Mathematical Thinking Matters

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IMG_5496Whether buying a new car, working in a research lab, applying the Pythagorean theorem on a construction site, or using spreadsheet formulas to plan how to pay off student loans most efficiently, mathematical thinking is a basic for graduates of our schools. What students must learn today goes well beyond the work of yesteryear’s arithmetic textbooks when members of earlier generations used to memorize rote fact families, repeat procedural recipes from long division to geometry theorems, and solve basic word problems.

It’s an expectation in Virginia that contemporary students take three or more years of high school math – a requirement far beyond the “just” Algebra I requirement of thirty years ago. That’s why developing critical reasoning skills in math is a key focus for today’s educators to make sure young people acquire the competencies they need for a lifetime of mathematical thinking.

This kind of mathematical learning does not happen by chance in schools. It demands teachers who deeply understand a range of mathematical disciplines and who skillfully use multiple teaching strategies to help learners of different competency levels learn to think mathematically as they solve complex math problems.

A high school principal recently shared that learners who once struggled with math are having significant success this year in Algebra I – by any measure. If a student can’t pass Algebra I and then take two more math courses beyond Algebra, they won’t graduate with a standard Virginia diploma. For an advanced diploma, the college admissions gold standard, four math courses are required.

When I met the lead teacher for the successful high school algebra team (a course in which parents and students routinely ask teachers, “when will I ever use algebra in life?”), she said three things which stood out to me: algebra problems must be real, multiple problem-solving strategies must be learned, and positive relationships between the teacher and learner are vital.

My conversation with her reminded me of a recent blog post by Walton Middle School math teacher Bill Doar who works to make sure every student in his class learns math concepts and competencies well. Teachers such as Mr. Doar create learning experiences so students learn math well and find themselves actually liking math.

Here’s a post from Mr. Doar on how he teaches middle school students to see math as a positive part of their day as they learn Virginia’s more rigorous standards.

Teaching for Perplexity by Mr. Bill Doar,
seventh grade math teacher

Walton MIddle School

The past two months have flown by.  On October 11th, my wife and I welcomed our first child – Will into the world.  It feels like September was just a short while ago and we were in Virginia Beach enjoying Labor Day.  Will is starting to smile, make cute baby ‘coo-ing’ and sleep for solid four-hour chunks at a time.  Those luxurious four-hour segments were not always the norm.  Sleep during the first month was scarce and I would often find myself watching Sportscenter or listening to sermons at 3 a.m. to pass the time while Will fell asleep.
One night several weeks ago I stumbled across a YouTube channel run by a math teacher I admire greatly – Dan Meyer.  I initially heard of Dan during my first year teaching in the Mississippi Delta and watched one of his more famous videos – ‘Math Class Needs a Makeover’.  I could immediately relate to his struggle of making math engaging.  In it he describes the math teacher – student relationship as follows:
“I sell a product to a market that doesn’t want it but is forced by law to buy it…”
I distinctly remember the moment during that first year when I realized, many of my students don’t like math, believe they can’t do it and don’t see any practical application of the workbook problems tdoarpic2hey’ve encountered since kindergarten. In the past five years of teaching I’ve worked hard to make math standards meaningful, engaging and applicable to real life. Through technology infusion in the classroom, the ‘maker curriculum’ and the push to make teaching more than just preparing for the SOL, I’ve tried to make my classroom one where the work we do has application that reaches beyond the annual standardized test.
A recent challenge posed while watching one of Dan Meyer’s videos at 3 a.m. holding Will was to change the progression of each lesson.  About 98% of the time I would start with a standard, students would take notes, work out problems, ask questions then try an enrichment/application level activity.  In Dan’s video ‘Teaching for Perplexity’ he challenges educators to start with a real life, engaging, thought-provoking question and embed the standards in the question.
[youtube=https://www.youtube.com/watch?v=EKdiXLIcqVQ]

Today in class, I handed my Core + students the 7th grade VDOE formula sheet when they walked in and told them to create the six shapes on the formula sheet and record the dimensions on a graphic organizer I created.  It’s been amazing to see the change in student engagement transitioning from the traditional ‘sage on stage’ teaching model to challenging students to create and ask probing questions along the way.  I’ve found that with this new model students can learn at their own pace and they genuinely want to ‘complete the challenge’ set before them. It also allows me to circulate the room and give more individualized attention.

The most astonishing aspect to this change though was that during our 40 minudoarpic1te activity today we were able to discuss evaluating expressions, order of operations, exponents, nets of 3D shapes, area, perimeter, volume and surface area.  When I am teaching in front of the class and students are working on a worksheet, it is incredibly difficult to teach more than one or two skills at a time.  This may prove to be the most important benefit to the change in classroom model.

In all honesty, I do not use this model everyday but am trying to implement it more and more each week.  I will leave you with a challenge Mr. Meyer posed during a recent TED talk.  Study the graph below that shows water consumption during the Olympic Gold Medal Hockey Game.

doargraph What caused the highs and lows?  Where is the math in this graph?  What standards could this graph be used to teach?

You can follow Bill Doar on twitter @MrDoarAtWalton

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As you can see from his post, Bill Doar works on students’ attitudes toward math, not just their math competencies. He knows students need both confidence and competence to advance their math knowledge and skills.

In the United States we tend to project a belief that some students are “good” in math –  but most aren’t. Boys are better at math. Girls aren’t. These beliefs play out at home and in school. We know from research families and educators around the world have a different mindset about the capability of children to learn to think mathematically. Adult beliefs about learners impact children’s beliefs about themselves as learners. Negative beliefs about some children’s potential to learn can become their destiny.

Math is a case in point. Let’s change that.