Writing in Mathematics
Reconnecting with Our Mathematicians
As you think back on the videos you’ve reviewed and reflected on, consider how the students in these videos are engaged in communicating and writing mathematically in ways that reflect the authentic work of mathematicians.
Mathematicians regularly write about their mathematical thinking, including the notes they take and the thoughts they have as they tackle a difficult problem or attempt a new proof. They need to be able to use this writing to consolidate and communicate their thoughts to others. Sometimes these communications are informal, including exchanging drafts of solutions or thoughts about obstacles and insights with colleagues and collaborators. Sometimes they are more formal, such as final papers that are presented to colleagues or submitted for publication.
This is true for applied mathematicians, who use mathematics to find solutions for problems in the real world, often as part of a team, where a variety of perspectives are shared and discussed and where solutions are finally laid out in the form of a report. This is also true for theoretical mathematicians, who work on rich mathematical problems or proofs that advance the field, are responsible for documenting their thinking processes as they work toward a solution or a proof, and need to be able to clearly and compellingly present these solutions or proofs to others.
As you reflect on what you saw in these videos, an important question to consider is how teachers provided structured opportunities for students to engage in mathematical writing. How did they organize and structure these opportunities? How were these opportunities situated in the larger context of small-group and whole-class discussion? What did the teachers seem to learn from the mathematical writing of their students? How was feedback provided on that writing? As you contemplate these questions, it is important to keep in mind that there are times when students may need to engage in mathematical writing on their own to document their thoughts and questions or take notes on what they are learning during class. There are also times when students engage in mathematical writing as part of a small-group effort to document and explain their thinking. Finally, there are times when there are more structured opportunities for students to engage in mathematical writing as they solve particular problems or work on particular proofs.
As you consider what you have seen in these videos, consider how you can use what you are exploring here to strengthen and support the engagement of your own students in the disciplinary literacy practice of writing mathematically on an ongoing basis.
Continue to Unit 8 – Bringing It All Together