The article describes the solution of a geometric problem and how this problem was formed. During the investigation process, I discovered that the inscribed parabola in a triangle, known as the parabola of Artzt, a mathematical subject developed almost 120 years ago, was the decisive idea which directed me towards the solution. Moreover, in the…

Analysis of integer structure and right-end-digits can illustrate why 3 and 5 are features of primitive Pythagorean triples. The results also utilize the triangular and pentagonal numbers. (Contains 5 tables.)

Can false memories have a positive consequence on human cognition? In two experiments, we investigated whether false memories could prime insight problem-solving tasks. Children and adults were asked to solve compound remote associate task (CRAT) problems, half of which had been primed by the presentation of Deese/Roediger-McDermott (DRM) lists…

Background: Internationally, there is a growing concern for developing STEM education to prepare students for a scientifically and technologically advanced society. Despite educational bodies lobbying for an increased focus on STEM, there is limited research on how engineering might be incorporated especially in the elementary school curriculum. A…

In this study we investigated how two different approaches to drawing free body diagrams influence the development of students' understanding of Newton's laws, including their ability to identify real forces. For this purpose we developed a 12-item two-tier multiple choice survey and conducted a quasiexperiment. This experiment included two groups…

Developing fluency in arithmetic facts is instrumental to mathematics learning. This study compares the effects of two practice conditions on children's fluency in simple multiplication facts. Third and fourth graders in the Netherlands (N = 282) practised in either a conventional "recall" condition where they produced answers to…

This paper describes a pedagogical framework that teachers can use to support students who are engaged in solving open-ended problems, by explaining how two Japanese expert teachers successfully apply open-ended problems in their mathematics class. The Open-Ended Approach (OPA) framework consists of two main sections: Understanding Mathematical…

Serious games are seen to hold potential to facilitate workplace learning in a more dynamic and flexible way. This article describes an empirical study into the feasibility of an online collaboration game that facilitates teachers-in-training to deal with classroom management dilemmas. A script to support these students in carrying out such…

This study measured the information gathering behaviors of high school students who had taken engineering design courses as they solved a design problem. The authors investigated what types of information students accessed, its quality, when it was accessed during the students' process, and if it impacted their thinking during the activity.…

The Physics Metacognition Inventory was developed to measure physics students' metacognition for problem solving. In one of our earlier studies, an exploratory factor analysis provided evidence of preliminary construct validity, revealing six components of students' metacognition when solving physics problems including knowledge of cognition,…

Management of "wicked problems", messy real-world problems that defy resolution, requires thinkers who can transcend disciplinary boundaries, work collaboratively, and handle complexity and obstacles. This paper explores how educators can train undergraduates in these skills through applied community-based research, using the example of…

This journal article discusses Advanced Mathematical Thinking (AMT) and how to enhance it. AMT is ability in representing, abstracting, creative thinking, and mathematical proving. The importance of AMT ability development in accord with government expectation who realize about the importance of mathematical competency mastery for student's life.…

Linear functions are an important part of the middle school mathematics curriculum. Students in the middle grades gain fluency by working with linear functions in a variety of representations (NCTM 2001). Presented in this article is an activity that was used with five eighth-grade classes at three different schools. The activity contains 15 cards…

The purpose of this study was to replicate similar instructional techniques of Jimenez, Browder, and Courtade (2008) using a single-subject multiple-probe across participants design to investigate the effects of task analytic instruction coupled with semi-concrete representations to teach linear algebraic equations to middle school students with…

This study solicits views about the goals of science education from a range of stakeholders within the science education community and society. It also compares students' needs, expressed through stakeholder expectations, with the current learning situation of gymnasium graduates. The study uses a Delphi method to solicit views with 111…