# Investigating middle school students' creative problem solving in numerical and spatial domains

## TL;DR

This study explores how middle school students solve math problems creatively in numerical and spatial contexts, finding that these skills are separate and often limited by conventional teaching methods.

## Contribution

The study reveals that numerical and spatial mathematical creativity are distinct and that students tend to rely on conventional solutions despite high creativity potential.

## Key findings

- No significant correlation was found between students' spatial and numerical creativity scores.
- Most students, regardless of creativity level, produced conventional solutions like right triangles or parity in tasks.
- High-creativity students showed more fluency and flexibility in generating diverse solutions.

## Abstract

This study aimed to investigate the relationship between creativity components in numerical and spatial mathematical problem-solving contexts and to identify the characteristics of products generated by students with different levels of creativity.

The study involved 167 sixth-grade students (aged 12–13) from eight public schools in Turkey. Data were collected using the Divergent Production Ability in Mathematical Problem Solving Test (DPAMPS). Students' responses were evaluated using a rubric adapted from established creativity frameworks, and statistical analyses were conducted to examine relationships between creativity constructs and to classify students into high and low creativity groups.

Findings revealed no statistically significant correlation between students' spatial and numerical creativity scores, suggesting that these domains function independently. Regardless of creativity level, most students produced prototypical responses, such as right triangles in spatial tasks and parity or divisibility in numerical tasks, indicating reliance on conventional representations. However, students with high creative ability demonstrated greater fluency and flexibility, generating more diverse and atypical solutions across both domains.

The results support the domain-specific nature of creativity in mathematical contexts and highlight how curricular and instructional practices may limit opportunities for students to express originality. Even high-ability students tended to reproduce familiar patterns, reflecting prototype-driven reasoning reinforced by curricular settings. The study underscores the need for open-ended, non-routine mathematical tasks that encourage divergent thinking and integration of spatial and numerical reasoning to better cultivate students' mathematical creativity.