Collaborative research: design and development of integer games to reduce barriers to algebra

George Fox University received a $343,330 Project Grant from the National Science Foundation's Division of Research on Learning in Formal and Informal Settings under the STEM Education program (CFDA 47.076), effective September 1, 2025, through February 28, 2029. This collaborative research initiative focuses on designing and developing educational games that introduce negative number concepts to elementary school students in grades 2-4. The project addresses a critical pedagogical gap wherein students' early experiences with only positive numbers often lead to mathematical misconceptions that later impede algebra learning. Through an iterative prototyping and testing process informed by expert consultation, the project team will develop game-based materials that align with students' cognitive development while building foundational understanding of integer principles and their connections to algebraic concepts.

The project deliverables include refined educational games produced through structured evaluation activities comprising a six-session study (pretest, four gameplay sessions, and posttest) with quantitative and qualitative assessment of student learning outcomes and motivation changes. By introducing negative number concepts earlier in the educational pipeline, this initiative aims to increase student motivation, strengthen mathematical understanding, and improve preparation for algebra and advanced STEM coursework. The research outcomes and refined game materials are designed to contribute to the broader National Science Foundation objective of advancing effective, evidence-based STEM education practices across formal and informal learning environments.

Abstract

Elementary school students' prolonged experiences with positive numbers and operations often lead to their overgeneralizations of rules (e.g., adding always makes larger numbers, subtracting always makes smaller numbers). These overgeneralizations can make learning algebra more difficult later, particularly when students must simultaneously learn algebra, negative numbers, and operations with negative numbers. The purpose of this project is to design and develop educational games centered on negative number concepts that target students before they learn algebra in middle school. Earlier exposure to and learning about negative numbers could increase students' motivation, understanding of connections between positive and negative numbers, and preparation for algebra. In the long term, this earlier exposure could lead to later success in advanced mathematics and improve science technology engineering mathematics (STEM) education. The project team will design and develop the educational games through an iterative process of prototyping and testing. During the prototyping phase, the project team will consult with experts about how the games' mechanics and rules align with and support second- to fourth-grade students' learning of integer principles. Next, they will test the games with students. Based on students' interpretations and uses of the rules, their interaction with the materials, and their feedback, the research team will refine the materials. During the testing phase, the project team will conduct a six-session evaluation study (pretest, four gameplay sessions, posttest) to examine the refined materials. The pretests and posttests will include a set of integer knowledge measures, along with mathematics and motivation measures, so the investigators can quantitatively and qualitatively analyze students' integer knowledge gains and changes in their motivation. Further, the investigators will qualitatively analyze the sessions to track and characterize students' levels of engagement and identify those mechanics that support learning of integer principles. During the project's final year, the set of print-ready educational games will be finalized and made freely available for teachers and families. This research will contribute to a greater understanding of students' learning about negative numbers as well as the mechanics of games that support mathematical learning. This project is supported by the discovery research prek-12 program (DRK-12) which seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by prek-12 students and teachers, through research and development of innovative resources, models and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.? This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the foundation's intellectual merit and broader impacts review criteria.- subawards are not planned for this award.