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…

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…

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…

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,…

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…

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…

The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across…

Students benefit from learning multiple procedures for solving the same or related problems. However, past research on comparison instruction has focused on comparing multiple formal procedures. This study investigated whether the benefits of comparing procedures extend to comparisons that involve informal and formal procedures. We also examined…

Short term memory is famously limited in capacity to Miller's (1956) magic number 7 plus or minus 2--or, in many more recent studies, about 4 plus or minus 1 "chunks" of information. But the definition of "chunk" in this context has never been clear, referring only to a set of items that are treated collectively as a single unit. We propose a new…

An account is made of the relationship between the convergence behaviour of a sequence and the accumulation points of the underlying set of the sequence. The aim is to provide students with opportunities to contrast two types of mathematical entities through their commonalities and differences in structure. The more set-oriented perspective that…

Argues that reasons for teaching geometry before second-year algebra include higher student achievement and attitude and better abstract thinking. (PK)

This study compared the effectiveness of teaching multidigit addition of whole numbers without regrouping prior to teaching it with regrouping to teaching multidigit addition with and without regrouping simultaneously. Pretest/posttest-delayed posttest results of second grade students (n=151) from seven randomly assigned classrooms indicated no…