Students Communicating What They Know

he talks in maths

Students struggle to share what they know about mathematics through writing, and it should not be surprise to anyone that students feel uncomfortable writing about mathematics. As math teachers, most of us don’t write about mathematics routinely (if ever). We were not expected to write as students, so we don’t have a lot of experience writing, and we do not have much (again, if any) training in the writing process.

When learning new content, students stumble over how to use the language, or how to describe a specific step in a process, or how they decide what step to do next within a problem. We provide ample opportunity in classes to talk about their understanding but as with any content there is a need to be able to express your understanding in written form as well as verbally. I believe it is important that we as mathematics teachers not only create opportunities to write in our classes but create routines in our classes that support students as writers.

In blogging about mathematics and math ed, I’ve done more writing than I have at any time in my life, other than when I am writing for college classes, and that writing has been for a very specific audience and has not been about mathematics, very often. This process is difficult for me and I acknowledge that it is not always eloquent prose, but it has helped me understand the increased need for writing in mathematics classrooms. Communication is a key skill in life and I want my students to be distinguished communicators of mathematics.

In a recent conversation with a teacher struggle with this exact issue, we developed a plan for supporting her students to become better thinkers and writers of mathematics. She has started having her students do short writes to organize their thinking and to let her know what they understood about what was happening in class. She is already working on techniques in her instruction that supported student thinking. She is having students represent concepts in multiple ways. With her latest topic, solving linear systems, it was very intentional that she had students represent the different types of systems symbolically, graphically, and with a brief description. This simple idea was designed so that students get used to seeing all three and be able to use all three representations to discuss the concepts.

The great step that Sue inserted next was to have her students develop questions they would ask others about the different systems; what makes the systems different, same, etc. Rather than ask the students questions she developed, Sue placed the task in the hands of the students. Creating the questions forced the students to think about the systems and to identify specific characteristics.

To end the activity, students were asked to do a quick write explaining what they knew about one of the system types. It was not surprising that the writings did not seem to express the same understanding that students were sharing in their discussions.

Sue is committed to having students write in her math classes to express their understanding. In brainstorming next steps some simple ideas surfaced. The writings are varied and some use the language that is expected, some make connections beyond the discussions in class, and some need help in many ways. Sue has decided to begin taking a few samples of sentences and identifying things she likes about them, and have students identify things they think are good in other student writings. Before moving on, the group will construct a couple of sentences together that use the concepts discussed. She is planning on using this kind of routine in her class regularly moving the work from whole group to small groups. She wants to move from creating one or two sentences together to creating multiple examples of sentences through small groups to individuals redrafting their own work to mirror the use of language, organized thinking, and consequently stronger writing.

By supporting writers to write more and to provide models for students Sue is hoping to increase her student’s ability to communicate what they are learning in her classroom. These are simple but effective strategies. She is also planning on posting student writing around her room to provide continued motivation and examples for students. The plan is to have students not only post writing in the displays but other representations that are important in mathematics as well. It is important that students can write about what they know and understand, but it is critical that they can connect manipulation of symbols, information from tables,  as well as read graphs.

Picture: “… he talks in maths” by Xenocryst @ Antares Scorpii, / CC BY-NC-ND 2.0

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