We compared self-regulatory processes and mathematics achievement with 138 elementary students across three conditions: learning by actually teaching (LAT), learning by preparing to teach (LPT), and learning for learning (LL). Students completed concept maps and then solved the problem. Students in the LAT condition created a teaching video, while…

Sets in the game "Set" are lines in a certain four-dimensional space. Here we introduce planes into the game, leading to interesting mathematical questions, some of which we solve, and to a wonderful variation on the game "Set," in which every tableau of nine cards must contain at least one configuration for a player to pick up.

Solving equations in finite algebraically structures (semigroups with identity, groups, rings or fields) many times is not easy. Even the professionals can have trouble in such cases. Therefore, in this paper we proposed to solve in the various finite groups or fields, a binomial equation of the form (1). We specify that this equation has been…

Counting problems have applications in probability and computer science, and they provide rich contexts for problem solving. Such problems are accessible to students, but subtleties can arise that make them surprisingly difficult to solve. In this paper, students' work on the Groups of Students problem is presented, and an important issue related…

Chemical processes can be fully explained only by employing quantum mechanical models. These models are abstract and require navigation of a variety of cognitively taxing representations. Published research about how students use quantum mechanical models at the upper-division level is sparse. Through a mixed-methods study involving think-aloud…

Problem-based learning is one of the promising innovative technologies for the educational process in the school. The study is based on system-activity and technological approaches. The study was based on the survey, which was attended by 185 teachers of physics, mathematics and computer science at general education schools of Mordovia. This…

This article concerns mathematical project work in the context of Finnish StarT project competition. The focus is on how well pupils achieve the learning objective of their project work: learning mathematics and practicing 21st century skills. Development of the learning objectives is considered from the viewpoint of Finnish national core…

Paper folding studies are quite effective in the development of students' visual and spatial skills. The "paper" used in these studies is a genuine tool that can support the development of geometric habits of mind as well as the visual-spatial skills. This is an action research aimed to investigate the potential of paper folding to…

This paper presents the results of an observational study developed on lessons taught by 128 teachers for a national teaching assessment program in Chile and whose practice was identified as outstanding. Specifically, we studied which strategies teachers used to promote students' self-regulation and autonomy during segments involving teacher-led…

What our century requires is an individual who can recognize and solve a problem, think in a critical manner, are productive, responsible, and open to innovation, and are capable of cooperating with others. The requirements of our era are also reflected on education. Education systems change and improve accordingly; thereby new education systems…

The teacher-researcher spent eight weeks as a participant observer in and advanced high school mathematics class in a small town in the southeast. The process of problem-solving was introduced to all twenty students from a combined IB Math SL and AP Calculus AB class. After the pretest, three students were selected, from under-represented groups,…

Perseverance, or initiating and sustaining productive struggle in the face of obstacles, promotes making sense of mathematics. Yet, engaging in struggle can be grueling and is avoided for some students. I investigate the effect of scaffolding mathematics tasks on student perseverance. The results show how prompting secondary students to…

Sometimes, in the teaching and learning of mathematics, open-ended problems posed by teachers or students can lead to a fuller understanding of mathematical concepts--a depth of understanding that no one could have anticipated. Interesting solutions and ideas emerged unexpectedly when the authors asked prospective and in-service teachers an "old"…

International and domestic mathematics teaching assistants (MTAs) are a critical part of mathematics education because they teach a substantial portion of low-level mathematics courses at research institutions. Even if there are several factors to build on MTAs' pedagogical practices, MTAs' beliefs significantly influence the MTAs' practices. The…

This case study explored how students disaffected with their school experience were scaffolded during their participation in a middle-school mathematics classroom. Of particular interest were the level of student engagement in discussion about the mathematics being presented by the teacher and the approach to doing mathematics being displayed by…