Functions are an essential concept in mathematics. The studies that have examined functions in advanced contexts have primarily focused on students' reasoning about specific types of functions (such as binary operations and isomorphisms) but not on the core characteristics of well-definedness and everywhere-definedness. Here, we report on a study…

Using a mixed methods approach, we explore a relationship between students' graph reasoning and graph selection via a fully online assessment. Our population includes 673 students enrolled in college algebra, an introductory undergraduate mathematics course, across four U.S. postsecondary institutions. The assessment is accessible on computers,…

This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students' behavior in these three stages of problem posing, especially focusing on investigating…

How to influence and assess whether students engage in conceptual thinking are longstanding methodological problems in mathematics education. Recently, eye-tracking technology has fueled a discussion on whether eye movement analysis can support valid inferences about mathematical thinking. This study investigates whether eye movement analysis can…

In this theoretical essay, I build on complexity theory and commognition to theorize the ways in which failure to teach/learn mathematics (FTLM) emerges through the dynamic interactions among teacher, learner, and curriculum demands. I focus on two main concepts of complexity theory: emergence in dynamic systems and attractor states (stable,…

Rational numbers, such as fractions and decimals, are harder to understand than natural numbers. Moreover, individuals struggle with fractions more than with decimals. The present study sought to disentangle the extent to which two potential sources of difficulty affect secondary-school students' numerical magnitude understanding: number type…

Many students persistently misinterpret histograms. This calls for closer inspection of students' strategies when interpreting histograms and case-value plots (which look similar but are different). Using students' gaze data, we ask: "How and how well do upper secondary pre-university school students estimate and compare arithmetic means of…