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Learning mathematics in a student-centered, problem-based classroom requires students to develop mathematical understanding and reasoning collaboratively with others. Despite its critical role in students’ collaborative learning in groups and classrooms, evidence of student thinking has rarely been perceived and utilized as a resource for planning and teaching. This is in part because teachers have limited access to student work in paper-and-pencil classrooms. As an alternative approach to making student thinking visible and accessible, a digital collaborative platform embedded with a problem-based middle school mathematics curriculum is developed through an ongoing design-based research project (Edson & Phillips, 2021). Drawing from a subset of data collected for the larger research project, we investigated how students generated mathematical inscriptions during small group work, and how teachers used evidence of students’ solution strategies inscribed on student digital workspaces. Findings show that digital flexibility and mobility allowed students to easily explore different strategies and focus on developing mathematical big ideas, and teachers to foreground student thinking when facilitating whole-class discussions and planning for the next lesson. This study provides insights into understanding mathematics teachers’ interactions with digital curriculum resources in the pursuit of students’ meaningful engagement in making sense of mathematical ideas.
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The Findings and Developed Tools from the Exploration of Procedural Pathways to Bolster Algebraic Knowledge
Algebra is essential for delving into advanced mathematical topics and STEM courses (Chen, 2013), requiring students to apply various problem-solving strategies to solve algebraic problems (Common Core, 2010). Yet, many students struggle with learning basic algebraic concepts (National Mathematics Advisory Panel (NMAP), 2008). Over the years, both researchers and developers have created a diverse set of educational technology tools and systems to support algebraic learning, especially in facilitating the acquisition of problem- solving strategies and procedural pathways. However, there are very few studies that examine the variable strategies, decisions, and procedural pathways during mathematical problem- solving that may provide further insight into a student’s algebraic knowledge and thinking. Such research has the potential to bolster algebraic knowledge and create a more adaptive and personalized learning environment. This multi-study project explores the effects of various problem-solving strategies on students’ future mathematics performance within the gamified algebraic learning platform From Here to There! (FH2T). Together, these four studies focus on classifying, visualizing, and predicting the procedural pathways students adopted, transitioning from a start state to a goal state in solving algebraic problems. By dissecting the nature of these pathways—optimal, sub-optimal, incomplete, and dead-end—we sought to develop tools and algorithms that could infer strategic thinking that correlated with post-test outcomes. A striking observation across studies was that students who frequently engaged in what we term ‘regular dead-ending behavior’, were more likely to demonstrate higher post-test performance, and conceptual and procedural knowledge. This finding underscores the potential of exploratory learner behavior within a low-stakes gamified framework in bolstering algebraic comprehension. The implications of these findings are twofold: they accentuate the significance of tailoring gamified platforms to student behaviors and highlight the potential benefits of fostering an environment that promotes exploration without retribution. Moreover, these insights hint at the notion that fostering exploratory behavior could be instrumental in cultivating mathematical flexibility. Additionally, the developed tools and findings from the studies, paired with other commonly used student performance metrics and visualizations are used to create a collaborative dashboard–with teachers, for teachers.
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- Award ID(s):
- 2142984
- PAR ID:
- 10596314
- Publisher / Repository:
- WPI eprojects
- Date Published:
- Format(s):
- Medium: X
- Institution:
- Worcester Polytechnic Institute
- Sponsoring Org:
- National Science Foundation
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