We introduce, motivate, and exemplify a proposed theoretical construct guiding the design and facilitation of collaborative geometry activities, conceptually generative perspectival complementarity (CGPC). Participants in CGPC activities learn content by negotiating their respective perceptions of situated features they manipulate to accomplish…

Previous studies have suggested that problem-posing activities could be used to improve the teaching, learning, and assessment of mathematics. The purpose of this study is to explore undergraduate engineering students' problem posing in relation to the integral-area relationship. The goal is to help fill a gap in tertiary level research about…

In Japan during the 1980s, there was an interesting debate about how to teach the area of a parallelogram effectively to primary school children. Yutaka Saeki criticized the standard method, which relies on a cut-and-paste procedure. He argued that the standard method inevitably failed to convince children because it does not provide any cogent…

Do young children understand the complex mathematics in the petals of a daisy, the Fibonacci sequence in the spiral of a pinecone, the fractal geometry in the leaves of a fern, or the "golden ratio" in the seed pattern of a sunflower? Probably not, but they certainly can observe and recognize the patterns and compare them to similar…

This article draws on the simple context of a two animal farm to create an engaging and mathematically meaningful problem solving task for students. It aims to encourage students to think systematically and to present their findings methodically. The task is structured sequentially, making it suitable for primary school students from Year 1 to…

This paper reports our efforts to develop a measure of pre-service elementary teachers' geometry knowledge for teaching 2-dimensional (2D) shapes and to evaluate the psychometric properties of this measure. Specifically, the GKT-2D scale was designed to assess pre-service elementary teachers' geometry content knowledge, knowledge of geometry and…

Background: Mastering fractions seems among the most critical mathematical skills for students to acquire in school as fraction understanding significantly predicts later mathematic achievements, but also broader academic and vocational prospects. As such, identifying longitudinal predictors of fraction understanding (e.g., mastery of numbers and…

In this study we examined the impact of four teaching sessions on the history of ancient Mesopotamian mathematics, in a 10th -grade classroom. The sessions were taught primarily with historical objectives by researchers in the history of ancient mathematics. We reconstructed historians' practices and ethos. The presence of the researchers provided…

The prime aim of the study was to investigate and understand first-year pre-engineering students' perceptions about mathematics teachers' knowledge and instruction. A case study method was employed as a mode of inquiry and a Likert-type survey for data collection. Participants included 158 first-year pre-engineering students and five mathematics…

Teaching geometry in the early years emerges along with maths activities but might be neglected sometimes. This research aims to identify preschool teachers' opinions on geometry teaching via using semi-structured interviews, and collected data analysed using content analysis. Seven female and three male preschool teachers were participated in the…

Professional learning communities (PLC) have increasingly attracted attention in research on teachers' professional development. The aim of this study is to identify contradictions that can occur and be manifested in PLCs in mathematics. Identifying contradictions in PLCs are important, as the identification and resolution of contradictions are…

Even though a substantial body of research suggests that adults' math talk fosters children's mathematics development and willingness to learn mathematics, little is known about how teachers make pedagogical decisions to communicate mathematics to young students. Supported by socio-constructivist and semiotic lenses, the study focuses on the close…

Tentativeness is often framed as a deficit, synonymous with timidity or a lack of confidence. In this article, I situate the notion of tentativeness in an enactivist framework and describe its role as both a strategy and affordance in a spatial visualization exercise. Drawing on insights from mathematics education and ecological psychology, I…

State exams frequently use word problems to measure mathematics performance, making difficulties with word problem solving a barrier for many students with learning disabilities (LD) in mathematics. Based on meta-analytic data for students with LD, five empirically validated word-problem strategies are presented, with components of model-based…

Educational apps can be considered a dominant medium for providing educational content to children. Parents are major stakeholders and mediators in the selection of apps (Dias & Brito, 2021). It is critical to know how they choose apps for their children and understand what indicates a quality educational app, as well-designed apps can support…