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…

In universities worldwide, there has been a movement away from mono-disciplinary towards multi-, inter- and transdisciplinary education, motivated by the notion that complex societal issues call for more than a single disciplinary perspective. To prepare students for a role in addressing these issues, flexibility within educational programs is…

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.

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…

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…

Increased use of computer-based assessments has facilitated data collection processes that capture both response product data (i.e., correct and incorrect) and response process data (e.g., time-stamped action sequences). Evidence suggests a strong relationship between respondents' correct/incorrect responses and their problem-solving proficiency…

Debugging is essential for identifying and rectifying errors in programming, yet time constraints and students' trivialization of errors often hinder progress. This study examines differences in debugging challenges and strategies among students with varying computational thinking (CT) competencies using weekly coding journals from an online…

In research practice, it is common to measure cognitive load after learning using self-report scales. This approach can be considered risky because it is unclear on what basis learners assess cognitive load, particularly when the learning material contains varying levels of complexity. This raises questions that have yet to be answered by…

Solving organic chemistry reactions requires reasoning with multiple concepts and data (i.e., multivariate reasoning). However, studies have reported that organic chemistry students typically demonstrate univariate reasoning. Case comparisons, where students compare two or more tasks, have been reported to support students' multivariate reasoning.…

While there have been many calls for teaching ethics and responsible computing, it is unclear how responsible computing instruction and technical learning interact. Some instructors even hesitate to include ethics in their courses, fearing it might distract students from learning technical computing content. An approach called…