The use of spatial reasoning to solve mathematical problems across number, algebra, and data and uncertainty domains among 8th-grade junior high school students

Abstract

Spatial reasoning has been widely studied, with evidence showing a strong relationship to students' mathematics achievement. However, most studies have focused on geometry and on primary/early-level students. Therefore, this study aims to explore students' use of spatial reasoning in solving mathematical problems across numbers, algebra, and data and uncertainty, which remains underexplored. This study employed a sequential mixed method design. In the quantitative phase, a predictive correlational design was used to examine the relationship between spatial reasoning and its constructs and students' mathematical problem solving performance across numbers, algebra, and data and uncertainty. The sample consisted of 213 8th-grade students from six public junior high schools in Depok City, selected through convenience sampling. Data were collected using the Mathematical Problem Solving Test (MPST) and the Spatial Reasoning Test (SRT), and were analyzed using regression analyses. In the descriptive qualitative phase, the participants consisted of 13 8th-grade students selected purposively to represent mathematics domains across numbers (n = 4), algebra (n = 5), and data and uncertainty (n = 4). The data were collected using the Mathematical-Spatial Problem Solving Test (MSPST) and a semi-structured interview instrument. The quantitative results revealed significant predictive relationships between overall spatial reasoning and overall mathematical problem solving performance. In terms of specific constructs, spatial visualization and mental rotation predicted students' algebra problem solving performance, while spatial orientation predicted performance in data and uncertainty. The qualitative findings indicated that spatial reasoning played an important role in supporting understanding of the problem context, facilitating the construction of mathematical models, terms, and symbols, and driving the planning of strategies or mathematical procedures. The findings also showed that students with developed spatial reasoning were able to construct effective mental representations to understand the problem, leading to appropriate problem solving, although procedural fluency remained an important factor. In contrast, students with less developed spatial reasoning or those who did not use spatial reasoning experienced difficulties in understanding the problem and determining appropriate problem solving strategies. In addition, the qualitative results showed that spatial language potentially enabled students to conceptualize objects and organize relational information, thereby initiating the construction of mental representations that support spatial reasoning. Then, visual representations functioned as operational tools that allowed students to externalize, manipulate, and mentally transform these representations, as well as serving as outcomes of the spatial reasoning process itself. Schematic imagery was found to be more effective in emphasizing spatial reasoning in mathematical problem solving. This study has several limitations, including the use of convenience sampling in the quantitative phase, an imbalanced qualitative sample that underrepresents performance in each mathematics domain, and the potential for interpretative bias in the qualitative analysis. Based on this study, future research may consider conducting intervention studies integrating spatial reasoning with procedural, exploring students' cognitive processes in constructing representations, and explaining the relationship between spatial language and visual representations to facilitate spatial reasoning.