A prevailing theory of mathematical problem solving predicts that children will be less accurate solving a + b = c + __ problems versus a + b = __ + c. However, this has never been tested directly. Because of low base rates, information combined from multiple studies can help improve estimation accuracy and precision. This study compared…

The development of universal learning actions [universal'nye uchebnye deystviya] in logic is one of the most important tasks of education. This article explores logical problems as an effective tool for developing logical thinking and the underlying universal learning actions. We outline the basic principles of learning to solve logical problems.…

We discuss teaching and learning situations that surfaced when computer programming and mathematics were brought together in a course where students write computer code to explore mathematics problems. Combining programming and mathematics creates a rich ecosystem which, on top of traditional mathematics activities (writing solutions, proofs,…

Through critical interpretation, this paper aims to critically think about some points of Paulo Freire's critical pedagogy and its educational implications. Firstly, this paper explores the influence of life experiences and the Frankfort School on the development of Freire's critical pedagogy. Secondly, it aims to critically assess some points of…

In this age of science, there is a need for rational individuals who are open to innovations to be able to limit and combine information and establish inter-system relationships. Problem solving is considered to be the most important cognitive activity that requires mental effort and will-power. The processes applied in mind when solving a…

An important but challenging problem-solving technique in introductory mechanics is that of using "tilted axes." For inclined plane and centripetal motion problems, using axes that are aligned relative to the ramp direction or the radial direction (rather than the horizontal and vertical) yields equations that are conceptually more…

The role that the mental, or internal, representation plays when people are solving hard computational problems has largely been overlooked to date, despite the reality that this internal representation drives problem solving. In this work we investigate how performance on versions of two hard computational problems differs based on what internal…

Studies of African indigenous games often focus on a specific game or on games from different regions. This article, rather, examines five popular African board games in order to find the similarities and differences among these games. The analysis shows similarities among them. However, these similarities do not necessarily mean that these games…

For students working on realistic complex modelling problems as autonomously as possible the support by a tutor is indispensable for the students. However, how this support can be realised is still a question that has not been sufficiently answered. Based on prior research, it turned out that teacher interventions based on heuristic strategies…

Based on Leader-Member Exchange and problem solving style theories, the purpose of the study was to test the hypothesis that teachers with perceived styles similar to their supervisors will have more positive perceptions of their supervisor-subordinate relationship. One-hundred ten teachers were recruited by Qualtrics to complete surveys about…

We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…

Mathematics educators advocate for the use of models as an instructional practice that can potentially aid in building students' understanding of difficult topics. Integers and integer operations are historically problematic for students and are critically important in both arithmetic and the future study of algebra. In this chapter, I explore one…

Some college students who experience discontent with the instructional experience engage in a complaining and problem-solving behavior called "instructional dissent." Three types of dissent have been identified: rhetorical, expressive, and vengeful. Student perceptions of "instructor power" influence if and how students…

The hypothesis that reduced accessibility to relevant information can negatively affect problem solving in a remote associate test (RAT) was tested by using, immediately before the RAT, a retrieval practice procedure to hinder access to target solutions. The results of 2 experiments clearly showed that, relative to baseline, target words that had…

The main objective of the research is to create and approbate a new way of reflection formation in future teachers, which would increase the level of classifying thinking to the theoretical one. The "Formation of equivalence groups" technique was modified to conduct the experiment. It was carried out both individually and in…