Grasping patterns of algebraic understanding: Dynamic technology facilitates learning, research, and teaching in mathematics education

Prior work has established that cognitive and perceptual processes influence students' attention to notational structures in mathematical expressions, which in turn affects their problem-solving approaches and performance. Advances in educational technology provide opportunities to further investigate these processes, improve student learning, and inform classroom instruction. Chapter 12 presents Graspable Math (GM), an online dynamic algebra notation system designed based on the research of cognitive, perceptual, and affective processes to support student learning. The log data recorded in GM offer a window into students' mathematical cognition, perceptual processes, and problem-solving strategies that can inform both research and instructional practice. First, we review the evidence of using GM to support algebra learning with elementary and middle school students. Next, we describe how log data from GM provide opportunities to research students' problem-solving processes and their uses of mathematical strategies. To conclude, we discuss how this work can inform classroom instruction and future research by providing teachers and researchers with in-depth feedback on students' use of mathematical strategies and understanding. Copyright © 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG.