This study investigates an exploratory teaching style used in an undergraduate geometry course to help students identify an ellipse. We attempt to probe beneath the surface of exploration to understand how the actions of teachers can contribute to developing students' competence in justifying an ellipse. We analyse the complex interactions between…

Problem posing in mathematics education is one of the most important skills. Since mathematics teachers are one of the most important parts of mathematics education and teaching, this research was conducted to evaluate their views on this important skill and the implementation process. The research was carried out by 56 mathematics teachers…

A successful instructional method is to engage learners with exploratory problem-solving before providing explanations of the canonical solutions and foundational concepts. A key question is whether and what type of guidance will lead learners to explore more productively and how this guidance will affect subsequent learning and transfer. We…

In this brief article, the author illustrates the flaws of FOIL (multiply the First, Outer, Inner, and Last terms of two binomials) and introduces the box method. Much like FOIL, the box method can become easy to use. Unlike FOIL, however, the box method is a more direct and visible link to using the distributive property to determine area, a…

The purpose of this mixed methods study was to determine how teachers use questioning techniques in their mathematics classrooms and if teacher questioning techniques correlate with student achievement in mathematics. As pacing and rigor increase and students learning styles vary, schools are challenged with finding new ways to make connections…

Visual problem solving is essential to highly visual and knowledge-intensive professional domains such as clinical pathology, which trainees learn by participating in relevant tasks at the workplace (apprenticeship). Proper guidance of the visual problem solving of apprentices by the master is necessary. Interaction and adaptation to the expertise…

One way to ease the solution of physics problems is to visualize the situation. However, by visualization we do not mean the pictorial representation of the problem. Instead, we mean a sketch for the solution of the problem. In this paper a new approach to solving physics problems, based on decomposing the problem into with and without gravity, is…

A new visual representation for insight problems permits 22 new quantitative measures; which leads to a detailed diagnosis of a person's (or team's) creative weaknesses; which then leads to prescribing targeted, effective counter-techniques for each weakness. Currently, only two measures are consistently used for insight problem solving: the…

It is critical for mathematics tasks to provide students with the opportunity to engage actively in reasoning, sense making, and problem solving so that they develop a deep understanding of mathematics. Learning mathematics while solving a problem can be like entering a dark room with a single small light. The objects are in the shadows, difficult…

In computer-supported collaborative learning research, studies examining the combined effects of individual level, group level and within-group differences level measures on individual achievement are scarce. The current study addressed this by examining whether individual, group and within-group differences regarding engagement and prior…

Mathematics and technology serve the health sciences as demonstrated in this article, cowritten by one of our calculus students. Creating a lesson based on dosing an antibiotic allows teachers and students to see the immediate value of high school calculus and technology.

Research shows that teachers and educators struggle to act when conflict appears in the classroom. This article argues that (political) conflict should not be avoided or eradicated. Teachers should enable conflict and attend to their pupils in the process, in order to enable further understanding of each other and their differences, as part of…

This study investigated the effectiveness of inquiry-based learning (IBL) approach in ratio and proportion on the mathematics reasoning skill of seventh-grade students. The study was carried out in a seventh-grade mathematics course in a middle school located in the Central Anatolia region of Turkey during the 2016-2017 academic year. The IBL…

Collaborative problem-solving (CPS) engages students in solving ill-structured problems, creating group knowledge, and developing self-regulation and collaboration skills. Different scaffoldings, such as minimal-guided, task-oriented, and idea-oriented, can be used to facilitate students' CPS activities, but their effects have not been…

Educational Scaffolding was first mentioned in 1976 by Wood et al. Several examples for scaffolding in chemistry are also known from the literature. As written scaffolds, stepped supporting tools to support students while solving problems in organic chemistry were developed, applied, and evaluated. Although the students rated the tool as very…