Many people find that solving story problems is challenging. A key source of the difficulty is symbolizing problem situations. In two experiments, we tested whether diagrams promoted successful symbolization of two-operator story problems, and we tested whether diagrams that depicted the integration of operations were more beneficial than diagrams…

Introductory mathematics courses at postsecondary institutions simultaneously function as gateways and gatekeepers to degrees and careers in Science, Technology, Engineering, and Mathematics (STEM) for historically minoritized and marginalized students. While these courses provide access to higher education, they also thwart student STEM pathways…

Efficient visualizations of computational algorithms are important tools for students, educators, and researchers. In this article, we point out an innovative visualization technique for matrix multiplication. This method differs from the standard, formal approach by using block matrices to make computations more visual. We find this method a…

This note presents a derivation of Viète's classic product approximation of pi that relies on only the Pythagorean Theorem. We also give a simple error bound for the approximation that, while not optimal, still reveals the exponential convergence of the approximation and whose derivation does not require Taylor's Theorem.

Students use a variety of resources to make sense of integration, and interpreting the definite integral as a sum of infinitesimal products (rooted in the concept of a Riemann sum) is particularly useful in many physical contexts. This study of beginning and upper-level undergraduate physics students examines some obstacles students encounter when…

In this study, we highlight the differences in classroom-, teacher-, and school-level factors in 8th and 9th grade algebra experiences along socioeconomic and racial/ethnic lines using nationally representative survey data from the American Mathematics Educator Study. Several takeaways emerge from our analysis. First, we show that highest-poverty…

Integrating information and communication technology (ICT) in mathematics education has been increasingly recognized as a powerful tool for increasing students' interest and performance. It is widely discussed that students' understanding of mathematical ideas is not satisfactory, especially in terms of conceptual understanding. Using narrative…

Manipulatives are an effective mathematical tool to support students with disabilities in the area of mathematics. Yet, there remain inconsistencies in terms of which type -- concrete or virtual -- is more effective for students with disabilities working on algebra related content and which type is preferred by students. The researchers used an…

The current study assessed whether adding worked examples with self-explanation prompts focused on making connections between mathematical principles, procedures, and concepts of rational numbers to a curriculum focused on invented strategies improves pre-algebra students' fraction number line acuity, rational number concepts and procedures.…

Although positive effects of lesson study on teachers learning are reported, only some studies have investigated teacher noticing as an analytical tool for supporting teachers with an explicit focus, as in LS, and more empirical evidence is needed. This qualitative interpretive case study design aims to investigate the noticing processes of a…

Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between…

Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between…

Purpose: The purpose of this journal-ready dissertation was to determine the extent to which Hispanic students differed in their performance on the Texas state-mandated Algebra I End-of-Course exam by their at-risk status. Specifically examined was the degree to which the at-risk status of Hispanic students was related to three grade level…

Proportional reasoning and knowledge of fractions are critical skills for completing algebra successfully, yet many students with mathematics learning disabilities (MLD) enter algebra classes without adequate prior knowledge of these skills. This study used a single-subject/case research, combined multiple-baseline and alternating-treatment design…

Geometry is used in different ways in the teaching of linear algebra. In this paper, I offer a typology of these ways, which I call varieties, and address three central questions. The first question is, "What varieties of use of geometry in the teaching of linear algebra exist?" This question is addressed through an analysis of six…