We report on an innovative design of algorithmic analysis that supports automatic online assessment of students' exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic…

Despite statistics learning becoming more important during this information explosion era, many students still deem the subject complex and challenging. Measures of dispersion, a critical component of statistical knowledge that students often struggle with, have received little attention in research on statistics education. The goal of this study…

For abstract concepts to be well understood, students need to be familiar with the concepts and able to associate them correctly. Students cannot make scientific explanations on the subject unless they can establish relationships. This study aimed to determine the understanding level of 11th-grade high school students on "gases" in terms…

To improve students' mathematics achievement, their errors should be treated as an opportunity to stimulate conceptual and procedural understanding. Using a teaching scenario, this study investigated 40 high school teachers' analyses of and responses to a student error(s) in solving a quadratic equation by using the factoring method. The teachers'…

Researchers and instructors have only recently embraced the role of errors as vehicles for learning in the algebra classroom. Studying a mixture of correct and incorrect worked examples has been shown to be beneficial relative to correct worked examples alone. This study examines the effectiveness of having students generate, or anticipate, errors…

Despite repeated discussions and practice, algebra students continue to make variable errors, in many ways, year after year. This same problem appeared thirty years ago in a list of common errors that math teachers today would immediately recognize, many involving exponents and distribution (Marquis 1988). Similar complaints even appeared in the…

This study investigates how students in England and Shanghai understand linear function. Understanding is defined theoretically in terms of five hierarchical levels: Dependent Relationship; Connecting Representations; Property Noticing; Object Analysis; and Inventising. A pilot study instrument presented a set of problems to both cohorts, showing…

The learning sciences community has made significant progress in understanding how people think and learn about complex systems. But less is known about how people make sense of the quantitative patterns and mathematical formalisms often used to study these systems. In this article, we make a case for attending to and supporting connections…

To improve mathematics achievement, students' errors should be treated as a source to stimulate their understanding of the conceptual and procedural basis of their errors. The study investigated 20 Chinese and 20 U.S. high school teachers' interpretations and responses to a student's errors in solving a quadratic equation. The teachers' responses…

This study examined Advanced Placement Calculus students' mathematical understanding of rate of change, after studying four years of college preparatory (integrated or single-subject) mathematics. Students completed the Precalculus Concept Assessment (PCA) and two open-ended tasks with questions about rates of change. After adjusting for prior…

The 12th iteration of the International Conference on Educational Data Mining (EDM 2019) is organized under the auspices of the International Educational Data Mining Society in Montreal, Canada. The theme of this year's conference is EDM in Open-Ended Domains. As EDM has matured it has increasingly been applied to open-ended and ill-defined tasks…