Blake Peterson, Keith Leatham and a former graduate student Lindsay Merrill along with other colleagues recently published an article titled “Clarifiable Ambiguity in Classroom Mathematics Discourse” in the journal Investigations in Mathematics Learning. Blake has answered a few questions about this article below:
Who were your co-authors on this article?
Keith Leatham, Lindsay Merrill, Laura Van Zoest, and Shari Stockero
Who would you say is the target audience for this article?
Both researchers and teachers.
What is the big problem you hoped to address with this article?
There are a lot of ways that communication can break down in a mathematics classroom. Are there ways that teachers can avoid or overcome such break downs?
What are some of the key ideas in the article?
In our verbal communication we tend to use a lot of pronouns or implied inferences to streamline the conversation. However, sometimes the object to which the pronoun is pointing is not clear. Some students may think the pronoun is referencing one thing and other students think it is referring to something else. Thus, if the referent isn’t cleared up, subsequent conversation is confusing for one group or another.
You might think that teachers would naturally address such situations but in our research we have found that even experienced teachers tend to assume that the students are interpreting these ambiguous situations the same way that they are so the teacher doesn’t take the time to seek clarification. In this paper, we emphasize the importance of teachers listening carefully to students to identify these situations then offer suggestions about how to best seek clarification.
What are some of the main ideas you hope your audience will take from the article?
Teachers need to adopt a lens of listening to their students as if they were another student in the class. Because of a teacher’s experience, they can probably infer what a student means but other students in the class may not be able to do so. If teachers can adopt this lens, they will better spot situations that need to be clarified.
Teachers should keep in mind that when they seek clarification, they should be very specific about what part of the student statement is ambiguous. When teachers ask for a generic clarification, we often see students clarify the part of their statement that wasn’t ambiguous. If, on the other hand, the teacher states what part of the student statement they did understand and then asks for clarification of the part of the student statement that they didn’t understand, the results are much better.
Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear in a relatively straightforward way if it were attended to. We argue for deliberate attention to clarifiable ambiguity as a critical aspect of attending to meaning and as a necessary precursor to productive use of student mathematical thinking. We illustrate clarifiable ambiguity that occurs in mathematics class- rooms and consider ramifications of not addressing it. We conclude the paper with a discussion about addressing clarifiable ambiguity through seeking focused clarification.