Brief experimental analysis (BEA) is a methodology of rapidly implementing interventions and observing the effect each has on student performance. Extensive research exists demonstrating the utility of BEA in identifying effective reading interventions for students, but comparatively little research exists regarding BEA and mathematics. The…

Felix Klein's Erlangen program classifies geometries based on the kinds of geometric transformations that preserve key properties of their figures, rather than focusing on the geometric figures themselves. This shift in perspective, from figurative to operative, fits Piaget's characterization of mathematical development. This paper considers how…

Inspiration from 'Confessions of a Shopaholic' led this team to explore how comics can be used for mathematics instruction about percentages. In this article, the authors describe how they conceptualised and developed a teaching package that uses comics to teach percentage concepts to Grade 7 students (age 13 to 14) in Singapore. It goes on to…

Spatial visualisation is an essential component of geometric thinking and measurement sense. It is a particular type of spatial skill that involves manipulation of spatial images and may not be naturally occurring for students. However, research shows that it is malleable and can be developed through instruction. This article presents an…

This professional practice paper is underpinned philosophically by the indisputable centrality of proof to the discipline of mathematics. Proof offers students the opportunity to deepen their own understanding of mathematical ideas, to construct and defend logical arguments, and to think critically about the veracity of mathematical statements.…

Learning rational number concepts is acknowledged as an important task but many learners find it difficult to make sense of them. This paper reports on a case study of the learning in a short (nine-lesson) learning programme for Grade 8 learners in a Namibian school, which sought to use visual models (circle area, bar area and number line) to…

This study focuses on emotion regulation in the challenging situation of collaborative learning. The aim is to explore what type of challenges trigger group-level emotion regulation and what kind of co- and socially shared emotion regulation strategies emerge in relation to these challenges. The participants are 62 higher education students, who…

Adult learners preparing for university level study have varying degrees of prior experience, confidence, ability, motivation and need when it comes to mathematical tasks. The development of numeracy skills is a core aspect of university preparation, with many university courses requiring a certain level of mathematical literacy. The standard…

Previous theoretical research has revealed conceptual similarities among a number of mathematical learning theories and theories regarding language acquisition. This intersection of ideas led to a novel framework defining four stages of mathematical learning: Receiving, Replicating, Negotiating Meaning, and Producing. Through qualitative research…

By modeling learning students enjoy learning and doing mathematics in new ways. This study aimed firstly to produce senior high school mathematics modeling tasks, lesson plan, and student worksheet for valid mathematical learning; secondly, to produce senior high school mathematics modeling, lesson plan, and student worksheet for practical…

The rational number knowledge of student teachers, in particular the equivalence of fractions, decimals, and percentages, and their comparison and ordering, is the focus of this article. An instrument comprising multiple choice, short answer and constructed response formats was designed to test conceptual and procedural understanding. Application…

Over the past 30 years, the way in which the first course in statistics has been taught has moved away from a mathematics mode to take account of the distinctiveness of statistics. This article considers exercises for the typical introductory course and gives some evidence that many of these look like somewhat expanded versions of mathematics…

We respond to a call to analyze issues of curriculum standards and to present alternative storylines by addressing criticisms of the Common Core State Standards in early childhood. We describe a storyline from multiple media and evaluate this storyline's criticisms, focusing on the criticism that the standards are developmentally inappropriate. We…

While tutoring his granddaughter in second-year algebra recently, the second author lamented that every textbook he could find expresses the quadratic formula as probably the most common form of the formula. What troubled him is that this form hides the meaning of the various components of the equation. Indeed, the meaning was obscured by the…

This paper presents the findings of a group of teacher candidates with undergraduate degrees in a STEM discipline who were followed through an intensive 1-year preparation program and their 1st year of teaching. We report on the affordances and challenges participants' discipline knowledge presented to developing pedagogical content knowledge…