Design and Development of Integer Games to Reduce Barriers to Algebra (Collaborative Research: Enzinger)

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.