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Creating Positive Change in Math Class

5 Mar 2020 7:44 AM | Kelli VanSetters (Administrator)

Creating Positive Change in Math Class

Moving Beyond the Covering Content Culture

By: David Coffey

Here in Michigan, the standardized-testing season is just around the corner. Starting in April, students in grades 3-11 will take some form of summative math test – M-STEP, PSAT, or SAT. This means that there’s a little more than a month left to cover all the content those students need to be successful on their respective test. At least that’s the conventional wisdom in a lot of math classrooms. But what if I told you there was another, a better way?

Pixabay.com – tjevans

As a middle school math teacher, I fell into the “covering content” trap. However, I came to realize that covering the mathematics they’d see on the test didn’t prepare my students to be mathematical thinkers. In fact, it did just the opposite. When I covered content, I sent the implicit message to my students that they couldn’t do a math problem unless I showed them how to do it first. How do I know that this was the lesson my students learned from covering content? They told me. They complained that a test question was unfair whenever I didn’t show them exactly how to do it beforehand.

Instead of covering content, we need to create learning environments that support the development of confident and capable problem-solvers. That way, when students encounter a math problem on a standardized-test that they have never seen before (and they will), they will roll up their sleeves and get to work instead of throwing up their hands and giving up. What will it take to create this positive change in math class? It depends, but here are three things that might help.


In designing our new math classes, we need a clear purpose. Simon Sinek, calls this our compelling Why. For example, why teach that math lesson I planned for today? If I don’t have a good answer, then it’s unlikely that the lesson will change anything. And coming up with a good answer is harder than you might think.

Norman Eng adapted Sinek’s work to create the One-Sentence Lesson Plan [OSLP]. We ask teachers to write OSLPs for to frame their math lessons. Almost all struggle with the last line – the Why. They usually focus on the how the content is on the test. But Sinek would say scoring well on a test is a result, not a compelling Why.

From Cult of Pedagogy Blog

Fortunately, the Michigan K-12 Mathematics Standards are filled with compelling Whys. They are called the Standards for Mathematical Practice and can be found beginning on page 6 – near the beginning of the document (start with Why, indeed). For our purposes, I will simply focus on the first one: Make sense of problems and persevere in solving them. If we are going to create positive change in our math classrooms, I cannot think of a better purpose.


Creating positive change around problem-solving in our math classrooms will also require a shift in our perspective. The covering content approach that predominates in our schools reflects a deficit-model of education: students lack some knowledge and skill which our lessons will impart. Instead, we need to focus on what our students can do and what they are trying to do. This asset-based approach will contribute to the positive change we are trying to create.

In Motivated, Dr. Ilana Horn identifies five key aspects of motivational classrooms. The one I want to concentrate on here is Competence. If we are going to change the way student think about what it means to be good at math, then we need to be willing to redefine mathematical competence. Getting correct answers on standardized-test questions in a fixed amount of time can no longer be the only thing we value in math class. Dr. Horn writes, “it is understandable why this particular mathematical competence has risen above others as a sign of mathematical ability. However, looking at the history of mathematics as a field, it is clear that other types of competencies have been key to the development of new ideas and discoveries (p. 63).”

At the end of each chapter, Dr. Horn includes an Audit for teachers to complete. The Competence Audit includes:

  • What kind of competencies are valued in you classroom? Where do student have a chance to show them? and
  • When you look at your class roster, can you identify at least one way that every student is mathematically smart?

For our purposes, with our Why in mind (Make sense of problems and persevere in solving them), we might ask how problem-solving is valued in our classroom, and what strengths each student already displays regarding problem-solving? Some examples of students’ strengths might be: asking questions; seeing patterns; doing research; coming up with wild ideas; making connections; and testing and reflecting on ideas. Designing assessments to identify such strengths and activities to support their development can seem a daunting task. Fortunately, you are not in it alone.


A key principle of human-centered design is creating with not for the people involved. For teachers, that means including their students as they try to create positive change in their math lessons. There are lots of ways to design problem-solving assessments and activities with students. Here are two examples

A preservice teacher I worked with was frustrated with his students. Only a few of them were doing their homework. We discussed some options, and he decided to focus on the power of choice. He realized that the only choice his students had regarding homework was to do it or not. But what if he asked them to pick the problems instead? He set some parameters (e.g. at least one problem from each section) and required the students to explain why they picked the problems they did. The number of student completing their homework went up significantly. Asking students to choose the problems they work on is a simple way for teachers to co-create positive change with them.

A second approach is a bit more complex. Dr. Christopher Emdin calls this strategy Co-generative Dialogues. He writes:

Co-generative dialogues—or cogens—are structured exchanges in which students and their teacher co-develop strategies for instruction that focus on the students' socioemotional and academic needs. The dialogues enable open communication concerning both the teacher's and students' perspectives on schooling.

The teacher meets with a small group of student to discuss the question: How might we improve problem-solving in our math class? The students might offer suggestions to the teacher or even design and teach a lesson to their peers. Throughout the school year different students cycle through the cogens. (You can learn more about this strategy in Dr. Emdin’s book, For White Folks Who Teach in the Hood … and the Rest of Y’all Too.)

Pixabay.com - dcondrey


If we are going to make a difference in our math classes, then we need to do things differently. Covering content is no longer good enough for our students – especially when most of the content is just a click away for our students. We need something different. This post has offered three ways that we might try to start making a difference: 1) identify a clear, compelling purpose to guide the choices we make; 2) see our students’ strengths, celebrated them, and build on them; and 3) invite our students to be a part of the re-design. These are not easy fixes, but they are necessary if want to change the way people think about what it means to “do math.”

David Coffey is a professor of Mathematics at Grand Valley State University. He will be presenting at the MCTM Conference in Grand Rapids July 28-30, 2020 in Grand Rapids, Michigan. 

Sign up for the conference by clicking HERE!


  • 8 Mar 2020 10:28 AM | Rusty Anderson
    Thanks Dave! I especially appreciate the thinking around cogens and how they can be a productive way to get feedback from those we serve on their learning experience. I feel like this is transferable to so many contexts both inside and outside of the classroom. For example, leaders could create cogens of teachers to gather insight about what might be working and gather their voice on how they might want to move forward. I am going to reread the cogen chapter ... Thanks for pushing me in this direction! @RAnderson_Math
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