The distinction between procedural and conceptual learning has long been a topic of discussion in mathematics education and the idea of compression into thinkable concepts that enable the individual make links between them (Tall, 2007). In addition to, the compression to thinkable concept was to be thinking mechanism arising naturally and…

Equation rearrangement is an important skill required for problem solving in mathematics and science. Eye movements of 40 university students were recorded while they were rearranging simple algebraic equations. The participants also reported on their strategies during equation solving in a separate questionnaire. The analysis of the behavioral…

The present research investigated whether an illustration and/or a warning could help students to (a) build a situational model of the problem situation and (b) solve problematic word problems (P-items) that require realistic thinking more realistically. In 2 similar studies conducted in Turkey and Belgium, the authors presented 10- to 11-year-old…

Emotions play important part in mathematical problem solving, yet the theories of their role are still at their preliminary stages. In our study, we introduce a method, where screen recordings and automatic emotion recognition software are used to study the emotional states of five upper secondary school students during a solitary GeoGebra problem…

Mental computation and mathematical reasoning are two intertwined top-level mental activities. In deciding which strategy to use when doing mental computing, mathematical reasoning is essential. From this reciprocal influence, the current study aims at examining the relationship between mental computation and mathematical reasoning. The study was…

Worldwide interest in Japanese Lesson Study as a vehicle to improve mathematics teaching practice through professional learning has left largely unanswered questions about the extent to which it can be replicated elsewhere. This paper reports on a small-scale research project, "Implementing structured problem-solving mathematics lessons…

This article focuses on the importance of activity-based teaching in understanding the mole concept and the vital role of basic mathematical operations. It describes needs-based training for teachers in a professional development programme in India. Analysis of test results before and after the training indicates that teachers improved their…

Proportional reasoning is both complex and layered, making it challenging to define. Lamon (1999) identified characteristics of proportional thinkers, such as being able to understand covariance of quantities; distinguish between proportional and nonproportional relationships; use a variety of strategies flexibly, most of which are nonalgorithmic,…

A recent international study of pre-service teachers identified that proportional reasoning was problematic for pre-service teachers. Proportional reasoning is an important topic in the middle years of schooling and therefore it is critical that teachers understand this topic and can rely on their Mathematical Content Knowledge (MCK) when…

Students in the United States demonstrate low proficiency in their math skills. One promising intervention, computer-assisted instruction, may be used for remediation. There is growing support that computer-assisted instruction is effective for increasing addition and multiplication accuracy and fluency, but more research is necessary in order to…

Self-efficacy is the belief an individual has about his or her capabilities to successfully complete an activity. Self-efficacy stems from four sources: verbal persuasion, physiological states, past experiences, and vicarious experiences. Increases in self-efficacy in education are connected with an increase in academic achievement. The current…

This is a descriptive research on the difficulties of Filipino high school students in translating algebraic word problems into mathematical equations. This research is composed of three parts: (1) development of an 11-page "Filipinized" questionnaire; (2) analysis of the mathematical thinking processes of the respondents based on the answers to…

The article deals with the way in which authority was established and interpreted by teachers and students in two Flemish sixth-grade mathematics classrooms. Problem-solving lessons during a seven-month observation period were analysed regarding three aspects of teacher-student interactions that explicitly or implicitly reflect who bears…

Much attention has been devoted in the literature to students' struggles with fraction division. With regard to the traditional invert and multiply algorithm, researchers and educators have examined such areas as typical errors, how to help students understand why this method works, and what alternatives are available that might be more intuitive.…

Mr. Carter is about to start a two-day lesson on subtraction of integers with his sixth-grade prealgebra students. He plans to use contextualized problems that will allow his students to develop an interpretation of subtraction that involves the idea of "difference." This article outlines one way to teach students develop number line…