Gestures are an integral component of mathematics classroom discourse. There is a need to
classify the types of gestures that teachers use according to their purposes towards supporting and extending students’ mathematical thinking. We analyzed 16 algebra tutoring sessions between pre-service teachers (PSTs) and high school students to categorize the PSTs’ gestures. We identified 10 categories of PST gestures that we roughly organized into three supercategories: gestures that facilitate shared attention and communication, gestures that emphasize written visual representations, and gestures that support verbal explanations. A taxonomy of gestures based on their purposes will enable further analyses of teacher gesturing and help preservice and practicing teachers use gestures in more purposeful ways.
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Posing questions is a direct way for teachers to push students to verbalize justifications and make connections among ideas, but this skill is difficult to learn. We recruited four pre-service special education teachers to participate in a semester-long professional development focused on developing mathematics knowledge and asking questions, while concurrently providing 1-1 tutoring to students with learning disabilities. The pre-service teachers increased their frequency of questions overall and of questions that probed students’ thinking or explored mathematical relationships. The pre-service teachers also developed strategies for shifting among different types of questions when students struggled. The findings of this study illustrate the potential for pre-service teachers to develop questioning routines that challenge students while scaffolding their progress towards new understanding.more » « less
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Categorizing mathematics teachers’ questioning: The demands and contributions of teachers’ questionsWe conducted a review of literature to answer the following research questions: (1) What types of questions do teachers pose in mathematical discussions? (2) What evidence exists of the effects of different types of questioning on students’ learning and participation? (3) What are the implications of existing research for teacher preparation? Existing literature can broadly be categorized according to studies that distinguish between higher order and lower order questioning, studies that characterize and distinguish probing questions, and studies that address teacher questioning in technology-rich environments. The demands of different types of questions need to be considered in light of the broader contributions that such questions make to students’ mathematical learning.more » « less
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We provide a detailed description of a purposefully sampled tutoring session during which a student with a learning disability displayed common tendencies we have seen in our work on algebra teaching. The student struggled with solving equations in general and especially with distribution and knowing how to distribute terms and what steps to take in the correct order. The tutor responded by helping the student offload information, gesturing while speaking with the student, and asking questions strategically to both support and challenge the student to think critically. The purpose of this paper is to provide, through a case study, an accessible description for teachers and researchers of how students with learning disabilities interact with algebra and how teachers can support and challenge these students in this context.more » « less
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Students with learning disabilities (LD), like other learners, show a range of resources and strategies for reasoning about complex concepts in mathematics. This study comes from a project in which a group of five ninth-grade students with LD participated in a once-weekly tutoring program with university pre-service teachers. We asked, what strategies did students use to reason about slope? Students drew upon knowledge of concepts related to constant covariation when given the opportunity. This study suggests that students with LD have rich conceptual knowledge that can be leveraged to improve their success in Algebra.more » « less
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