This work provides a characterization of the learning of graph theory through the lens of the van Hiele model. For this purpose, we perform a theoretical analysis structured through the processes of reasoning that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. We…

Cognitive processes are procedures for using existing knowledge to combine it with new knowledge and make decisions based on that knowledge. This study aims to identify the cognitive structure of students during information processing based on the level of algebraic reasoning ability. This type of research is qualitative with exploratory methods.…

Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form--where form could be a tree, ring, chain, grid, etc. (Kemp & Tenenbaum, 2008). Although this approach…

One line of research on student understanding of complex systems has tended to emphasize discontinuities between common misconceptions and relatively more sophisticated understandings. Other work has focused on instruction while acknowledging the existence of other ways of understanding complex systems, but less emphasis has been on examining the…

We report our qualitative study of twenty-four students enrolled in the second-semester of a second-year undergraduate (sophomore-level) organic chemistry course, Organic Two. We asked the research participants to propose the product and electron-pushing mechanism of elementary mechanistic steps in the absence and presence of the corresponding…

Electromagnetic induction is an important, yet complex, physics topic that is a part of Croatian high school curriculum. Nine Croatian high school students of different abilities in physics were interviewed using six demonstration experiments from electromagnetism (three of them concerned the topic of electromagnetic induction). Students were…

Current theories and models of education often argue that instruction is best administered when knowledge is situated within a context. Problem-based learning (PBL) provides an approach to education that has particularly powerful affordances for learning disciplinary content and practices by solving authentic problems within a discipline. However,…

The sequence in which problems of different concepts are studied during instruction impacts concept learning. For example, several problems of a given concept can be studied together (blocking) or several problems of different concepts can be studied together (interleaving). In the current study, we demonstrate that the 2 sequences impact concept…