How Do Gestures Influence Thinking and Speaking? The Gesture-for-Conceptualization Hypothesis.

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Assessing knowledge conveyed in gesture: Do teachers have the upper hand?

Children's gestures can reveal important information about their problem-solving strategies. This study investigated whether the information children express only in gesture is accessible to adults not trained in gesture coding. Twenty teachers and 20 undergraduates viewed videotaped vignettes of 12 children explaining their solutions to equations. Six children expressed the same strategy in speech and gesture, and 6 expressed different strategies. After each vignette, adults described the child's reasoning. For children who expressed different strategies in speech and gesture, both teachers and undergraduates frequently described strategies that children had not expressed in speech. These additional strategies could often be traced to the children's gestures. Sensitivity to gesture was comparable for teachers and undergraduates. Thus, even without training, adults glean information, not only from children's words but also from their hands

Does Comparing Informal and Formal Procedures Promote Mathematics Learning? The Benefits of Bridging Depend on Attitudes Toward Mathematics

Students benefit from learning multiple procedures for solving the same or related problems. However, past research on comparison instruction has focused on comparing multiple formal procedures. This study investigated whether the benefits of comparing procedures extend to comparisons that involve informal and formal procedures. We also examined how learner characteristics, including prior knowledge and attitudes toward mathematics, affect learning from comparing procedures. We addressed these issues in college students\u27 learning procedures for solving systems of equations problems in algebra. Learners who liked mathematics learned equally well whether they received comparison or sequential instruction. However, among learners who did not like mathematics, instruction that included support for comparisons between the formal and informal procedures led to greater gains in conceptual knowledge than did sequential instruction of the procedures

Gesture analysis for physics education researchers

Systematic observations of student gestures can not only fill in gaps in students' verbal expressions, but can also offer valuable information about student ideas, including their source, their novelty to the speaker, and their construction in real time. This paper provides a review of the research in gesture analysis that is most relevant to physics education researchers and illustrates gesture analysis for the purpose of better understanding student thinking about physics.Comment: 14 page

Middle School Students’ Conceptual Understanding of Equations: Evidence from Writing Story Problems

This study investigated middle school students’ conceptual understanding of algebraic equations. 257 sixth- and seventh-grade students solved algebraic equations and generated story problems to correspond with given equations. Aspects of the equations’ structures, including number of operations and position of the unknown, influenced students’ performance on both tasks. On the story-writing task, students’ performance on two-operator equations was poorer than would be expected on the basis of their performance on one-operator equations. Students made a wide variety of errors on the story-writing task, including (1) generating story contexts that reflect operations different from the operations in the given equations, (2) failing to provide a story context for some element of the given equations, (3) failing to include mathematical content from the given equations in their stories, and (4) including mathematical content in their stories that was not present in the given equations. The nature of students’ story-writing errors suggests two main gaps in students’ conceptual understanding. First, students lacked a robust understanding of the connection between the operation of multiplication and its symbolic representation. Second, students demonstrated difficulty combining multiple mathematical operations into coherent stories. The findings highlight the importance of fostering connections between symbols and their referents

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

Grounded and embodied theories of cognition suggest that both language and the body play crucial roles in grounding higher-order thought. This paper investigates how particular forms of speech and gesture function together to support abstract thought in mathematical proof construction. We use computerized text analysis software to evaluate how speech patterns support valid proof construction for two different tasks, and we use gesture analysis to investigate how dynamic gestures—those gestures that depict and transform mathematical objects—further support proof practices above and beyond speech patterns. We also evaluate the degree to which speech and gesture convey distinct information about mathematical reasoning during proving. Dynamic gestures and speech indicating logical inference support valid proof construction, and both dynamic gestures and speech uniquely predict variance in valid proof construction. Thus, dynamic gestures and speech each make separate and important contributions to the formulation of mathematical arguments, and both modalities can convey elements of students’ understanding to teachers and researchers

Gesture production and comprehension in children with specific language impairment

Children with specific language impairment (SLI) have difficulties with spoken language. However, some recent research suggests that these impairments reflect underlying cognitive limitations. Studying gesture may inform us clinically and theoretically about the nature of the association between language and cognition. A total of 20 children with SLI and 19 typically developing (TD) peers were assessed on a novel measure of gesture production. Children were also assessed for sentence comprehension errors in a speech-gesture integration task. Children with SLI performed equally to peers on gesture production but performed less well when comprehending integrated speech and gesture. Error patterns revealed a significant group interaction: children with SLI made more gesture-based errors, whilst TD children made semantically based ones. Children with SLI accessed and produced lexically encoded gestures despite having impaired spoken vocabulary and this group also showed stronger associations between gesture and language than TD children. When SLI comprehension breaks down, gesture may be relied on over speech, whilst TD children have a preference for spoken cues. The findings suggest that for children with SLI, gesture scaffolds are still more related to language development than for TD peers who have out-grown earlier reliance on gestures. Future clinical implications may include standardized assessment of symbolic gesture and classroom based gesture support for clinical groups