In this paper, we build on a previously developed notion of 'learning as Making' to examine mathematics thinking and learning in a highly transformative and technological Making environment: one that involves a handheld 3D printing technology which enables 3D models to be created instantly via one's moving hand. In particular, we present two…

Paper folding, or origami in Japanese, is a traditional craft that has been enjoyed by both children and adults for hundreds of years. Mathematicians have long studied the mathematics of paper folding. They use square papers to construct mathematical shapes (for example, folding an equilateral triangle from a square paper or trisecting an angle),…

This article reports a study of educators differentiating aspects of mathematical knowledge for teaching in preschool as part of a further-education programme. Eight Swedish preschool educators participated in focus group discussions about documentations from their own practice during a school year, to enhance their awareness of their mathematics…

Lesson study is a professional development activity that increases teachers' attention to student thinking. However, coordinating teachers' live observations of a lesson can be challenging. Using the framework of "distributed cognition," we investigate whether technology supports teachers' examination of student thinking and aids the…

The increasing availability of new technologies in schools provides new possibilities for the integration of technology in mathematics education. However, research has shown that there is a need for new kinds of task that utilize the affordances provided by new technology. Numerous studies have demonstrated that dynamic geometry environments…

This pilot case study of two teachers and their learner groups from Adult and Community settings, investigates how numeracy teachers, working with adult learners in discrete numeracy classes, motivate and enable learners to build on their informal skills and apply new learning to their own real-life contexts. Teachers used a range of abstract and…

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…

This article presents an examination of the language demands of cognitively demanding tasks and proposes an initial framework for the language demands of higher-order mathematics thinking practices. We articulate four categories for this framework: "language of generalisation," "language of comparison," "language of proportional reasoning," and…

This article gives a general overview of an alternative instructional sequence that can be used to teach integer concepts and operations. The sequence follows three heuristics from Realistic Mathematics Education (RME) that encourage curricula to be reinforced with real-world applications (financial net worth): move students gradually, yet…

This book provides a landscape of learning that helps teachers recognize, support, and celebrate their students' capacity to structure their worlds algebraically. It identifies the models, contexts, and landmarks that facilitate algebraic thinking in young students and provides insightful and practical methods for teachers, math supervisors, and…

In this article, the author believes that a visual image of the number system is helpful to everyone, especially children, in understanding what is, after all, an abstract idea. The simplest model is the number line, a row of equally spaced numbers, starting at zero. This illustrates the continuous progression of the natural numbers, moving to the…

In the project described in this article, students work together to model real-life phenomena. They also think about the modeling process as they develop rubrics for evaluating their peers' work.

This paper describes research into the framework of Computer Analysis Relationship (CAR) and its methodology together with software such as Scientific Notebook in a teaching and learning problem-solving environment to support student investigation as well as to enhance student logical thinking. CAR aims to motivate students how to subdivide a…

Illustrates how upper elementary grade students can develop an understanding of the invert-and-multiply algorithm. (CCM)

Several researchers have noted how children's whole number schemes can interfere with their efforts to learn fractions. An Australian study found that children who were successful with the solution of rational number tasks exhibited greater whole number knowledge and more flexible solution strategies. Behr and Post (1988) indicated that children…