SRCD 2019 Biennial Conference
March 21-23, 2019
Title: Using Visual Comparison to Facilitate Students’ Proportional Reasoning Learning (Poster
Session: Education, Schooling
Authors: Kelly Trezise, Bryan Mattien, Emily A. Lyons, Ellen Klostermann Wallace, Lindsey Richland
Abstract: Acquisition of proportional reasoning concepts is both fundamental for higher level mathematics, and difficult for many students. Proportional reasoning is cognitively demanding and requires use of prior knowledge (e.g., multiplication and division skills). Children with poorer executive functioning experience greater difficulty learning proportional reasoning (Begolli, Richland, Jaeggi et al, 2018). Given difficulties in proportional reasoning acquisition, can instruction be adapted to improve students’ ability to learn proportional reasoning? Research indicates learning can be improved by reducing task cognitive demands and better prior knowledge representations (Doumas, Morrison, Richland, 2018; Paas , Renkl & Sweller, 2003). The current study examines whether changes in students’ proportional reasoning accuracy and strategies is affected by cognitive demands and/or prior knowledge representations.
Two hundred sixty-seven 5th grade students from five schools in the Chicago area completed the study. Visual support during learning was used to reduce cognitive demands; instruction for long division was used to strengthen prior knowledge representations. Students were assigned to both a Familiarity (Familiar, Unfamiliar) and a Comparison (Visual, Indirect) condition. Students in the Familiar condition completed a worksheet containing step-by-step instructions for solving long division problems. The Unfamiliar condition worksheet contained division problems without instruction. Several days after the familiarity manipulation, all students completed a video lesson on solving proportional reasoning problems using least common multiple (LCM) and division strategies. In the Visual Comparison condition, during the video lesson the LCM and division problem solving strategies remained onscreen, in parallel, throughout the lesson, and the teacher used linking gestures comparing the two strategies. In the Indirect Comparison condition, strategies were not shown at the same time, and linking gestures were not shown. The teachers’ speech for the two video lessons were identical: only visual content was manipulated. Students’ proportional reasoning accuracy and strategy were assessed before, immediately after, and one week after the lesson (pretest, immediate- and delayed-tests).
All groups showed improved performance on the immediate and delayed tests, compared to the pretest (see Figure 1). Planned comparisons showed no difference between Familiarity or Comparison conditions at pretest. Accuracy in the immediate and delayed test was higher for students in the Visual Comparison condition; there was no effect of Familiarity and no interaction between Familiarity and Comparison. Examination of change in strategies shows many students changed from invalid strategy or (incorrect) subtraction strategy at pretest, to LCM or division strategies as immediate test. A multinomial regression shows that when accounting for pretest strategy, Visual Comparison predicted use of LCM but not division at the immediate test. The findings indicate instructional techniques aimed at reducing cognitive load (e.g., visual support) can improve students’ proportional reasoning learning. However, visual support appears to be more useful for some proportional reasoning strategies than others. This suggests visual support may be used as an instructional technique to facilitate students’ procedural proportional reasoning learning, but the impact on conceptual learning remains unclear.