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Mathematics Learning From Instructional Gestures: Do Executive Functions or Cognitive Reflection Matter?

Fri, April 9, 3:15 to 4:15pm EDT (3:15 to 4:15pm EDT), Virtual

Abstract

Instructional gestures have been shown to benefit learning in a number of domains, including mathematics, science, and language. For example, instruction about the meaning of the equal sign (i.e., mathematical equivalence) that includes gesture improves student understanding greater than speech-only instruction (Cook et al., 2013; Cook et al., 2016; Koumoutsakis et al., 2016; Singer & Goldin-Meadow, 2005). Despite the overall efficacy of instructional gestures, many children fail to learn from either instructional format. The present research examines whether individual differences in two domain-general cognitive resources previously shown to correlate with mathematical equivalence understanding (executive function and cognitive reflection; Young & Shultman, 2020) predict students’ learning from instructional gestures.

Fifty-three 2nd-5th graders participated in an online pretest-intervention-posttest study via Zoom. Students completed 12 mathematical equivalence problems with operations on both sides of the equal sign (e.g., 2 + 3 + 8 = _ + 6) at pretest and posttest (unique items for each test). Students were also asked to provide a definition of the meaning of the equal sign, a common conceptual measure of mathematical equivalence understanding. Most U.S. elementary students provide incorrect operational definitions of the equal sign (e.g., “it means put the answer”) rather than a correct relational definition (e.g., “it means both sides have the same amount”; Hornburg et al., 2018). Students were randomized to speech-only or speech+gesture instructional videos used by Koumoutsakis et al., 2016.
In a classroom setting, Koumoutsakis found both videos improved overall student understanding, but speech+gesture led to greater learning. Prior to the pretest, students also completed a developmental measure of cognitive reflection (i.e., the tendency to reflect on one’s own thinking; Young & Shtulman, 2020) and measures of executive function (set shifting and working memory).

Bayesian regression modeling yielded three main results. First, there was no overall effect of instruction type, students’ equivalence problem solving and conceptual definitions improved similarly with speech-only and speech+gesture instruction. Second, measures of cognitive reflection, executive function, and student age did not interact with the learning effects of instruction type. Third, cognitive reflection was broadly implicated in students’ understanding. Cognitive reflection predicted equivalence problem-solving at pretest and at posttest (adjusting for executive function, age, and pretest score). Cognitive reflection also predicted conceptual learning, such that more reflective students were more likely to learn a correct relational definition from pretest to posttest.

The present results suggest individual differences in executive function and cognitive reflection are not implicated in students’ differential learning from instructional gestures over speech-only instruction. Cognitive reflection did predict conceptual learning from both instructional formats, suggesting cognitive reflection supports the construction of an accurate relational conception of the equal sign. However, these findings should be considered tentative as the current data suggest the well-documented benefits of instructional gesture may not necessarily generalize to online instruction (at least over Zoom). Data collection is ongoing during the Covid-19 pandemic, however these data highlight that researchers need to consider whether in-person research findings generalize to online settings and vice versa.

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