This paper describes a model of mathematics bianshi teaching using one problem with several solutions, changes, and applications in an inquiry-based classroom. Based on the model of mathematics bianshi teaching, the author discusses a class-room experience where one Chinese mathematics teacher takes a simple plane geometry problem to guide…

In the context of a rapid digital transformation, digital competence is now regarded as a fourth cultural skill complementing reading, writing, and arithmetic. We argue that a well-structured and sound competence model is needed as a shared foundation for learning, teaching, pedagogical diagnostics and evaluative schemes in the school system.…

The learning of mathematics generally undergoes a less effective and less appealing learning process, resulting in students' perceived lack of mastery of the material. Consequently, students' insufficient understanding of the concepts leads to a lack of folding back. In the process of understanding, it influences individual characteristics, where…

Despite continued efforts to address this issue, many students still exhibit misunderstandings regarding Newton's laws. These misconceptions include beliefs, such as every movement requires a force, that force is directly proportional to velocity, and that action-reaction forces can differ in magnitude. To mitigate these misunderstandings,…

This conceptual paper discusses two frameworks, developed independently by the lead author, that will provide the conceptual foundation for the identification and evaluation of mental computation strategies students demonstrate during an upcoming research project entitled Mental Computation in Year 5. These frameworks will be used by the lead…

The aim of this paper is to present a teaching proposal for the theoretical part relating to the first- and second-order linear difference equations with constant coefficients suitable for the first-year students at various types of universities. In contradistinction to the methods often applied (memorization of algorithms without a proper…

This article presents a task providing college students opportunities to build on their high school knowledge of trigonometry to explore parametric equations and inverse trigonometric relationships within a contextual learning ladder problem.

Idea evaluation is a critical activity in the creative process due to its role in making a decision about what idea(s) should be developed further and implemented, or whether more ideas should be generated. Confidence in the correctness of the evaluation plays a key role in making that decision. Emerging evidence suggests that inner speaking, the…

We discuss an investigation of student sensemaking and reasoning in the context of degenerate perturbation theory (DPT) in quantum mechanics. We find that advanced undergraduate and graduate students in quantum physics courses often struggled with expertlike sensemaking and reasoning to solve DPT problems. The sensemaking and reasoning were…

Through instructional tasks, teachers can present content in ways that require students to apply critical thinking, problem-solving, and other cognitive skills. The purpose of this mixed methods collective case study was to determine how teacher-assigned instructional tasks in mathematics impact students' learning of mathematical concepts. In this…

The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…

Electricity and magnetism are fundamental areas of physics and are integral to science curricula at various educational levels. However, this area has been reported to contain several concepts that students find challenging, leading to perspectives that diverge from scientifically accepted views. This study examines the errors made by physics…

Engineering and technology teachers have advocated using robotics and coding to cultivate students' computational thinking and problem-solving skills at PreK-12 levels. Understanding teachers' perceptions of how preschool children develop strategies and skills for engaging in robotics and coding activities is crucial for promoting the early use of…

Problem-solving before instruction has been shown to be a more effective learning design than traditional tell-and-practice for several mathematical concepts at the secondary school level. In particular, the more a problem-solving before instruction design follows the productive failure principles, such as comparing and contrasting…

Metacognition, or the ability to "think about thinking," plays a significant role in the performance of first-year design students. Although the number of studies that focus on metacognition has increased in the past decade, additional studies are needed to more fully investigate metacognition and the use of metacognitive strategies in…