Making Thinking Visible in Math Classrooms

"When we help teach our kids how to work together, contribute their ideas and critique the thinking of others, we are teaching them to be problem solvers in a rapidly"


Solving Problems in Study Teams

Classrooms today emphasize collaboration to solve problems. When we help teach our kids how to work together, contribute their ideas and critique the thinking of others, we are teaching them to be problem solvers in a rapidly-changing world where solutions to problems appear to be more complex than ever.  Study Teams is just a name for cooperative learning groups where structure adds roles to each person on the study team.  The reusable Wipebook Flipcharts provide the Canvas for Study Teams to visually show their ideas and collaboration. As a classroom teacher, my job is to push their thinking. Rather than answering questions about how to solve a problem, I ask them questions about their approach so far and clarify questions about math concepts they would like to use as a math expert.


Students working on Flipcharts to solve problems


Questions we might ask:

  • What skills in your mathematics toolkit could you possibly use to attack this problem?
  • What have you discussed so far as a team?  Tell me your thinking so far.
  • I notice that you have a lot of the key components that you need…I am wondering how to can piece those together to solve the problem.


It’s About Looking for Patterns

I grew up in a time when math class emphasized memorizing formulas and applying math to solve routine problems, often without any context. This left me without the real reason why we study mathematics…to search for meaningful patterns that can be expressed as equations that can be used to make predictions about things that may happen (or be prevented) in the future (algebra) and be able to convince others in a sequential and logical manner that your equations, called models, will prove to solve a problem (geometry).


Solving math problems on the Flipcharts


Today in the news, current events are filled with the need for patterns to solve problems. We use them to make decisions about COVID-19, explain the future of the planet with global warming and carbon emissions as well as predict which stocks may perform the best over the next several months. 


I like that students have a large space to generate ideas, removing or editing them as they see they need to be rethought or modified.  They don’t have to worry about pencil erasers or making sure that they have all copied their work on their own paper.  Being able to record their responses in the app makes sharing their thinking with each other relatively easy…and allows me to have a copy of their thinking as well, which prevents me from having to collect paper copies. The best eco-friendly solution to school paper waste.


Example of Wipebook Scan app being using


Questions we can ask without taking away the thinking from the problem:

  • What information do we know about the problem? What question are you trying to answer?
  • How could you organize the data in a way that helps you look for patterns?
  • What types of things would you need to know if you wanted to write an equation for this situation?
  • What evidence are you presenting to your audience to prove to them that your solution is correct?
  • How well will the audience be able to understand your thinking based on what you have shown them?


Making Accountability Visible Too

Students complete tasks in a variety of ways in my room. Sometimes, it is on paper; other times they draw on their desks with whiteboard markers when they are doing foundational learning with math skills. When I want students to collaborate and solve a problem together, the Wipebook Flipcharts add a different dimension to classroom engagement. I purposely switch up how students communicate their thinking depending on the purpose of the learning.

I notice that when students use Wipebook Flipcharts, they are engaged in a different way. Since I can see their work easily without having to walk around and look at tables or desks, I can more easily monitor which Study Teams may need guidance, and which need redirection when they are off-task.  Additionally, middle schools have a heightened awareness of how they “fit in” with the whole group. This helps because they are also aware that other students can also see their thinking.


Solving math problems on the Flipcharts


Both of these aspects help keep Study Teams accountable for their work.


Things we can say to promote accountability:

  • Be sure that every team member would be able to explain what the team has communicated.
  • It looks like you may be struggling…is it a math issue or a social issue that I need to help with.
  • Tell me what each of you has contributed to the solution I am seeing.
  • I am wondering how you can ensure that everyone’s ideas are being valued.


Steven Koponen, Teacher, Warner Middle School


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