opportunities of many for the actions of a few. Maybe this option can be earned?</span></li></ol><div><span style="font-family: georgia;">There are many other ideas or thoughts to make education better. It should be noted that <u>none of these</u> are curricular or instructional. There was little mention of videos to support learning or giving students voice and choice. Little mention of how we structure our communication or the specific expectations we hold our students up to. What I unfortunately believe is that if in 2021-22 we start the year as we did in 2019-20 our opportunity to make a major move in the innovation of education could be missed. </span></div></div><div><span style="font-family: georgia;"><br /></span></div><div><span style="font-family: georgia;">Let's not delay. Let's begin the hard work of planning quality learning for all students!</span></div><div><br /></div><p></p>Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-49349336170522634102020-09-13T20:33:00.001-07:002020-09-13T20:33:11.702-07:00Summarizing the Initial Weeks of COVID Era Instruction<p> <img alt="Ponder Pondering GIF - Ponder Pondering Hmm - Discover & Share GIFs" src="data:image/jpeg;base64,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" /> <img alt="281,899 Banging Your Head Against A Wall Stock Photos, Pictures & Royalty-Free Images - iStock" src="https://encrypted-tbn0.gstatic.com/images?q=tbn%3AANd9GcSItaDZi2yQ45iAixG0o_7AoRFpJu_s4ElN6w&usqp=CAU" /></p><p>So weeks 1 and 2 are in the books. We meet with the students every other day and Friday is designed to call in students who need additional support or extension. If you were to ask me my concerns prior to starting the year they would have been:</p><p></p><ul><li>The students remembering what it means to learn</li><li>Trying to figure out how to teach a year of material <u style="font-weight: bold;">with depth of understanding</u> while only seeing the students half the time.</li><li>Figuring out how to personally get to know each student</li><li>Safety</li></ul><div>As it turns out, safety is the one I feel comfortable with. My classes are typically filled with sound but this year, with masks, you could hear a pin drop on my carpet. </div><div><br /></div><div>I spent a good deal early in the year in the pose of the upper left image and last Friday lived in the pose in the upper right. Essentially, I will have spent the same amount of class days on a topic I did last year, which means it is going to go <u>twice</u> as long because of the every other day process. This is <i>not an option!</i> Furthermore, every time I tried to condense or trust their at home learning skills I was disappointed. And now, I feel very much like I want to do this:</div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/Ja1CuACuEOM" width="320" youtube-src-id="Ja1CuACuEOM"></iframe></div><br /><div>You see, I needed feedback. I gave the students an online portion of homework (I love DeltaMath) and a short, thinking-based 10 question online formative. FYI - last year when we were face-to-face daily I had similar expectations with excellent results. This year, of the 105 students I have in Algebra 2:</div><div><ul><li>53 didn't attempt the formative</li><li>33 haven't started any of the homework (due tomorrow morning - it is now after 10pm)</li><li>7 - yes SEVEN finished it</li></ul><div>So here I sit, typing when I should be reading or dare I say sleeping, trying to get these thoughts out of my brain as it works overtime. I've been continually going over this for the past several hours (ok it has been days of this but I didn't want anyone to think I was obsessed) and coming to the same conclusion. If the students aren't going to do anything when I am not there to encourage and support them this will not work. Now that I type that I realize it is the same as when we are face-to-face daily but seriously! We are being asked to do the impossible. Teach students who forgot what it means to learn and be a student, in an environment that is unwelcome, in half the time...all while accomplishing the same goals in learning. </div><div><br /></div><div>So what do I do now....</div><div><ol><li>We are reviewing the concepts from the useless formative because ultimately there are 52 students who need quality feedback.</li><li>I am slowing down to make sure they get the information I need them to this week. If they are struggling with this the rest of the year is going to feel like climbing Mount Everest.</li><li>I created a DESMOS activity to support learning that I am giving them for Friday as a pre-teaching session. I can track who has gone through it. It has a coding glitch but frankly it is so small I bet only I see it. If you want to check it out, <a href="https://teacher.desmos.com/dashboard/5f5a8aaa9abff0346a588dca#summary" target="_blank">here</a> it is.</li><li>I am calling in students (all of them) who didn't finish the formative and/or the homework on Friday. I am guessing this will be most of my classes. That should be fun...(sarcasm alert). Oh, and we have been told attendance may be sketchy on Friday's due to travel inability (I kinda get), home life (starting to not totally agree) or work needs (NOPE - sorry, I cannot get behind that). </li><li>Monday, we are having a little heart to heart. Maybe I should just email them this blog and let that do the work for me. It might be more effective. </li><li>Then, and finally, we are going to press a bit. I am going to force the issue my making the non face-to-face day more rigorous. Up until now it has been practice and reflection which should have amounted to 30ish minutes a day. </li></ol></div>As a truly dedicated, creative and dedicated teacher (yup, said that twice) this is maddeningly frustrating. It needs to work. There is no option and I totally agree this form of instruction is the best we could do at this time. However, that doesn't mean those of us who care about the kids won't get frustrated. We will and do. This is one massive, high risk puzzle. Last year we patched together a quarter and the outcomes were not great. This year, we can't do that. Studies say that 1-year with a bad teacher can take 2 or more to recover from. Imagine 5 quarters of partial instruction where the issue isn't the teachers effort or ability but the students. Can one recover from that?</div><div><br /></div><div>Now, I will pick up a book, read for a while and see if the brain is willing to shut down long enough to recharge. Then, go to work and see what I can make the day bring. After all, it is another chance to solve this puzzle.</div>Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-85866336277029441212020-08-12T20:11:00.001-07:002020-08-12T20:12:06.926-07:00Equity, Standards, Pathways, and Options Part 2<p> <b style="color: #333333; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px;"><span style="font-size: x-large;">Equity, Standards, Pathways, and Options </span></b></p><div style="background-color: white; color: #333333; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px;"><b><span style="font-size: x-large;">Part 2</span></b></div><div style="background-color: white; color: #333333; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px;"><b><span style="font-size: x-large;"><br /></span></b></div><div style="background-color: white; color: #333333;"><span style="font-family: verdana;">After a week of reflecting on the most recent meeting I am ready to discuss what we met about on the standards revision committee.</span></div><div style="background-color: white; color: #333333;"><span style="font-family: verdana;"><br /></span></div><div style="background-color: white; color: #333333;"><span style="font-family: verdana;">The 2+1 model is clearly the way we are heading and rightfully so. The idea of two core classes (more than likely Algebra 1 and Geometry, not necessarily in that order, or an integrated approach to the two) makes so much sense for so many students. Then, choosing the course that means something for the student. This could be a UW-Gateway course such as College Algebra (Algebra 2 equivalent), Quantitative Reasoning or Statistics. It could also be a different elective a school offers. However, all of this is dependent on the standards.</span></div><div style="background-color: white; color: #333333;"><span style="font-family: verdana;"><br /></span></div><div style="background-color: white;"><span style="font-family: verdana;"><span style="color: #333333;">To that end, we started looking specifically at the standards. The overwhelming consensus from the statewide feedback was that major changes were not necessarily needed but there was cleanup that needed to be done. The initial question: Is a + standard a standard? I don't believe it is and the longer I consider that idea the more I settle on that realization. It is by definition "beyond the core." Therefore, not a standard. Does that mean it is not meant for instruction? Not necessarily. It can and should be instructed for students seeking a career in STEM. Not for students who are <u>not</u> desiring a career in STEM. These are courses beyond the 2+ level.</span></span></div><div style="background-color: white;"><span style="font-family: verdana;"><span style="color: #333333;"><br /></span></span></div><div style="background-color: white;"><span style="font-family: verdana;"><span style="color: #333333;">What are some of these standards we are discussing? They are things like complex numbers. We are still working through the standards but complex number concepts are common standards that are discussed regularly. Does every student need to know and understand what a complex number is? Or is it enough that they understand when real solutions do not exist. So far, the latter is a stronger argument.</span></span></div><div style="background-color: white;"><span style="font-family: verdana;"><span style="color: #333333;"><br /></span></span></div><div style="background-color: white;"><span style="font-family: verdana;"><span style="color: #333333;">Tomorrow, I personally am looking forward to the additional discussions and reviewing the remaining standards. If we can reduce them to a more manageable quantity while focusing them without drastically changing them, it will help students. If, while doing this we can organize them in a manner that promotes equity while maintaining rigor we have a major win. </span></span></div><div style="background-color: white;"><span style="font-family: verdana;"><span style="color: #333333;"><br /></span></span></div><div style="background-color: white;"><span style="font-family: verdana;"><span style="color: #333333;">I actually feel we will get there soon!</span></span></div>Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-25412670718186074882020-08-01T19:08:00.006-07:002020-08-01T19:08:38.125-07:00Equity, standards, Pathways, and Options<div><b><font size="5"><div class="separator" style="clear: both; text-align: right;"><br /></div>Equity, Standards, Pathways, and Options </font></b></div><div><b><font size="5">Part 1</font></b></div><div><br /></div>This past year and now into the next year I have had the opportunity to participate on the WI-University System Math Initiative. The initiative is a multi-institutional collaboration of UW faculty, staff, and administrators working to improve student success by helping incoming students successfully complete their gateway mathematics course by the end of their first two semesters of study. In addition, I am currently on the WI-State Mathematics Standards Revision team. The overlapping concepts, along with striving for more equitable pathways for students while also increasing the quality of instruction, has caused my brain to spin, and it feels great! For the first time in my 24 years in education I feel like the alignment of all the moving parts is happening. We just need to convince everyone that the moment has arrived for math to finally make the needed changes we have been waiting for.<br /><br /><div>Although I was purely in an advisory role during the UW-University System Math Initiative, the results were very promising. The creation of gateway courses: <a href="https://www.wisconsin.edu/math-initiative/download/Math-Initiative-CA-Description-and-LO-with-Pre-Req-9.20.18.pdf" target="_blank">College Algebra</a>, <a href="https://www.wisconsin.edu/math-initiative/download/Math-Initiative-QR-Description-and-LO-9.20.18.pdf" target="_blank">Quantitative Reasoning</a>, and <a href="https://www.wisconsin.edu/math-initiative/download/Math-Initiative-Stats-Description-and-LO-9.20.18.pdf" target="_blank">Statistics</a> allow the secondary schools to alter their offerings and standards alignment while truly, possibly for the first time, understanding the expectations of the post-secondary schools. </div><div><br /></div><div>For many years we have seen the issues in secondary math instruction. Perpetual struggle, lack of interest, ongoing remediation and much more that we don't need to reiterate here. This has happened not because there is a lack of quality instruction, not because teachers haven't kept up with the times (although in fairness there is some of that in all schools), but because students don't see the value of mathematics. In most cases, they are correct. Technology has advanced to make the computing of math obsolete. This is not to say that pure mathematics isn't needed. It is...for less than 5% of the population. The very same population we have been focusing all of our curriculum on. Sure, there are plenty of remedial courses but they are based on the same foundations of Algebra, Geometry and Algebra 2. It is only after Algebra 2 that we begin to get creative with our course offerings.</div><div><br /></div><div> I am excited for math because we may now have the ability to change the entire paradigm in the above paragraph. Since this is the first blog in what I expect is a series of reflections as the standards revision process starts, I will keep it short. I wish to leave it with my early goals in the process.</div><div><br /></div><div>I hope:</div><div><ul style="text-align: left;"><li>we can eliminate several standards at the 9-12 level in mathematics further focusing our content. The clear place to start is the + standards. These are extensions of the CCSS and thus not a standard of instruction. However, in addition to the + standards we need to rethink concepts like complex numbers, logarithms, etc... Are these really for ALL students or for STEM students? </li><li>we can organize the 9-12 standards similar to the grade level standards in K-8. My concern is it may direct districts to a specific set of pathways which may cause unintentional controversy in light of local control. At minimum, I would like to see a more defined appendix that gives clarity to which standards should be taught by year.</li><li>we can develop core years of math, through 10th grade allowing students to choose a pathway that includes STEM options that instructs some of the content in a normal Algebra 2 course after grade 10 or an assortment of other pathways that are not STEM related.</li><li>we can either emphasize statistics or define a broader category of quantitative literacy that is integrated in year 1 and 2 of 9-12 math instruction. Actually leading to its instruction.</li></ul><div>These are purely initial thoughts. We have a long way to go and honestly a very short time to complete it. Stay tuned for updates.</div><div><br /></div></div>Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-48530261563003018192018-03-01T13:16:00.001-08:002018-03-01T13:16:21.058-08:00How would I react in a catastrophe?<span style="font-family: "trebuchet ms" , sans-serif;">During the past several weeks after yet another school catastrophe, this time in Florida, I have been quietly contemplating as we wait for the reaction that comes. What doesn't surprise me, that seems to surprise most of the public, is the impressive nature of the students who survived. It seems that, as adults we seem to forget how smart our children are. We allow them to be smart as young children, hope they become more than we are, and finally get annoyed when they come back from college believing they are smarter than us. This is all fine when they are "our" children. When they are someone else's child who is trying to tell us what to do then we don't seem to believe they know enough to do that. Rather ironic isn't it.</span><br />
<span style="font-family: "trebuchet ms" , sans-serif;"><br /></span><a href="https://1.bp.blogspot.com/-vDlVyWDa4Wk/WpdoedeVS-I/AAAAAAAABfU/RVmIaM8nDBMDlGRCZ1_1jyOelzgazOOZgCLcBGAs/s1600/smart.jpeg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="183" data-original-width="275" height="212" src="https://1.bp.blogspot.com/-vDlVyWDa4Wk/WpdoedeVS-I/AAAAAAAABfU/RVmIaM8nDBMDlGRCZ1_1jyOelzgazOOZgCLcBGAs/s320/smart.jpeg" width="320" /></a><span style="font-family: "trebuchet ms" , sans-serif;">The thing is, as teachers we know how smart all of "our" children are. Even those students we struggle with are really quite intelligent. "Our" children work, often not as hard as we want them to until they find a reason to show what they are capable of. "Our" children speak, often not as well as we want them to, until they find a cause that forces them in front of an audience. "Our" children show passion, too often about things that we don't want them to be passionate about, until they show us the true power of passion. </span><br />
<span style="font-family: "trebuchet ms" , sans-serif;"><br /></span><span style="font-family: "trebuchet ms" , sans-serif;">"Our" children mean a whole lot to me. Most of my energy goes to trying to figure out how to harness their potential and create the best child they can become. Because of that, it bothers me that I don't know how I would react to a similar catastrophe in my building. Would I do whatever I could to save their life? I have jumped up and saved a choking baby on a plane. I have done CPR to a referee at a basketball game. I have given the Heimlich to a choking adult. It seems I have had too many opportunities to be around when a life is on the line. </span><br />
<span style="font-family: "trebuchet ms" , sans-serif;"><br /></span><span style="font-family: "trebuchet ms" , sans-serif;">But none of these were my life...</span><br />
<span style="font-family: "trebuchet ms" , sans-serif;"><br /></span><span style="font-family: "trebuchet ms" , sans-serif;">Would I give my life for another student? I really don't know. My thoughts go to my family, my two boys who I have yet to finish raising. My thoughts go to my wife, whom I look forward to growing old with. My thoughts go to myself, and the experiences I really would like to have. Am I willing to sacrifice those for the sake of someone else? </span><br />
<a href="https://2.bp.blogspot.com/-Iihs357i1xk/WpdnxH9-KFI/AAAAAAAABfI/XZCCeWVTToEnJqDGiKHvPzVqPxIXi9EIQCLcBGAs/s1600/trust.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="600" data-original-width="1600" height="150" src="https://2.bp.blogspot.com/-Iihs357i1xk/WpdnxH9-KFI/AAAAAAAABfI/XZCCeWVTToEnJqDGiKHvPzVqPxIXi9EIQCLcBGAs/s400/trust.jpg" width="400" /></a><span style="font-family: "trebuchet ms" , sans-serif;"><br /></span><br />
<span style="font-family: "trebuchet ms" , sans-serif;">Is this what I got into education for...</span><br />
<span style="font-family: "trebuchet ms" , sans-serif;"><br /></span><span style="font-family: "trebuchet ms" , sans-serif;">The answer is clearly no. Educators are educators because they want to empower students through the use of their mind. One of our biggest assets is trust. We gain the trust of our students through a long, focused, and persistent process to get to know them and show them we care. Can I gain a students trust with a gun strapped to my hip as I am now told I, or a few of my colleagues should do? It seems that would get in the way of a trust building exercise. If given the choice of being by someone with a gun or without, I would always choose without. Wouldn't some, if not most of my students feel the same way? Arming schools is not the solution to fixing this problem. Making our schools "tougher" is not the solution. Each of the children who have executed these shootings wouldn't respond well to tougher or more strict schools. It is not discipline that fixes this. </span><br />
<span style="font-family: "trebuchet ms" , sans-serif;"><br /></span><span style="font-family: "trebuchet ms" , sans-serif;">It is compassion...</span><br />
<span style="font-family: "trebuchet ms" , sans-serif;"><br /></span><a href="https://1.bp.blogspot.com/-xLhXzZPcu8g/Wpdn4crHU4I/AAAAAAAABfM/MFYNZGwe2oseThfV3gMi_llcuAhUHzuwQCLcBGAs/s1600/compassion.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="132" data-original-width="383" height="136" src="https://1.bp.blogspot.com/-xLhXzZPcu8g/Wpdn4crHU4I/AAAAAAAABfM/MFYNZGwe2oseThfV3gMi_llcuAhUHzuwQCLcBGAs/s400/compassion.jpeg" width="400" /></a><span style="font-family: "trebuchet ms" , sans-serif;">We need to listen to our young adults speaking in front of the microphones. It is interesting that what we hear on the news is all about the officer outside the building, the lack of a gun in the building, etc... What we don't hear is what the true problem is, and there are several. Why do these weapons exist? Why do we have such easy access to them? How does a child obtain them without one, if not many other people knowing? Who do these children confide in? How do they plan something like these acts and not tell anyone? Who did these children trust?</span><br />
<span style="font-family: "trebuchet ms" , sans-serif;"><br /></span><span style="font-family: "trebuchet ms" , sans-serif;">We need Congress to help us equip our teachers with the time and talents to get to know the children they have in their classrooms. We need parents to be an active part of the learning process, not just trusting that teachers can teach their child everything they need to know. We need Congress to look in the mirror and consider that part of the problem may be themselves. Finally, we need everyone to open their ears and minds and learn from the same children we have been trying to teach. The generation we have heard so many concerns about is telling us they have learned. They have learned and are now ready to teach us.</span><br />
<span style="font-family: "trebuchet ms" , sans-serif;"><br /></span>Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-51648691735124585402017-01-03T19:30:00.003-08:002017-01-03T19:30:50.339-08:00The Truth Behind the Standard Algorithm
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For as long as I can remember seeing in pictures, reading in
books, and watching old TV shows, the standard algorithm has been the staple of
mathematics during the elementary years.
These algorithms are burnt into our brain through images of the old
school house, blackboards, and crummy movies.
However, they have maintained in instruction for an assortment of
reasons. <o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]-->1.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span><!--[endif]-->They help most students calculate math.<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]-->2.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span><!--[endif]-->Our parents learned through them so therefore,
children have also.<o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]-->3.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span><!--[endif]-->Teachers tend to teach the way they are
taught…thus the algorithms continue.<o:p></o:p></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]-->4.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span><!--[endif]-->The Common Core has them stated as necessary
parts to instruction in grades 3-6.<o:p></o:p></div>
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<br /></div>
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Recent instructional pedagogy has produced strong data to
support no longer using the standard algorithm as the main form of
instruction. The changes started in the
late 1990’s and are now being pushed further by people such as Jo Boaler. Their efforts are based off an understanding of
mathematics rather than just calculation.
With all of our advancements, the United States continues to be one of
the few remaining developed countries that use the standard algorithm as the
main form of instruction. <o:p></o:p></div>
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<br /></div>
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Personally, I couldn’t agree more with the changes being
pushed in recent years. Since starting
as a K-12 Math Coordinator we have been discussing, developing, creating, and
presenting alternatives to these algorithms that have more to do with
understanding than calculating. We have
been working against traditional math trying to encourage students to do more
than calculation. I believe we can
expect so much more from our children than rote mathematics. I believe we need to focus on the “why”
rather than giving students the “how.”<o:p></o:p></div>
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<br /></div>
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Lets go on a journey through some of the biggest reasons why
teachers keep emphasizing these algorithms and why we as professionals need to
make the decision to move on.<o:p></o:p></div>
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<br /></div>
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<u>The methods in the algorithms are needed to learn the
upper levels of mathematics<o:p></o:p></u></div>
<div class="MsoNormal">
Forgive me but I started with my favorite reason most people
give to keep the algorithms. It is not
enough to say that after grade 6 or 7 calculators are doing the vast majority
of the dirty work in calculating math.
It is more important to understand that the methods used in the
algorithms are not used in upper levels of math. The only algorithm that reappears
consistently is the division algorithm, which comes back when dividing
polynomials. Even that method for
dividing polynomials is an inefficient method as compared to synthetic division
or graphing solutions. In all of these
cases there are apps that can do much of the computation for us. This doesn’t mean it isn’t important to know
how to do these steps but that its’ importance is minimal as compared to the
much larger picture of what the outcome of the division means.<o:p></o:p></div>
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<br /></div>
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The standard algorithm for multiplication is purely
gone. For some time area models have replaced
the algorithm. Even that is an
incomplete comparison because we are comparing polynomials with multiple terms,
not numbers. Polynomial multiplication
is closer to the partial products method than the standard algorithm. Furthermore, the methods used emphasize the
meaning of multiplication. Not just
calculating for a solution.<o:p></o:p></div>
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<br /></div>
<div class="MsoNormal">
<u>It is the methods parents know so we must teach it that
way to help with home-school communication<o:p></o:p></u></div>
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It is ironic that statements similar to this one surface
about math when they don’t surface about reading or writing. I believe it has much more to do with the
procedural drill and kill approaches taken when current teachers/parents were
learning math. In schools, we used to
teach keyboarding at the high school level.
We taught students lattice multiplication in the late 1990’s and early
2000’s. We went through phonics, to
whole language, and back again. <o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
This goes to show that times change and we need to move with
them. With the technology of today we
can communicate our methods of instruction with parents and more importantly
the reasons why instructional methods are changing. We need to emphasize instructing parents as
much as instructing our students.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
To be clear, we own this problem. The problem is communication, not knowledge.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<u>The algorithms work.
Why change what is working?</u><o:p></o:p></div>
<div class="MsoNormal">
I would argue that the algorithms are not working. In third grade, students learn to add
multi-digit numbers together. This
addition should be fluent by the end of the year. However, in fourth grade teachers are always
re-assessing and arguing that the students don’t know how to add multi-digit
numbers. The same is true in fifth
grade, sixth grade and so on. <o:p></o:p></div>
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<br /></div>
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Is the problem that students don’t know how to do it or are
not retaining the knowledge? The answer,
based on student performance is obvious. Students are proficient at the skill in each
grade level but when reassessed the following year no longer show the same
level of proficiency. The students don’t
retain the process. However, when using
alternative methods such as partial sums they not only retain the ability to
add they perform it at a fluency level doing much of the calculations in their
head. They learn that adding the
hundreds, tens and then ones makes it easier to get the solution. It also gives them a much better understanding
of place value which means when the students transfer into multiplication it
makes more sense. <o:p></o:p></div>
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<br /></div>
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I leave this blog with a final thought. Watch a student as they progress through
Kindergarten to first and then second grade.
Students don’t naturally develop the traditional algorithms for addition
or subtraction. Instead, they focus on
concepts that deal with place value. The
traditional algorithm must be learned through a teacher that directly teaches
it. That alone should tell us what we
should be doing. I believe there is a
place for these algorithms. However,
only if they are taught after the sense making methods are discovered. <o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
As always, I don’t consider my opinion to be fact. Because of that I have linked a few articles
that support both sides of this story.
Enjoy the reads and come to your conclusion. Please share it with me. Hopefully we can learn together.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<a href="http://www.theproecenter.info/uploads/2/2/5/5/22551316/van_de_walle_algorithm_article.doc">Do
we Really Want to Keep the Traditional Algorithms for Whole Numbers? </a> John A. Van de Walle<o:p></o:p></div>
<div class="MsoNormal">
<a href="http://www.commoncoretools.me/2015/01/08/wheen-the-standard-algorithm-is-the-only-algorithm-taught/">When
the Standard Algorithm is the Only Algorithm Taught </a> Jason
Zimba<o:p></o:p></div>
<div class="MsoNormal">
<a href="http://www.fmd.uni-osnabrueck.de/ebooks/erme/cerme1-proceedings/papers/g2-hedren.pdf">The
Teaching of Traditional Standard Algorithms for the Four Arithmetic Operations
versus the use of Pupil’s own Methods </a> Rolf Hedren<o:p></o:p></div>
<!--EndFragment-->Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-8355068876623745772016-12-08T07:39:00.001-08:002016-12-08T07:39:50.242-08:00What do I feel all new math teachers need to know...<span style="font-family: Trebuchet MS, sans-serif;">I have the opportunity to talk to prospective Elementary teachers at the University of WI - Stevens Point today. The talk is focused on problem solving and how it integrates into the classroom. However, we are going to talk about much more than that. I am bringing a few examples of things with me. Such as a few articles I wrote, some Math Thinkers to demonstrate problem solving, some sample assessments, and a basic form that I use to evaluate instruction in a classroom. I am also bringing a few books that I feel are important for every new (and existing) teacher to read. The goal is to expose these current students to what we are going to expect from them as they become professionals leading our future students.</span><br />
<br />
<ul>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0Qm5mY3drUFBZbWM" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">How to Teach in a Group Centered Classroom</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0Ylc0VFl4SURZSG8" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Elementary Math Instruction "Look-For's"</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0a0x0OGtTMXNKalE" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Task - Picnic Lunch for 3rd Grade</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0MG0zazV5dVR6LTA" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Task - New Fish Tank for 3rd Grade</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0N0tGby1VdXpMNU0" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Task - How Much Does it All Cost for 5th Grade</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0Q2dVQnJoTUJyamM" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Formative Activity - Going to the Movies for 5th Grade</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0RGYxTWtLUDJlZU0" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Grade 1 Assessment - Adding and Subtracting Multiples of 10</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0aHpsRlFacmxRSm8" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Grade 3 Assessment - Place Value and Addition and Subtraction</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0dndfYXdqQk5JcFU" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Grade 3 Performance Task - Arcade Tickets</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0SjhKbThFb1NYTUE" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Grade 5 Assessment - Multiplying Whole Numbers and Decimals</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0Q2NiVXFrMjJZMTA" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Grade 5 Assessment - Multiplying and Dividing Fractions and Mixed Numbers</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0SS1OWHZWUDA5RTQ" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Task - Who is Correct for 1st Grade</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0bHA5NkJvbFFScDA" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Task - IPod Usage for 3rd Grade</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0TDN6S00wQ0dCUVE" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Grade 1 Assessment - Working with Equality</span></a></li>
<li><a href="https://drive.google.com/open?id=0B9nQxOSHG8M0a2ViWDRCdHlXM2s" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Unfinished Task - Shriners Donation from the Packers - Grade Unknown</span></a></li>
<li><a href="https://www.amazon.com/Whats-Math-Got-Transform-Mathematics/dp/0143128299/ref=sr_1_1?ie=UTF8&qid=1481211168&sr=8-1&keywords=whats+math+got+to+do+with+it" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Book - What's Math Got to Do With It by Jo Boaler</span></a></li>
<li><a href="https://www.amazon.com/Accessible-Mathematics-Instructional-Student-Achievement/dp/0325026564/ref=sr_1_1?s=books&ie=UTF8&qid=1481211200&sr=1-1&keywords=accessible+mathematics" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Book - Accessible Mathematics by Steve Leinwand</span></a></li>
<li><a href="https://www.amazon.com/Principles-Actions-Ensuring-Mathematical-Success/dp/0873537742/ref=sr_1_1?s=books&ie=UTF8&qid=1481211215&sr=1-1&keywords=principles+to+actions+ensuring+mathematical+success+for+all" target="_blank"><span style="font-family: Trebuchet MS, sans-serif;">Book - Principles to Actions by NCTM</span></a></li>
</ul>
<div>
<span style="font-family: Trebuchet MS, sans-serif;">This is a whole lot of stuff. However I want the future teachers to understand thinking at different grade levels. The key to the whole conversation is not the tasks but the thinking the tasks promote and how a teacher promotes it. Something that cannot be explained by a sheet of paper. This year I have been lucky enough to be able to be in more classrooms than ever. It just makes it more obvious that as teachers, we think a whole lot more than our students. At first read that sounds like a "duh" statement but the reality is it needs to be the other way around. In fact, we don't even let them get to the thinking because we "save" them from failure.</span></div>
<div>
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span></div>
<div>
<span style="font-family: Trebuchet MS, sans-serif;">We, as professionals need to realize that the sage on the stage can no longer be a viable instructional method at any level. We need to realize that the more math (please don't confuse this word with calculation - instead read it as pattern finding) students are doing in the classroom the more math they will learn. </span></div>
<div>
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span></div>
<div>
<span style="font-family: Trebuchet MS, sans-serif;">My hope with these conversations is the new instructional force coming into the field understands the expectations and can hit the ground running. The reality is this will take some time. If you are a prospective teacher just reading this blog for the first time, check out some of the links on the right. They are resources from great teachers. More than anything, be creative and try something new. If you have talked for 10 minutes or more while teaching a classroom...you have talked for too long. </span></div>
<div>
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span></div>
<div>
<span style="font-family: Trebuchet MS, sans-serif;">For the experienced teachers reading this blog, post a comment that you feel new teachers could benefit from. </span></div>
Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-25504152219787091482016-07-18T08:35:00.002-07:002016-07-18T08:35:41.340-07:00A New Perspective...Can we look at post-Algebra 1 Math Differently?<span style="color: #262626; font-family: Roboto, arial, sans-serif;"><span style="background-color: white;">A question was posed rather carefully on a previous </span>blog that needs to be addressed. </span><br />
<div style="text-align: center;">
<span style="color: #262626; font-family: Roboto, arial, sans-serif;"></span><br /><span style="color: #262626; font-family: Roboto, arial, sans-serif;"></span></div>
<div style="text-align: center;">
<i><span style="color: #262626; font-family: Roboto, arial, sans-serif;">"R</span><span style="background-color: white; color: #262626; font-family: Roboto, arial, sans-serif;">unning the risk of inciting the ire of math teachers across the world, "What qualifies as "post-Geometric" math?" Does it have to be Pre-Calculus and Calculus? Does Statistics count? What about a class like Machinist Math, where the application of the mathematical concepts ties directly to the problem solving process directly related to operating and maintaining manufacturing machines? Is it possible to address the fundamental skills that math allows us to practice with a different kind of math curriculum than the "standard?"</span></i></div>
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<tr><td class="tr-caption" style="text-align: center;"><a class="_ZR irc_hol i3724" data-noload="" data-ved="0ahUKEwjN4uCMo_3NAhVIxoMKHXqCCF8QjB0IBg" href="https://en.wikipedia.org/wiki/Group_theory" jsaction="mousedown:irc.rl;keydown:irc.rlk" style="color: #7d7d7d; cursor: pointer; font-family: arial, sans-serif; text-align: start; text-decoration: none;" tabindex="0" target="_blank"><span class="irc_ho" dir="ltr" style="margin-right: -2px; overflow: hidden; padding-right: 2px; text-overflow: ellipsis;">en.wikipedia.org</span></a></td></tr>
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<span style="background-color: white;"><span style="color: #262626; font-family: Roboto, arial, sans-serif;">Let's start with some background since this question really reminds me of a Rubik's Cube. Depending on the way you look at it there are several answers. There is little to no disagreement that Algebra </span><span style="font-family: Roboto, arial, sans-serif;">1 is necessary to understand for all students. It is a gateway, not only to math but other subjects. According to KnowRe, </span></span><span style="background-color: white;"><span style="font-family: Open Sans, Arial, Helvetica, sans-serif;">Algebra 1 presents students with academic challenges they have not yet had to face. Algebra is often the first course in which students deal with abstract reasoning and problem solving. This abstract reasoning helps connect the dots between historical events and what is currently happening in the world. It opens areas of science that cannot be explored without it. It has direct links to music and art along with a litany of applications in sports. </span></span><br />
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<span style="background-color: white;"><span style="font-family: Open Sans, Arial, Helvetica, sans-serif;">What about Geometry? Is that necessary. Prior to 2010 it would not be difficult to say yes. However, with the adoption of the Common Core State Standards, much of Geometry has moved into 5th - 8th grade where it is used as an application of current learning. This should remove a significant portion of the years learning as long as students are retaining knowledge (which is a major issue in all subject areas). The remaining portions of Geometry would be ground-level knowledge for trigonometry, applications in circles, etc... Knowledge that the current U.S. citizen walking down the street doesn't have. Should they have it? That is the debate. </span></span><br />
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<tr><td class="tr-caption" style="text-align: center;"><a class="_ZR irc_hol i3724" data-noload="" data-ved="0ahUKEwjG3OvQov3NAhVE54MKHfAXCBgQjB0IBg" href="http://www.hwporter.org/teacher_pages/guidance/student_success_plan.php" jsaction="mousedown:irc.rl;keydown:irc.rlk" style="color: #7d7d7d; cursor: pointer; font-family: arial, sans-serif; text-align: start; text-decoration: none;" tabindex="0" target="_blank"><span class="irc_ho" dir="ltr" style="margin-right: -2px; overflow: hidden; padding-right: 2px; text-overflow: ellipsis;">www.hwporter.org</span></a></td></tr>
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<span style="background-color: white;"><span style="font-family: Open Sans, Arial, Helvetica, sans-serif;">When I have the opportunity to attend a math conference my thinking typically falls with the majority of others. However, when I am in my district or visiting other districts working with secondary math teachers, my thinking tends to be the minority. Why that is would qualify for another blog. Regardless, there is a much bigger question here that needs to be answered. That said, the answer is complicated. </span></span><br />
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<i style="font-family: 'Open Sans', Arial, Helvetica, sans-serif;">What does the student need to succeed in their career/life?</i><span style="background-color: white; font-family: 'Open Sans', Arial, Helvetica, sans-serif;"> </span></div>
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<span style="background-color: white;"><span style="font-family: Open Sans, Arial, Helvetica, sans-serif;">Every time I am posed with student placement decisions this is my go to question. What makes this so hard is a few conditions we cannot change.</span></span></div>
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<li><span style="font-family: Open Sans, Arial, Helvetica, sans-serif;"><span style="background-color: white;">Many students have no idea what they want to do after high school.</span></span></li>
<li><span style="font-family: Open Sans, Arial, Helvetica, sans-serif;"><span style="background-color: white;">If a student does have an idea of what they want to do, too many parents steer students away from their choice. </span></span></li>
<li><span style="font-family: Open Sans, Arial, Helvetica, sans-serif;"><span style="background-color: white;">Career choices are changing so fast most of the careers our current students will have don't exist currently.</span></span></li>
<li><span style="font-family: Open Sans, Arial, Helvetica, sans-serif;"><span style="background-color: white;">Some of the most growing fields are seen as "manual labor" when the reality is they are highly specialized (Machinist) involving lots of mathematics.</span></span></li>
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<span style="background-color: white;"><span style="font-family: ff-dagny-web-pro, Arial, sans-serif;">The Common Core State Standards <u>do not</u> require a student to pass Algebra 2. They require some of the skills in a typical Algebra 2 course but not all of them. Therefore, Algebra 2 is not required. In fact, most, if not all of the skills are taught in the 1st semester of a typical Algebra 2 course. The remainder of the skills are instructed as the next set of foundations needed for further study in mathematics. </span></span><span style="background-color: white; font-family: ff-dagny-web-pro, Arial, sans-serif;">"Taking and successfully completing an Algebra II course, which once certified high school students' mastery of advanced topics in algebra and solid preparation for college-level mathematics, no longer means what it once did," </span><span style="color: black; font-family: ff-dagny-web-pro, Arial, sans-serif;"><a href="http://www.brookings.edu/blogs/brown-center-chalkboard/posts/2013/09/04-algebra-coursetaking-loveless" style="text-decoration: none;">writes Tom Loveless of the Brooking Institution</a> </span><span style="background-color: white;"><span style="font-family: ff-dagny-web-pro, Arial, sans-serif;">in a blog post. "The credentialing integrity of Algebra II has weakened." Tom Loveless bases this statement on a correlation between the number of students passing an Algebra 2 course and the nations NAEP scores. The Algebra 2 barrier has been a sticking point with post-secondary education. For many institutions, it is required for entrance. Even for students with no interest in mathematics.</span></span><br />
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<span style="background-color: white;"><span style="font-family: ff-dagny-web-pro, Arial, sans-serif;">So if Algebra 2 is not something all students should have what is? The answer in my mind is </span><i style="font-family: ff-dagny-web-pro, Arial, sans-serif;">nothing</i><span style="font-family: ff-dagny-web-pro, Arial, sans-serif;">. This is not to mean </span><u style="font-family: ff-dagny-web-pro, Arial, sans-serif;">no</u><span style="font-family: ff-dagny-web-pro, Arial, sans-serif;"> math class. It means there should not be one answer to this question. Lets face some facts. The important learning that happened in my life to get me where I am now did not happen in high school or college. It happened after several years in my </span></span><span style="font-family: ff-dagny-web-pro, Arial, sans-serif;">field when I realized, "Wow, I really need to know more about that." I took courses, attended workshops, and read. When I was done I read some more. The constant for students who struggle in school is a lack of interest. It goes back to the question listed above. </span><i style="font-family: 'Open Sans', Arial, Helvetica, sans-serif; text-align: center;">What does the <u>student</u> need to succeed in their career/life? </i><span style="text-align: center;"><span style="font-family: Open Sans, Arial, Helvetica, sans-serif;">Note, the question is not "What do we currently have that we can put the student in?"</span></span></div>
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<span style="font-family: Open Sans, Arial, Helvetica, sans-serif;">By no means do I imply that students should not take Algebra 2, Pre-Calculus, Statistics or Calculus. I mean they should take what interests them. If a student has no interest in math but can't wait to corner someone in order to argue politics. They are more than likely not going into a field where Calculus will make a difference. It is quite possible their path may need to go through a more formal statistics course (which needs more math background than Algebra 1 but not a full year of Algebra 2). As the original questioner stated, what about a Machinist course? Definitely! Consider for a moment that student who doesn't do his/her homework but spends time in the wood/metal shop "playing" with materials. Currently they don't need Algebra 2. Although, it should be noted that much of a machinist job lies in content of a 1st semester Algebra 2 course. In my district we did a small challenge this year. The Machine Tool course was working on some models, determining the lengths and angles needed to make a part. It should be noted that the math is completely integrated into the course. The teacher took the same schematic to his Algebra 2 class and gave them a period to find the necessary measurements. After a period, they were no farther than when they started. The Machine Tool students, who would never pass an Algebra 2 class, had it all figured out. </span></div>
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<span style="font-family: Open Sans, Arial, Helvetica, sans-serif;">Here is my answer to a long thought process. We don't need all students to take anything past Algebra 1. However, we need all students to take the math they need to move forward in what they want to do. We need instructional options for all students. An abbreviated upper algebra course for those students who don't now need everything Algebra 2 has to offer but yet might entice them to go farther if they so desire. We need courses such as Calculus for those students who know their path lies in mathematics. I once read a report that only 9% of college majors require calculus. Then why is that where the crown of mathematics is held. We need the upper level mathematics courses to continue to move innovation because that content will possibly be helpful in the next innovation. However, not everyone is an innovator in that way. The key is to find where that child wants to be innovative, then tailor the plan to set the student on a path towards their goal. </span></div>
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<span style="font-family: Open Sans, Arial, Helvetica, sans-serif;">There are far too many resources available to not allow a student to tailor their own path.</span></div>
Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-36487733527927356892016-07-16T20:43:00.002-07:002016-07-16T20:43:21.852-07:00Why do we Continue to Teach...Part 2<div style="background-color: white; color: #333333; font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 16px;">
Well, it took a bit longer to get to part 2 than I had planned. Things like finishing a school year and planning for next year took some precedence. Regardless, if you need a refresher on part 1, <a data-mce-href="http://blog.discoveryeducation.com/blog/2016/05/17/why-do-we-continue-to-teach/" href="http://blog.discoveryeducation.com/blog/2016/05/17/why-do-we-continue-to-teach/">here</a> it is. The premise of the problem is "Why do we continue to teach math that has little application to a “normal” person?" The first post went the route of justifying why people are asking the question and the problems with the foundation of the question. This post now leads into what other teachers are saying. To clarify, I polled my staff and some of other math teachers around Wisconsin. Their thoughts ranged from dumbfounded, to overly traditional, to outright angry. Most of the teachers had very similar comments. Finally, my closing thoughts on this topic. I must say, it ranks up there as one of my least favorite questions to answer.</div>
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<strong>The overly traditional teacher</strong>:</div>
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I must admit that this teacher is the one I would not want discussing this prompt with others. Why must we teach post Geometry mathematics when there are programs that can do it for us? "Because students need to know this information. It is important for being a mathematician. It is what pure mathematics is about."</div>
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Personally, I feel these teachers are so far off base it is scary. Why does a student need to know this information? Where can we show students they will actually apply these concepts. In my life, as a math teacher, outside of school I have not had the pleasure of factoring a degree 3 polynomial. Nor do I ever feel like I will. The final two comments made from what I am calling the overly traditional teacher bother me the most. It is rare that we have "mathematicians" come out of school. It is one of the highest need majors in careers yet one of the least populated in post-secondary education. Being a mathematician isn't even about pure mathematics. A general mathematician doesn't sit around solving proofs on his coffee table. A mathematician applies mathematical theories and techniques to solve practical problems in business, engineering, the sciences, and other fields (www.bls.gov). Overly traditional teachers tend to feel they are producing life-long math people. They miss the point of mathematics. It is an area of study that can enhance other fields by making them more efficient and effective. Since they miss the point, they also miss many of the best ways to meet the needs of their students. Their flaw is not with a lack of instructional ability but with a lack of knowledge of their students and because of that, instruction that can engage students.</div>
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<strong>The Politically Correct teacher</strong>:</div>
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It was a struggle to put a name to these responses. Partly because I agree with their answer to the question but don't feel they have hit it all. These teachers believe we need to teach post Geometry mathematics because we are working on their "Critical thinking skills." When they get in the real world (no matter what their job is) they are going to be required to think critically and solve problems on the fly. The better their critical thinking skills are the better chance they have of advancing in their career.</div>
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On the whole it is hard to disagree. However, there are many, far more engaging ways to teach critical thinking skills than higher level mathematics. Why would we teach the math and be so specific to the solutions and methodologies if it was about critical thinking? Critical thinking skills can be taught in many ways. Sites such as <a data-mce-href="http://www.criticalthinking.org" href="http://www.criticalthinking.org/">www.criticalthinking.org</a> list numerous strategies that engage students without teaching mathematics. Math in itself doesn't teach critical thinking. Students will perform better if they have the ability to think critically. It is much more of a shared relationship. Does math help develop these skills. There is no question about it. I would argue more than any other subject in Secondary instruction.</div>
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<strong>The honest Abe with a touch of angry teacher</strong>:</div>
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The responses from these teachers were all well stated and...long. It makes the most sense to simply put one of their responses in here since I cannot say it better.</div>
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<em>"I was hoping not to reply to this, as this whole line of questioning just reflects how little these people know, understand or care about math and it is very frustrating. We have to justify ourselves...why math? Really? Why do we teach anything then? </em></div>
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<em>My first response would be how little they care about the development of our students reasoning and logical thinking ability as they develop their minds in adolescence. Yes I understand a Geometry proof or multistep complex type solving equation my never be directly used in that students future, but the ability to think and reason clearly is very important. Do they wish our students to never know how to make a political candidate decision based on logic, or decide if as a family they should spend a large amout to have surgery on a pet, or let the animal pass. We need thinking skills and math helps in that development.</em></div>
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<em>Second, I would offer to come over to their house, dismantle their TV dish or cable, ask for their cell phone, and tell them you will be happy to dispose of them since math is so unimportant. Lets' take away some of those benefits that have been given since you don’t' care why they exist.</em> <em>Okay, so not every student is going to come up with the next and best greatest math idea. But should we not at least proceed on the premise that someone could be that person. We should at least give them a chance to improve the next generations lives, maybe figure out pollution problems, energy usage, etc... No math, no improvements!</em></div>
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<em>Finally, I would tell them how sorry I feel for them. They truly do not see math for the beauty and wonder it offers in their lives. Math is everywhere. It is integral part of all our lives if you just know where to look, and be open for it. If you have no base understanding, like Geometry and Algebra you will never see that wonder. If they choose to close their minds to what is all around them, then just let them know how you feel sorry for their loss, but don't let your close mindfulness affect our students."</em></div>
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Although the anger clearly spews from this particular teacher the depth of the response is precious. I can't make this better than it is. What needs to be said is that I side closest with this teacher. We teach post Geometric math because we need people who can make the change in the world they want to see. We don't know who they are or when or if they will gain an interest in math. What I can guarantee you is that if we don't teach these topics we won't have those who can make the advancements we want to see. This is a question that needs to be put to rest. Math has the same importance as reading in many ways. Each subject by itself doesn't mean much. However, tied to other content and math and reading become of such an importance that without them progress would subside.</div>
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Instead of asking why we need to teach them, we should be listing all the things that would happen if we didn't. I don't think there is enough room on a blog for that though.</div>
Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-42709000312862915462016-07-16T20:41:00.003-07:002016-07-16T20:41:51.894-07:00Why do we Continue to Teach...Part 1<div style="background-color: white; color: #333333; font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 16px;">
Recently, a common question has been repeatedly posed to me, one which makes me uncomfortable on several levels. The first being that the answer seems so simple that it begs me to wonder why bother asking it. The second being that the answer, although simple, makes me wonder if we are doing the best we can, or if we are simply giving someone verbal justice.</div>
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Why do we continue to teach math that has little application to a “normal” person?</blockquote>
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This question begs at the systemic problem of post Geometry mathematics: “Those who do not understand mathematics, feel it is unimportant.” Dispensing with the simplistic, selfish nature of the question, the lack of vision of the person posing the question, and the refusal to answer it with “because we always have”, on its surface, the answer seems simple.</div>
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The logic associated with the late secondary mathematics allows students to engage in careers they would not be able to engage in without it. Essentially, it opens doors. The technological advancements that have prompted this question are things such as Photomath and other internet sites, along with the theory that we need to prepare students for what they will be doing in their careers, not a general path of instruction.</div>
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Let’s tackle these one at a time. The first argument typically presented is that if apps such as Photomath or sites such as Google can solve the problem, why do I need to learn about it? (see a previous blog for more introduction). This argument is fraught with problems, the least being with the instructor who is allowing students to live in simple DOK 1 styles of questioning. Those are the only questions that these apps can handle. Anything related to an actual scenario to utilize the math is well beyond the capabilities of these programs.</div>
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Furthermore, if we isolate the problem to a DOK 1 situation, as shown below, it opens up an additional area of concern.</div>
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1/3 (x+3/6)=1/3</blockquote>
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Using apps such as Photomath produces a solution like the one shown below.</div>
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<img alt="Screen Shot 2016-05-10 at 9.30.48 PM" class="aligncenter wp-image-69555 size-full" data-mce-src="http://blog.discoveryeducation.com/wp-content/uploads/2016/05/Screen-Shot-2016-05-10-at-9.30.48-PM.png" height="430" src="https://blog.discoveryeducation.com/wp-content/uploads/2016/05/Screen-Shot-2016-05-10-at-9.30.48-PM.png" style="display: block; height: auto; margin-left: auto; margin-right: auto; max-width: 100%;" width="766" /></div>
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The goal of a problem such as this is to see if students understand the conceptual nature of mathematics. We want students to understand the solution process so that they can open the door to higher levels of mathematics. However, if they understand number sense, they can quickly see that (x+1/2) must be equal to one because 1/3(1) = (1/3). Therefore, the only way (x+1/2) = 1 is if x = 1/2. What takes photomath 17 steps can be solved in less than three.</div>
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Knowing “math” is not only more efficient, it is more effective. When I teach math, I want students to understand the solving process, or what most people believe upper mathematics is about. That said, I want them to understand mathematics so much more than I even care about the process.</div>
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The second argument is more daunting and more bothersome. Adults who have struggled in math, or never truly understood mathematics, believe it is solving equations for the sake of solving equations. They believe it is completing proofs for things that have no meaning, so they can somehow be more fulfilled by the process of just doing the proof. They see math careers as teachers, professors, and engineers. The reality is so far from this perception. It is the equivalent of telling someone that they know how to make an automobile because they know how to drive one.</div>
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Kiplinger listed the top 10 college majors for 2015-16. Each of the top 10 has a major focus, if not entire focus on mathematics. In addition, CareerCast lists the top 10 professions to enter. Of those professions, seven are focused on mathematics.</div>
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This isn’t math for the sake of doing math. It is math for the purpose of what math is. It is about seeing a pattern, or a logical process, in a situation and either finding a solution or a pathway to improving that situation.</div>
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In the past few years, math has helped solve problems in heath care, computers, and safety. In the near future, math will help to solve efficient energy solutions, global warming, and many more issues of our time.</div>
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Some would argue that science will be responsible for solving these problems. But I would argue that science is a subset of mathematics. Math by itself doesn’t solve problems, which is why many school districts are implementing STEM initiatives. One of the most significant realizations among educators over the past several years is that there are really two core subjects in education — English and mathematics. Without a solid foundation in both of these, career opportunities become drastically limited.</div>
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Beyond these responses, what is the best way to respond to the question of, “why do we continue to teach courses like Algebra 2, Pre-Calculus, and so on?”</div>
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Is there a better way?</div>
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I thought about my answer to this question a lot for this blog post. I plan to split my response across three parts. In part two, I will convey how my staff feels about the question and some of their responses. And in the final post, I will cover some possible answers to the question.</div>
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<em>Look for part two of this blog post soon!</em></div>
Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-53528032343668822182016-03-06T18:46:00.000-08:002016-03-06T18:46:35.703-08:00Give Students the Tools needed to Solve Problems...<div class="p1" style="color: #58595b; font-family: Lato; font-size: 16px; margin-bottom: 10px;">
<span class="s1">In my previous blog, <a href="http://blog.discoveryeducation.com/blog/2016/01/24/a-new-perspective-asking-questions-that-spark-student-engagement/" style="-webkit-transition: 0.2s; color: #328eca; outline: 0px !important; text-decoration: none !important; transition: 0.2s;"><span class="s2">Questions that Spark Student Curiosity</span></a>, I discussed ways to ask questions that would engage students. France Snyder commented, “What is the best way to evaluate our students? What is the effect on our students’ engagement, retention, and transference of skills? What is overall best for our students?” I’ve thought a lot about how we evaluate students over the past few weeks, as we have just completed first semester final exams. </span></div>
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<span class="s1">While prepping my students for their final exams, I fielded questions from students about how to access the study guide, the best way to study at home, and how many class periods would be dedicated to finals exam review. My response was consistent with past years. “Every one of you is aware of what we discussed in class. You are also aware of how to access the resources we used in class. To study for the final exam, consider our conversations and reflect on them.”</span></div>
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<span class="s1">When the final exams came, I chose to spend an extra day administering the exam over two full hours so students could consider their responses thoughtfully without time constraints. After I distributed the exam on the first day, students responded “It’s only 8 questions. Why would it take 2 hours to complete?” Shortly after exams were over and students had a chance to reflect, I asked them what they thought of the exam and their responses reaffirmed my final exam strategy. “It wasn’t hard but my answers were not the same as those of my friends. We knew you would not accept a simple ‘yes’ or ‘no’ so we really had to think about all the options and justify our responses.</span></div>
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<span class="s1">To me, final exams aren’t for the sole purpose of determining what knowledge a student has attained and what facts that student has memorized. They are an integral part of the learning process. For many decades, we have asked Webb’s Depth of Knowledge (DOK) 1 and DOK 2 questions: those questions with a single correct answer that leads students through a single path of thinking. Now, we are focused on DOK 3 levels of thinking, so we know there is a better way to evaluate student learning. Yet, we still fall back to the familiar ‘yes’ or ‘no’ style of questioning in many of our final exams.</span></div>
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<span class="s1">I was on Facebook the other day and saw a post that made me stop and smile. “Don’t ask kids what they </span><span class="s3">want to be</span><span class="s1"> when they grow up but </span><span class="s3">what problems they want to solve</span><span class="s1">.” This is a perfect example of changing a question from a one-word DOK 1 answer to a thoughtful, considerate DOK 3 response. What problems do we want our students to solve? I don’t want them to solve a problem in which the answer is known. We need to stop training our students to accept DOK 1 questions as the norm. Life doesn’t contain these simple problems, and neither should education. Any question that ever told me anything about a student was a question I didn’t know how they would answer it and more importantly, how they would explain their answer.</span></div>
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<span class="s1">While working with one of my teachers responding to an email from a disgruntled parent about the lack of “math” being taught we decided to dig a little deeper. The parent described how he retaught his daughter using proper math and how she now completely understands everything we were trying to get through to her. We did what any good teachers would do. We asked her to explain her understanding. She could explain parts, but after a few steps, she could not explain the next procedure and, most telling, couldn’t explain her goal. DOK 1 questioning that we have been doing for years promoted a recipe style of mathematics. Our students don’t retain it and, most importantly, they don’t like it.</span></div>
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<span class="s1">Webb’s DOK is not just a method of questioning for the sake of questioning. It is a way to help students attain a higher level of understanding. At the same time, it is a method that encourages student engagement. Encouraging students with questions that make them consider multiple options and different perspectives to solving mathematics will only aid them in enjoying what they are doing, which in turn will make for better mathematicians.</span></div>
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<span class="s1">It’s not about just teaching for recitation. It’s about giving students the tools to solve the problems they want to solve.</span></div>
Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-89895880735233572962016-03-06T18:39:00.000-08:002016-03-06T18:39:36.928-08:00Walter Wick bringing a New Perspective to Math...<div style="background-color: white; color: #333333; font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 16px;">
On a Sunday afternoon that the family finally had a free moment, my wife took the family to the <a data-mce-href="http://www.lywam.org" href="http://www.lywam.org/" target="_blank">Woodson Art Museum</a> to view the <a data-mce-href="http://www.walterwick.com" href="http://www.walterwick.com/" target="_blank">Walter Wick</a> exhibition. Walter Wick is the photographic illustrator of the <em>I SPY</em> series, and the author/illustrator of the <em>Can You See What I See?</em> series. Besides see some amazing photography and reflecting on a bit of my own past, I had so many moments of game changing instructional opportunities. <img alt="balancing act" class="wp-image-68045 alignright" data-mce-src="http://blog.discoveryeducation.com/wp-content/uploads/2016/03/balancing-act-130x130.jpg" height="172" src="http://blog.discoveryeducation.com/wp-content/uploads/2016/03/balancing-act-130x130.jpg" style="float: right; height: auto; margin: 0.5em 0px 0.5em 1em; max-width: 100%;" width="172" /></div>
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The first came from a pair of photos called <em>Balancing Act, </em>of which one is pictured at the right. The photo shows many objects seemingly placed at random all balancing on a single piece of LEGO. Mr. Wick mentions the process of getting everything to balance took over a week with much trial and error and several crashes along the way. What I saw was the amount of math that could be extracted and then performed from such a starting image. From 7th grade ratios and proportions to symmetry all the way through the upper levels of mathematics. What intrigues me the most is that almost every student will have objects similar to these sitting in their home.</div>
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<img alt="Slide-SortingClassifying" class="size-medium wp-image-68049 alignleft" data-mce-src="http://blog.discoveryeducation.com/wp-content/uploads/2016/03/Slide-SortingClassifying-1-217x130.jpg" height="130" src="http://blog.discoveryeducation.com/wp-content/uploads/2016/03/Slide-SortingClassifying-1-217x130.jpg" style="float: left; height: auto; margin: 0.5em 1em 0.5em 0px; max-width: 100%;" width="217" />Next to this photo was another called <em>Sorting and Classifying</em> from the <em>I SPY School Days</em>. From my experience teaching Geometry to planning earlier math lessons the concept of a Venn Diagram is not the easiest concept to grasp when applying it to mathematics. However, what if the class started with a photo of <em>Sorting and Classifying</em> followed by the simple question, "What is the purpose of the rings?" Instead of teaching students what the Venn Diagram is, allow students to discover its' purpose and what they sort in this situation.</div>
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The final photo that<img alt="mirrors" class="size-medium wp-image-68050 alignright" data-mce-src="http://blog.discoveryeducation.com/wp-content/uploads/2016/03/mirrors-216x130.jpg" height="130" src="http://blog.discoveryeducation.com/wp-content/uploads/2016/03/mirrors-216x130.jpg" style="float: right; height: auto; margin: 0.5em 0px 0.5em 1em; max-width: 100%;" width="216" />I felt it was important enough to share is <em>Mirror Maze</em>. This photo is created by using mirrors in the shape of an equilateral triangle to make the maze. I sat in front of this photo for at least 15 minutes just following the reflections and identifying where I felt there could be inconsistencies while also looking for justifications of the inconsistencies. This is the type of thing that would make Geometry much more intriguing. The number of places it could fit in during the year is almost limitless.</div>
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All these are just pieces to a puzzle I have been trying to solve in my head and in the classroom for some time. Students have a limitless amount of stimulus throughout the day that take their attention away from the classroom. However, rarely do they find something that they could just stare at and be intrigued. The other piece to these photos is not only the depth of the mathematics but the access to many other levels of math. For example, most of a typical Geometry course could be made up with just these three photos and connecting the concepts between them.</div>
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My thoughts now settle on the art that I am missing to further enhance mathematics. On a side note and for our M.C. Escher enthusiasts. Check out <em>Going Up </em>and <em>Tricky Triangle. </em>These are not drawings, which often lead students to find M.C. Escher "cool" but not with the same curiosity as something real. These are photographs of real objects. Go ahead and find the intrigue.</div>
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<img alt="paradoxical pavillion" class="wp-image-68052 aligncenter" data-mce-src="http://blog.discoveryeducation.com/wp-content/uploads/2016/03/paradoxical-pavillion-104x130.jpg" height="194" src="http://blog.discoveryeducation.com/wp-content/uploads/2016/03/paradoxical-pavillion-104x130.jpg" style="display: block; height: auto; margin-left: auto; margin-right: auto; max-width: 100%;" width="155" /> <img alt="IMG_1254" class="wp-image-68053 aligncenter" data-mce-src="http://blog.discoveryeducation.com/wp-content/uploads/2016/03/IMG_1254-173x130.jpg" height="182" src="http://blog.discoveryeducation.com/wp-content/uploads/2016/03/IMG_1254-173x130.jpg" style="display: block; height: auto; margin-left: auto; margin-right: auto; max-width: 100%;" width="242" /></div>
Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-31814413208507361782016-02-12T18:37:00.002-08:002016-02-12T18:37:19.031-08:00Why a Retake doesn't enhance Learning...<div style="background-color: white; color: #333333; font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 16px;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMYcb2-g9t46E0dDuSmG3zxzONK-LUHrmrGBGsfpGmuX6xqv-a7sA8877GxT6yn_PFtKJ9UrY4gAcih5lhmQk1H7Bd36vo5UuMbRYuShVGiEz2rCytZCaxMS6leUEmRs3gWtFvtcHY770N/s1600/CB106388.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="213" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMYcb2-g9t46E0dDuSmG3zxzONK-LUHrmrGBGsfpGmuX6xqv-a7sA8877GxT6yn_PFtKJ9UrY4gAcih5lhmQk1H7Bd36vo5UuMbRYuShVGiEz2rCytZCaxMS6leUEmRs3gWtFvtcHY770N/s320/CB106388.jpg" width="320" /></a>Recently, a post on a listserv I am part of was discussing retakes at the secondary level and how different schools have structured them. The thread was well responded to and well thought out. We had responses from giving them in every case no questions asked to not ever allowing a retake. Some schools require certain things before a retake can begin, others allow a certain maximum number of retakes in a semester.</div>
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Throughout the thread, I read, but didn't respond. I wanted to know if my thoughts about retakes were unique, or being rather reflective, on the right track. In my experience, retakes have been frustrating to say the least. The culture of the my school has changed so drastically since the advent of the retake, it puts in question the core concept of should retakes happen. It has been pointed out to me that I never statistically determined that the retake is the cause of the cultural issues. Nope, I haven't. Personally, I don't feel I need to. When student's respond on the first assessment of the year that they "just want to look at it and take the retake tomorrow," I don't need a statistical analysis to determine there is a cultural issue and retakes, at minimum have something to do with it.</div>
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My beliefs about retakes are simple. Not only should they happen but they are an essential component of education. My guess is you may be a little surprised at that statement.</div>
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Retakes and RTI need to go hand in hand. If a student is retaking an exam, the question really needs to be why, not what percentage it should take in the grade. We should also be asking questions such as: What did the student do to not earn a passing grade? Do they have prior gaps preventing them from learning? Do they have poor work habits? Is our test based on work habits or learning? How can we design their day to best help enable them to succeed? Could the issue be a home issue and this is a one time instance? Or, is there a different underlying issue?</div>
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I feel it is too easy to pull the student responsibility card and much harder to look at it from an individual student perspective. It is important to remember that these are kids we are working with even though in most cases we want them to act as adults. This doesn't mean there are no consequences from poor choices. On the contrary, it means the complete opposite. If a student legitimately didn't do anything prior to the exam the true reaction should be they don't take the original assessment. Wouldn't this be more effective than allowing the student to fail initially. The retake needs to be used as a teaching tool, not a gift. Retakes don't lead to learning. If a retake needs to happen what is the reason. That is where the learning occurs. Should they happen, yes...after we have figured out what the root cause of the lack of learning is. Otherwise we are just perpetuating a viscous circle.</div>
Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-85221410371527221062015-12-01T20:49:00.001-08:002015-12-01T20:49:08.261-08:00Most Likely to SucceedSo here I sit late at night while sleep evades me. Not because it normally does but because of a movie. I read the book <i>Most Likely to Succeed</i> but the movie was far more powerful. Still not as powerful as a brief few words by an administrator at NTC but powerful. <br />
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Never am I one to swing the pendulum too far to one side. Let me explain. I see most of the "new things" in education as advancements that have both good and bad to them. Taking a look as some of the most recent best practices such as the flipped classroom and personalized learning leads to some very interesting conclusions. First, neither is showing much for results. Second, both are dependent on the right student culture. Third and most important both are only as strong as the teacher in the classroom. I like aspects of the flipped classroom just like I can see value in parts of personalized learning. I just don't see sustained success in either one individually. <br />
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Today's student is a new breed. Taking out the top 1/3 of the students that would succeed regardless of how they were instructed we are left with a mixed bag of students. Most of which would rather sit at home playing video games than trying to dig into something new. These students have a rather large issue coming at them. For the first time in my almost 2 decades of teaching I believe the world they are entering has the potential to be vastly different than the one we were in. I just don't think other teachers see this yet. For the past several decades not much has changed. Don't get me wrong, tons has but most people have a job, went on to school and became what they wanted to become. Now, unemployment is sustaining at a high rate in part I believe because technology is replacing people at a much faster rate than in the past. Furthermore, the climate of business almost promotes these changes. Normal manual labor is still necessary and to a degree will always be there. However, the jobs that are harder to find are the more skilled positions. Computers are taking those jobs and keeping them. <br />
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Most math teachers have a certain pride in our level of expertise to teach math. I must admit I really don't believe the students I produce become mathematicians. I just want them to be thinkers. Regardless nobody does the math we teach anymore. To respond to the pundits out there, yet some do but play the math game. Maybe 1 out of your entire building, not classroom, will go on to actually calculate/create using the math we teach. Computers do all the work. So why do we teach all of it? Why even bother? <br />
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Speaking for one I am done teaching the stuff that really doesn't matter. I am tired of preparing students to take an assessment that shows zero student success past the first year of college. I want to prepare students to succeed in life. My problem is where is the midpoint of all this transition. We can't just give up on all math. Students/Families will require us to have certain cognitive understandings. While at the same time I really want to see students thinking, creating, doing... How do we determine where to begin? <br />
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Where is the balance between enough background skill and enough group interactive skills to ensure a child succeeds? Then, even when we find it how do we communicate it? <br />
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Oh so many questions. I think it is going to be a long night...Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-69668444465391728932015-11-30T19:13:00.002-08:002015-11-30T19:13:12.994-08:00Making Retention Systematic<div style="background-color: white; color: #333333; font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 16px;">
It has been said for many years. "I'm not sure last years teachers did such a great job. Students don't even know (fill in your major topic that students should remember from a previous year)." Teachers had very little way of fixing this without practically going to last years teachers and accusing them of poor instruction (Even though this is an extreme situation it is far from uncommon).</div>
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Maybe this doesn't have to be the case anymore. The Common Core State Standards have had many advantages in the classroom. The most prominent may be a basic set of expectations that all teachers at a specific grade level should see in their classrooms. This base-level has made it possible for sites such as <span data-mce-style="text-decoration: underline;" style="text-decoration: underline;"><a data-mce-href="http://jeffbaumes.github.io/standards/" href="http://jeffbaumes.github.io/standards/">http://jeffbaumes.github.io/standards/</a></span> to make retention more than just a lucky happening. Not only does this site show clearly what standards your current instruction will lead to but easily identifies the "end" of a topic. It also has the ability to identify those topics that make one think...why do we need this taught at this grade level?</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRwkQLQ0Xo43wJ2JcowhANkGYavQFs2oSGbjZTPxncoONQNlfwSBE8Es4-RscMc1GDr71uEdE0BNGlCzDCX9Gv5jAvJ1HNC4sp15qYrBtDDl3VAe-i-bOkmXoJu3OswkSZUpZdOt-ClmGl/s1600/Screen+Shot+2015-11-30+at+8.08.38+PM.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="163" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRwkQLQ0Xo43wJ2JcowhANkGYavQFs2oSGbjZTPxncoONQNlfwSBE8Es4-RscMc1GDr71uEdE0BNGlCzDCX9Gv5jAvJ1HNC4sp15qYrBtDDl3VAe-i-bOkmXoJu3OswkSZUpZdOt-ClmGl/s320/Screen+Shot+2015-11-30+at+8.08.38+PM.png" width="320" /></a>After spending a while looking at the matrix, many of the standards I question happen to be Geometry standards. For example, 5.G.4 asks students to classify two-dimensional figures. Often, this is discussed in High School Geometry where inevitably we hear the words from teachers claiming students should know this "stuff" already. Should they? If we teach Geometry in 10th grade and the last time properties of 2-dimensional shapes is mentioned is in grade 5, a full half-decade earlier...should they remember? The same argument could be made for angle measurement, another common topic in 10th grade Geometry. Prior to Geometry the last time it was mentioned in the standards was in 4th grade. Using a protractor is such a foreign tool to begin with. Since it doesn't come up again until the 10th grade it makes sense that students struggle with what is perceived as a very basic task. Instructionally this begs 2 questions, the first of which I would rather not tackle.</div>
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Why is this topic in the grade if it not important enough to expand on for 5-6 full years?</div>
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How can this help us form instruction to enhance retention?</div>
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This site makes it quite easy to see what leads into your current topic (provided you are teaching in K-8). Take for example 7.G.2. This standard has no prior skills attached to it. Therefore we know that <span data-mce-style="text-decoration: underline;" style="text-decoration: underline;">all</span> the vocabulary is new, all the concepts are new, and that we clearly need to attack this standard from step #1. Taking a different perspective 6.EE.3 discusses the distributive property. Any elementary teacher will tell you how often the distributive property is instructed, used, discussed from multiplication algorithms, to area models, and many more concepts. The site confirms this. In 6th grade the teachers role should be to access its previous uses and expand on them working their way into algebraic expressions.</div>
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In education, too often we get caught up on the goal. Sometimes it makes more sense instructionally to look at learning from the students perspective and ask some important questions.</div>
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When was the last time this topic was discussed?</div>
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What was its context?</div>
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How can I expand on that context to tie it to the new standard?</div>
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It is those types of connections that make instruction effective. So thank you Jeff Baumes and Jason Zimba for your work on the dependencies in mathematics. Hopefully we can make effective use of your time.</div>
Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-50581677517717738152015-11-17T19:49:00.000-08:002015-11-17T19:49:17.292-08:00A New Persepctive...Inquiry Based Learning<div style="background-color: white; color: #333333; font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 16px;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzNJo_eEw3dljpZQ_h04CAkgZzDr7xyIfOMmr4m_mocV7ZP0Laaqh6B7dJ9B0h4zZD0A0jcO7mLJ_g9KBFIKUn4WXZwAS79jhXamAC0PatCynhwEzfkadrpXIkx_bhTiYa77kWVFgTPDaJ/s1600/images.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="212" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzNJo_eEw3dljpZQ_h04CAkgZzDr7xyIfOMmr4m_mocV7ZP0Laaqh6B7dJ9B0h4zZD0A0jcO7mLJ_g9KBFIKUn4WXZwAS79jhXamAC0PatCynhwEzfkadrpXIkx_bhTiYa77kWVFgTPDaJ/s320/images.jpg" width="320" /></a>There are numerous studies that point to the need for instruction to be inquiry based. Personally I cannot disagree. What a student can figure out on their own versus being told will stick with them for years to come. However I cannot help but think it is not just the inquiry process that enables the learning. In fact, it may not have anything to do with it. It is the changes in instruction forced by that process that matter the most. In John Hattie's research about educational practices anything with an effect size greater than 0.7 is foolish not to incorporate into teaching and learning. Anything </div>
above a 0.5 is a medium effect size and still should be implemented. Looking at Hattie's research things such as reciprocal teaching, self-verbalization/questioning, problem solving techniques, and cooperative learning all have effect sizes of 0.59 or greater. These strategies are the same strategies that would be implemented with inquiry based learning. Today we call this high quality discourse. <br />
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As we delve further into an inquiry based model of instruction we find that there are limitations that need to be addressed. Teaching students to think deeply is essential. However, so is preparing them conceptually to proceed to the next grade level. In writing this blog I don't want to debate the K-12 industrial system we call education. The reality is almost every school in this great nation uses a grade level advancement system where one grade level has certain expectations or standards that need to be addressed. The Common Core is built off this understanding. Therefore, I'll put a non-negotiable out there that the Common Core State Standards need to be instructed and understood by all students at the appropriate grade level. Inquiry instruction takes time. A lot of it. The great mathematicians of the past didn't discover this stuff we call mathematics in a 42 minute period. </div>
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My question is how much time should we devote to discovering things that have already been discovered versus applying those things in a context that could be used today?</div>
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The reality is we don't have the time to discover every topic. We have to decide which topics just need to be directly instructed and which can be found through an inquiry process. By the way, direct instruction has an effect size of 0.59 according to Hattie which is the same as cooperative learning. Once we admit that not everything can be discovered, or needs to be, it begs the question of what gets learned through an inquiry model? What are the most important concepts for students to dig into as deeply as possible? Once we have determined that, then determine what is the most engaging way I can instruct these topics enabling students to not only be able to complete the concept but more importantly, understand and apply it in a timely manner.</div>
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Inquiry is a form of instruction but the methodologies are what make it strong. Using those same methods in a non-inquiry form of instruction will speed things up but also should enable students to continue to retain the knowledge. The most important thing, until the industrialized version of education changes, is that students have an opportunity to engage, inquire, and retain the information necessary to move forward. Where ever forward is.</div>
Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-50479475166144046782015-09-04T12:23:00.002-07:002015-09-04T12:26:04.222-07:00What "this" means for Math Education???<div style="background: white;">
<span style="font-family: Trebuchet MS, sans-serif;">It wasn't that long ago that Math was the subject that never
changed. We had our postulates, theorems, graphs, and our clear steps to
solving equations. The advent of the graphing calculator was about the
biggest event in math education since, well, forever. Sadly, even today
some teachers still resist its use.<br /><br />It seems now math is the subject in schools that doesn't stop
changing.<br /><br />The change may have
coincided with the Common Core State Standards but that was not the push.
It started well before that but only is gaining traction in the last few
years. The change is causing educators to rethink how we teach, what we
teach, the tools we use to teach and what students have the potential to do.
The change isn't just one thing but an onslaught of instructional
opportunities. An interesting piece of technology that came out a short
while ago as improved to the point of being interesting is <i><a href="https://youtu.be/WvIoYUr1SWI" target="_blank">Photo Math</a>.</i></span></div>
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<tr><td style="text-align: center;"><span style="font-family: Trebuchet MS, sans-serif;"><img alt="" border="0" height="186" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEKmo46Be3_qmHzlbQVvCD_8XJiDe8c4x4qx57DW0JFsxCu9Sw7xSs76SxJ6o513BuVmyjoM7hI9EGRIXrgjJEgNp_ZoOArGrommPDkIOwSa4ACZEkey85h8FNVOsD-6WtugTATGROhcrR/s320/Screen+Shot+2015-09-03+at+9.28.41+PM.png" style="margin-left: auto; margin-right: auto;" title="Photo Math" width="320" /></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Trebuchet MS, sans-serif;">Photo Math <a href="https://youtu.be/WvIoYUr1SWI" id="LPlnk487318" previewinformation="1" style="background-color: white; font-family: wf_segoe-ui_normal, 'Segoe UI', 'Segoe WP', Tahoma, Arial, sans-serif; font-size: 15px; text-align: start;" target="_blank">https://youtu.be/WvIoYUr1SWI</a></span></td></tr>
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<span style="font-family: Trebuchet MS, sans-serif;"><i>"Photo Math</i> reads and solves mathematical problems by using the camera of your mobile device in real time. It makes math easy and simple by educating users how to solve math problems." Not sure about the educating portion but it truly works. Typed equations of almost any kind can be solved with all of their steps shown in a blink of an eye. I tried it on a traditional Algebra 2 textbook. It solved everything from multi-step equations to logarithms to systems of equations with 3 variables. It solved it all. So what does this mean for math education. Are we to put our slide rulers away and just take a seat on the side? Is our career in jeopardy?</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;">The answer lies in math. What is math truly about? It's not about solving equations and multiplying correctly. It is about patterns and logical reasoning. This occurs outside everything everyone thinks is math. It's about continuing the direction we are heading and making it stick. Apps like <i>Photo Math</i> won't help solve an applied problem. They won't help visually show why the best price point for a product is $8.57 according to a set of supply and demand equations. They won't help analyze data or learn why higher mathematics is important to learn. </span><br />
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<span style="font-family: Trebuchet MS, sans-serif;">The easy solution is to ban the phone from the classroom or lock the iPad to only use a basic calculator upon entering the classroom. The short sightedness of that is scary. To ignore the opportunities to truly understand and enhance math through the plethora of available apps is to ignore an entire generation of students who are able to play and learn higher levels of mathematics than we dreamed possible before. Not the math of algorithms. The math of applications. </span><br />
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<span style="font-family: Trebuchet MS, sans-serif;">We live in a world where application is now easy. Video, sound, photo are all made readily available by the same phone that makes a skill and drill problem useless. We are entering a new playing field. It is time to take our skills-based DOK 1 and 2 style questions out of our summative assessments, place them as learning skills and formative assessments throughout a unit and focus on how to apply those same skills in a setting that means something to students. People like Dan Meyer began the momentum several years ago and we started to listen. Then others joined the game like Jo Boaler who decided to not just focus on tasks but on how we instruct and what we expect. Now programs such as the Discovery Math TechBook change the way we offer instruction using a constructivist style learning with an emphasis on real applications. We are finally seeing the combination of resources and quality instruction.</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjDnbCpCTRANs_ik_LJWvk0yX3cMtHLabL-c71Fu1F-pfsEghc_pD4bGnA9VKRzp6Er1UbSmzhxIqgX8t80JDVTyiAfLXN47-lfhqDrHgaJMA6SqQ-KQAHQg0DVmvRJvGcLoX8I24qk5gH/s1600/discovery.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjDnbCpCTRANs_ik_LJWvk0yX3cMtHLabL-c71Fu1F-pfsEghc_pD4bGnA9VKRzp6Er1UbSmzhxIqgX8t80JDVTyiAfLXN47-lfhqDrHgaJMA6SqQ-KQAHQg0DVmvRJvGcLoX8I24qk5gH/s320/discovery.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Discovery Education <a href="http://www.discoveryeducation.com/what-we-offer/techbook-digital-textbooks/math/index.cfm" target="_blank">Math TechBook</a></td></tr>
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<span style="font-family: Trebuchet MS, sans-serif;">For the first time in history technology and resources are catching up to classroom pedagogy. It's up to us as teachers to make math instruction be what it was always meant to be. A search for a better more efficient way to the find the solution to any problem life throws at them.</span><br />
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<br />Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-48024439186475292192014-11-06T07:54:00.000-08:002014-11-07T13:00:48.732-08:00Confessions of a constructivist/pragmatic teacher.<div>
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<span style="font-family: 'Segoe UI'; font-size: 10pt; font-stretch: normal;">I did a major application today. It is below. <span class="Apple-converted-space"> </span><br /><br />The goal was to engage the students in the topics we are trying to get them to understand (determining profits - new topic). Of course, a simple application doesn't cut it. The plan was small group work for 10 minutes, then every 1-2 minutes a new group would come up and "add to the problem" slowly forming the process and understanding. Periodically I would interject and ask questions but mostly I just talked group to group<span class="Apple-converted-space"> </span></span><span style="font-family: 'Segoe UI'; font-size: 10pt; font-stretch: normal; text-decoration: underline;">never</span><span style="font-family: 'Segoe UI'; font-size: 10pt; font-stretch: normal;"><span class="Apple-converted-space"> </span>saying an answer was correct. <span class="Apple-converted-space"> </span><br /><br />Here are my results:</span><br />
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<li><span style="font-size: 10pt;">The students HATED the large "real" numbers. (my response was that they were the reality, not fake school numbers - they got past this)</span></li>
<li><span style="font-size: 10pt;">Period 1 did awesome - fully engaged except for 1 child who is making poor choices. They really liked it.</span></li>
<li><span style="font-size: 10pt;">Period 2 did fine but their struggles indicated a lack of knowledge in the pre-steps (served as a great formative - with things I can address tomorrow)</span></li>
<li><span style="font-size: 10pt; font-stretch: normal;">The<span class="Apple-converted-space"> </span></span><span style="font-size: 10pt; font-stretch: normal; font-weight: bold;">discussions</span><span style="font-size: 10pt; font-stretch: normal;"><span class="Apple-converted-space"> </span>in the small groups cannot be understated. They are the backbone to why we<span class="Apple-converted-space"> </span></span><span style="font-size: 10pt; font-stretch: normal; text-decoration: underline;">need</span><span style="font-size: 10pt; font-stretch: normal;"><span class="Apple-converted-space"> </span>to do these applications. Priceless.</span></li>
<li><span style="font-size: 10pt;">I was bombarded with questions after each class - the kids wanted to know the results - To be continued into tomorrow.</span></li>
<li><span style="font-size: 10pt; font-weight: bold;"> NO TIME WAS LOST because this method replaced a lesson. In fact, I would estimate time was SAVED giving more time for depth!</span></li>
<li><span style="font-size: 10pt; font-stretch: normal;"><span style="color: red;">My kids stink at problem solving. If they are not handed the process they quit. This in unacceptable to me. MP #1</span></span></li>
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</span><span style="font-family: 'Segoe UI'; font-size: 10pt; font-stretch: normal;">These applications do not always work in our content. However, they work more than I feel we say they do simply because we are at times afraid to make that leap of faith that a lesson that is not the norm will work. Today, was a leap of faith for me. Not because I have never done this but the task was so rigorous for this clientele. My class is clearly not advanced (more on the remedial side for a senior - they are not "math" kids). <span class="Apple-converted-space"> </span></span></div>
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<span style="font-family: 'Segoe UI'; font-size: 10pt; font-stretch: normal;"></span><span style="font-family: 'Segoe UI'; font-size: 10pt; font-stretch: normal; font-weight: bold;">By the way: This problem was not found - it is not in any book - I made it on my own time using Google to find numbers. Unfortunately, what every study says in regards to quality math instruction is not what textbooks produce. They produce what the public wants. We need to challenge the norm and apply our math. </span></div>
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Apple Inc. sells its 16GB iPhone 5S for $649. It costs Apple $335.00 to manufacture the iPhone including packaging, labor, freight, and warranty renewals according to a report published by<span class="Apple-converted-space"> </span><a href="http://online.wsj.com/public/quotes/main.html?type=djn&symbol=UBSN.VX"><span style="color: #218db4;">UBS</span></a><span class="apple-converted-space"> </span>AG. Apples fixed cost is in excess of $5 billion dollars. However, they sell many more products than the iPhone. Assume for this situation that their fixed costs are $7.4 million dollars. The iPhone is a highly sought after phone in the SMART phone market. The demand function is<span class="Apple-converted-space"> </span><span class="Apple-converted-space"><!--[if !mso]>
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Given this information, use your classes know-how to help determine if Apple Inc. has priced its iPhone correctly. <b>What should the price of the iPhone be in order for Apple to maximize its profit?.</b><br />
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Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-72283514880100654592014-07-02T04:20:00.001-07:002014-07-06T14:22:25.683-07:00Enrichment #1 - 3rd - 6th Grade (Taipei-101)This is the first in what is hopefully a series of enrichment problems at different grade levels. The goal is to take a problem that has potential and make is something better. All the problems can be used at different grade levels with different expectations. <br />
<br />
Collaboration is the key. Post how you would edit the problem. I will edit it as the week goes on. The initial problem will be up for 1 day without any edits. Be creative - think outside the box. What would make this problem a much better problem or task? Can we differentiate the problem to meet a broader audience? What would make it more rigorous and meet the needs of the 21st century learner?<br />
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<b><span style="color: blue;">Taipei-101</span></b><br />
<b><span style="color: blue;"><br /></span></b>
<span style="color: blue;">Taipei-101 is the 2nd tallest building it the world. The building has 101 floors averaging 22 steps per floor. If you were to walk from the 1st floor to the top of the building, how many steps would you have to climb?</span><br />
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<b>EDITS - let me know what you think...</b><br />
<b><br /></b>
3rd Grade: https://drive.google.com/file/d/0B9nQxOSHG8M0Q3JGT29nR29Cdmc/edit?usp=sharing<br />
4th Grade: https://drive.google.com/file/d/0B9nQxOSHG8M0UW9WM0kxQ1ZUdUE/edit?usp=sharing<br />
5th Grade: https://drive.google.com/file/d/0B9nQxOSHG8M0cFhHVGZzdFUtQnM/edit?usp=sharing<br />
6th Grade: https://drive.google.com/file/d/0B9nQxOSHG8M0M0JxSllLYnRfczA/edit?usp=sharingMark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-26092781557666200732014-06-11T09:07:00.002-07:002014-06-12T07:37:05.108-07:00Equal Sign Survey<span style="font-family: Trebuchet MS, sans-serif;">This question was given to all 2nd - 8th graders in my district. I found this survey at the WI Math Conference and wanted to see what the students understanding of the equal sign was. <span style="color: blue;"> </span><span style="color: blue; font-weight: bold;">I learned so much more</span>...</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxME_vvK0Nu8plo1Aes-1sVxVamvJxcc2YFmjYoyWEHJMBmikUrB4yI5kuFrlR1OWjmfA4DK5rmZfXFPGi-Xo4jrsks9O8Yll_w5nzHdRFKg4_JEDmr10oAGRv12nthdHuchfiMvmukLHo/s1600/equal+sign.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxME_vvK0Nu8plo1Aes-1sVxVamvJxcc2YFmjYoyWEHJMBmikUrB4yI5kuFrlR1OWjmfA4DK5rmZfXFPGi-Xo4jrsks9O8Yll_w5nzHdRFKg4_JEDmr10oAGRv12nthdHuchfiMvmukLHo/s1600/equal+sign.png" height="140" width="400" /></a></div>
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<u style="font-family: 'Trebuchet MS', sans-serif; font-weight: bold;">The Data Results</u><span style="font-family: 'Trebuchet MS', sans-serif;">:</span></div>
<span style="font-family: Trebuchet MS, sans-serif;">First, for the data geeks, the data set is 400-450 students per grade level and over 50% were scored for each level. </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span>
<span style="font-family: Trebuchet MS, sans-serif;">As hoped, the proficiency of students increased on the correct answer by grade level with the exception of 8th grade. However, the statistical significance may be irrelevant. </span><span style="font-family: 'Trebuchet MS', sans-serif;">Regardless</span><span style="font-family: 'Trebuchet MS', sans-serif;">, we are at 90% correct. That is pretty good.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaVnhdHpgUtjAknJyOTLzw3-vFLvR2Qyh-b7en80QQJOKKYbLDYKie3d2MpGjoQ6LUtQ7iBl84WRvKEIXqLYtpzopEgoa_1rxV-ZuSxnI9tdxvC45w1q245Oj2AULuF5tzQy_aoWK59G8A/s1600/Data+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaVnhdHpgUtjAknJyOTLzw3-vFLvR2Qyh-b7en80QQJOKKYbLDYKie3d2MpGjoQ6LUtQ7iBl84WRvKEIXqLYtpzopEgoa_1rxV-ZuSxnI9tdxvC45w1q245Oj2AULuF5tzQy_aoWK59G8A/s1600/Data+1.png" /></a></div>
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<span style="font-family: Trebuchet MS, sans-serif;">The more <b style="color: blue;">interesting</b> data is the quality of the explanations. Here is how the scoring worked.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"> 0 - No explanation </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"> 1 - Significant logical errors in the explanation</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"> 2 - Logic was acceptable but the explanation either had errors, was only calculation</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"> based or was guess and check</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"> 3 - Explanation was the process used. It either explained how they achieved the </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"> solution (algorithm) or implied an equality of the two sides.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"> 4 - </span><span style="font-family: 'Trebuchet MS', sans-serif;">Student specifically stated that the left side of the equation had to equal the right. </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"> It was not just implied.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaBqJALrEeljzBwgiuWyf69DdgnXcxdEHtZIwr0iH2-4sCD1UR4JK93Fl7699KuzvO2nB5gdRIULZfobg3E_bre3A_0rXVKf_b9nFUbmDlH3R5zEn4Z8P6qg7z2ckFy6Ap4i_705aFQNfj/s1600/data+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaBqJALrEeljzBwgiuWyf69DdgnXcxdEHtZIwr0iH2-4sCD1UR4JK93Fl7699KuzvO2nB5gdRIULZfobg3E_bre3A_0rXVKf_b9nFUbmDlH3R5zEn4Z8P6qg7z2ckFy6Ap4i_705aFQNfj/s1600/data+2.png" /></a></div>
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span>
<span style="font-family: Trebuchet MS, sans-serif;">The understanding of what the equal sign means varied greatly not only by grade level but by school. The chart below is bothersome for a few reasons. The first is the red square which represents almost 1 in 10 students didn't even bother to put an explanation down. <span style="color: blue;">How would those students perform on the SMARTER Balanced Assessment? </span><b style="color: blue;"> </b>The remaining parts that bother me have more to deal with the quality of the explanation than anything. Students, at minimum, should have been able to explain to a level of 3. The amount of students that only put down calculations increased as they got older (Schools A and B). Also, the clarity of how each building emphasizes how to explain something is supported in this question. </span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><span style="color: blue;"><b><br /></b></span></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju6vcURy4Mb238EC_Kp-0XX_K50s8bjZCbLJ5f-7AuV866rEOPD-d4IFkBlIVORdryprdBuT3Byxspd3XLzasHkG9nmpS3mXjxwXt3DbSJm432CJrXSZycYM63KRFb8k7s5Gf0bMu7AfK0/s1600/Data+C.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEju6vcURy4Mb238EC_Kp-0XX_K50s8bjZCbLJ5f-7AuV866rEOPD-d4IFkBlIVORdryprdBuT3Byxspd3XLzasHkG9nmpS3mXjxwXt3DbSJm432CJrXSZycYM63KRFb8k7s5Gf0bMu7AfK0/s1600/Data+C.png" height="85" width="400" /></a></div>
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span>
<span style="font-family: 'Trebuchet MS', sans-serif;">Students who were incorrect most commonly answered 18 or 23. However, other incorrect answers were 0, 1, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 19, 20, 22, 24, 25, 26, 28 and 78. A challenge would be to figure out how they worked out all those answers.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><b><u>Where do we go from here?</u></b></span><br />
<span style="font-family: Trebuchet MS, sans-serif;">The number of students who answered 18 and 23 is alarming and indicates a teaching error. In other words - WE OWN THIS PROBLEM. Students did not show a clear understanding of what the equal sign means. One can only assume that when we teach the math operations we run a string and continue to add numbers to the right. <b>Mathematically - this is incorrect. </b></span><br />
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<span style="font-family: Trebuchet MS, sans-serif;">12 + 6 = 18 is a correct statement</span></div>
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<span style="font-family: Trebuchet MS, sans-serif;"><br /></span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">However, if we add more: 12 + 6 = 18 + 5 = 23</span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">This is no longer correct because the values are <span style="color: red;">not equal</span>. </span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">12 + 6 is not equal to 18 + 5</span></div>
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<span style="font-family: Trebuchet MS, sans-serif;"><br /></span></div>
<div>
<span style="font-family: Trebuchet MS, sans-serif;">To write this correctly, we would make a new row.</span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">12 + 6 = 18</span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">18 + 5 = 23</span></div>
<div style="text-align: center;">
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">The other portion that we own is how our students explain things. Explanations in math should not just be the math process in words. See the <a href="https://docs.google.com/file/d/0B9nQxOSHG8M0dm43RzhMb2ZwNGs/edit" target="_blank">exemplars</a> for more clarity.</span></div>
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<span style="font-family: Trebuchet MS, sans-serif;"><br /></span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">So, I pose to you...</span><b style="font-family: 'Trebuchet MS', sans-serif;">how are you teaching your math?</b></div>
Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-8869764293337463342014-06-06T07:35:00.006-07:002014-07-02T04:32:58.505-07:00Jump Starting the Summer...<span style="font-family: Trebuchet MS, sans-serif;">Smiling while I write this...Did you know there are 2,970 2nd - 8th graders. I did, but didn't really think how many 2 part assessments that is to correct. I am about 18 inches in interoffice folders from having them all corrected. </span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span>
<span style="font-family: Trebuchet MS, sans-serif;">While everyone waits in <span style="color: red;">unabated anticipation</span> 8-) take a moment and wager a guess on the polls at the right. </span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span>
<span style="color: blue; font-family: Trebuchet MS, sans-serif;">If you are curious - the scoring went as follows:</span><br />
<span style="color: blue; font-family: Trebuchet MS, sans-serif;"> obviously the correct answer was noted</span><br />
<span style="color: blue; font-family: Trebuchet MS, sans-serif;"> For the explanation a student:</span><br />
<span style="color: blue; font-family: Trebuchet MS, sans-serif;"> 4 - <u>had</u> to state the two sides needed to be equal in words - not just imply it</span><br />
<span style="color: blue; font-family: Trebuchet MS, sans-serif;"> 3 - had the right idea - it was more a process explanation than anything</span><br />
<span style="color: blue; font-family: Trebuchet MS, sans-serif;"> 2 - had the concept was there but there was an error in it</span><br />
<span style="color: blue; font-family: Trebuchet MS, sans-serif;"> 1 - had an improper process</span><br />
<span style="font-family: Trebuchet MS, sans-serif;"><br /></span>
<span style="font-family: Trebuchet MS, sans-serif;">What I know already is that <b>we own these errors in student thinking. </b> More on that later.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCUwcAB7fRWyaz6AZRGXL11ktNsNuMa5T3bbrOHHwMUD1VhByI9orDN-83MoTNLTQjAfKEipvvs_HrK1IEgZ_T5n0m7PFcuR47yn3JddfkxcPpAje0C2w2lcqHSRyxjBtyeG0qRW1IwzPr/s1600/equal+sign.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCUwcAB7fRWyaz6AZRGXL11ktNsNuMa5T3bbrOHHwMUD1VhByI9orDN-83MoTNLTQjAfKEipvvs_HrK1IEgZ_T5n0m7PFcuR47yn3JddfkxcPpAje0C2w2lcqHSRyxjBtyeG0qRW1IwzPr/s1600/equal+sign.png" height="224" title="" width="640" /></a></span></div>
Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-26649476596339665122014-05-22T08:42:00.002-07:002014-05-22T08:42:33.624-07:00Have the World's Best Athletes Improved?<span style="font-family: Trebuchet MS, sans-serif; font-size: x-small;"><span style="color: red;">Pardon the interruption from typical blogging but I need to get my students some web sites and trust this resource to do that. </span> </span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz8jVaxOu07nWIKUoW1MSLFYNHYli_2nS3LzBCIc2kF3l8tPBCqwA1ZK1yR16fZy40ROYTQuuI2e4kdoMRLSw9Di__MxXejTAKXUNkqcpzDO_Vb9drAPlTPql7h7zXlEdjQSVltPEvj-_M/s1600/olympic.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Trebuchet MS, sans-serif; font-size: x-small;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz8jVaxOu07nWIKUoW1MSLFYNHYli_2nS3LzBCIc2kF3l8tPBCqwA1ZK1yR16fZy40ROYTQuuI2e4kdoMRLSw9Di__MxXejTAKXUNkqcpzDO_Vb9drAPlTPql7h7zXlEdjQSVltPEvj-_M/s1600/olympic.png" height="215" width="320" /></span></a></div>
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<span style="font-family: Trebuchet MS, sans-serif; font-size: x-small;">Have the world’s elite
athletes improved?<o:p></o:p></span></div>
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<span style="font-family: Trebuchet MS, sans-serif; font-size: x-small;">The
100 meter dash has been run at the summer Olympics for decades. Using the data provided, determine if humans
are getting faster, slower, or staying about the same. A solid statistical analysis must be provided
to support your position. <o:p></o:p></span></div>
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<span style="font-family: Trebuchet MS, sans-serif; font-size: x-small;"><b>Data:</b><o:p></o:p></span></div>
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<u><span style="color: red;"><span style="font-family: Trebuchet MS, sans-serif; font-size: x-small;"><a href="http://en.wikipedia.org/wiki/Athletics_at_the_1952_Summer_Olympics_%E2%80%93_Men's_100_metres">http://en.wikipedia.org/wiki/Athletics_at_the_1952_Summer_Olympics_%E2%80%93_Men's_100_metres</a><o:p></o:p></span></span></u></div>
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<u><span style="color: red;"><span style="font-family: Trebuchet MS, sans-serif; font-size: x-small;"><a href="http://en.wikipedia.org/wiki/Athletics_at_the_1972_Summer_Olympics_%E2%80%93_Men's_100_metres">http://en.wikipedia.org/wiki/Athletics_at_the_1972_Summer_Olympics_%E2%80%93_Men's_100_metres</a><o:p></o:p></span></span></u></div>
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<u><span style="color: red;"><span style="font-family: Trebuchet MS, sans-serif; font-size: x-small;"><a href="http://en.wikipedia.org/wiki/Athletics_at_the_2012_Summer_Olympics_%E2%80%93_Men's_100_metres">http://en.wikipedia.org/wiki/Athletics_at_the_2012_Summer_Olympics_%E2%80%93_Men's_100_metres</a><o:p></o:p></span></span></u></div>
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;"><b>Requirements:</b></span></div>
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<li><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">·
</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">Lists, summaries, conclusion, and anything
else should be typed</span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">·
</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">Graphical displays should be neatly
written or done on the computer</span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">·
</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">Typed paper supporting your position</span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">·
</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">Organized mathematical proof supporting
your position (does not need to be typed)</span></li>
</ul>
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<span style="font-family: Trebuchet MS, sans-serif; font-size: x-small;"><b>Scoring:</b><o:p></o:p></span></div>
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<li><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">·
</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">The score of your project will depend on
the quality of your analysis, the presentation, and the overall </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">quality of your
writing. </span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">·
</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">See the back of this page for the scoring
rubric.</span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">·
</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-indent: -0.25in;">This project will count towards the core
knowledge portion of your last assessment.</span></li>
</ul>
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<br />Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-8442974366458439412014-04-16T18:30:00.001-07:002014-04-16T18:30:11.422-07:00Doing it the Right Way!<span style="font-family: Trebuchet MS, sans-serif;">Call me a dreamer, call me anything you want but I see no purpose in doing things (even if ultimately I think they are flawed) only to get them done. Educator Effectiveness (EE) is a perfect example of a major opportunity to just check something off the list and have it not affect student performance.</span><div>
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<span style="font-family: Trebuchet MS, sans-serif;">I am not sure I totally agree with the premise behind Educator Effectiveness. I am sure I disagree with the time commitment necessary to do it because every minute spent on it is another minute spent away from kids. However, be that as it may it is a state mandate and optional was not a word I read anywhere. We have spent a decent amount of time talking about Student Learning Outcomes (SLO's) and choosing SLO's that will be manageable but more importantly have an opportunity to not only affect our instruction but student learning. Several schools are deciding to use purchased screeners such as SMI, AIMSweb, MAPS or STAR. The problem with each one of them is we didn't write them. We don't control what is on them and we have zero control over the rigor. All of them are multiple choice and therefore will give the teacher no information on how deeply a student understands a concept. The CCSS is very clear that students not only need to conceptually understand a topic but also need to be able to apply it. </span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">So back to our SLO's. So far I can say I am proud of our PLC's. Each PLC, after lots of thought and debate have chosen to assess prerequisite skills necessary for success and either student understanding of a major concept of overall understanding of the core concepts needing to be learned in class. Why are these important? First, we will know what information our students are coming in with and creating interventions to meet the needs of those who struggle and those who need a greater challenge. Ensuring that <u>all</u> students know the prerequisite skills (I would rather call them prerequisite understandings) will pay major dividends throughout the year. Secondly, having an emphasis on concept proficiency is an easy goal since that is the same goal we have each year. However, this focus has many byproducts. For example, what is proficiency? At what level of rigor? Should they have to explain their solution? Should it be applied? When should proficiency be determined? The discussions extending from this SLO are changing instruction and assessment for the better every day. </span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">Ideally, one would think that these discussions should happen regardless and I would totally agree. What I know is we don't control what makes something important to one person and not to another. We also don't exactly know what is going to make someone change their ways and analyze how they are going about their instruction. I do know that if I do my best with everything, never just trying to check it off a list eventually, I will find something that is that right trigger for everyone. </span></div>
Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-37200198908029947092014-03-20T19:50:00.001-07:002014-03-20T19:50:16.857-07:00What works in Math Education?<span style="font-family: Trebuchet MS, sans-serif;">We know that starting a lesson with an engaging aspect that ties students into what they have been learning or what they will be learning. </span><br />
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<span style="font-family: Trebuchet MS, sans-serif;">We know that a teacher who understands students and gets to know them at a personal level gains their effort, their attention and most importantly their respect. </span><br />
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<span style="font-family: Trebuchet MS, sans-serif;">We know that just assigning homework has little effect on kids. However, giving practice to students that ties to their level of learning and then provides quality feedback enables students to challenge themselves and to understand where they can continue to improve. </span><br />
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<span style="font-family: Trebuchet MS, sans-serif;">We know that a teacher who finds creative ways to reach students through interactive collaborative lessons ends up with students who understand what it means to learn and in the end...learn.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;">We think we know a lot about math education. However, do we have proof that it works? John Hattie says we do. Can we do it better? What else should we be looking at?</span><br />
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<span style="font-family: Trebuchet MS, sans-serif;">John Hattie determined that any effect size over 0.4 has positive effects but an effect size over 0.7 simply needs to be done in the classroom. After reading <i>Visible Learning</i>, I have taken his list and focused it on the math classroom. What should we be doing?</span><br />
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<li><span style="font-family: Trebuchet MS, sans-serif;">Students self-reporting their grades (1.44)</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">Formative assessment (1.28)</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">Acceleration (0.88) - Personally I don't agree with this one</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">Teacher Clarity (0.75)</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">Differentiated Practice (0.71)</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">Meta-Cognitive Practices (0.69)</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">Vocabulary Programs (0.67)</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">Problem Solving Teaching (0.61)</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">Cooperative vs. Individualistic Learning (0.6)</span></li>
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<span style="font-family: Trebuchet MS, sans-serif;">These are some of the best practices for the general classroom. If these are great practices then where does typical math instruction fit in?</span></div>
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<li><span style="font-family: Trebuchet MS, sans-serif;">Direct Instruction (0.59)</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">Mastery Learning (0.58)</span></li>
<li><span style="font-family: Trebuchet MS, sans-serif;">Worked Examples (0.57)</span></li>
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<span style="font-family: Trebuchet MS, sans-serif;">It takes only a quick reference to realize that these strategies are still effective strategies and students will learn. Imagine if we did less of the traditional instruction and more of the practices listed above as a general rule in education. </span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">Where could are kids be then?</span></div>
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<br />Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0tag:blogger.com,1999:blog-1689618624018786848.post-70911342446556903972014-02-23T19:48:00.000-08:002014-02-23T19:48:01.651-08:00Update on senate bill<br />
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<span style="background-color: rgba(255, 255, 255, 0);">Thank you all for your time and energy in reaching out to the legislature regarding SB 619 and AB 617. I know that many people made calls, forwarded my initial email, and made their voices heard. Several things have happened since I wrote, and I'd like to update you on them and make another call to action.</span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">On Wednesday, Assembly Bill 617 was amended to match Senate Bill 619, which in brief is the bill intended to create a legislatively-appointed board to create new model academic standards. On Thursday, the Assembly Education Committee indefinitely tabled consideration of the bill, but it could be reconsidered at any time (and I understand it is likely to be brought back next week). There is still some significant push behind bringing this bill to a vote. I do believe that our efforts in part slowed down this process and gave us more time and opportunity to be heard.</span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">Erin Richards, the excellent reporter at the education desk of the Journal Sentinel, managed to uncover who is behind this bill. According to her story, the bill was drafted by the Walker administration, in consultation with legislators, and was handed to Senator Vukmir for introduction. See story here:<a href="http://www.jsonline.com/news/education/standards21-b99209908z1-246343221.html">http://www.jsonline.com/news/education/standards21-b99209908z1-246343221.html</a></span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">Tony Evers, on Wednesday, issued a call to action, describing the bill and its impact. Watch his 3 minute message here:</span></div>
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<a href="https://www.youtube.com/embed/Z7fNt5HocvY?list=PL6361FCDE05564015" style="background-color: rgba(255, 255, 255, 0);"><span style="color: black;">https://www.youtube.com/embed/Z7fNt5HocvY?list=PL6361FCDE05564015</span></a></div>
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<span style="background-color: rgba(255, 255, 255, 0);">Senator Paul Farrow, in response, wrote a scathing open letter to Dr. Evers with a number of stern accusations. I'm attaching that memo. In it, he cited NEA opposition to the Common Core, in the form of a letter from NEA President Van Roekel. You can read his letter here, which is in my view inaccurately represented in Senator Farrow's letter.</span></div>
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<a href="http://neatoday.org/2014/02/19/nea-president-we-need-a-course-correction-on-common-core/?utm_source=nea_comms&utm_medium=email&utm_content=dvr_ccss&utm_campaign=140219neacomms" style="background-color: rgba(255, 255, 255, 0);"><span style="color: black;">http://neatoday.org/2014/02/19/nea-president-we-need-a-course-correction-on-common-core/?utm_source=nea_comms&utm_medium=email&utm_content=dvr_ccss&utm_campaign=140219neacomms</span></a></div>
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<span style="background-color: rgba(255, 255, 255, 0);">We also know that Representative Theisfeldt was instrumental in not only bringing the Assembly bill into line, but leaking the details to the Common Core opposition (Stop Common Core in Wisconsin Facebook group) to ramp up support.</span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">Finally, DPI's attorneys has reviewed the bill and weighed in on the implications. They concur that the bill as written gives the legislature the power to set standards. See memo attached.</span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">We are still at risk and we need to make our voices heard. </span></div>
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<b style="background-color: rgba(255, 255, 255, 0);">Here is my request for action.</b></div>
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<span style="background-color: rgba(255, 255, 255, 0);"><span style="font-style: italic;">-</span>Read the bills and the supporting documents I've linked here. Also read Senator Farrow's memo and my annotations in red with rebuttal points (link below), and the DPI legal memo on the implications (link below).</span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">-Contact your senator and representative again. My own were completely uninformed about the two bills when I called on Wednesday.</span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">-Make two more calls if you can to members of the Senate and Assembly Education Committees. (If you can contact them all, contact them all.) Links below.</span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">-Distribute this information far and wide.</span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">I've drafted a set of talking points that you may find useful in crafting your argument (link below). At the end are some questions that we should be asking of any legislator we talk to, and encouraging others to ask. Calls are best, but if you can't call, emails are an excellent option. I know you are all very busy people and you may not have time to set aside to make the calls. Many offices now have the ability to take voice messages, so you may be able to get some work done on this over your weekend.</span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">Please don't hesitate to contact me with questions. Remember also that DPI, by rule, cannot lobby for this, so our colleagues at the Department are counting on us to be their voice in this fight.</span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">Have a great weekend, and thank you for all that you do for the children of Wisconsin.</span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">-Mike</span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">Links to resources:</span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">Farrow letter <a href="https://www.dropbox.com/s/56p0t8xe8fig8h3/0220farrow_01.pdf">https://www.dropbox.com/s/56p0t8xe8fig8h3/0220farrow_01.pdf</a></span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">Farrow letter with my annotations<a href="https://www.dropbox.com/s/1ir3tl7nu8ga1b6/0220farrow_01%20annotated.pdf">https://www.dropbox.com/s/1ir3tl7nu8ga1b6/0220farrow_01%20annotated.pdf</a></span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">DPI legal analysis<a href="https://www.dropbox.com/s/mnwojpui09tm4zh/Legal_Memo_SB_619.pdf">https://www.dropbox.com/s/mnwojpui09tm4zh/Legal_Memo_SB_619.pdf</a></span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">Talking points<a href="https://www.dropbox.com/s/vmvtsv6yf6b2pev/SB%20619%20and%20AB%20617%20talking%20points.pdf">https://www.dropbox.com/s/vmvtsv6yf6b2pev/SB%20619%20and%20AB%20617%20talking%20points.pdf</a></span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">Senate education committee: <a href="http://legis.wisconsin.gov/pages/comm-info.aspx?c=1045">http://legis.wisconsin.gov/pages/comm-info.aspx?c=1045</a></span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">Assembly education committee: <a href="http://legis.wisconsin.gov/pages/comm-info.aspx?c=1093">http://legis.wisconsin.gov/pages/comm-info.aspx?c=1093</a></span></div>
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<span style="background-color: rgba(255, 255, 255, 0);">--------------------------------<br />Michael D. Steele<br />Associate Professor, Mathematics Education<br />Department of Curriculum and Instruction, University of Wisconsin-Milwaukee</span></div>
Mark Schommerhttp://www.blogger.com/profile/09589038746262061530noreply@blogger.com0