This paper analyses student views on an e-learning intervention that incorporated a content development tool and computer algebra systems, aimed at improving performance and applicability of mathematics knowledge. The study deliberately relied on open source tools, with high usability both online and offline, that can be customized to address the…

Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. Positive and negative…

The ways teachers understand mathematics that is useful for teaching, known as mathematical knowledge for teaching (MKT), has been a center of attention for the research and policy communities. A teacher's MKT has been shown to be a significant factor in predicting student outcomes and positively related to the quality of mathematics instructional…

In this paper, we explore how students' algebraic noticing's and explanations changed across a two-year period with the introduction of designed instructional material. The data in this report is drawn from n=53 Year 7-8 students' responses to a free-response assessment task across two different years. Analysis focused on how students noticed and…

This study explores high school students' and their mathematics teachers' mathematical discourses on the equal sign and variables in the classroom context. The participants in this case study were ninth graders and their mathematics teachers. The data were analyzed in terms of participants' routines, specifically ritual and explorative routines in…

The purpose of this study was to determine the extent to which professional development on assessment for learning improves pre-service teachers' self-regulated learning. Helping students develop self-regulation abilities in learning and assessment remains difficult due to the widespread culture of summative assessment in teacher education. A…

Pattern recognition is an important skill in computational thinking. In this study, an equation puzzle game was developed by combining pattern recognition with algebraic reasoning, and scaffolding was designed to support learners' learning. Sixty participants were enrolled in this study, divided into a control group and an experimental group to…

This study examines the perceptions of first-year, mathematics graduate teaching assistants (GTAs) participating in a six-week summer course designed to deepen their knowledge of collegiate mathematics teaching practices before being assigned to instruct undergraduate students in the subsequent fall semester. Through hybrid deductive-inductive…

Generalizing patterns is an important feature of algebraic reasoning that is accessible to students across grade-levels because it connects their numerical reasoning to algebraic reasoning. In this article, the authors describe how teachers can use the game Crack the Code to introduce generalizing to their students or can extend students'…

The Math Immersion intervention was designed to aid the transition-to-proof phase of the undergraduate mathematics major. The Immersion was co-taught by two instructors, one for Intro to Proofs and Abstract Algebra and another for Probability and Statistics and Linear Algebra. This case study documented that efficiency gains directly attributable…

We investigate the beliefs that influence middle and high school algebra teachers' appraisals of contextual problems having diverse mathematical and pedagogical features. We asked six teachers to analyze six contextual algebra tasks and indicate how they would apportion instructional time among the six tasks based on their structure, pedagogical…

High school chemistry is essential. Every citizen needs basic chemistry background to understand current events, and millions more can benefit from further study. Nevertheless, students do not always continue learning chemistry, even when they could do so. The loss of potential learning is significantly more common for girls, economically…

Student focusing and noticing, which drive reasoning, are important but under researched aspects of student learning. Quadratic functions representations are perceptually and conceptually complex and thus, offer much for students to focus on and notice. Our study compared a teacher's goals for student focusing and noticing during quadratic…

In the era of 21st century learning, many secondary students with learning disabilities continue to struggle with mathematics problem solving. Emerging evidence suggests self-regulated strategy development can be combined with existing evidence-based and promising practices during mathematics instruction. These practices include explicit…

Cognitive development of eighth-grade students, as identified by Jean Piaget, occurs during a time when many of them are transitioning between concrete operations and formal operations where the ability to think in abstract concepts becomes possible. Because of this period of transition, many eighth-grade students find difficulty in demonstrating…