The application of ethnomathematics and mathematical modelling allow us to see a different reality and give us insight into mathematics accomplished holistically. In this context, a pedagogical action that connects ethnomathematics and the cultural aspects of mathematical modelling with its academic features is referred to as ethnomodelling. This…

The purpose of this study was to examine the epistemological beliefs of middle school students in rural area and their attitudes toward solving mathematical problems according to gender and class level variables. It was also necessary to determine whether the epistemological beliefs of middle school students in rural area had predicted their…

The higher education system of the Republic of Kazakhstan emphasizes the need for the development of institutional science, including the field of information technology, with a priority on fundamental research. Professional training of future computer science teachers requires them to know the range of tasks related to computer graphics, and the…

The study reported in this article sought to explore and observe how grade 9 learners solve real-wor(l)d problems (a) without real context and (b) without real meaning. Learners' abilities to make sense of the decontextualised word problems set in the real world were investigated with regard to learners' use of common sense in relation to problem…

Mathematical problem solving is one of the most valuable aspects of mathematics education. It is also the most difficult for elementary-school students (Verschaffel, Greer, & De Corte, 2000). Students experience cognitive and metacognitive difficulties in this area and develop negative emotions and poor motivation, which hamper their efforts…

In this article on introductory calculus, intriguing questions are generated that can ignite an appreciation for the subject of mathematics. These questions open doors to advanced mathematical thinking and harness many elements of research-oriented mathematics. Such questions also offer greater incentives for students to think and reflect.…

This article seeks to illustrate the analysis of episodes of chat sessions based on Charles Sanders Peirce's triadic sign relation. The episodes are from a project called "Math-Chat", which is based on the use of mathematical inscriptions in an experimental setting. What is characteristic of this chat setting is that pupils are required to…

Many students or teachers ask themselves: Being given a natural number n, how many non-isomorphic groups of order n exists? The answer, generally, is not yet given. But, for certain values of the number n have answered this question. The present work gives a method to determine of all non-isomorphic groups of order 16 and gives descriptions of all…

Many integrals require two successive applications of integration by parts. During the process, another integral of similar type is often invoked. We propose a method which can integrate these two integrals simultaneously. All we need is to solve a linear system of equations.

Various stakeholders in mathematics education have called for increasing the role of reasoning and proving in the school mathematics curriculum. There is some evidence that these recommendations have been taken seriously by mathematics educators and textbook developers. However, if we are truly to realize this goal, we must pose problems to…

An important goal of school mathematics is to enable students to formulate, approach, and refine problems beyond those they have studied, allowing them to organize and consolidate their mathematical thinking. To achieve this goal, students should be encouraged to develop expertise in a variety of areas, such as problem solving, reasoning and…

Cognitively demanding tasks (CDT) (Stein et al. 2000) are necessary for the development of students' mathematical reasoning skills. Research is unequivocal on the importance of giving students opportunities to engage in such tasks. Although current reform efforts call for mathematics learning for "all" students, learners who…

This study explored the extent to which domain-specific knowledge predicted proportional word problem-solving performance. We tested 411 seventh-grade students on conceptual and procedural fraction knowledge, conceptual and procedural proportion knowledge, and proportional word problem solving. Multiple regression analyses indicated that all four…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

It has been well-documented that many students do not understand the meaning of the equal sign. Thus, researchers have called for instruction that specifically addresses misconceptions about the equal sign, and have indicated that such work must start at the elementary level. In response to these recommendations, some state curriculums require…