# Constructed Learning in Elementary Mathematics

#### Abstract

Math manipulatives are an exciting way to interest elementary school students. Which designs are most useful for young children? In what way(s) do manipulatives affect the learning process? After researching the literature math manipulatives for elementary students (Furner & Worrell, 2017) I designed several 3D models for mathematics lessons. Factors affecting the design, such as color (Dzulkifli & Mustafar, 2013), size, shape, and 3D print materials (resin and filament) were essential in creating an attractive, usable, and affordable manipulative. The experimental manipulative produced was a 1-inch filament-printed hollow, stackable octagon. Primary colors of yellow, red, and blue, no matter the designated unit, were chosen most often for use to solve a mathematical equation. The mathematics lessons, with the experimental and control manipulatives, were delivered to Kindergarten (N=20) and first grade (N=30). The first day was addition, second day tens places, and third day money skills both factual and with theoretical exchange rate. Results from both classrooms indicated that students were skilled with addition and subtraction (80% accuracy). Fewer students (50%) were skilled with ones, tens places. Kindergarten students had about 30% accuracy with tens place money calculations. Money exchange equations were embedded within a commercial text which were provided to students in both English and Spanish versions. Students were asked to exchange imaginary currency based on tens exchange. As this was an extension lesson not covered through standard curriculum, it was highly surprising to find that nearly 30% of all students were able to accurately complete the equations. The 3D manipulatives were, on the whole, not a determining factor for processing mathematical inquiry. Although 20% of students used the manipulatives as requested with place values, the majority of students regarded both equally as single units.

*This paper has been withdrawn.*

Constructed Learning in Elementary Mathematics

Math manipulatives are an exciting way to interest elementary school students. Which designs are most useful for young children? In what way(s) do manipulatives affect the learning process? After researching the literature math manipulatives for elementary students (Furner & Worrell, 2017) I designed several 3D models for mathematics lessons. Factors affecting the design, such as color (Dzulkifli & Mustafar, 2013), size, shape, and 3D print materials (resin and filament) were essential in creating an attractive, usable, and affordable manipulative. The experimental manipulative produced was a 1-inch filament-printed hollow, stackable octagon. Primary colors of yellow, red, and blue, no matter the designated unit, were chosen most often for use to solve a mathematical equation. The mathematics lessons, with the experimental and control manipulatives, were delivered to Kindergarten (N=20) and first grade (N=30). The first day was addition, second day tens places, and third day money skills both factual and with theoretical exchange rate. Results from both classrooms indicated that students were skilled with addition and subtraction (80% accuracy). Fewer students (50%) were skilled with ones, tens places. Kindergarten students had about 30% accuracy with tens place money calculations. Money exchange equations were embedded within a commercial text which were provided to students in both English and Spanish versions. Students were asked to exchange imaginary currency based on tens exchange. As this was an extension lesson not covered through standard curriculum, it was highly surprising to find that nearly 30% of all students were able to accurately complete the equations. The 3D manipulatives were, on the whole, not a determining factor for processing mathematical inquiry. Although 20% of students used the manipulatives as requested with place values, the majority of students regarded both equally as single units.