The ability to solve physics problems that require multiple concepts from across the physics curriculum--"synthesis" problems--is often a goal of physics instruction. Three experiments were designed to evaluate the effectiveness of two instructional methods employing worked examples on student performance with synthesis problems; these…

Young children have been taught simple sequences of alternating shapes and colors, referred to as "patterning", for the past half century in the hope that their understanding of pre-algebra and their mathematics achievement would be improved. The evidence that such patterning instruction actually improves children's academic achievement…

This mixed method study was aimed at examining the influence of dual processing (Type 1 and Type 2 thinking) on the development of high school students' nature of science (NOS) views. Type 1 thinking is intuitive, experiential, and heuristic. Type 2 thinking is rational, analytical, and explicit. Three research questions were asked: (1) Do the…

This mixed methods, action research case study sought to investigate the effects of incorporating LEGO robotics into a seventh grade mathematics curriculum focused on the development of proportional reasoning through the lens of Social Constructivist Theory. Quantitative data was collected via pre- and post-tests from the mathematics class of six…

We develop a theory of grounded and embodied mathematical cognition (GEMC) that draws on action-cognition transduction for advancing understanding of how the body can support mathematical reasoning. GEMC proposes that participants' actions serve as inputs capable of driving the cognition-action system toward associated cognitive states. This…

Currently, instruction pays little attention to the development of students' sampling variability reasoning in relation to statistical inference. In this paper, we briefly discuss the especially designed sampling variability learning experiences students aged about 15 engaged in as part of a research project. We examine assessment and…

This research investigated whether symbolic understanding of pictures in low-functioning children with autism is mediated by iconicity and language. In Experiment 1, participants were taught novel words paired with unfamiliar pictures that varied in iconicity (black-and-white line drawings, greyscale photographs, colour line drawings, colour…

The purpose of this study is to analyse the feasibility of an evidential reasoning (ER) method for portfolio assessments and comparison of the results found with those based on a traditional holistic judgement. An ER approach has been incorporated into portfolio assessment of an undergraduate engineering design course delivered as a project-based…

The objective of this article is to contribute to research on teachers' probabilistic knowledge and reasoning. To meet this objective, prospective mathematics teachers were presented coin flip sequences and were asked to determine and explain which of the sequences was least likely to occur. This research suggests that certain individuals, when…

The purpose of this study was to study the impact of conformity to Statistical Reasoning Learning Environment (SRLE) principles on students' statistical reasoning in Advanced Placement statistics courses. The study encompassed ten different schools in the Southeast United States over a school year. A quasi-experimental design was used to compare…

In our last critical thinking column we introduced the idea of intellectual standards and pointed out that all natural languages are repositories for such standards, which, when appropriately applied, serve as guides for assessing human reasoning. We argued that intellectual standards are necessary for cultivating the intellect and living a…

In 2 experiments, we tested a strong version of a dual process theory of conditional inference (cf. Verschueren et al., 2005a, 2005b) that assumes that most reasoners have 2 strategies available, the choice of which is determined by situational variables, cognitive capacity, and metacognitive control. The statistical strategy evaluates inferences…

This article reports results from two studies of how people answer counterfactual questions about simple machines. Participants learned about devices that have a specific configuration of components, and they answered questions of the form "If component X had not operated [failed], would component Y have operated?" The data from these…

I discuss a teaching experiment that sought to characterize precalculus students' angle measure understandings. The study's findings indicate that the students initially conceived angle measures in terms of geometric objects. As the study progressed, the students formed more robust understandings of degree and radian measures by constructing an…

The psychology of reasoning is increasingly considering agents' values and preferences, achieving greater integration with judgment and decision making, social cognition, and moral reasoning. Some of this research investigates utility conditionals, ‘"if 'p' then 'q'’" statements where the realization of "p" or "q" or…