Reasoning is considered to be an important proficiency in national mathematics curricula both in Australia (ACARA, 2014) and Malaysia (MOE, 2013). However, the nature of reasoning that supports learning and problem solving in mathematics is an area that requires further study (Schoenfeld, 2013). In this study we explored the link between…

The objective of the present study is to describe how students discover rules underlying a certain phenomenon under question and the process in which they mathematically justify such discovery by way of utilizing tables and graphs in the use of the cell reference function of spreadsheets when a problem is not easily solved through simple symbol…

The two research projects described and discussed in the special issue provided much needed longitudinal empirical data to show the curricular influence on classroom instruction and student learning outcomes. The findings have helped to advance our understanding of whether the reform curricula can bring about positive changes in classroom…

Teaching mathematics associated with the repaying of loans has always been an awkward task--it seems superficially easy, but it contains pitfalls both for the learner and for the unwary teacher. This short article reviews some of the mathematics, and notes an interesting result.

With the notion of governmentality, this article considers how the equal sign (=) in the U.S. math curriculum organizes knowledge of equality and inscribes cultural rules for thinking, acting, and seeing in the world. Situating the discussion within contemporary math reforms aimed at teaching mathematics for all, I draw attention to how the…

This report summarizes the results of a scale-up project funded by the Institute of Education Sciences in 2006. "Scaling up TRIAD: Teaching Early Mathematics for Understanding with Trajectories and Technologies" was a project that took a preschool mathematics intervention to scale across three sites, following children from their…

Comparison is a powerful tool that has been shown to improve learning in a variety of domains. In both laboratory studies and small-scale classroom studies, having learners compare and contrast worked examples has been shown to reliably lead to gains in students' knowledge. Comparison is also integral to "best practices" in mathematics…

One-third of the current A-level mathematics curriculum is determined by choice, constructed out of "applied mathematics" modules in mechanics, statistics and decision mathematics. Although this choice arguably involves the most sizeable instance of choice in the current English school mathematics curriculum, and it has a significant…

This study introduces a new set of weighting procedures for revealing the mediation mechanism in multi-level settings. These methods are illustrated through an investigation of whether the impact of a system-wide policy change on student outcomes is mediated by policy-induced peer composition change. When the policy changed not only…

Why have an organisation like MERGA? This question will be addressed from past, present and future perspectives (1976, 2012, and 2025). One focus of the paper will be the need to improve mathematics curricula, and to improve the teaching and learning of mathematics, at all levels. I shall argue that we have not done enough to make sure that MERGA…

Competence in early mathematics is crucial for later school success. Although research indicates that early mathematics curricula improve children's mathematics skill, such curricula's impacts on oral language and early literacy skills are not known. This project is the first to investigate the effects of an intensive pre-kindergarten mathematics…

Equivalence is mostly associated with the strand of Number and Algebra and is fundamental in both of the substrands. Equivalence is considered a key and foundational concept of algebra, and whereas an assumption might be made that equivalence is a relatively "easy" concept; studies have shown that when asked to balance an equation such…

Spatial ability has been recognized as one of the most important factors affecting the mathematical performance of students. Previous studies on spatial learning have mainly focused on developing strategies to shorten the problem-solving time of learners for very specific learning tasks. Such an approach usually has limited effects on improving…

In considering mathematics problem solving as a model-eliciting activity (Lesh & Doerr, 2003; Lesh & Harel, 2003; Lesh & Zawojewski, 2008), it is important to know "what" students are modeling for the problems: situations or solutions. This study investigated Grade 3 students' mathematization process by examining how they modeled different…

Preservice Secondary Mathematics Teachers (PSMTs) were surveyed to identify if they could connect early-secondary mathematics content (Grades 7-9) in the Common Core State Standards for Mathematics (CCSSM) with mathematics content studied in content courses for certification in secondary teacher preparation programs. Respondents were asked to…