Enhancing Engagement and Learning Through Interactive Conceptual Learning Tools for Mathematics

• In Event: Advancing Math Motivation, Engagement and Persistence: Insights from Digital Interventions and Research-Practice Partnerships

Abstract

This poster presents findings from two experiments examining how redesigned conceptual learning tools in the [math software] intelligent tutoring system can support student engagement and improve learning outcomes.
Study 1: Understanding Circle Area: The first study investigated a redesigned tool designed to engage students in understanding circle area components through interactive manipulation, compared with a business-as-usual (BAU) static image in a [math software] non-mastery (concept builder) workspace.
Students answered questions referring to the conceptual model in the concept builders (CBs), then moved to a mastery workspace (identical in both conditions) focused on solving area and circumference problems without direct model reference.
Students using the new tool completed the workspace 0.64 minutes faster than the BAU group (95% CI: [-55.68, -20.61], t(9536.908) = -4.264, p < 0.001), contrary to expectations that exploration might require more time. However, these students made 0.34 more errors during the exploration phase (95% CI: [0.08, 0.60], t(9794.604) = 2.574, p < 0.01).
While there was no difference in number of problems needed to reach mastery in either condition, p = 0.232, students who used the interactive tool in the CB had 0.54 times increased odds of mastery in the subsequent mastery workspace compared to BAU students (z = 2.101, p = 0.04), suggesting that that initial engagement with an interactive tool may build the motivation necessary for continued success.
Study 2: Operations on Signed Numbers: The second study examined an interactive kangaroo metaphor tool for teaching signed number operations, designed to engage learning more dynamically than an abstract BAU number line manipulative.
Like Study 1, students answered questions referring to the conceptual model in the CBs, then moved to a mastery workspace focused on solving problems without direct model reference.
In the CB, students using the kangaroo manipulative completed the workspace 5.11 minutes faster than the BAU group (95% CI: [-3.64, -1.62], t(3391.54) = -12.09, p < 0.001), indicating improved efficiency. These students made 2.6 fewer errors during the exploration phase (95% CI: [-356.90, -257.27], t(3397.637) = -5.113, p < 0.001).
In the mastery workspace, students who had used the kangaroo manipulative had 0.29 times increased odds of mastery compared to BAUs (z = 2.643, p = 0.008), requiring 0.48 fewer problems to reach mastery, (95%CI [-0.933, -0.025], t(-2.069), p = 0.0386), suggesting that initial engagement with the interactive tool may create a positive feedback loop to sustain learning momentum.
Implications and Conclusions: Both studies provide evidence that interactive conceptual learning tools can improve mastery of math skills, even when the mastery problems do not explicitly reference the tools. The efficiency gains observed in both studies—faster completion times with improved learning outcomes—suggest that interactive tools can support both engaged learning and, potentially, motivation for success, reinforcing prior research showing that when students are motivated through strong conceptual instruction, acquisition of procedural knowledge is enhanced (Rittle-Johnson & Alibali, 1999).

Authors

• Steven Ritter, Carnegie Learning, Inc.

• April Murphy, Carnegie Learning, Inc.