Thursday, November 6, 2014

Confessions of a constructivist/pragmatic teacher.

I did a major application today.  It is below.  

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 
never saying an answer was correct.  

Here are my results:

  1. The students HATED the large "real" numbers.  (my response was that they were the reality, not fake school numbers - they got past this)
  2. Period 1 did awesome - fully engaged except for 1 child who is making poor choices.  They really liked it.
  3. 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)
  4. The discussions in the small groups cannot be understated.  They are the backbone to why we need to do these applications.  Priceless.
  5. I was bombarded with questions after each class - the kids wanted to know the results - To be continued into tomorrow.
  6.  NO TIME WAS LOST because this method replaced a lesson.  In fact, I would estimate time was SAVED giving more time for depth!
  7. My kids stink at problem solving.  If they are not handed the process they quit.  This in unacceptable to me.  MP #1
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).  
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.  


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 UBS 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 q=-3000p+5628000.
Given this information, use your classes know-how to help determine if Apple Inc. has priced its iPhone correctly. What should the price of the iPhone be in order for Apple to maximize its profit?.

Wednesday, July 2, 2014

Enrichment #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.

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?


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?

EDITS - let me know what you think...

3rd Grade:
4th Grade:
5th Grade:
6th Grade:

Wednesday, June 11, 2014

Equal Sign Survey

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.  I learned so much more...

The Data Results:
First, for the data geeks, the data set is 400-450 students per grade level and over 50% were scored for each level.  

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.  Regardless, we are at 90% correct.  That is pretty good.

The more interesting data is the quality of the explanations.  Here is how the scoring worked.

    0 - No explanation  
    1 - Significant logical errors in the explanation
    2 - Logic was acceptable but the explanation either had errors, was only calculation
         based or was guess and check
    3 - Explanation was the process used.  It either explained how they achieved the 
         solution (algorithm) or implied an equality of the two sides.
    4 - Student specifically stated that the left side of the equation had to equal the right. 
         It was not just implied.

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.  How would those students perform on the SMARTER Balanced Assessment?  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.  

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.

Where do we go from here?
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. Mathematically - this is incorrect.  
12 + 6 = 18 is a correct statement

However, if we add more:  12 + 6 = 18 + 5 = 23

This is no longer correct because the values are not equal.  
12 + 6 is not equal to 18 + 5

To write this correctly, we would make a new row.
12 + 6 = 18
18 + 5 = 23

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 exemplars for more clarity.

So, I pose to are you teaching your math?

Friday, June 6, 2014

Jump Starting the Summer...

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.  

While everyone waits in unabated anticipation 8-) take a moment and wager a guess on the polls at the right. 

If you are curious - the scoring went as follows:
     obviously the correct answer was noted
     For the explanation a student:
          4 - had to state the two sides needed to be equal in words - not just imply it
          3 - had the right idea - it was more a process explanation than anything
          2 - had the concept was there but there was an error in it
          1 - had an improper process

What I know already is that we own these errors in student thinking.  More on that later.

Thursday, May 22, 2014

Have the World's Best Athletes Improved?

Pardon the interruption from typical blogging but I need to get my students some web sites and trust this resource to do that.  

Have the world’s elite athletes improved?

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. 


  • ·         Lists, summaries, conclusion, and anything else should be typed
  • ·         Graphical displays should be neatly written or done on the computer
  • ·         Typed paper supporting your position
  • ·         Organized mathematical proof supporting your position (does not need to be typed)

  • ·         The score of your project will depend on the quality of your analysis, the presentation, and the overall quality of your writing. 
  • ·         See the back of this page for the scoring rubric.
  • ·         This project will count towards the core knowledge portion of your last assessment.

Wednesday, April 16, 2014

Doing it the Right Way!

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.

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.  

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 all 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.  

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.  

Thursday, March 20, 2014

What works in Math Education?

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.  

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.  

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.  

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.

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?

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 Visible Learning, I have taken his list and focused it on the math classroom.  What should we be doing?

  • Students self-reporting their grades (1.44)
  • Formative assessment (1.28)
  • Acceleration (0.88) - Personally I don't agree with this one
  • Teacher Clarity (0.75)
  • Differentiated Practice (0.71)
  • Meta-Cognitive Practices (0.69)
  • Vocabulary Programs (0.67)
  • Problem Solving Teaching (0.61)
  • Cooperative vs. Individualistic Learning (0.6)
These are some of the best practices for the general classroom.  If these are great practices then where does typical math instruction fit in?
  • Direct Instruction (0.59)
  • Mastery Learning (0.58)
  • Worked Examples (0.57)
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.  

Where could are kids be then?

Sunday, February 23, 2014

Update on senate bill

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.

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.

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:

Tony Evers, on Wednesday, issued a call to action, describing the bill and its impact. Watch his 3 minute message here:

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.

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.

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.

We are still at risk and we need to make our voices heard. 
Here is my request for action.
-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).
-Contact your senator and representative again.  My own were completely uninformed about the two bills when I called on Wednesday.
-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.
-Distribute this information far and wide.

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.

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.

Have a great weekend, and thank you for all that you do for the children of Wisconsin.

Links to resources:

Michael D. Steele
Associate Professor, Mathematics Education
Department of Curriculum and Instruction, University of Wisconsin-Milwaukee

Sunday, February 16, 2014

Highest effect sizes in the Math Classroom

As teachers we always believe we know what is right for students in the classroom.  We work hard, practice our skill, and care about kids.  However, if you take the time to look from classroom it is apparent we go about our skill in different ways.  This is fine for the most part but as more studies are done, and the results repeat themselves it becomes obvious there is a science to our art called education.  The studies have been done irregardless of grade level and there is some background to understand the numbers.

     - An effect size greater than 0.4 has a positive effect.
     - An effect size between 0.5 - 0.6..."your crazy not to do it."
     - and an effect size of 0.7 needs to beg the question "why are you not doing this already."

As it turns out, the teacher staple that smaller class sizes help instruction holds no merit.  Good teachers succeed in any class size.  The statistical effect for class size is 0.27.  This correlates to showing no positive effect at all.  Sorry...

On the contrary, if you would like to start off simple get your kids up and around.  The simple act of physical movement shows an effect size of 0.54 (your crazy not to do it).  The trick is, how can we structure the time with our students that gets them up and moving?

The three highest effect sizes should come as little to no surprise if you have been engaging in professional development.  

  1. Spaced vs. Mass Practice (0.71)  -  Mass practice is all students do 1 - ???.  Spaced is differentiated.  Some students do #1, ...  Other students do a different set or an entirely different practice depending on their level of understanding or areas of interest.  By doing this practice it opens the door to knowing your students well enough to differentiate.  
  2. Assessment as a Process of Formative Feedback (0.75) - Everyone knows what formative assessment is.  However, lots of teachers (math in particular) are still stuck on the summative assessment being the be all end all of student learning.  Challenge yourself to consider when learning is completed and what our job is as teachers?  If my sole job is to rate/rank my students then I am drastically selling short my abilities.  We are hired to inspire learning and engage students in a manner that causes them to dig deeper and do things they don't always feel comfortable doing.  Something called learning.  Formative assessment gives me the information necessary to know exactly where my students are at and determine the instruction necessary to get them to where we need them to be.
  3. Classroom Discourse (0.82) - Getting a discussion going in your classroom about the topic you are working on has an effect size higher than the category labeled "why are you not doing this already."  To often as math teachers we feel teaching is us talking.  In reality, the more we talk the less they learn.  Clearly there are those topics we need to describe.  The challenge is how you can get a deep discussion going about the topic.  These discussions, if done properly by letting the students do the talking will greatly increase the depth of your topic while also performing a large degree of the formative assessment needed to understand where your students are at.
The basic gist that everyone needs to hear is simple.  Do not "try" these classroom strategies.  DO THEM.  The better we do them the higher the effect.

Sunday, January 12, 2014

The Student Effort Conundrum...

Every year it seems as teachers we lament the way students "try" to learn.  We know they complete homework for the sake of checking it off their list instead of learning the material.  We know that the students who struggle rarely complete their homework, if they attempt it at all which then makes determining whether it is student effort or academic deficiency that leads the student to failure.

In year 17 of teaching and year 4 of administration I can honestly say students are giving less effort than they were 4 years ago, and probably 10 years ago.  What is our answer?

Note:  where is says "homework" it could say "effort."  I am trying to use them interchangeably.

All theories in education say students need to know the purpose of homework otherwise why would they do it.  Our reaction is to devalue homework by removing it from the grading categories, currently it is valued at 5% of the overall grade or lower.  Then, by differentiating the homework and explaining its connection and purpose to students will enable them to give full effort and focus on the learning, not just complete it.  However, what is happening in many cases is the students reaction is then to realize it means nothing on the overall grade and in turn, don't pay much attention to it.  

The intention is strong but the execution is weak.  For a student to understand that doing homework is for learning purposes and students should focus on homework/effort in class for the long-term learning in the course is reaching the highest level of Maslow's heirarchy.  They are reaching self-actualization.  It means they are fulfilling their potential and becoming all that they are capable of being.  It is to assume that all students are reaching Maslow's top tier or self-actualization.  Just to even write that is to realize how unattainable this theory is in practice.  Most adults don't reach this level in Maslow's hierarchy of needs.

What would be a better option?  

First, not all courses are equal.  For this blog - math is the course of preference.  
We need to teach students the importance of practice for learning.  It is what promotes fluency in math and ease of future skill development.  DO NOT READ THIS AS "SKILL  HOMEWORK IS WHAT WE NEED."  In reality it is the exact opposite and reading most any other post on this blog will reinforce the need for engaging activities that connect students to the use of the math skills in terms of high end applications.  Second, differentiation is the key to homework.  Regardless, in the primary grades students need to understand the importance of homework and set the stage to what homework does.  This will help build the culture of homework/effort as learning.  

As students get older they naturally have other barriers to effort/homework.  Peer pressure, 10-12 year old issues, increased student work load, etc...  These things start to really kick in from 3rd - 6th grade.  This is where I feel we are making our largest mistake in theory to practice.  These grade levels need the reinforcement of homework as learning but this age of student needs a little more hand holding.  They need the added incentive and perks to completing homework beyond just the understanding or learning they achieve.  They need the incentives for completion, and learning can follow.  Furthermore, this age is where math skill is "cemented in" and the foundation is set for years to follow.  Fluency practice is essential in grades 3-6.  

In grades 7-9, Algebra is the goal and having a clear foundation is essential.  Students will need significant practice but more importantly they need to have practice at their level of learning.  This means differentiated homework.  At these ages, students still need hand holding but need to understand the importance of assessments.  Gradual release is the key.  Lessen the percentage weight of homework but make sure completion/effort is achieved.  

In grades 10-12, homework should take almost no weight (in reality - 0%).  Culturally this needs to be set at a young age with students understanding why they should practice and give effort.  

The key for me is meeting the needs of all kids where they are at in their years of growth.  I would love for homework to not be needed in that students are working to achieve on their own.  However, I don't see this happening.  A structure that progresses with students as they grow might make sense.  

I am anxious to hear your thoughts.

Wednesday, January 1, 2014

Are we doing homework wrong?

I just finished reading the book The Perks of Being a Wallflower and it made me consider how we treat our talented students.  This is not to say that it didn't cause thinking about other things such as how crazy high school can be, that Charlie lived a very different high school experience than I did, that I hope drugs are not that prevalent (but pretty much acknowledge that they are)...

Regardless, Charlie was an extremely intelligent boy who ran into a teacher that truly cared about him.  In that caring was giving him additional books to read and essays to write about them.  Charlie didn't see these as extra work or even a labor to do.  He enjoyed doing them.  Is that so different than our classrooms?  There are students in our classrooms that depending on the subject area have an interest that goes well beyond the normal student.  For this student, we expect of them the same as every other student.  We expect them to do the normal work, at the normal standard level the same as every other student.  We don't give them any other work or tasks to meet their needs because we are told by so many people that too much homework is bad especially in the elementary grades.

However, for students like Charlie, extra reading and essays are not more work.  Its playtime.  Its a time to think like they want to think.  Its an opportunity to explore an area they already love to work in.  We can't keep thinking of an assignment as a prototypical assignment but as an opportunity to take them further.

This work cannot be more problems but a deeper experience with math.  If you've read previous posts I obsessively talk about Math Tasks.  We have them.  They are provided in our tables we use for our topics.  We just need to give them to our students either in selective groups or as a classroom.  Regardless, just like the caring teacher in the The Perks of Being a Wallflower it's all about how the discussion after the task.  Charlie's discussions were always with his teacher.  Our discussions could be with us as teachers but more importantly should be with other students.

We need to treat all students as individuals.  Some need the standard level of instruction, others need additional help because they struggle.  Still there are those others who can sneak through the cracks.  Not because they end up struggling but because we never approach them to see if they could do more.