Background: Creativity requires both divergent and convergent thinking. Previous research established that "divergent" thinking relates to mathematics performance, but generally ignored the role of "convergent" thinking and, hence, leaves it unclear how both might interact when children work on mathematical tasks. This study…

Background: Functional thinking is characterized as a specific way of thinking in relationships, dependencies, and changes. Hence, beyond mathematics, it is also crucial for other (STEM) disciplines as well as for everyday situations. In particular, dealing with different representations of functions and changing between them are core…

Studies in mathematics education have shown interactions between a variety of emotions and the quality of learning. Research has found that positive emotions are among the main factors that engender a sense of well-being. In the current study, we focused on emotions that may be aroused while coping with mathematical challenges, and sought to…

Assessment for Learning (AfL) has long been identified as effective in supporting teachers to modify their teaching and learning with the aim of improving attainment but AfL practices are rarely applied to mathematics homework. Parental involvement in learning is also a key ingredient to success. This paper explores the benefits of using AfL…

How dyslexia students solve number operations is still challenging to unravel. This study aimed at revealing the types of errors conveyed by a dyslexic student in performing fractional operations on mathematical tasks that combined non-verbal text (symbols and pictures) and verbal text. The data were collected using a task-based interview with a…

Though the curriculum reform movement that began in 1989 has had a significant impact on calculus pedagogy and content (Windham, 2008), the question remains to what extent reform-based calculus textbooks reflect these reforms. This paper explores this question by analyzing the mathematical content and pedagogical approach of the chapter on…

Gifted students are individuals who show extraordinary development in at least one area compared to their peers. The common feature of gifted students is their creativity. The gifted students need training to improve their skills. If they do not receive such training, their abilities will fade out over time. Problem posing is one of the activities…

During the past 20 years, numerous studies examining the use of problem posing in mathematics instruction have documented positive outcomes in terms of students' problem-solving skills, creativity, and attitudes and beliefs regarding the study of mathematics. However, despite these promising results, problem posing in mathematics instruction has…

In this study, the mathematics of carpet will be introduced by presenting the lifestyle of two expert carpet-weavers from Kerman, Iran, who work for many years in carpet-weaving activities through an explanation of carpet weavers' culture. This explanation reveals that carpet weavers can do mathematics and solve related real-world problems without…

Methods of teaching differential equations (DE) have long focused on rote analytic solution methods that align poorly with more industry-relevant numerical and computational methods. Engineering and mathematics educators agree that there is a need to shape DE curricula to reflect the mathematical practices of the disciplines whose students take…

Word problem solving is the premise for students to generalize their problem solving skills to real world problems. This includes students with autism spectrum disorder (ASD) and intellectual disability (ID). Modified Schema-based Instruction (MSBI) is one strategy that research has shown is effective for teaching students with ASD/ID to acquire…

A method is presented which can be used to obtain analytical solutions for boundary value problems (BVPs) using the matrix exponential and Maple. Systems of second order, linear differential equations are expressed as two or more first order equations in matrix form, and their solutions are obtained using the matrix exponential, matrix…

Compare problems are the most difficult type of word problems among primary school students, especially inconsistent problems, when the relational term is not consistent with the arithmetic operation required for the solution. The present study examines whether different methods help students successfully solve them and how these approaches…

Visualization and argumentation are central processes in the learning of geometry, giving rise to specific lines of research in mathematics education. However, it is worth asking whether they should be developed independently or if it is possible and in what way an articulation between them can be promoted. The objective of this paper is to search…

The solution and verification of single-digit multiplication problems vary in speed and accuracy. The current study examines whether the number of different digits in a problem accounts for this variance. In Experiment 1, 41 participants solved all 2-9 multiplication problems. In Experiment 2, 43 participants verified these problems. In Experiment…