This article describes emerging perspectives on contextualizing, complementizing, and complexifying--three processes involved when individuals ascribe meaning to mathematical objects of their thinking. The article is oriented toward a dialectic between theory and empirical research and is structured in two parts. The first part focuses on an…

We show that the total distance traveled by an under-damped oscillating spring mass system with sinusoidal displacement results in a nice, closed-form expression.

We engaged five mathematicians who conduct research in the domain of complex analysis or use significant tools from complex analysis in their research in interviews about basic concepts of differentiation and integration of complex functions. We placed a variety of constructivist, social-constructivist, and embodied theories in mathematics…

In this article we are analyzing which spherical symmetry groups can be found and which ones cannot among the eggs with wax-resist patterns most frequently used in the Carpathian Basin. We are also trying to answer the question why exactly these symmetry decorations can be found. Before that, we are providing a review on the history of decorating…

Fragile understanding is where new learning begins. Students' understanding of new concepts is often shaky at first, when they have only had limited experiences with or single viewpoints on an idea. This is not inherently bad. Despite teachers' best efforts, students' tenuous grasp of mathematics concepts often falters with time or when presented…

There is a long tradition of teaching science through inquiry, with broad agreement about the form it should take. Students should investigate researchable questions; gather and analyse data; and develop and represent evidence-based claims. Authoritative teacher or textbook representations are generally used to guide this learning (Buckley &…

If chosen carefully according to teaching purposes and incorporated into the curriculum, games can enhance teaching and learning. The use of didactic games while teaching maths can support students' motivation and performance during the lesson. Therefore, educational games should be preferred in maths classes as an alternative teaching method. In…

The present study tests two predictions stemming from the hypothesis that a source of difficulty with rational numbers is interference from whole number magnitude knowledge. First, inhibitory control should be an independent predictor of fraction understanding, even after controlling for working memory. Second, if the source of interference is…

Using simulation approaches when conducting randomization tests for comparing two groups in the context of experimental studies has been promoted as a beneficial approach for supporting student learning of statistical inference. Many researchers have suggested that the data production process in simulations for the randomization test intuitively…

The authors share the results of a research project involving the use of mathematics to develop students' Numeracy General Capabilities. The current article delves into an example of a teacher supporting 'good habits of mind' through focussing on the Critical Learning Disposition of accuracy.

The math education community has made strides in understanding how math teachers help students develop a conceptual understanding of math ideas. In-the-moment instructional decisions are essential for helping students develop a conceptual understanding of important math ideas (Carpenter et al., 2003; NCTM, 2000). However, math instruction centered…

A learning trajectory as a sequence of mathematical activities that could facilitate the growth of students' understanding of learning goals. This research aimed to produce an instructional sequence to learn the concepts of translation and reflection and to investigate how students develop their understanding informally using a South Sumatra dance…

Extant research has demonstrated that problem-posing and problem-solving mutually affect one another. However, the exact nature and extent of this relationship requires a detailed elaboration. This is especially true when adidactical problem-posing arises within a problem-solving context. In this study, we analyze the scripting journey used by two…

The aim of the present study was to examine the kinds of developmental profiles of arithmetic fluency skills that can be identified across Grades 1-9 (ages 7-16) in a large Finnish sample (n = 2,518). The study also examined whether membership in the developmental profiles could be predicted using a comprehensive set of kindergarten-age factors,…

Traditional rote learning methods often fail to adequately develop reasoning skills in mathematics, particularly among pre-university students. This study addresses challenges in fostering mathematical reasoning abilities, as evidenced by declining TIMSS results and resistance to pedagogical innovations. My online teaching with GeoGebra (MyOT_G+)…