This paper presents data from the first of three iterations of teaching experiments conducted with secondary teachers. The purpose of the experiments was to investigate how teachers' combinatorial reasoning could support their development of algebraic structure, specifically structural relationships between the roots and coefficients of…

This introduction presents Active Learning Methodology, surveying its history, main existing tools and supporting evidence, with an emphasis on mathematics and higher education, in particular engineering studies. This work is part of the DrIVE-Math project, developing innovative mathematical teaching strategies in engineering studies.

The author presents a child-centered approach to teaching, developed through longtime connections with colleagues, which concentrates on the children and provides them time to make their own connections, to learn, to think, and to develop at their own pace with the support of their classmates. Two examples of how mathematics interlaced into…

The need to understand the differences in the self-efficacy of K-12 mathematics teachers based on teachers' characteristics and school factors is imperative because research has shown teachers' self-efficacy to be a mediating factor on students' academic achievement. As such, education policymakers and school administrators need to understand…

The present study aimed to determine the effectiveness of the concrete-representational-abstract instruction strategies employed in the direct instruction of fractions to students with learning disabilities. Furthermore, the generalization of the instruction to different settings and tools, the follow-up data for one and three weeks after the…

Schools across the country are struggling to retain STEM teachers, particularly secondary math and science teachers. Mentoring has been a successful tool to help build the confidence of novice teachers and to help lower attrition rates. Further, because it takes time and support to develop robust pedagogical content knowledge (PCK), the mentoring…

In mathematics, the keyword strategy involves identifying a keyword (e.g., "altogether") and using that keyword to determine the operation needed to find a word problem's solution. We analyzed 747 high-stakes released items across Grades 3, 4, 5, 6, 7, and 8 from the Partnership for Assessment for Readiness for College and Careers and…

Many students in the United States are not proficient in mathematics. Mathematics vocabulary is one area that may impact students' understanding of and engagement with mathematics. This dissertation investigated the implementation, effectiveness, and teacher's perceptions of a program for teaching mathematics vocabulary necessary for fourth grade…

This quasi-experimental design study aimed to examine how exposure to supporting productive struggle teaching practice impacts students' conceptual understanding, procedural fluency, and strategic competence when solving high-demanding quadratic functions problem solving tasks. Results suggested that students in the supporting productive struggle…

Math achievement is frequently measured by various assessments. These assessments are then used to determine student and school success, often leading to high stakes decision making. Therefore, it is important to understand ways in which educators can improve student math achievement. Students with a growth mindset, as defined by Dweck (2006),…

Technology is shaping our personal and professional lives every day, yet many educators struggle with its implementation and therefore are not using it to the fullest potential. The purpose of this single-case study was to analyze how a teacher's participation in a Professional Development (PD) initiative influenced the implementation of mobile…

Summer bridge programs are the second most common student support program in the United States. Though they vary in design, most are focused on supporting students who are at risk. Programs vary in terms of their curricular offerings as well. This study examined the ex post facto data from a summer bridge program at Manchester Community College in…

This study explores the relationship between play-based learning and achievement in mathematics in Palestinian elementary school children. Forty teachers from eight schools received training in play-based pedagogies and follow-up support visits from programme staff (intervention group); four matched schools served as the control group.…

A simple forward approach for solving linear Diophantine equations is presented, which does not involve using backward substitutions. It is suitable for teaching undergraduate students as an alternative to the backward substitution method commonly described in mathematics textbooks.

Inspired by the "Batman Equation" of 2011, this article presents a challenging and engaging process for graphing complicated designs from just a single parametric equation pair. Reinforces numerous analytic geometry skills. Works in popular graphing software such as Desmos or GeoGebra, or even graphing calculators.