Early Elementary Students’ Use of Shape and Location Schemas When Embedding and Disembedding

Laura Bofferding,Sezai Kocabas,Lizhen Chen,Mahtob Aqazade

doi:10.3390/educsci12020083

Laura Bofferding, Sezai Kocabas + Show 2 more

Open Access

https://doi.org/10.3390/educsci12020083

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Abstract

Elementary students’ early development of embedding and disembedding is complex and paves the way for later STEM learning. The purpose of this study was to clarify the factors that support students’ embedding (i.e., overlapping shapes to form a new shape) and disembedding (i.e., identifying discrete shapes within another shape) through the use of filled shapes as opposed to shape frames. We recruited 26 Grade 1 students (~6–7 years old) and 23 Grade 3 students (~8–9 years old), asked them to work on two layered puzzle designs from the Color Code puzzle game, and interviewed them about their thinking processes. The first graders had higher success rates at fixing and embedding the tiles correctly, and students at both grade levels improved on the three-tile design when encountering it a second time about two months later. The four-tile design was more difficult, but students improved if they could identify a correct sub-structure of the design. Successful students used a combination of pictorial shape strategies and schematic location strategies, systematically testing tiles and checking how they could be embedded. The results suggest that helping students focus on sub-structures can promote their effective embedding.

Highlights

There is no separate embedding learning trajectory, the current learning trajectories for shape composition and for disembedding [10] involve a progression from students using pictorial schemas toward using schematic schemas [10–12]
Between the ages of four and seven, the learning trajectory for disembedding geometric figures progresses from students being able to identify non-overlapping frames of shapes—only pictorial schemas needed, shape frames embedded inside of other shape frames, secondary frames created from embeddings [10]—focused on schematic schema use
The results of this study provide an interesting addition to current trajectories [10] and research on pictorial and schematic schemas

Summary

Introduction

Current standards in the United States explicitly call for kindergarteners and first graders to have opportunities to compose shapes, to make compositions using those composite shapes, and to decompose shapes into equal parts [1]. Between the ages of four and seven, the learning trajectory for disembedding geometric figures progresses from students being able to identify non-overlapping frames (i.e., outlines) of shapes—only pictorial schemas needed, shape frames embedded inside of other shape frames (e.g., a triangle inside a rectangle on a geoboard [13]), secondary frames created from embeddings [10]—focused on schematic schema use. Missing from this trajectory is the consideration of filled shapes (i.e., the result of disembedding a filled shape from a layered design)

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