Problems involving rotating systems analysed from an inertial frame, without invoking fictitious forces, is something that freshman students find difficult to understand in an introductory mechanics course. In this article we try to see what could be the factors that lead to this difficulty and propose a set of arguments that could be used to…

Productive failure has shown positive effects on conceptual and transfer measures, but no clear effects on procedural measures. It is therefore an open question whether, and to what extent, productive failure methods may be used to enhance the learning of procedural skills. A typical productive failure study focuses on a single, complex concept;…

This study involved an intervention designed to examine whether employability prospects for STEM students studying mathematics could be improved. It incorporated use of non-routine problem solving in second-year mathematics courses at two New Zealand universities. From a theoretical standpoint, we conceptualised a novel construct called…

This study aims to determine the effect of an instruction dealing with non-routine problem solving on fifth graders' strategy flexibility and success in problem-solving. For this aim, a quasi-experimental pre-test-post-test design without a control group was designed. The sampling method of the research is convenience sampling. There were 65 fifth…

Drawing on research around the utility of worked examples, we examine how 29 first- and 27 third-grade students made sense of integer subtraction worked examples and used those examples to solve similar problems. Students first chose which of three worked examples correctly represented an integer subtraction problem and used the example to solve a…

In the context of a multiplicative problem, our study investigated young children's ability to visualise and draw equal groups. This paper reports the results obtained from 18 Australian children in their first year of school (age 5-6 years). The task "12 Little Ducks," taught by their classroom teacher, provoked children to visualise…

Statistics is taught in mathematics courses in all school levels. We suggest that using rich tasks in statistics can develop statistical reasoning and create both intra and interdisciplinary links in students. In this paper, we present three case studies where middle school mathematics teachers used different tasks in lessons on pie charts. We…

The present study summarized three studies of schema-based instruction (SBI), a research-based Tier 1 mathematics program implemented in general education classrooms. We evaluated the efficacy of SBI in improving the mathematics achievement of seventh-grade students, including students with or at risk for mathematics disabilities (MD). The three…

Problem solving is an important yet neglected mathematical skill for students with autism spectrum disorder and intellectual disability (ASD/ID). In addition, the terminology and vocabulary used in mathematical tasks may be unfamiliar to students with ASD/ID. The current study evaluated the effects of modified schema-based instruction (SBI) on the…

Statistics standards found in the Common Core (CCSSI 2010) and other state standards require considerable instructional time and focus for students to develop the depth and breadth of understanding necessary. In this article, the authors offer an approach to teaching a statistics unit that combines student choice with authentic and sustained…

The National Council of Teachers of Mathematics (NCTM) has called on teachers to create supportive and equitable classroom environments, to steadfastly advocate that all students can learn mathematics, to hold high expectations for all students and to adopt practices that offer students the opportunity to excel (NCTM 2014). The overarching aim of…

Word problems require students to read a language-based problem, identify necessary information to answer a prompt, and perform calculation(s) to develop a problem solution. Solving word problems proves particularly challenging for students with mathematics difficulties because skill in reading, interpretation of language, and mathematics is…

Collaborative gestures in the mathematics classroom occur when multiple learners coordinate their bodies in concert to accomplish mathematical goals. Collaborative gestures show how cognition becomes distributed across a system of dynamic agents, allowing for members of groups of students to act and gesture as one. We explore ways high school…

In this paper, we present a design experiment in a "Teaching Mathematics" course for prospective elementary teachers where we sought to develop a "measurement approach" to fractions. We focus on the conceptualization of the mathematical content of the approach. We attribute our progress in the conceptualization to our efforts…

The sheet resistance of a conducting material of uniform thickness is analogous to the resistivity of a solid material and provides a measure of electrical resistance. In 1958, L. J. van der Pauw found an effective method for computing sheet resistance that requires taking two electrical measurements from four points on the edge of a simply…