The use of written or graphic representations is essential in mathematics. Graphic representations are mainly used and researched as instruments for problem solving. There is a gap in research for interventions that use learner-generated graphic representations as documents for reflection processes for promoting the development of children's…

Industrial design (ID) education involves students with different cognition types. This study aims to explore and compare the design activities of problem-driven and solution-driven students and examine the stability of the design process of the two classifications regarding constraints. Based on the P-S index derived from…

In this article, we consider certain minimization problems. If d[subscript 1], d[subscript 2] and d[subscript 3] are the distances of a boundary or inner point to the sides of a given triangle, find the point which minimizes d[subscript 1][superscript n] + d[subscript 2][superscript n] + d[subscript 3][superscript n] for positive integer n. These…

In this article, the authors describe an algebra 2 class activity, called the Exponent Maze, that had students practice many mathematics problems, display their creativity, and work together collaboratively by creating their own mazes. The authors discuss how they introduced the activity, what the students created, and how creating mazes can be…

The study of loops and spaces in mathematics has been the subject of much interest among researchers. In Part 1 of "The Theory on Loops and Spaces," published in the "Mathematics Teaching Research Journal," introduced the concept and the basic underlying idea of this theory. This article continues the exploration of this topic…

Process data from educational assessments enhance the understanding of how students answer cognitive items. However, effectively making use of these data is challenging. We propose an approach to identify solution patterns from operation sequences and response times by generating networks from process data and defining network features that…

Playing games can be one of the most important activities for children to improve their social problem-solving (SPS) skills. Studies that have examined the empirical evidence of playing games concerning children's SPS skills have tended to focus on the function of a single game. Therefore, an overview study is needed to generalize the data by the…

Young children with limited knowledge of formal mathematics can intuitively perform basic arithmetic-like operations over nonsymbolic, approximate representations of quantity. However, the algorithmic rules that guide such nonsymbolic operations are not entirely clear. We asked whether nonsymbolic arithmetic operations have a function-like…

This paper introduces the basic knowledge of integral factors of first-order ordinary differential equations and Lie symmetry analysis. It then discusses the principle of constructing an integral factor of the first-order ordinary differential equation by the Lie symmetric method. Finally, it presents some examples to show the process of…

Eddie Woo discusses the importance of problem solving in mathematics education. He points to the need for teachers to carefully consider the approaches they use to best support the growth of problem-solving abilities in students.

While never a loved organisation, Ofsted's reputation has perhaps never been so low. Amid a myriad of calls for reform or abolition, former HMI Adrian Lyons reflects on his 20 years of inspection with over 16 years employed by Ofsted as an HMI. He concludes that one of the biggest problems with Ofsted is its frequent change in policy, activity and…

Creativity is increasingly seen as a key human capability that can be deliberately developed. Correspondently, a proliferation of tools, techniques, and methods are available in the academic and popular literatures. Creative problem-solving (CPS) is one framework among these, and has a 70-year history of research and development. This essay…

My concern in this article is how the university might become more distributed, less concentrated in particular places and times, and more permeable to different sorts of interests. In order to do this, I have written a partly autobiographical reflection on an attempt to practice the work of the university differently. It is the early story of a…

Purpose: This paper engages Olaf Zawacki-Richter and Insung Jung in a frank and penetrating conversation that seeks to ground, frame, and problematise research in the field conceptualised as "open, distance and digital education" (ODDE). Taking as starting point the recent publication of the landmark "Handbook of Open, Distance, and…

Early interventionists may frequently encounter ethical dilemmas due to the complex nature of early intervention (EI) service delivery (e.g., EI system infrastructure and building and sustaining collaborative relationships within the system). Therefore, the purpose of this research study was to explore the experiences of EI professionals related…