This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…

Tasks involving real-world contexts offer opportunities for teachers to engage students in mathematical practices (Standards for Mathematical Practice; NGA Center and CCSSO 2010). The practice of reasoning abstractly and quantitatively requires students to decontextualize and contextualize a task. Decontextualizing a task involves representing it…

This paper presents a praxeological analysis, based on ATD (Anthropological Theory of the Didactic), of the topic of Fourier series, as this topic is introduced and used in mathematics and in electrical engineering, more precisely in signal theory. The analysis is based mainly on one widely used textbook in mathematics for engineers, and a…

Using the High School Longitudinal Study of 2009, we examine the association between taking Algebra I by the eighth grade and students' later achievements and advanced mathematics course-taking. To explore our research questions, we employ three distinct methods--regression analysis, fixed effects models, and propensity score matching. In all our…

The present paper describes beautiful conservation relations between areas formed by different geometrical shapes and area relations formed by algebraic functions. The conservation properties were investigated by students at an academic college of education using a computerized technological tool and were subsequently accompanied by justified…

One of the fundamental topics taught in the microeconomics class is minimizing economic costs. It includes understanding the concept of derivatives and applying them. However, most of the first-year undergraduate students find calculus difficult to understand, which also results in poor knowledge of optimization. We use the method based on the…

It is widely assumed that teachers play a key role in providing high-quality learning opportunities to students and fostering students' learning. Yet it is still unclear how specific teacher knowledge facets as part of their professional competence contribute to classroom processes and learning outcomes. Focusing on mathematics education at the…

The purpose of this work was to explore how elementary pre-service' teachers (PSTs) responded to a volume task that asked for a coordination of changes in one dimension with changes in volume. We carried out both written pre-assessments and follow-up interviews with seventeen PSTs, focused on exploring volume content knowledge. Our findings…

The aim of the present study was to examine the effects of Technology-Assisted Learning (TAL) and Project-Based Learning (PjBL) approaches upon students' attitudes toward mathematics and their academic achievements. A quasi-experimental research design was employed including pre-tests, post-tests and a retention test. The findings of the research…

The purpose of this study was to investigate the affordances and constraints of a technological tool to foster pre-service teachers' (PSTs) noticing skills including attending to, interpreting, and responding to students' mathematical work. Participants were 99 junior or senior PSTs in a mathematics pedagogy course at a large university. Using…

Evaluations of professional development programmes often seek to represent definitive outcomes, with phenomena posited as discrete, bounded and independent entities, and researchers positioned as external actors. An alternative is to understand the complexity of these relationships as entanglements by applying Baradian concepts. The value of this…

There is an emerging research base exploring the relation between mathematics vocabulary and achievement; therefore, we conducted a pilot study of a mathematics vocabulary intervention for first-grade students with mathematics difficulty (MD). At posttest, the vocabulary intervention group scored significantly higher than the active control on…

In this paper we discuss students' opportunities to learn to pose mathematical problems, based on a historical analysis of problem posing in the area of number and algebra in six series of Chinese primary school mathematics textbooks published since the 1950s. We examine changes in the proportion and distribution of the problem-posing tasks, and…

The purpose of this study was to investigate how teachers understand one specific aspect of proportional reasoning. We were interested in understanding the extent to which practicing teachers were able to make sense of reasoning that involved the fixed number of variable-sized parts perspective. We used two items, drawn from a larger dataset, that…

"Nature-based learning" is learning through exposure to nature and nature-based activities (Jordan and Chawla 2019). Nature and mathematics can be connected through teaching and learning with natural materials (objects from nature) or teaching and learning in outside spaces. In this article, the authors elaborate on the rationale for…