Unit 3: Reasoning and Explaining (MP2 and MP3)

# Taxonomy of Questions in Mathematical Discourse

...students' explanations are a starting point for classmates to develop mathematical arguments that support, refine, or possibly refute his ideas."

Whitenack & Yackel, 2002

Take a few minutes to review the taxonomy of questions in mathematical discourse below:

 Question Type Description External authority Answers are attributed to someone else, teacher, parent, or "I just knew it." Confirm - Is it? Agree or disagree. Choose. Categorize Recall - What is it? Knowledge produced from memory (e.g., facts, calculations, definitions). Explain - What is true? Produces new learning. Gives solutions with enough clarity and detail to be understood. Gives examples. Convinces others. Justification - Why is it true? Provides evidence for and against claims. Relates concepts to situations and concepts to questions, and introduces new concepts. Generalization - Is it always true? Communicates reasoning about commonalities in patterns, procedures, structures, and relationships. Adapted from Mendez (1998) and Nathan & Kim (2007)

The patterns of language in teacher questions and student responses were collected and synthesized into the table below :

 Questions Responses External (Any question) Last year's teacher told me. My brain just knows it. Confirm Do you agree? Disagree? Is it ... or ...? Yes/no Thumbs up/thumbs down Recall How many ...? What did ...say? It is ... The answer is ... Explain How did you ...? Can you explain ...? And then what did you do? How are they the same? Different? First I... then I... and then... They are ... because ... Justify Why does that work? Is there another way? What do you think? If ... then ... because ... If ... so ... because ... So it would be ... because ... Generalize Why? Does it always work? Is there a rule Sentences combined with a Justification: It will always ... Every time .

When students make their thinking visible, they are organizing their thoughts, connecting to previous understandings, and recognizing and correcting gaps in their logic. An awareness of language patterns enables the teacher and other students to access student thinking which helps to develop a public knowledge base. This awareness is especially helpful in supporting English learners and students with special needs.