Writing in Mathematics
Mathematical Writing as Formative Assessment
Mathematical writing can also provide teachers with insights into the mathematical thinking of their students, including their level of proficiency with mathematical vocabulary and notation and their fluency with important models and representations. When doing formative assessments, teachers might ask themselves, What do students understand about the mathematics associated with the problems and tasks they are being asked to solve? How well do they articulate justifications for their solutions or identify their reasons for each step in a proof? How are students making connections across important mathematical ideas as they write reflectively about a mathematics topic? How do students communicate their analyses of the range of solution strategies that might arise as they examine and respond to the mathematical thinking of others? Having students engage in mathematical writing also allows confusions or misconceptions to surface so they can be discussed and addressed.
Feedback to students on their writing, either from the teacher or from other students, can often help students become more powerful mathematical writers. This feedback can consist of questions about anything that is not clear in the mathematical writing, suggestions for improving the writing, or comments on what is powerful in the writing. All these different kinds of feedback provide students with opportunities to revisit and reengage with their mathematical thinking and how effectively they are communicating that thinking.
An additional strategy that can help students strengthen their writing is to show them examples of strong mathematical writing and have discussions about the features that make it strong as well as to share anonymous examples of writing that needs to be strengthened and have discussion about how it might be strengthened. The use of rubrics that identify the features of strong mathematical writing, particularly with regard to solutions for “open response” items or rich tasks, can also be extremely helpful.
When mathematical writing is intended to serve as a personal log of students' own mathematical thinking, including questions and confusions as well as new mathematical insights, and not a communication to others, expressing a genuine interest in their writing and providing encouragement may be more powerful and appropriate than giving feedback on the writing itself.