Conventional coordinate systems are often considered representational tools for reasoning about mathematical concepts. However, researchers have shown that students experience persistent difficulties as they engage in graphing activity. Using examples from research and textbooks, we present a framework based on a conceptual analysis of the use of…

Special relativity theory (SRT) has recently gained popularity as a first introduction to "modern" physics thinking in upper level secondary physics education. A central idea in SRT is the absolute speed of light, with light propagating with uniform speed relative to the reference frame of the observer. Previous research suggests that…

The aim of this research is to analyse students' sense-making regarding matrix representation of geometric transformations in a dynamic geometry environment (DGE) within the perspective of semiotic mediation. In particular, the focus is on students' reasoning on the transition from the notion of function to transformation and to matrix…

This study examined middle and secondary mathematics teachers' knowledge structures, informal inferential reasoning (IIR), and pedagogical content knowledge (PCK) for statistics. Using task-based clinical interviews (Goldin, 1997) and cross-case analysis (Creswell, 2013), a stratified purposeful sample (Patton, 2002) of nine teachers responded to…

If we admit that students must be prepared for life and work in increasingly culturally-diverse and ever changing contexts through core curricula which are the competences that must be prioritized? What competences are 'strong candidates' to be considered as trans-regional and can lead to inclusive excellence in higher education? Does, this,…

In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

Teachers readily welcome instructional materials that situate mathematics in the real world because they provide the relevance of mathematics to students who genuinely seek the answer to the question, "When are we ever going to use math in real life?" Although using the real world as a motivational hook is often effective for engagement,…

Ambridge argues that there is widespread agreement among child language researchers that learners store linguistic abstractions. In this commentary the authors first argue that this assumption is incorrect; anti-representationalist/exemplar views are pervasive in theories of child language. Next, the authors outline what has been learned from this…

Argument-based interventions in science education have largely been motivated by the perspective that students lack knowledge of argument. Recent studies, however, suggest that contextual factors influence students' argument quality. The authors hypothesize that a key limiting factor lies in students' abilities to recognize when to employ…

This research asks whether analogical processing ability is present in human infants, using the simplest and most basic relation--the "same-different" relation. Experiment 1 (N = 26) tested whether 7- and 9-month-olds spontaneously detect and generalize these relations from a single example, as previous research has suggested. The…

In this paper, we present a novel approach to defining, teaching, and assessing creativity by examining its origins and delineating the processes involved. The rationale for introducing this framework developed from studying existing thinking and questioning the current metrics for measuring creativity, which we posit are unfit for purpose. We…

The present study investigates the effects that concreteness fading has on learning and transfer across three grade levels (4-6) in elementary school science education in comparison to learning with constantly concrete representations. 127 9- to 12-years-old elementary school students studied electric circuits in a computer-based simulation…

One of the central goals of modern science and chemistry education is to develop students' abilities to understand complex phenomena, and productively engage in explanation, justification, and argumentation. To accomplish this goal, we should better characterise the types of reasoning that we expect students to master in the different scientific…

The periodic table is recognized as one of the most powerful tools in science. While it is included in virtually all high school and undergraduate general chemistry curricula, it remains a mystery to many chemistry students who find it impossible to decode. Students are often able to predict periodic trends concerning atomic radius, ionization…

Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.