In teaching proportion, the teachers usually give the students a formal formula, such as cross-multiplication, without providing them the meaning of proportionality. Thus, the students just apply it in order to solve proportional problems. However, it does not connote that they understand what proportionality means. In this paper, the authors…

The data for this study were gathered from an assignment consisting of 10 number sense related mathematics problems completed in an algebra course at developmental level. The results of the study suggest that a majority of developmental mathematics students use routine algorithmic procedures rather than mathematical reasoning to solve problems.…

The simulation of human mind often helps in the understanding of abstract concept by representing it in a realistic model and simplistic way so that a learner develops an understanding of the key concepts. Bian (1873) and James (1890) in their work suggested that thoughts and body activity result from interactions among neurons within the brain.…

This article describes an exciting exploration-based activity in which students develop an alternative definition of factor that can help them solve problems like the one presented above. Students work in groups to collect data, analyze the data to make conjectures, and then spend a significant amount of time debating and justifying their…

An important aspect of PBL problems is the affordances that they hold for engaging students in discussion of important content knowledge. In this paper, I argue that one can analyze a problem in terms of a deep problem space and a broader learning space to identify the conceptual ideas for potential engagement. The problem space refers to the…

A plethora of laboratory studies have shown that including the study of worked examples during problem-solving practice improves learning (Sweller, 1999; Sweller & Cooper, 1985). While most worked-example research focuses on the use of correct examples, recent work suggests that asking children to explain a combination of correct and incorrect…

This study expands contemporary theorising about students' conceptions of equality. A nationally representative sample of New Zealand students' were asked to provide a spoken numerical response and an explanation as they solved an arithmetic additive missing number problem. Students' responses were conceptualised as acts of communication and…

The ubiquitous practice of providing worked solutions to exercises in mathematics education has been under-researched. Little is known about what elements of a worked solution are valued by students. This exploratory study sought in-depth feedback from six undergraduate students who experienced a range of worked solutions designed to encourage…

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…

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…

Manipulatives are considered a best practice for educating students with disabilities, but little research exists which examines virtual manipulatives as tool for supporting students in mathematics. This project investigated the use of a virtual manipulative through the National Library of Virtual Manipulatives--polynominoes (i.e., tiles)--as a…

We can now get purposefully directed in the way we assess our learners in light of the emergence of evidence from the field of neuroscience. Why higher-order learning or abstract concepts need to be the focus in assessment is elaborated using the knowledge of semantic and episodic memories. With most of our learning identified to be implicit, why…

The "Everyday Mathematics®" curriculum aims to provide students in prekindergarten through grade 6 with multiple opportunities to learn math concepts and practice skills. Since the release of the WWC's 2010 Everyday Mathematics report, the curriculum continues to be widely used and evaluated. This updated review includes 30 studies that…

Undergraduate science, technology, engineering, and mathematics (STEM) curriculum emphasize project-based learning (PBL) with peer assessment/on-line peer assessment (PA/OPA). Many studies have stressed that students did not improve over two rounds in PBL with OPA studies and PBL with PA have to adopt team mutual cooperation to reap effective…

Flipped instructional approaches are innovative instructional practices that focus on students reviewing the lecture materials outside of class and working on homework problems during class time. A growing body of research highlights the effectiveness of flipped instructional approaches in improving student performance in statistics courses.…