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Writing to Learn Math

March 27, 2019

By Nina Sudnick

You walk quietly into room 244. You don’t want to disturb the sixth-grade math class; you just want to see what’s going on today. You have been here before when the students were engaged in a lively discussion about finding the area of different types of quadrilaterals. You watched as students cut apart the shapes and pieced them back together into rectangles or parallelograms to find the area. Today, however, is different. The room is quiet. So quiet that you hear your shoes squeak as you walk around the room. It almost looks like you’ve walked into a literacy class because the students are writing in journals. Not only are they writing, but they are writing very intently, stopping occasionally to ponder. You wonder what they are writing and decide to peak over some shoulders. Here is what you see:

“It was like we [the team] had a hard time putting 1/8 into a decimal. How are we going to do 1/16, 1/32 and 1/64? Then we realized a pattern . . .”

Well, that’s interesting. They seem to be journaling about the challenges their team had with a math problem about converting fractions to decimals. Maybe they just completed the lesson and are writing about the challenges. You decide to move on to another student across the room and glance at their journal.

“At that point my mind was kinda going crazy and I was wondering why |-8| = |8|. Then I reread the paragraph about what absolute value really was.”

OK, so they seem to be writing about their own challenges about various problems. You take one more look just to confirm.

“I thought this problem was fun for a few reasons. My first reason was when I first started the problem, I was always bad at these kinds of problems. At first this one was no different but after a few seconds of looking over the problem I realized I had been overthinking it. What really helped me was thinking back to the group problem from yesterday where there was [a] similar pattern.”

So, it seems like they are writing about challenges and how they overcame them. You wonder if that is the only thing they are journaling about. You also wonder how the teacher, Miss Sudnick, responds to the journals. Does she read each journal? What does she do with the information from the journal? It seems as if this would be a wonderful way to truly understand what students are thinking about when they are working in math class. This is so very different from the math classes you were in as a child. You were basically shown how to do a problem, and if you were confused, well, good luck with it. What if your teacher had asked you about what challenged you or what you did to overcome the challenge? Would it have helped build your confidence in math? Maybe you would have made more connections with what you were learning instead of seeing math as a checklist of things to learn that only lived in math class. Maybe you would have understood math at a much deeper level.

You make a note to come back to talk to Miss Sudnick about the math journals and why and how she uses them. You are also eager to learn about how the students feel about writing. You leave feeling uplifted that today’s young mathematicians are learning math in a way that makes sense to each one of them in their own way. Math that makes sense. Now there’s a novel idea!

…

This introductory narrative is a snapshot of a visit to my classroom by my principal, Andrea Bobo, as well as my own experience with my students as I have incorporated writing, in the form of math journals, into my classroom. To promote students’ understanding of math, my approach has changed 180 degrees from teacher-centered to student-centered. Student-centered math means giving students problems to work on individually and as small teams and then getting together to share our understandings. I am always on a quest to expand students’ learning processes, and in that quest a particular instructional idea kept showing up—writing to learn math.

When I found out I had the honor of becoming a Heinemann Fellow I knew immediately that this would be the focus of my action research project, and I have since developed the following research question: In what ways might middle-grade (sixth-grade) students’ math agency deepen by writing about their learning or discoveries in math class, including, but not limited to, journaling, explaining math ideas, and writing conjectures and proofs about their mathematical discoveries?

As I began to dabble with writing in math, I searched for professional books to deepen my understanding of why it’s valuable and how to incorporate it. Here are the three books that inspired my work:

Writing to Learn by William Zinsser (Harper, 1988)
Writing to Learn Mathematics by Joan Countryman (Heinemann, 1992)
Writing in Math Class by Marilyn Burns (Math Solutions, 1995).

Let’s start with a bird’s-eye view of writing to learn with the ideas of William Zinsser. He believes that “Writing is how we think our way into a subject and make it our own.” Throughout Zinsser’s career he used writing to understand the world around him and to share that understanding with readers through his journalistic works and numerous books. Simply stated, Zinsser believed in the value of writing across the curriculum. “Writing organizes and clarifies our thoughts. Writing enables us to find out what we know—and what we don’t know—about whatever we’re trying to learn.”

In Writing to Learn, he devotes a whole chapter to writing in mathematics. His words were so inspiring to me. When I thought back on my own learning experiences, I realized that writing did help me make sense of my learning across the disciplines. It’s magical to see what you understand appear before you on paper. I want this for my students. I want them to see their own thinking, to see how much they know, how much they are learning, how they’ve persevered and conquered math ideas they never knew would be possible. It is a learning journey where writing helps them “think their way into” math and make it their own.

Once I decided to have students write to learn math, I had to decide what types of writing we would do. There are multiple ways students can write to learn about math and to share their thinking. In Marilyn Burns’ book Writing in Math Class, she shares four ways to incorporate writing into math class:

Keeping journals or logs;
Explaining how they solved a math problem;
Explaining math ideas;
Creative writing and math.

I have used all four ideas over the years, but for my action research project I decided to focus on math journals. My students author amazing personal narrative writing in their language arts class, so I thought journals would be a secure scaffold for writing in math. One approach is to ask students to select one homework or in-class problem to write about and to explore why the problem was challenging or interesting to them. When I ask my students to write about their thinking, they jump in and start writing in their dedicated math composition book (which has graph paper versus lined paper). They write what they’re thinking about—not a topic I’ve chosen for them. It is their own thinking in their own words.

The journaling has provided the students and me with detailed information about their thinking. It ranges anywhere from how they now actually understand a concept, such as the area of a triangle, to how a simple mistake can derail our math work or thinking. One student shared her developing understanding of how to create common denominators to combine fractions. Another student shared how finding a decimal equivalent for 1/8 gave her an idea on how to do the same for 1/16, 1/32, and so forth. This kind of information helps us create discussions in our classroom where we can share these ideas and deepen our understanding of the content. The thoughts students share are invaluable to me. My hunch is that they value the time to write as well. I hear a lot of “Do we get to journal today?” and that is music to my ears.

ninasudnick Nina Sudnick believes in continually striving to make math enriching and engaging for her students, school district, and community. Her math leadership journey began over decade ago when she was asked to teach a middle school math class to a group of struggling students. She currently teaches 6th Grade Math and Science at East Elementary in Athens, Ohio. Nina is also a co-founder of the Southeastern Ohio Math Teachers Circle, serves of the Board of the Ohio Math Education Leadership Council, is the leader of her district's Math Leadership Team and in 2014 was the keynote speaker at the Annual STEM Symposium at Ohio University.