This paper reports on a two-part investigation into how students think about and use summation (sigma) notation. During an instructional design experiment, two participating students struggled with this notation, but also reasoned about it in creative ways. This motivated a follow-up study in which we administered a free-response three-item survey…

Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the…

Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

This study investigates the performance of GPT-4, an advanced AI model developed by OpenAI, on the force concept inventory (FCI) to evaluate its accuracy, reasoning patterns, and the occurrence of false positives and false negatives. GPT-4 was tasked with answering the FCI questions across multiple sessions. Key findings include GPT-4's…

In this study, we have explored the effectiveness of two instructional approaches in the context of the motion of objects falling at terminal speed in the presence of air resistance. We ground these instructional approaches in dual-process theories of reasoning, which assert that human cognition relies on two thinking processes. Dual-process…

The current study expands on previous research on gender differences and similarities in science test scores. Using three different approaches -- differential item functioning, differential distractor functioning, and decision tree analysis -- we examine a high school science assessment administered to 3,849 10th-12th graders, of whom 2,021 are…

Fraction arithmetic facility is fundamental to learning more advanced math topics. However, attaining the ability to add and subtract fractions is hard for many students. The present longitudinal study examined students' growth on simple addition and subtraction word problems between fourth and sixth grades (N = 536). Latent class growth analyses…

Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated…