This paper describes our work to determine the naturalistic images that first-time second-semester university calculus students possess for series convergence. We found that the students we interviewed most frequently determined whether a series converged by imagining a process of appending summands into a running total and examining whether this…

[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] Research in physics education has contributed substantively to improvements in the learning and teaching of university physics by informing the development of research-based instructional materials for physics courses. Reports on the design of these…

The study explored various facets of the intuitive style and its relevance to learning and education from a dual-processing perspective, namely how it relates to other style constructs (analytical; visual and verbal; local and global), gender, and superstitious reasoning and how these are likely to impact upon learning in educational and…

Students' informal inferential reasoning (IIR) is often inconsistent with the normative logic underlying formal statistical methods such as Analysis of Variance (ANOVA), even after instruction. In two experiments reported here, student's IIR was assessed using an intuitive ANOVA task at the beginning and end of a statistics course. In both…

This article explores 11- to 16-year-old students' explanations for phenomena commonly studied in school chemistry from an inclusive cognitive resources or knowledge-in-pieces perspective that considers that student utterances may reflect the activation of knowledge elements at a range of levels of explicitness. We report 5 themes in student…

This article reports on a case study from a design-based research project that investigated how students make sense of the disciplinary tools they are taught to use, and specifically, what personal, interpersonal, and material resources support this process. The probability topic of binomial distribution was selected due to robust documentation of…

The purpose of this paper is to address the concept of "intuition of education" from the pragmatic viewpoint so as to assert its place in the cognitive, that is inferential, learning process. The structure of the paper, consistent with the spirit of Charles Sanders Peirce's triadic semiotics, is threefold. As a point of departure, the author…

The purpose of this study was to determine the nature of teachers' implicit in-action mental models about children's minds and learning, as inferred through the ways they teach. The work was based on the theoretical works of D. Schon, L. Shulman, and P. N. Johnson-Laird. Study participants included 24 student, novice, and experienced teachers. All…

External representations have a great impact on what and how students learn. One key manner in which environments can operate upon novices' knowledge is through helping them ground their problem solving in an understanding of the situation embodied by the problem. In this paper, students' difficulties in microeconomics problem solving were…