Keith Leatham and Blake Peterson recently had a paper titled “Articulating the Student Mathematics in Student Contributions” published in the conference proceedings for the Psychology of Mathematics Education – North America (PMENA) conference. Blake has answered a few questions about this paper below:
Who were your co-authors on this paper?
Laura Van Zoest – Western Michigan University, Shari Stockero – Michigan Technological University, and Joshua Ruk – Western Michigan University.
Who would you say is the target audience for this paper?
This work would be useful for both researchers and practicing teachers.
What is the big problem you hoped to address with this paper?
When students share their thinking as part of a class discussion, it is sometimes difficult for the teacher to make sense of exactly what they are saying. This paper describes four types of student contributions and provides suggestions on how teachers might respond to each type.
What are some of the main ideas you hope your audience will take from this article:
One of the main ideas that comes out of this article is the importance of teachers listening carefully to what their students are saying. Oftentimes, teachers have an idea of where they want the lesson to go and what kind of student contributions they are hoping the students will make. Thus, there can be a tendency for teachers to infer something about what the student has said but that is not what they actually said.
If a teacher is at all unsure of what a student is saying, they should seek clarification. Just because the teacher may be able to infer what the student is saying, it cannot be assumed that other students in the class are able to make the same inference. Thus, when a teacher seeks clarification to solidify their inference, they are also clarifying it for everyone in the class. If a teacher attempts to have a discussion about a contribution that has not been adequately clarified, the discussion will likely be unproductive.
Finally, we have found that experience articulating the student mathematics of student contributions has the potential to develop a “habit of listening” and increase teachers’ abilities to notice student thinking during instruction.
Abstract:
We draw on our experiences researching teachers’ use of student thinking to theoretically unpack the work of attending to student contributions in order to articulate the student mathematics (SM) of those contributions. We propose four articulation-related categories of student contributions that occur in mathematics classrooms and require different teacher actions:(a) Stand Alone, which requires no inference to determine the SM; (b) Inference-Needed, which requires inferring from the context to determine the SM; (c) Clarification-Needed, which requires student clarification to determine the SM; and (d) Non-Mathematical, which has no SM. Experience articulating the SM of student contributions has the potential to increase teachers’ abilities to notice and productively use student mathematical thinking during instruction.