Abstract

Examining Children’s Use of Different Types of Concrete Representations in a Novel Numeration System
By Aryann Blondin
Concrete materials, also called manipulatives, are used in the elementary classroom (e.g., Blondin, Tomaszewski, & Osana, 2017; Moyer, 2001) to illustrate a wide variety of abstract mathematical notions, yet little is known about how the differences in the materials affect the mathematical learning (Belenky & Schalk, 2014). This study examined the differences between concrete proportional and non-proportional models in the context of base-four problems. The aim was to examine the effects of the manipulatives’ proportionality on learning and transfer measures, and to see if there were any effects of prior knowledge of numeracy and place value. Following prior knowledge assessment, 52 second-graders were randomly assigned to either the proportional condition (n = 26) or the non-proportional condition (n = 26). Students in the proportional condition used base-four blocks for the instructional intervention and the testing. Students in the non-proportional condition used colored chips. Next, students received an instructional intervention with the manipulatives and completed learning and transfer measures. No condition effects were found. Prior knowledge accounted for a significant portion of the variance on two of the learning measures and one of the transfer measures, but no interaction effects were found. The present study reminds teachers that prior knowledge is important to consider when choosing appropriate tools in the classroom to meet their students’ needs. Additionally, the present study reminds researchers that assessing prior knowledge is an important factor when examining the effects of manipulatives. The results of this study contribute to the literature on external knowledge representations.