We explored transformations that teachers made to modify geometry proof problems into investigation problems and analyzed how these transformations differ in teachers who use a dynamic geometry environment (DGE) in their classes and those who do not. We devised a framework for the analysis of problem transformations and types of teacher-generated…

Innovation is central to modern industry. It can and should be taught in schools. Not only does providing students a background in innovation benefit them later in life and industry, but it also promotes and further develops their critical thinking and collaboration skills. Despite the need for innovation, many have struggled with how to teach it.…

In this article, the author applies Makiguchi Tsunesaburo's (1871-1944) perspectives to language policy and planning (LPP). One theoretical question in LPP theory is why individuals opt to use particular languages and varieties of languages in certain contexts. The author contends that Makiguchi's theory of value can be used to systematically…

The importance of students' problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students' mathematical content knowledge could be highly…

Although official curriculum documents make cursory mention of the need for problem posing in school mathematics, problem posing rarely becomes part of the implemented or assessed curriculum. This paper provides examples of how problem posing can be made an integral part of mathematics teacher education programs. It is argued that such programs…

The goal of this research was to investigate the extent to which young children use the past reliability of another person's statements to make inferences about the accuracy of that person's claims about a hidden toy. When children interacted with a previously reliable speaker, both 30- and 36-month-olds searched in the new location of the toy, in…

Classification problems ("find the odd-one-out") are frequently used as tests of inductive reasoning to evaluate human or animal intelligence. This paper introduces a systematic method for building the set of all possible classification problems, followed by a simple algorithm for solving the problems of the R-ASCM, a psychometric test derived…

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…