THEME: INSTRUCTION AND GESTURE

### TALK SESSION #4

**Facilitator: Martha W. Alibali**

**Janet Walkoe - Teacher Noticing of Student Thinking as Expressed Through Gesture and Action**

Teacher noticing has been identified as an important facet of teacher cognition. In particular, if teachers are able to attend to the disciplinary substance of students’ ideas, students are more likely to have access to and engage with important ideas in the discipline. Historically, however, the work on teacher noticing has focused primarily on students’ verbal or written expression. In this talk, I will discuss two lines of work that call for a research agenda that attends to ways teachers notice and build upon students’ multi-modal expression of mathematical ideas. One line focuses on teacher noticing in of students’ actions and gestures while watching classroom video clips. A second line explores the opportunities embedded in lesson design for teachers to attend to students’ multi-modal expressions. I will discuss early findings and implications for the design of classroom lessons and teacher PD.

**Martha Alibali - Understanding the Role of Teachers’ Gestures in Students’ Learning: Lessons from a Teacher Avatar**

This talk describes a program of research involving a computer-animated teacher avatar that produces gestures as she speaks. We used the avatar to test hypotheses about the role of teacher gestures in students’ mathematics learning, with a focus on the role of gesture in (1) guiding students’ attention to relevant elements of instructional material, and (2) helping students learn about links between representations. Teachers’ gestures were not always helpful for student learning. However, there was strong evidence that teachers’ gestures foster students’ encoding of instructional material. We consider the overall pattern of findings and the function of teachers’ gesture “in the moment” in interactions between students and teachers.

**Susan Wagner Cook - Individual Differences in Learning with Hand Gesture: The Role of Visual-Spatial Working Memory**

When teachers use hand gestures to support instruction, students learn more than others who learn the same concept with only speech. Individual variation in working memory capacity is also known to influence math learning, with individuals with greater working memory capacity learning more rapidly than individuals with lesser capacity. We investigated the relation between mathematical learning with or without gesture and individual variation in working memory capacity. Students observed a videotaped lesson in a novel mathematical system that either included instruction with speech and gesture or instruction in only speech. When gesture was present, learning was related to visuospatial working memory. When gesture was absent, learning was related to verbal working memory. Thus, adding gesture to instruction can change the processes supporting learning. Effective instruction will match designs to capabilities.

**Nicole Engelke Infante - Communicating Calculus: Two Sides of the Equation**

Calculus is the study of motion. As such, when we are communicating about these advanced mathematical ideas, gesture naturally arises to supplement the spoken word. My research focuses on how instructors use gesture to highlight information about these complex ideas for students and how students use gesture to support their problem-solving activities. There are great variations in what instructors do; this raises the question of what is most beneficial for student learning. Coming from a constructivist perspective of embodied cognition, the gestures students make during their problem-solving processes (e.g., modeling, diagram construction) are equally critical for constructing their understanding. I will share brief vignettes from both sides of this critical equation.

**Caroline Yoon - Metaphor Tangles in an Inverse Problem Calculus Task**

An inverse problem begins with results produced by a system, and asks solvers to find the parameters that produced the results. The problem of finding an antiderivative (rather than an integral) of a given function can be thought of as an inverse problem, requiring solvers to imagine the function that differentiated to the given function. When two participants worked on a sequence of antiderivative tasks, they performed the mechanical steps required of the inverse procedure almost as easily as those of the forward direction. What was more challenging was overcoming their strong inclination to work in the forward direction, and orient themselves to the inverse direction instead. I discuss how the participants relied on a tangle of metaphors, gestures and diagrams to orient themselves in the inverse direction. I also share my own struggles to make sense of this data using a tangle of cognitive linguistics, semiotics, and inclusive materialism.