Undergraduate students' understanding of function continuity has not been explored broadly in previous research. The relevant findings in the literature are predominantly concerned with calculus students' understanding and misconceptions of continuity. Many of these misunderstandings are tied to the relationships which continuity has with limits…

Equipping teachers with the knowledge, skills, and dispositions deemed necessary to work with students from diverse populations is a documented need that plagues teacher education. Furthermore, the influx of students from diverse backgrounds enrolled in United States schools intensifies the need to prepare the future generation of teachers to be…

In response to recent interest in K-12th students' mathematics identity formation and its implications for achievement, the present study examines the relationship between learners' mathematics identity and student achievement while simultaneously accounting for teacher-enacted instructional practices in mathematics. Drawing from HSLS:2009, a…

Numerous states use research-based mathematics curricula as a teaching tool to enhance mathematics performance outcomes on state assessment scores. Despite implementation of the Eureka curriculum, students at the study site were still struggling to master Algebra 1 skills sufficiently to pass the Louisiana state exam. The aim of this basic…

The purpose of this comparative study was to determine if and to what extent there was a statistically significance difference in college students' motivation--amotivation, external regulation, introjection, identification, intrinsic motivation--to learn Algebra I between in-person instruction and online instruction in Central Arizona. The theory…

Representations are used throughout school mathematics for students to both think through a problem and communicate their ideas. Students also often come to mathematics class with a repertoire of representations. This article presents the ideas of different and multiple representations with conceptual connections as their underlying distinguishing…

This study compares the impact of two New York State mathematics Regents-level course sequences on the number of secondary mathematics courses taken by New York City Department of Education (NYCDOE) students and explores the potential that programming decisions could increase or diminish the mathematics learning opportunity and achievement of…

Felix Klein's notion of "double discontinuity" between university mathematics and secondary school mathematics has persisted in mathematics teacher education. Situating this study in Hong Kong, we investigated three prospective secondary teachers' experiences in higher education and secondary mathematics classrooms, including their…

In numerical cognition research, the operational momentum (OM) phenomenon (tendency to overestimate the results of addition and/or binding addition to the right side and underestimating subtraction and/or binding it to the left side) can help illuminate the most basic representations and processes of mental arithmetic and their development. This…

This study investigated the effects of a place value intervention with third-grade students with learning disabilities. The intervention added content to a research-based intervention using the concrete-representational-abstract (CRA) sequence. The added content reflected current mathematics standards for third grade. Students' place value…

New perspectives on executive functions propose a greater involvement of context. These perspectives have implications for research in mathematical cognition. We tackle the problem that although individuals clearly exercise inhibitory control in mathematical contexts, researchers find that the relations between inhibitory control and mathematics…

This paper explains teaching modern geometry for schools using software called Surfer and converting the algebraic surfaces into Batik motifs as one example of teaching mathematics with the integration of STEAM. Typical algebraic surfaces known in schools were, for example, cylinders and spheres which are identified as traditional geometry in this…

The transition from school to university is a challenging process for many students which is reflected in high dropout and low examination success rates during the first year at university. Qualitative studies have found hints that students' beliefs play an important role during the transition. Due to their dialectic nature with cognitive as well…

The use of the algebraic method for solving word problems is a challenging topic for secondary school students. Students' difficulties are usually associated with extracting the problem's network of relationships between quantities and with formalizing these relationships into algebraic language in a problem model. Both sources can coexist and…

This article presents a task providing college students opportunities to build on their high school knowledge of trigonometry to explore parametric equations and inverse trigonometric relationships within a contextual learning ladder problem.