Undergraduate students are expected to produce and comprehend constructive existence proofs; yet, these proofs are notoriously difficult for students. This study investigates students' thinking about these proofs by asking students to validate two arguments for the existence of a mathematical object. The first argument featured a common structural…

This study examined college calculus instructors' preferences in solving two calculus tasks to examine college calculus instructors' use of important cognitive roots in understanding derivatives of function. Our results showed that only one instructor consistently uses cognitive roots while other instructors either focus on algebraic methods or…

Research on mathematics interventions for college students with learning disabilities (LD) is sparse, yet mathematics is critical for post-secondary success. Prior research indicates that many effective strategies for teaching mathematics to secondary students with LD (e.g., manipulatives and cognitive strategies) can also improve the mathematics…

This study is aimed to investigate the effectiveness of problem-based learning combined with simulation on students' problem-solving and creative thinking skills. By employing a quasi-experimental design, this study used essay and problem-based tests as the instruments to evaluate problem-solving and creative thinking skills of 192 students. These…

Recent scholarship around teaching elementary mathematics supports the learning of early algebra with 5- to 12-year olds. However, in spite of the recognition of the affordances of early algebra, issues about how to introduce it remain open. Within this context, Davydov's work is often cited as a source of impressive demonstration of young…

Background & aims: In recent years, there has been an increased interest in analyzing the mathematical performance of students with learning difficulties in order to provide them with teaching methods adapted to their needs. In particular, the importance of studying the type of informal strategy that students use when solving problems has been…

Mathematical literacy and numeracy are critical for students during school and post-graduation, however, many U.S. students do not develop the mathematical skillset needed for college or the workplace, despite curricular importance placed on solving problems encountered in mathematics classrooms and spaces. Part of this skillset for critical…

What does it mean to "make sense" of physics? It's not a simple question. Most people have an intuitive feeling for when things do (or do not) make sense to them. But putting this feeling into words--especially actionable words--is another task entirely. Generally speaking, there are two ways in which we commonly use the term "make…

In this article we show that the electrostatic field intensity of a uniformly charged straight line equals that of the corresponding arc of a circle charged with the same linear density. This new method greatly simplifies the calculation of the electrostatic field of a system consisting of uniformly charged straight lines.

While project-based learning can be traced back to centuries-old theory, new research shows how it is linked to a variety of efforts for change in innovative schools.

The study aimed to develop some insights into whether science teachers are aware of films that contain socioscientific issues, the influence of the films they watch on their perception on these issues and whether they would like to use these films as teaching materials in the classroom. Therefore, in the study, the perception of science teachers…

In mathematics classrooms, it is common practice to work through a series of comparable tasks provided in a textbook. A central question in mathematics education is if tasks should be accompanied with solution methods, or if students should construct the solutions themselves. To explore the impact of these two task designs on student behavior…

Research has shown there are algebra concepts elementary teachers can introduce that help prepare elementary students for the eventual transition to algebra (e.g., the relational interpretation of the equal sign). "Early algebra" refers to the use of informal approaches to introduce such concepts to elementary students. "Strip…

Education 4.0 strongly promotes the development of communication, collaboration, critical thinking, and creativity (4C) skills among students. Consequently, it is crucial for mathematics teachers to integrate activities that facilitate the cultivation of these skills. However, the scarcity of resources, such as recommended instructional…

Video instruction has been widely studied and is generally considered as effective as live instruction for teaching scientific concepts and procedures. However, there is limited research on the effectiveness of prerecorded videos for teaching more challenging content. This study conducted a controlled experiment on over 300 high school students to…