Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

Differentiating instruction can be difficult, however, when higher performing students yearn to be stretched and lower performing students benefit from scaffolded support. One way to meet these students' learning needs and everyone in-between is to embrace the notion of novel exploration in support of critical school mathematics concepts. Novelty…

Two common interest-enhancement approaches in mathematics curriculum design are illustrations and personalization of problems to students' interests. The objective of these experiments is to test a variety of illustrations and personalization approaches. In the illustrations experiment, students (n = 265) were randomly assigned to lessons with…

The author discusses how to teach students to extend economic models using in-class scaffolding assignments, supported by discussions and workshops. Methods include discussions of a model's strengths and weaknesses; small group, in-class assignments that provide steps toward model extension; informal presentations of the work resulting from these…

Purpose: This paper aims to deal with the skills for sustainable development in engineering courses. The main objective is to identify which competences should be developed in these courses to contribute to the resolution of conflicts related to sustainability, as well as the means used by universities for their development.…

The purpose of this replication study was to provide replication evidence not currently available of the effects of a research-based mathematics program, schema-based instruction, on the mathematical problem-solving performance of 7th-grade students. The replication was implemented in 36 schools in 5 districts; 59 mathematics teachers and their…

Although generic skills have received widespread attention from both policymakers and educationalists, little is known regarding how students acquire these skills, or how they should best be taught. Hence, the aim of this study was to identify what kinds of pedagogical practices are behind the learning of eight particular generic skills. The data…

The Australian Science Teachers Association offers an innovative international professional development program for science teachers called the Science Teachers Exchange -- Japan. The program offers Australian and Japanese teachers an opportunity to travel to the corresponding country, allowing the teachers to grow in their knowledge of the…

This paper examines whether using "From Here to There!" (FH2T:E), a dynamic game-based mathematics learning technology relates to improved early algebraic understanding. We use student log files within FH2T to explore the possible benefits of student behaviors and gamification on learning gains. Using in app measures of student…

Children's literature can provide useful contexts for teaching mathematics. In this article, the authors discuss the use of the children's book "Measuring Penny" (Leedy 1997) to support Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) related to length measurement. The authors first describe three types of misconceptions…

Ensuring students correctly understand the notion of equality is a fundamental problem in teaching mathematics. Is it possible to teach arithmetic in such a way that students do not misinterpret the equal sign "=" as indicating the result of an arithmetic operation and, consequently, viewing the arithmetic operation symbols (+, -, or x)…

Organizations governing education in the health professions have recently called for changes in teaching to promote students' use of critical thinking (CT). Expectations for CT in courses to train educators should be aligned with the expectations of student use of CT. A growing number of certificate and master's-level programs are being developed…

This study aimed to synthesize theoretical and designing framework of Virtual Immersive Learning Environments (VILEs) based on digital storytelling to enhance deeper learning for undergraduate students. Documents analysis and survey research were employed in this study. The procedures were as follows: (1) to examine and analyze the principles,…

The goal of this paper is to present a succinct consolidation of the why, what and how of the 'Model' method as there is a lack of such documentation for researchers, practitioners and policy makers thus far. The 'Model' method is a tool for representing and visualising relationships when solving whole number arithmetic (WNA) word problems. The…

This randomized control treatment study investigated the role of generative paraphrasing interventions on word problem-solving (WPS) accuracy in English language learners (ELL) who were at risk for math difficulties (MD). One hundred and forty-two third-grade monolingual and English language learners were randomly assigned to either an untreated…