The increased Simon effect with increasing the ratio of congruent trials may be interpreted by both attention modulation and irrelevant stimulus-response (S-R) associations learning accounts, although the reversed Simon effect with increasing the ratio of incongruent trials provides evidence supporting the latter account. To investigate if…

This study extends past research on students' understanding of slope by analyzing college students' mistakes on routine tasks involving slope. We conduct quantitative and qualitative analysis of students' mistakes to extract information regarding slope conceptualizations described in prior research. Results delineate procedural proficiencies and…

In contrast to previous studies on Spontaneous Focusing on Quantitative Relations (SFOR), the present study investigated not only the "extent" to which children focus on (multiplicative) quantitative relations, but also the "nature" of children's quantitative focus (i.e., the types of quantitative relations that children focus…

We present the results of an in-depth qualitative study that examined ninth graders' conceptual and procedural knowledge of fractions as well as their approach to mathematics learning, in particular fraction learning. We traced individual differences, even extreme, in the way that students combine the two kinds of knowledge. We also provide…

We investigated how the updating function supports the integration process in solving arithmetic word problems. In Experiment 1, we measured reading time, that is, translation and integration times, when undergraduate and graduate students (n = 78) were asked to solve 2 types of problems: those containing only necessary information and those…

Researchers have argued that students can develop foundational understandings for a variety of mathematical concepts through quantitative reasoning. I extend this research by exploring how students' quantitative reasoning can support them in developing meanings for inverse relations that influence their inverse function meanings. After summarizing…

Research over the past few decades points to ways precalculus and calculus courses can be strengthened to improve student learning in these courses. This research has informed the development of the Algebra and Precalculus Concept Readiness (APCR) and the Calculus Concept Readiness (CCR) assessments. In this article, the authors present three…

Does solving subtraction problems with negative answers (e.g., 5-14) require different cognitive processes than solving problems with positive answers (e.g., 14-5)? In a dual-task experiment, young adults (N=39) combined subtraction with two working memory tasks, verbal memory and visual-spatial memory. All of the subtraction problems required…

The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…

A reverse engineering approach to automatic item generation (AIG) was applied to a figure-based publicly released test item from the Organisation for Economic Cooperation and Development (OECD) Programme for International Student Assessment (PISA) mathematical literacy cognitive instrument as part of a proof of concept. The author created an item…