This study examined the effects of training involving spatial versus nonspatial representations of numerical magnitude for promoting arithmetic fluency. The key goal was to advance theoretical understanding of the relation between spatial and math learning, while simultaneously laying the groundwork for the development of future educational…

Many elementary education programs have only one mathematics methods course designed for preservice teachers (PTs). Such courses typically cover a range of content and present a challenge for mathematics teacher educators (MTEs) who strive to prepare their PTs to teach mathematics in equitable and humane ways. Due to the "stand-alone"…

In this meta-analysis of 54 longitudinal studies with over 58,000 students in kindergarten through 12th grade, we examined the predictive nature of early numeracy measured at or before the first year of formal schooling in relation to later mathematics. Results showed that early numeracy significantly predicted mathematics measured after 6 months…

Scholarly interest about how students learn and retain learned skills is vast. Cognitive psychologists have recommended various techniques used to increase retention. One technique, spaced retrieval practice, involves extending opportunities to retrieve course content beyond a customarily short window following the initial learning process. Our…

This research examined the impact of the Cognitive-Communicative (C-C) model as a pedagogical strategy for teaching algebraic word problems (AWPs). The C-C model integrates structured dialogue, concept clarification, and systematic problem-solving steps to enhance students' comprehension and reasoning. Employing a mixed-methods framework, the…

To understand the ways that manipulatives might support changes in students' reasoning about algebraic generalizations, a constructivist teaching experiment was conducted with two sixth-grade students. The students interpreted numerical situations with units of one and could construct units of units in mental activity. Initially, the students'…

In this theoretical essay, I build on complexity theory and commognition to theorize the ways in which failure to teach/learn mathematics (FTLM) emerges through the dynamic interactions among teacher, learner, and curriculum demands. I focus on two main concepts of complexity theory: emergence in dynamic systems and attractor states (stable,…

In this paper we present a novel adaptation of a tri-phase assessment tool, originally devised to investigate students' linear equations-related strategy flexibility, to evaluate Danish grade-six students' multidigit arithmetic-related strategy adaptivity and flexibility. Participants, 731 students, median age 12 years and drawn from 20…

Assessments play a pivotal role in Mathematics education, serving as vital gauges of students' mathematical proficiency and informing teaching strategies. Despite calls for contextualization, some educators still rely on abstract teaching methods and decontextualized tasks. This study aims to address these concerns by designing and implementing a…

Background/Context: Current course-taking plans for high school students are often not optimized to support every student's success in math. Since math course-taking can influence important outcomes (e.g., math achievement, college enrollment), and these effects may vary by students' characteristics (Byun et al., 2015), it is crucial to develop…

This study investigated the impact of discussing mathematical events on in-service Mathematics teachers' professional noticing of geometric definitions. Fifty-two teachers engaged in discussions in which they analyzed students' thinking regarding rhombus definitions and the teachers' noticing skills were assessed through pre- and post-tests…

The lived experiences of university mathematics students are an emerging area of mathematics education research. In this article, we discuss findings from a study about the experiences of undergraduate students in mathematics degree programs at two Australian universities. We analyzed two participants' interview data using the Listening Guide…

Calculus is perhaps the most widely taught and researched upper-secondary/post-secondary mathematics subject the world over. The research literature is amassing greater clarity around students' understandings of calculus, yet calculus instruction tends to be at odds with this literature, maintaining a focus on procedural aspects of the subject.…

In the United States, calls for improved K-12 learning opportunities in mathematics have shifted focus in school district offices from bureaucratic pursuits to instructional improvement efforts. Yet, district leaders often receive little guidance on how to achieve these goals. Further, although widely recognized that content-specificity matters in…

This paper focuses on the definitions and the mis-out and mis-in examples of rational numbers that four prospective elementary teachers presented while working on rational number assignments. The participants were first asked to respond, individually, to an Individual Rational Number Assignment, consisting of items aiming at detecting their…