Writing to Learn Mathematics

By Yetunde Zannou, RME Postdoctoral Research Fellow

As a mathematics teacher, were you ever blind-sided by students’ performance on an assessment when they seemed so knowledgeable in class? I most certainly was! I decided to do an action research project in several of my classes to better understand that gap and how to bridge it.

My initial investigation led me to look more closely at my assessment techniques and what other teachers were doing to “know what their students know.” I decided to deliberately, and regularly, incorporate writing into my mathematics instruction as a tool to help me support students during the learning process, not near the end of a unit. Writing ultimately helped me to help my students learn.

Some Benefits of Writing to Learn Mathematics

Writing to learn mathematics benefits students and teachers. For students, the process of writing can help them think through and explain their reasoning, which may not always happen when the goal is to find a solution. Students learn over time how to be good note-takers, but often struggle to apply their notes meaningfully. Writing about their thinking forces this process to happen. For instance, instead of asking students to find a solution, ask them to evaluate whether a solution is correct or not and to justify their reasoning. Students have to examine a solution carefully, identify whether or not there are any errors, and explain their position. This type of assignment requires students to access their knowledge in a new way, which facilitates real ownership of new knowledge, not just regurgitation.

As a teacher, my students’ writing made clear where they struggled with a concept or procedure. Particularly as someone who understands mathematics and enjoys it, it was difficult to see some of the little things that may confuse students. However, their writing made those visible to me. As a result, I could address common misconceptions in future classes, provide additional specific support for individual students, and strategically reorder problems in consideration of possible challenges.

Practical Application

There is a wealth of information available on using writing to learn mathematics. In the upper grades, students may be unaccustomed to writing about their mathematical knowledge; however, with sufficient guidance, clear examples, and regular opportunities to practice, they can do well. A good initial writing activity is a mathematics biography. I’ve seen this done primarily with numbers or as a history of students’ experiences in mathematics. I used it as a history and gained valuable insight into my students’ feelings about their mathematical ability. It may be helpful to write your own and share! Writing can be used at almost any stage of a lesson or unit. I’ve used writing to get students thinking about previous lessons and connections between concepts at the beginning of class. I’ve also used writing as an on-the-spot assessment, as well as on summative assessments. Here are my top five assessment prompts:

1. Evaluate a problem and its solution for accuracy and justify your response
2. Create a problem to certain specifications (solvable or not), include a correct response, and identify possible errors a friend might make
3. Write a note to a friend who was absent, describing what you learned today. Include an example problem, solution, and detailed steps to solve
4. Describe how you would solve a problem and your reasoning without including the answer. Great for scale problems
5. Describe what would happen if… This is a good prompt for geometry, proportions, rate, and many others

At the end of a lesson sometimes I would ask students to describe: one thing you know well, one thing you sort of get, and one thing you don’t get at all. I’d use these to revamp the next day’s lesson.

Making it Work

For writing to learn mathematics to work, you and your students have to “buy in.” Students have to understand the value of writing as a tool to help them “know what they know,” as well as a way to assist you in determining how to proceed. You have to be committed to learning from students in this way. Incorporating writing takes class time and time to evaluate assignments. Here are some suggestions to make it work:

• Plan writing assessments in advance. Students will take the writing exercises seriously when they see that you do. Avoid using writing as a way to “pass time” or “on the fly.” Even if you decide an on-the-spot writing assessment is needed, you should already have an idea of a prompt to use or a question that could work as a written assignment.
• Make sure prompts are clear and direct. Writing alone does not guarantee these benefits. Make sure instructions clearly communicate what you want so that students know how to respond and their writing serves as an effective assessment tool.
• Decide in advance how and when you will evaluate it. Planning to write should accompany a plan for evaluation and action. The likelihood of reviewing a written assignment in a timely manner increases when you know what you’re looking for. If you want to know common errors across classes, sampling entries is better than reading each students.’  I’ve given written assignments in lieu of traditional homework problems at times and discussed them in class the next day before moving on.
• Provide feedback, individually or to the class. Even if you don’t provide each student with a detailed response, students should be aware that you are reading their answers. This will help them to see the value of their writing efforts and the immediate impact it has on your instruction.

What are some other advantages of using writing to learn and assess in mathematics? What might be challenges to incorporating it into your instruction? What supports are available to make it work?