This article presents a networking of two theories, the Extended Theory of Mathematical Connections (ETC) and the Onto-semiotic Approach (OSA). In particular, concordances and complementarities are identified in the respective conceptions of mathematical connections, as a result of applying these theoretical frameworks to a student's response…

This research aims to describe the expectations of prospective teachers for students' mathematical thinking processes in solving problem-based on the Polya model. This model is perceived by the theory of mathematical thought processes proposed by Mason. A descriptive method with a qualitative approach was used in this research. The research…

This aim of this study is to describe the process of local conjecturing in generalizing patterns based on Action, Process, Object, Schema (APOS) theory. The subjects were 16 grade 8 students from a junior high school. Data collection used Pattern Generalization Problem (PGP) and interviews. In the first stage, students completed PGP; in the second…

This study is part of ongoing research in undergraduate mathematics education. The study was guided by the belief that understanding the mental constructions the pre-service teachers make when learning matrix algebra concepts leads to improved instructional methods. In this preliminary study the data was collected from 85 pre-service teachers…

Semantic studies on diagrammatic notations (Barwise & Etchemendy,; Shimojima,; Stenning & Lemon, ) have revealed that the "non-deductive," "emergent," or "perceptual" effects of diagrams (Chandrasekaran, Kurup, Banerjee, Josephson, & Winkler,; Kulpa,; Larkin & Simon,; Lindsay, ) are all rooted in the…

This study examined how working memory plays different roles in open-ended versus closed-ended creative problem-solving processes, as represented by divergent thinking tests and insight problem-solving tasks. With respect to the analysis of different task demands and the framework of dual-process theories, the hypothesis was that the idea…

Research has demonstrated that instruction that relies heavily on studying worked examples is more effective for less experienced learners compared to instruction emphasizing problem solving. However, the guidance associated with studying some worked examples may reduce the performance of more experienced learners. This study investigated…

This paper provides a critical examination of the current state and future possibility of formal cognitive theory for insight problem solving and its associated "aha!" experience. Insight problems are contrasted with move problems, which have been formally defined and studied extensively by cognitive psychologists since the pioneering…

This article proposes a unified framework for understanding creative problem solving, namely, the explicit-implicit interaction theory. This new theory of creative problem solving constitutes an attempt at providing a more unified explanation of relevant phenomena (in part by reinterpreting/integrating various fragmentary existing theories of…

This article is concerned with how computer science, and more exactly computational complexity theory, can inform cognitive science. In particular, we suggest factors to be taken into account when investigating how people deal with computational hardness. This discussion will address the two upper levels of Marr's Level Theory: the computational…

The worked example effect within cognitive load theory is a very well-established finding. The concrete effectiveness of worked examples in a learning situation, however, heavily depends on further moderating factors. For example, if learners improve their processing of worked examples by actively explaining the worked examples to themselves, they…

The 3 most often-used performance measures in the cognitive and decision sciences are choice, response or decision time, and confidence. We develop a random walk/diffusion theory--2-stage dynamic signal detection (2DSD) theory--that accounts for all 3 measures using a common underlying process. The model uses a drift diffusion process to account…

Cognitive load theory (CLT) is one of the most important theories in educational psychology, a highly effective guide for the design of multimedia and other learning materials. This edited volume brings together the most prolific researchers from around the world who study various aspects of cognitive load to discuss its current theoretical as…

Can children genuinely create new knowledge, as opposed to merely carrying out activities that resemble those of mature scientists and innovators? The answer is yes, provided the comparison is not to works of genius but to standards that prevail in ordinary research communities. One important product of knowledge creation is concepts and tools…

In the present article, we articulate three assumptions underlying theories proposing that restructuring processes play a key role in insightful problem solving: representational difficulty, representational change, and discontinuity in solution processes. We argue that these assumptions need empirical validation to justify the proposition of…