What could be or could have been...

 

 

In a Year What are Going to

 Remember from COVID?

What could be or could have been...

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.

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?  

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.

Let's take a moment and review some of what we have learned:

• Students need more students around to help with social/emotional needs
• Having a day for reflection for students, with a proper amount of support can be powerful in retention and creating depth in learning.
• Yearly instructional goals can be achieved with a drastically reduced schedule
• Students without support, along with those with other needs, can be drastically disadvantaged without daily contact in school.
• Teachers have the ability to provide support at very high levels through the use of technology.
• 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.
• For the majority of students, current academic performance is comparable to the performance in a 5-day face to face environment.

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:

• It took me a semester to refine my methods and figure out how to make this system work for almost all of my students.
• Structure for the students was vital with clear expectations including deadlines.
• Students, like always, want to learn but need a connection to the teacher to be successful.
• Students, like always, want to feel like they have some ownership of their learning.
• We can release content, focusing on depth, with greater results than in previous 5-day schedules.  
• Students, when they are not in class daily, are excited to come to class.
• There are still students who will make choices that prevent them from succeeding.
• 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.  
• Students come to class eager because they know that class time is effective and important.
• 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.

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.  

1. 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 would negatively affect all students ability to succeed.  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.
2. 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. 
3. 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.
4. 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!
5.  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.
6. 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?

There are many other ideas or thoughts to make education better.  It should be noted that none of these 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.  

Let's not delay.  Let's begin the hard work of planning quality learning for all students!

Summarizing the Initial Weeks of COVID Era Instruction

                            

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:

• The students remembering what it means to learn
• Trying to figure out how to teach a year of material with depth of understanding while only seeing the students half the time.
• Figuring out how to personally get to know each student
• Safety

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.  

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 twice as long because of the every other day process.  This is not an option!  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:

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:

• 53 didn't attempt the formative
• 33 haven't started any of the homework (due tomorrow morning - it is now after 10pm)
• 7 - yes SEVEN finished it

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.  

So what do I do now....

1. We are reviewing the concepts from the useless formative because ultimately there are 52 students who need quality feedback.
2. 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.
3. 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, here it is.
4. 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).  
5. 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.  
6. 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.  

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?

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.

Equity, Standards, Pathways, and Options Part 2

 Equity, Standards, Pathways, and Options 

Part 2

After a week of reflecting on the most recent meeting I am ready to discuss what we met about on the standards revision committee.

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.

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 not desiring a career in STEM.  These are courses beyond the 2+ level.

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.

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.  

I actually feel we will get there soon!

Equity, standards, Pathways, and Options

Equity, Standards, Pathways, and Options 

Part 1

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.

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:  College Algebra, Quantitative Reasoning, and Statistics 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.  

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.

 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.

I hope:

• 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?  
• 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.
• 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.
• 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.

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.

How would I react in a catastrophe?

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.

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.  

"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.  

But none of these were my life...

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?  


Is this what I got into education for...

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. 

It is compassion...

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?

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.

The Truth Behind the Standard Algorithm

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. 

1.     They help most students calculate math.

2.     Our parents learned through them so therefore, children have also.

3.     Teachers tend to teach the way they are taught…thus the algorithms continue.

4.     The Common Core has them stated as necessary parts to instruction in grades 3-6.

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. 

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.”

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.

The methods in the algorithms are needed to learn the upper levels of mathematics

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.

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.

It is the methods parents know so we must teach it that way to help with home-school communication

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. 

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.

To be clear, we own this problem.  The problem is communication, not knowledge.

The algorithms work.  Why change what is working?

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. 

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.  

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. 

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.

Do we Really Want to Keep the Traditional Algorithms for Whole Numbers?  John A. Van de Walle

When the Standard Algorithm is the Only Algorithm Taught  Jason  Zimba

The Teaching of Traditional Standard Algorithms for the Four Arithmetic Operations versus the use of Pupil’s own Methods   Rolf Hedren

What do I feel all new math teachers need to know...

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.

• How to Teach in a Group Centered Classroom
• Elementary Math Instruction "Look-For's"
• Task - Picnic Lunch for 3rd Grade
• Task - New Fish Tank for 3rd Grade
• Task - How Much Does it All Cost for 5th Grade
• Formative Activity - Going to the Movies for 5th Grade
• Grade 1 Assessment - Adding and Subtracting Multiples of 10
• Grade 3 Assessment - Place Value and Addition and Subtraction
• Grade 3 Performance Task - Arcade Tickets
• Grade 5 Assessment - Multiplying Whole Numbers and Decimals
• Grade 5 Assessment - Multiplying and Dividing Fractions and Mixed Numbers
• Task - Who is Correct for 1st Grade
• Task - IPod Usage for 3rd Grade
• Grade 1 Assessment - Working with Equality
• Unfinished Task - Shriners Donation from the Packers - Grade Unknown
• Book - What's Math Got to Do With It by Jo Boaler
• Book - Accessible Mathematics by Steve Leinwand
• Book - Principles to Actions by NCTM

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.

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.  

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.  

For the experienced teachers reading this blog, post a comment that you feel new teachers could benefit from.  

A New Perspective...Can we look at post-Algebra 1 Math Differently?

A question was posed rather carefully on a previous blog that needs to be addressed.  

"Running 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?"

en.wikipedia.org

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 1 is necessary to understand for all students.  It is a gateway, not only to math but other subjects.  According to KnowRe, 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.  

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.  

www.hwporter.org

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. 

What does the student need to succeed in their career/life? 

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.

1. Many students have no idea what they want to do after high school.
2. If a student does have an idea of what they want to do, too many parents steer students away from their choice.  
3. Career choices are changing so fast most of the careers our current students will have don't exist currently.
4. Some of the most growing fields are seen as "manual labor" when the reality is they are highly specialized (Machinist) involving lots of mathematics.

The Common Core State Standards do not 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.  "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," writes Tom Loveless of the Brooking Institution 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.

So if Algebra 2 is not something all students should have what is?  The answer in my mind is nothing.  This is not to mean no 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 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.  What does the student need to succeed in their career/life?  Note, the question is not "What do we currently have that we can put the student in?"

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.  

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.  

There are far too many resources available to not allow a student to tailor their own path.

Why do we Continue to Teach...Part 2

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, here 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.

The overly traditional teacher:

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."

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.

The Politically Correct teacher:

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.

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 www.criticalthinking.org 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.

The honest Abe with a touch of angry teacher:

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.

"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?  

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.

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.  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!

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."

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.

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.