Five Ways to Spark Flexible Thinking and Courage in Math Class…and Beyond

April 22, 2019 |

By Courtney Dickinson

What if math was a place where kids’ problem solving and deep thinking skills could come alive, and a place where they grow in their confidence and adaptability?   

Mathematics learning at school can be authentically engaging, and it is the perfect place for students to take on the much sought after “growth mindset.”  Rather than focusing on “getting the right answer,” math class can be an incredible place to bring about flexible thinking skills.

How can we, as educators, make this happen for every student?  

  1. Create an atmosphere of growth

Most students think about school as a place where they “show what they know” rather than as a place where they “show that they can learn.” As educators, though, we need to change that paradigm. We need to model and show that we make mistakes, and give them room to make mistakes.

Historically, math is a place where there is “one right answer.” The risk, here, is that students can easily fall into a habit of thinking that the goal is solely to “get all the answers right,” and that there is only one way to get there. 

Math class is a particularly compelling time, each day, when the concept of a being in a growth mindset can be consciously taught, and modeled. What if the primary purpose of a math test is to determine what is next best to focus on and teach and practice in class — as the teacher — rather than to “judge” a student as being smart enough or good enough or better or worse than their peers? Speed and intelligence, after all, are not the same things. Yet the typical framework of timed math tests makes it seem like they are.  

Additionally, we should seriously consider de-coupling how we give credit around understanding concepts and solving problems as very different from being accountable to bring in assignments and turn in homework; mathematical and conceptual problem solving and conceptual thinking skills are not the same things as good organization and executive functioning skills.   

They would give extra credit for students who have more than one way to solve a problem.  And maybe, just maybe, they’d give multiple ways kids could show mastery of concepts — via projects they make, or video descriptions and tutorials they create. . .having options beyond just a “timed” test.  And what if we gave guidance for how long it “should” take but we gave everyone extra time for an assessment, so they are focused on solving math problems and showing what they can do rather than focusing on their stress and anxiety about a clock?   

Additionally, Instead of focusing on “right” and “wrong” we should instead focus on giving students chances to engage in challenging and applications-based math material — concurrently learning math while readily showing what they don’t know, and while showing that they can improve and learn and grow.  What if they got “points” for demonstrating “growth mindset” in math class by the comments they make, the mistakes they make public, by sharing their struggles and points of confusion out loud, by asking for help?

  1. Encourage flexible thinking

There is always more than one way to solve every problem. A key part of fluency is not just knowing a fact but also knowing how to think about solving a problem most efficiently, and picking the best strategy to get there.  Students get to engage deeply in a way that fits their capacity, and experience the authentic satisfaction which comes from trying hard, figuring things out, balancing that equation just right, and solving a problem. That kind of intellectual satisfaction creates an appetite for trying new and more challenging things. When habits of flexible thinking start to hatch, they can be generalized to other areas of learning and life.  

  1. Make it relevant to the real world

Students learn more authentically when things are relevant — when they matter for a real world need or situation, or connect deeply to something the student cares about.  Relevance ups the ante, supporting the student to try harder and do the work, which results in better learning. It is a snowball effect of a virtuous cycle of acquiring new habits of mind, new skills, and new commitment to make impact because of awareness about why the learning matters and what difference it can make.  An example? Young elementary students practice their math facts as part of a “store” they set up one day in school, at lunch, perhaps a bake sale fundraiser for the school PTO. Students of all ages buy goods from their youngest school mates, and students ages 5-7 get copious practice adding and subtracting while making change, making profits, and making friends.  The real-world facets of this are further increased if a teacher frames this unit more broadly within the context of a service learning project in which students share information and education their school mates in a persuasive, compelling way, and hand out brochures about their cause — perhaps advocating for school-wide adoption of “Meatless Monday” – -concurrent with their cookie sale campaign?   In this case, perhaps the funds raised go towards a relevant non profit they’ve researched and chosen as a class? When learning becomes linked across disciplines and to real world problems kids have chosen as important to them, the urgency to learn new skills and the sense of meaning in the learning changes in fundamental ways.

  1.  Have an individual learning plan for every child; ideally, math groups are ability based.

What if, in school, each child’s growth was compared with where they started at the start of the year, with goals for growth that fit defined by what they are ready to learn — rather than by a fixed set of learning objectives determined by their age or a textbook?  What if we actually evaluate and wrap goals around students which truly fit them, regardless of their grade designation?  What if part of their learning plan including their unique needs and learning profile, as well as their interests, so that math problems and challenges can be set in a context that matters to them?   The invitation? Test kids to the ceiling of what they know. And engage them where they are, even if what they are capable of does not align with age expectations.

Ideally, in order to best optimize this for math, schools would organize math classes by ability, not age. 

Students should have the runway at school to show what they know, what they can do, and what they are ready next to learn. When a school year starts with a series of math problem-solving exercises, offered up in an encouraging way with adults who observe and coach them along, kids can — sometimes for the first time — show what their potential is!  

And this, then, can correlate with placement in math classes which honor their capacities and needs, instead of just placing students into math programs based upon their age. Ability-based math classes become feasible through a simple scheduling framework of holding math classes at the same time across multiple classrooms and, ideally, multiple grades. Teachers can then define groups which fit the students’ capabilities, placing students in the right level and right learning style/approach to best suit them in what they are ready to learn.

In this type of math school schedule and framework, new possibilities open up for math experiences for all kids. These kinds of experiences then generate a new sense of self and new capabilities which far surpass math alone, and inform the adults they will become!  

  1.  Recognize courage

Some students feel anxious about being exposed for what they don’t know. Or are perfectionistic. Or don’t like math. We want math class — and application of mathematical concepts within any project or situation — to be times when kids try it out, even if they are nervous, or not feeling confident, or identify as if they don’t like it or aren’t good at it. This is brave. This can and should be supported, honored, and encouraged!  

The way to support this is not through timed tests, where speed is valued over thoughtful problem-solving. It is not through a “points off” mindset, but rather through a setting where math is useful, contextual, and woven into imaginative scenarios. The most progressive teacher might also considering giving some sort of credit or at the least praise for students who share the mistakes they make, publicly, for all to learn.

To get the best out of all students and foster more girls into STEM fields, we should move the emphasis away from math being timed, corrected, and graded. Instead, we need to shift into a new zone where students feel coached, excited to show what they can figure out and why it matters, and encouraged to share where they are stuck so they can keep learning.

Students will model after a teachers’ example, and can become freed up from “getting it right” or tapping into a perfectionistic and rigid way of thinking, and instead start to engage as a “learner” rather than a “knower.”   Additionally, when teachers unleash kids to try lots of different ways to solve problems, kids become more invested to figure it out and to define which tools best suit them. This approach sets them up for discussions about mathematical ideas.  Practicing this approach enables more people to come up with a pathway to solve a problem; it opens’ students’ perspectives and gives us a concrete way to see that — as is true in all things — there are lots of ways to solve every problem.  Math class can, then, pattern a new way of engaging in the world – a place and time where kids try things out even if they don’t work, and a place where lots of different points of views and approaches are respected and heard.  Math, then, surprisingly, can be a place where every student can find their voice. And this can be a pattern that they can keep and grow in all aspects of their lives.