Our previous work interpreted single-lognormal fits to inter-gaze distance (i.e., "gaze steps") histograms as evidence of multiplicativity and hence interactions across scales in visual cognition. Bogartz and Staub (2012) proposed that gaze steps are additively decomposable into fixations and saccades, matching the histograms better and…

Box plots are frequently used, but are often misinterpreted by students. Especially the area of the box in box plots is often misinterpreted as representing number or proportion of observations, while it actually represents their density. In a first study, reaction time evidence was used to test whether heuristic reasoning underlies this…

We produce a continuum of curves all of the same length, beginning with an ellipse and ending with a cosine graph. The curves in the continuum are made by cutting and unrolling circular cones whose section is the ellipse; the initial cone is degenerate (it is the plane of the ellipse); the final cone is a circular cylinder. The curves of the…

Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.

Research has shown that forest plots are a gold standard in the visualization of meta-analytic results. However, research on the general interpretation of forest plots and the role of researchers' meta-analysis experience and field of study is still unavailable. Additionally, the traditional display of effect sizes, confidence intervals, and…

AMOEBA is a unique tool to support teachers' orchestration of collaboration among novice programmers in a non-traditional programming environment. The AMOEBA tool was designed and utilized to facilitate collaboration in a classroom setting in real time among novice middle school and high school programmers utilizing the IPRO programming…

To prepare students for participation in our society, where interpreting, representing, and manipulating of dynamic phenomena are becoming key activities, we believe that one should start developing a mathematical understanding of change at an early age. We therefore started a design research project to teach the concept of instantaneous speed in…

Graphing is a fundamental part of the scientific process. Scales are key but little-studied components of graphs. Adopting a resources-based framework of cognitive structure, we identify the potential intuitive resources that six undergraduates of diverse majors and years at a public US research university activated when constructing scales, and…

Modeling and argumentation are two important scientific practices students need to develop throughout school years. In this paper, we investigated how middle and high school students (N = 512) construct a scientific argument based on evidence from computational models with which they simulated climate change. We designed scientific argumentation…

The quest to contextualise education in Africa has been on-going for a while and many countries have been making efforts towards it. During this time of educational review, conscious efforts should be made to identify problematic levels of some subjects that are dreadful to the learners to pave the way for curriculum re-design for context…

Students with cerebral palsy (CP) without severe intellectual impairments often experience difficulties in mathematics performance. Given the high prevalence of learning difficulties in students with CP, few studies have examined interventions to improve the math competency of these students (Jenks et al., 2009). A single-subject reversal design…

This paper describes investigations in visualizing logpaths of students in an online calculus course held at Florida State University in 2014. The clickstreams making up the logpaths can be used to visualize student progress in the information space of a course as a graph. We consider the graded activities as nodes of the graph, while information…

This article reports on a study of six Grade 11 learners' levels of understanding of concepts related to the function definition and representation. Task-based clinical interviews were used to elicit the learners' interpretations and reasoning when working with these function-related concepts. Indicators for Action-Process-Object-Schema (APOS)…

The research described in this article concludes that the widely cited U-curve hypothesis is no longer supported by research data because the adjustment of international postgraduate students is a complex phenomenon that does not fit easily with attempts to define and categorize it. Methodological issues, different internal and external factors,…

Algebra has been explicit in many school curriculum programs from the early years but there are competing views on what content and approaches are appropriate for different levels of schooling. This study investigated 12-13-year-old Australian students' algebraic thinking in a hybrid environment of functional and equation-based approaches to…