In this study, we explored elementary school teachers' experiences working on open-ended mathematics tasks during a 10-day professional development (PD) workshop. Teachers engaged with the tasks daily in a session call Morning Math (MM). Thirty-two elementary teachers from three school districts in the USA participated in a 2-year professional…

This article reports on a qualitative investigation into students' thinking about a differential equations problem posing task; i.e. an initial value problem. Analysis of written and verbal responses to the task indicate that only four of the 34 students who participated in the study were successful in posing problems. Furthermore, only one of the…

Elementary (5 [approximately] 11 years old) students with mathematics difficulties often struggle with word-problem solving. This systematic review and network meta-analysis aimed to examine the comparative effectiveness of various instructional strategies and their combinations for improving word-problem solving skills in this population. We…

This study focuses on equivalent transformations of equations in the context of secondary school education. Solving (determining the solution set of an equation), normalizing (transforming an equation to reach a certain form), and reorganizing equations (isolating variables in formulae) are discussed as different possible applications of these…

As early as first grade, some children are more likely than others to perform arithmetic using inefficient or other overt counting strategies. To partially address this problem, the primary investigator developed a skill hierarchy with procedures based on applied behavior analysis. The novel early-intervention program included a combination of…

This research centers on implementing Quantitative Reasoning (QR) within a differential equations course at an urban public community college. As a participant in the Numeracy Infusion for College Educators (NICE) faculty development program, I sought to integrate QR skills into my curriculum. Students in the course were introduced to QR goals…

A teacher of mathematics knows mathematics as a teacher and as a mathematician. Whilst the existing research on teacher knowledge contributes to our understanding of the ways of knowing mathematics as a teacher, little is known about ways of knowing mathematics as a mathematician. Guided by the conceptual framework of mathematical practices (MPs)…

High school teachers often encounter incorrect solutions from students, especially when teaching combinatorics. This study investigates the ability of prospective mathematics teachers to assess the correctness of solutions to combinatorial problems and to falsify incorrect ones. 39 second-year prospective teachers participated in the experiment,…

This Spotlight explores effective strategies for improving math instruction and enhancing student achievement in K-8 classrooms. From making math more relevant and engaging and mastering word problem-solving to deepening conceptual understanding of fractions and nurturing students' ability to tackle challenges, these articles offer valuable…

Symbolic and situational mathematics are the two major representations of mathematical knowledge. Although previous literature has studied the relationship between the two from the perspective of teaching practice, learning effectiveness and behavioural performance, there is still a lack of empirical psychological research on cognitive mechanisms…

Graph theory allows the student to work on problems that require imagination, intuition, systematic exploration, conjecturing, and reasoning. It implies that mathematical investigation skill is essential to be proficient in Graph Theory. In this study, we conduct empirical research that deals with associational research. There were 97 students…

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…

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…

Collaborative learning is a group learning paradigm in which individuals or students work together to solve problems or complete tasks, exemplifying the essence of collective educational efforts. There are a lot of collaborative learning methods available; however, finding one that is suitable for the complex nature of mathematical problem-solving…

For decades, mastery ambitions related to processes like problem-solving, modelling, and reasoning have been incorporated in mathematics curricula around the world. Meanwhile, such ambitions are hindered by syllabusism, a term I use to denote a conviction that results in mastery of a subject being equated with proficiency in a specific subject…