Conceptualized in France during the sixties, the Theory of Didactical Situations [TDS] is a pivotal framework for developing mathematics teaching and learning processes. Despite the increasing qualitative studies over the last ten years, there remains a dearth of analysis of its effects on mathematics education. Through a Grounded Formal Theory…

This paper explores magical realism as a theoretical lens for analysing mathematics classrooms. Traditional frameworks often overlook the complexities of teaching and learning, focusing solely on measurable aspects. Inspired by magical realism -- a literary genre blending the fantastical and the everyday -- I propose a new perspective on how…

Traditional mathematics instruction often fails to address the diverse learning needs of students, leading to frustration and disengagement. This study proposes personalized learning, emphasizing sequential learning, diagnostic assessments, and technology to tailor instruction. This research examines the potential of personalized learning to…

The study of mathematics is often described as the science of patterns (Resnik 1981), and the cognitive tasks involving the search, recognition, and assessment of patterns are fundamental to learning mathematics. Patterning activities lead students to a better understanding of dependent relations among representations, create a transparent way for…

Current literature indicates the significance of embodied scaffoldings in enhancing the effectiveness of interactive learning technologies for STEM conceptual learning and relevant cognitive skill development. However, there is limited research on pedagogical approaches for integrating mixed embodied scaffoldings in learning with interactive…

The objective of the study was to characterise how pre-service kindergarten teachers used a Hypothetical Learning Trajectory on length and its measurement to notice children's mathematical thinking. A total of 64 pre-service kindergarten teachers enrolled in an Early Years Education mathematics teaching course were asked to notice teaching…

This study aims to examine the changes in students' mental constructions of function transformation based on the designed activities, classroom discussions, exercises (ACE) teaching cycle in the light of the action, process, object, schema (APOS) theoretical framework. The study was conducted by seven volunteer students who were enrolled in…

The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

Both recent evidence and research-based early mathematics curricula indicate that repeating patterns--predictable sequences that follow a rule--are a topic of major importance for mathematics development. The purpose of the current study was to help build a theory for how early repeating patterning knowledge contributes to early math development,…

We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…

Many mathematics departments have instituted transition-to-proof courses for second semester sophomores to help them learn how to construct proofs and to prepare them for proof-based courses, such as abstract algebra and real analysis. We have developed a way of getting students, who often stare at a blank piece of paper not knowing what to do, to…

Learning mathematical thinking and reasoning is a main goal in mathematical education. Instructional tasks have an important role in fostering this learning. We introduce a learning sequence to approach the topic of integrals in secondary education to support students mathematical reasoning while participating in collaborative dialogue about the…

This article explores the potential use metacognitive skills learned in computer games to teach mathematics. This study explored the similarities and differences in the learning of metacognitive skills between computer games and mathematics education. A mixed-methods approach was employed in which a quantitative survey (students, n=174) and a…

Southern Cross University (SCU) educators and local teachers have developed a five-lesson instructional sequence built around fluke identification as a way of resolving the question: How fast do humpback whales travel up the east coast of Australia?

This article describes part of a study in which researchers designed lesson sequences based around using a string number line to help teachers support children's development of relative thinking and understanding of linear scale. In the first year of the study, eight teachers of Years 3-5 participated in four one-day professional development…