Scholars propose that contextual problems can be used to ground students' understanding of mathematical ideas, and recent curricular trends have resulted in a plethora of resources that introduce and develop new mathematical ideas through contextual problems (CPs). Given the tension between this approach and the traditional role of CPs as…

One major issue in mathematics teacher education regards the role of university-level mathematics in teacher knowledge. In the context of a design-based research project, an advanced mathematics teacher education course aimed at strengthening the connections between university-level mathematics and school mathematics was developed. In this paper,…

This paper examines whether using "From Here to There!" (FH2T:E), a dynamic game-based mathematics learning technology relates to improved early algebraic understanding. We use student log files within FH2T to explore the possible benefits of student behaviors and gamification on learning gains. Using in app measures of student…

Science and engineering departments face high student attrition due to perceived difficulty of courses in these disciplines. To subdue student attrition, students need to be guided by individual tutors to help them learn, practice and test their understanding of concepts. However, due to the exorbitant cost and time involved, this is not…

In this article, the authors applied profile analysis to Maths exam data to demonstrate how different exam forms, differing in difficulty and length, can be reported and easily interpreted. The results were presented for different groups of participants and for different institutions in different Maths domains by evaluating the balance. Some…

Online math videos for student learning are abundant; yet they are surprisingly uniform in their monologic, expository mode of presentation and their emphasis on procedural skill. In response, we created an alternative model of online math videos that feature the unscripted dialogue of secondary school students, who convey sources of confusion and…

A common challenge among mathematics professors is to structure a course so that students are motivated to complete enough work to master the material without creating an unmanageable grading workload. We will discuss a strategy that the author devised to successfully confront this challenge (after many other failed attempts): using online surveys…

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…

This paper reports the factors that three Year 11 mathematics students identified as influencing their choice to use a Computer Algebra System (CAS) for solving selected problems, some of which were expected to be outside their pen-and-paper (p&p) range. In individual interviews, the students were presented with eleven algebra problems and…

The purpose of this study was to determine if the size of a public school district or the amount allocated per-pupil in the state of Texas made a difference in student academic outcomes for special education students. The data evaluated in the study were the State of Texas Assessments of Academic Readiness (STAAR) Algebra I score and the Public…

We present a mathematical analysis that distinguishes two quantitative perspectives on ratios and proportional relationships: Multiple Batches and Variable Parts. We argue that (a) existing research on proportional relationships has addressed Multiple Batches but has largely overlooked Variable Parts, (b) Multiple Batches makes the co-variation…

This paper presents a research framework for investigating the role of language use in mathematics learning. The paper draws on the wider M[superscript 2]EID study, which explores whether differences in languages (English and Irish) and their use by bilingual mathematical students have a differential impact on their mathematics meta-level…

We investigated how high school mathematics course placement contributes to inequalities in college preparation for students categorized as "English Learners" (ELs), especially "long-term" English Learners (LTELs). We devised a base-2 enumeration approach that allowed us to process complex transcript data from one school…

Academic discourse communities and learning circles are characterized by collaboration, sharing commonalities in terms of social interactions and language. The discourse of these communities is composed of jargon, common terminologies, and similarities in how they construe and communicate meaning. This study examines the extent to which discourse…

Background: The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic…