Through post-observation and general discussions our preservice teachers thought they were asking good questions by asking "why?". While these questions are important, "why?" questions are not always effective, especially when a student responds with "I don't know". Such questioning techniques must be explicitly…

This paper proposes a novel application of knowledge space theory for identifying discrepancies between the knowledge structure that experts expect students to have and the real knowledge structure that students demonstrate on tests. The proposed approach combines two methods of constructing knowledge spaces. The expected knowledge space is…

In this paper we report on a survey designed to test whether or not students differentiated between two different types of problems involving combinations--problems in which combinations are used to count unordered sets of distinct objects (a natural, common way to use combinations), and problems in which combinations are used to count ordered…

Mistakes can be a source of frustration for teachers and students in mathematics classrooms because they reveal potential misunderstandings or a lack of learning. However, increasing evidence shows that making mistakes creates productive pathways for learning new ideas and building new concepts (Boaler 2016; Borasi 1996). Learning through…

Few studies have applied Skinner's (1953) conceptualization of problem solving to teach socially significant behaviors to individuals with developmental disabilities. The current study used a multiple probe design across behavior (sets) to evaluate the effects of problem-solving strategy training (PSST) on the target behavior of explaining how to…

Making as a design-centered learning activity has recently received significant attention in education. We use literacies--how individuals use representations to learn--to explore the STEM literacy practices of experienced designers and makers. Describing makers' representational practices in STEM contexts can inform the design of literacy…

The European Commission Science Hub has been promoting Computational Thinking (CT) as an important 21st century skill or competence. However, „despite the high interest in developing computational thinking among schoolchildren and the large public and private investment in CT initiatives, there are a number of issues and challenges for the…

It is important for students to connect with real life in mathematics courses. The aim of this study is to investigate the activities which are written by prospective primary school teachers in the context of Realistic Mathematics Education. This research is a case study of which data were collected by qualitative methods. The participants of the…

Purpose: This paper aimed to present the design of a teaching module on mathematical problem solving for the upper primary mathematics. Method: The module used Pólya's and Schoenfeld's problem solving models as the theoretical framework. The researchers introduced problem-solving processes through specialized mathematics "practical"…

Research has shown that once a potential solution to a problem has settled into one's mind, it can be difficult to break from the original idea and move in a different direction (Cardoso & BadkeSchaub, 2009; Jansson & Smith, 1991). When designers are given examples (whether as models, photographs, sketches, or drawings), they often fixate…

The goal of this paper is to illustrate different ways that cardsorting activities (or "card stacks") can be implemented in the introductory physics classroom, along with various tips and resources for getting started. My first attempt at developing a card stack came about from simply wanting to try out a fun way to change student…

The 1969 version of "The Italian Job" is used as context for teaching turning forces and introducing or enhancing the understanding of equilibrium and Newton's Third Law of Motion. A Harrington Legionnaire coach is used as the getaway vehicle for a gold heist and the film ends on a genuine cliffhanger, with the rear half of the coach…

The Next Generation Science Standards states that "science begins with a question." (NGSS Lead States [2013] "Next generation science standards: For states, by states". Washington, DC: National Academies Press). Yet scientific inquiry among students and scientists alike often begins without a clear question. In this article, we…

The aim of this research was examining the mathematical thinking of athletes who are actively engaged in sports in a sports club in terms of various variables. The research was designed as a screening model. The sample of the study consisted of 229 licensed athletes in various clubs. The "Mathematical Thinking Scale" developed by Ersoy…

Contributing to a growing body of research on undergraduate students' quantitative reasoning, the study reported in this article used task-based interviews to investigate business calculus students' quantitative reasoning when solving two optimization tasks situated in the context of revenue and profit maximization. Analysis of verbal responses…