Embodied truths: How dynamic gestures and speech contribute to mathematical proof practices

A comparative study of high school mathematics teachers' audible teaching language: A student satisfaction perspective

Teachers' audible teaching language is essential for organizing classroom instruction. This study used a questionnaire to compare expert, skilled, and novice high school mathematics teachers' audible teaching language from the perspective of student satisfaction. The sample was selected using a purposive sampling technique, and the participants were students from a key high school in Changsha, China. A research framework and research instrument with good reliability and validity were constructed for this study. The data were analyzed using SPSS 22.0 and AMOS 22.0. The results showed 263 valid questionnaires, good measurement model fit, and high reliability and validity of the questionnaire. It was found that: (1) students were highly satisfied with the audible teaching language of high school mathematics teachers; (2) student satisfaction with the audible teaching language of skilled, expert, and novice mathematics teachers declined in order, but there was no significant difference overall; (3) students were more satisfied with expert mathematics teachers than with novice teachers in terms of the tone and adaptability of the audible teaching language. The researchers discussed the study's results, suggested how pre-service and post-service mathematics teachers can improve the quality of their audible teaching language, and pointed out the value and limitations of the study.

The roles of motion, gesture, and embodied action in the processing of mathematical concepts

This article discusses perspective and frame of reference in the metaphorical description of mathematical concepts in terms of motions, gestures, and embodied actions. When a mathematical concept is described metaphorically in terms of gestures, embodied actions, or fictive motions, the motor system comes into play to ground and understand that concept. Every motion, gesture, or embodied action involves a perspective and a frame of reference. The flexibility in taking perspective and frame of reference allows people to embody a mathematical concept or idea in various ways. Based on the findings of past studies, it is suggested that the graphical representation of a mathematical concept may activate those areas of the motor system that are involved in the production of that graphical representation. This is supported by studies showing that when observers look at a painting or handwritten letters, they simulate the painter's or writer's hand movements during painting or writing. Likewise, the motor system can contribute to the grounding of abstract mathematical concepts, such as functions, numbers, and arithmetic operations.

The Effect of Cognitive Relevance of Directed Actions on Mathematical Reasoning

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the cognitive relevance of particular body states to associated math concepts. We test competing models of action-cognition transduction to investigate the cognitive relevance of directed actions to students' mathematical reasoning in the area of geometry. The hypotheses we test include (1) that cognitively relevant directed actions have a direct effect on performance (direct cognitive relevance hypothesis), (2) that cognitively relevant directed actions lead to more frequent production of gestures during explanations, which leads to improved performance (mediated cognitive relevance hypothesis), and (3) that performance effects of directed actions are influenced by the presence or absence of gesture production during mathematical explanations (moderated cognitive relevance hypothesis). We explore these hypotheses in an experiment where high school students (N = 85) evaluated the truth of geometry conjectures after performing cognitively relevant or cognitively irrelevant directed actions while playing a movement-based video game. Contrary to the direct and mediated cognitive relevance hypotheses, we found no overall differences in performance or gesture production between relevant and irrelevant conditions. Consistent with the moderated cognitive relevance hypothesis, cognitive relevance influenced mathematical performance, as measured by the accuracy of students' intuitions, insights, and the validity of their proofs, provided that students produced certain kinds of gestures during mathematical explanations (i.e., with explanatory gestures as the moderator). Implications for theories of grounded and embodied cognition and the design of embodied forms of educational interventions are discussed.