Many rules taught in mathematics classrooms "expire" when students develop knowledge that is more sophisticated, such as using new number systems. For example, in elementary grades, students are sometimes taught that "addition makes bigger" or "subtraction makes smaller" when learning to compute with whole numbers,…

A common critique of teacher education centres on the gap between coursework and schools, with ample evidence that novice teachers seldom bring ambitious forms of instruction into classroom placements. We describe a 6-year design experiment conducted in a university teacher education program secondary mathematics methods course focused squarely on…

Semiotic representations have been an important topic of study in mathematics education. Previous research implicitly placed more importance on the development of institutional representations of mathematical concepts in students rather than other types of representations. In the context of an extensive research project, in progress since 2005,…

Students with Autism Spectrum Disorders (ASD) have unique educational needs. The concrete representational abstract (CRA) instructional sequence has been shown effective in teaching students with mathematical difficulties. The purpose of this study was to examine the effects of the CRA sequence in teaching students with ASD. A multiple baseline…

For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

The article focuses on mathematics for toddlers in preschool, with the aim of challenging a strong learning discourse that mainly focuses on cognitive learning. By devoting more attention to other perspectives on learning, the hope is to better promote children's early mathematical development. Sweden is one of few countries to have a curriculum…

This study reports teachers' insights and challenges after one year of adopting a curricular material designed to move students through carefully engineered, small steps and encourage learners through success and accessible challenges. The analysis of interviews showed that teachers 'followed' the material in different ways, not necessary in-line…

To succeed in college, career, and life, students need to become financially literate. But understanding the basics of a long-term investment or a short-term loan is not enough without the math skills to make financially sound choices. In the already full curriculum of middle schools today, how can teachers find room to include financial literacy?…

Mathematical engagement is a complex process of interaction between the person and the world. This interaction is strongly influenced by the concepts and structure of the mathematical field, by the practical and symbolic tools of mathematics and by the focus of investigation in the world. This paper reports on research that involves a detailed…

This paper concerns communities of learners and teachers that are formed, develop and interact in university mathematics environments through the theoretical lens of "Communities of Practice." From this perspective, learning is described as a process of participation and reification in a community in which individuals belong and form…

Education professionals, regardless of their specialist area, are broadly aware of the importance of numeracy. Internationally, definitions of numeracy (known elsewhere as mathematical literacy or quantitative reasoning), describe "an individual's capacity to formulate, employ and interpret mathematics in a variety of contexts... reasoning…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) define what children should understand and be able to do in K-grade 12. This document also includes a description of key mathematical processes and proficiencies, the Standards for Mathematical Practice (SMPs), which provide an important overview for the kind of robust thinking…

A story problem about borrowing money, presented in this article, may be represented with positive or negative numbers and thought about in different ways. The authors describe ideas related to integers (both positive and negative) and how students used them in relation to a story problem, and how they related these ideas to equations.

Concern has been expressed that many commencing undergraduate mathematics students have mastered skills without conceptual understanding. A pilot study carried out at a leading Australian university indicates that a significant number of students, with high tertiary entrance ranks, have very limited understanding of the concept of function,…

The first idea that must be understood by the students to learn the concept of concept of conservation of area is recomposing shape. In recomposing shape, the students will see the fact that the shape can be transformed into a different form without adding or losing the part of the shape. So the students could conclude that the area of the shape…