Reversibility thinking carried out mentally in mathematical operations has an important role in the process of understanding concepts as it involves developing a thinking process from beginning to end and from end to beginning. This qualitative research aims to describe students' reversible thinking processes in solving algebra problems,…

STEM Problem solving necessitates a substantial amount of specialized domain knowledge. An important element of problem-solving within the domain includes how knowledge is structured and organized in memory to facilitate efficient retrieval of relevant information and future problem solving. In previous studies, however, problem solving and…

Online metacognitive skills are the real-time awareness of cognition, which can effectively promote science learning and improve performance in solving scientific problems. Therefore, it is important to enhance and diagnose students' online metacognitive skills in science education. This study aimed to evaluate ninth-grade students' online…

The ability to solve complex problems successfully represents a key competence for students' educational success and beyond. While strategy application and metastrategic knowledge constitute two underlying components that drive successful complex problem solving (CPS), little is known about how these two facets develop individually and jointly in…

This study investigated how motivational strategies predict ninth graders' mathematical problem-solving achievements. The students were grouped based on their school types as students who have high and moderate academic achievements. Quantitative data were collected by motivational strategies for Learning questionnaire and routine/nonroutine…

Schematic chunks denote patterns, schemes, or sophisticated rules and knowledge stored in the long-term memory in the form of chunks. We investigated whether schematic chunking is effective in improving the performance of students with math difficulties (MD) and students at risk of math failure, and how the complexity level of geometry problems…

Collaborative gestures in the mathematics classroom occur when multiple learners coordinate their bodies in concert to accomplish mathematical goals. Collaborative gestures show how cognition becomes distributed across a system of dynamic agents, allowing for members of groups of students to act and gesture as one. We explore ways high school…

This research aimed to develop a computer detective game for science education to provide students in experiencing real-world problem-solving after learning electricity-related knowledge, and to explore the effects of designing the guidance of process constraints and prompts into this game. To explore the effects of guidance, two different game…

This case study contrasts the strategies used by two students in solving bilateral symmetry and reflection tasks, based on the differential properties they attended to. The ninth grader focussed on congruence of sides as the main property of reflection whereas the eighth grader focussed on perpendicularity and equi-distance, as is the normative…

The purpose of this study was to examine the differences between Finnish and Taiwanese textbooks for grades 7 to 9 on the topic of solving systems of linear equations (simultaneous equations). The specific textbooks examined were TK in Taiwan and FL in Finland. The content analysis method was used to examine (a) the teaching sequence, (b)…

The present study investigates the empirical separability of mathematical (a) content domains, (b) cognitive domains, and (c) content-specific cognitive domains. There were 122 items representing two content domains (linear equations vs. theorem of Pythagoras) combined with two cognitive domains (modeling competence vs. technical competence)…

Making decisions about the production and use of chemical substances is of central importance in many fields. In this study, a research team comprising teachers and educational researchers collaborated in collecting and analyzing cognitive interviews with students from 8th grade through first-year university general chemistry in an effort to map…

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…

The present study investigated (a) whether the perceived cognitive load was different when geometry problems with various levels of configuration comprehension were solved and (b) whether eye movements in comprehending geometry problems showed sources of cognitive loads. In the first investigation, three characteristics of geometry configurations…

A major goal of education is to help learners store information in long-term memory and use that information on later occasions to effectively solve problems (Vockell 2010). Therefore, this author began to use the Rubik's cube to help students learn to problem solve. There is something special about this colorful three-dimensional puzzle that…