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  • Pam Koutrakos

Writing in Math: 4 Steps That Make Math Learners the Heroes of Their Own Journeys

Once upon a time, as pure as a fairy tale, it seemed as if math was all about algorithms and right answers. But times, they are a’changing. It is no longer enough for math learners to correctly compute. Today, the expectation is for students to have a full-bodied, rich understanding of math concepts and the ability to communicate their knowledge. It’s part of a broader trend in education to to develop problem-solving and critical thinking—a noble pursuit. Throughout this transition, however, many of us have witnessed learners struggle with how to communicate their math processes. Some students show anxiety and say they are not good at math. This is a clarion call, telling us that we need to make this journey more accessible and successful for all students, so we can leave that heartbreaking, “I’m no good” fixed mindset in the dust.

Writing workshop to the rescue! Seriously, I have leaned on structures I know and love from writing workshop to help classroom mathematicians develop the skill sets and mindset of a practiced problem solver. I had a lot of success (and a great deal of fun) using these components to help students competently communicate their math ideas.

Check out this photo-sequence that will help you transform a student’s “ughhh” mindset to an “I got this” identity as a math learner:

Step 1: Modeled Writing

In modeled writing, not only do you think aloud as you solve a math problem, you also explain your thinking process visually and in words. Typically, I write on chart paper or screen so work is easily visible to all. In as little as 5-10 minutes, I create a verbal and visual model for learners that they will soon try for themselves. I purposefully say aloud my wonderings, my wait-a-minutes, with language like, “maybe I’ll divide these two numbers...but actually, that won’t work so I’ll try this instead.” In the gradual release method, this step is the “I go” phase, so I make the most of my time in the spotlight.

As you see in this photo, students listen to me think aloud and watch me jot. Afterward, students share their noticings, thoughts, and questions about what they observed.

Step 2: Shared Writing

Now, I share the work with students. I think of this step as “I go with a little we go,” because I’ve found learners in all grades benefit from teacher modeling. This builds the confidence to take on process-oriented and reflective writing without getting overwhelmed. For example, while using shared writing, I hand over a bit of the responsibility by asking students to turn and talk; discussing what I could jot down next to show my math thinking. In this step, the students provide the ideas, but I still handle the actual physical writing on the page.

I listen in to student partnerships as they share math thinking. I then credit students, use their ideas, and write down what I heard students saying.

Step 3: Interactive Writing

Next, I give students “low stakes” first steps in initiating explanations. Interactive Writing is a true “we go” practice. Together, we think and compose a text. I often invite students to participate by first sharing what I could write and then helping me actually jot down specific parts. Sometimes I share the pen with students as we create a model to help visualize the problem. Sometimes students help with writing the number sentence, and in other instances, I ask students to help me reflect on and list our process. Students love adding a bit of their own flair to our collaborative composition.

During this digital interactive writing session, I wanted students to build a habit of using math language, so students took ownership of writing the math words included in our response. I purposely let the students guide more and more of the work, sometimes tweaking, but never overhauling their ideas.

Step 4: Partner Practice

Finally, it’s “you go!” time—students are now ready to use the processes they’ve learned, and persevere in the face of a new challenge. To support success, I keep class examples of shared and interactive writing visible by hanging them on the walls. Students choose the math problem they want to work on. I tend to offer simple problems at first so that students can focus on the process of explaining math thinking. However, we soon follow up with more challenging “partner persevere problems.” This helps students feel confident in the way jotting in math helps them become more focused and successful problem solvers. This also reinforces the idea that in math, talking, sketching, and writing are tools—not something “extra” we ask students to do. Afterward, we celebrate the many different ways students shared their math thinking.

Students take on writing that is developmentally appropriate and practical as a tool to problem solve.

Tip for Success: Vary the Rate of Release

Even with thoughtful, well-planned instruction, the path to proficiency may not be smooth. The four steps outlined above are not just right for every group of students. There are times I move a bit more quickly in my release of responsibility. There are also times I zig and zag… dipping in and out of steps in this process as students learn to trust themselves and feel prepared to persevere when working independently. Although writing in math supersedes any particular content, I also sometimes back up in reverse when the class begins to focus on a new strand or cluster of math curriculum.

It is helpful to look beyond grade-level standards and seek out strengths in place —there is often variation in readiness among different classroom learners or different classes at one particular grade. Start from what is in place and slowly build strategies over time. Remember that it is not only okay, but also expected, to personalize instruction for different groups of students. If I notice a pattern among the majority of classroom learners, I follow up with some whole class instruction. If I have a smaller amount of students showing a common readiness, I meet with a small group for some short-term practice. If I observe a unique next step, I support this student with one-on-one conferring.

I am supporting a small group of learners showing a common readiness in this process.

By offering these four steps, we can empower learners with strategies and mindsets that are more powerful than magic and wiser than prior decades’ focus on right answers. Why? Because these four steps equip students to be independent, flexible problem solvers. They develop learners’ resiliency and readiness to forge through the bumps and hurdles that come their way. No need to wait to be saved: they got this!

Stay tuned for Part 2 of this blog where we explore the following questions: What happens next? How might we help students reflect on how things are going? How could we support the continued development of writing in math?

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