According to the author, the "Australian Curriculum: Mathematics (AC:M) requires primary school students to measure the attributes of angle, time, temperature, length, area, capacity and mass. This article outlines some misconceptions held by primary school students which appear to stem from them not understanding terminology concerning the…

Grade 8 students were given a task that had pairs of shapes that had been transformed (i.e., preimages and images). Students were to identify which of the three rigid transformations--reflections, rotations, or translations--were used to map the preimage to the image. Students were also asked to give a justification for their choice of…

This chapter is a case study examining the symbiotic relationship among an Arts and Sciences mathematics department, a school of education, and a large urban public school district, as a context for the development of pedagogical content knowledge in the curriculum. Specifically, Hunter College, CUNY, has a long-standing master's program in…

The Carnegie Learning Cognitive Tutor curricula are based on cognitive models, which include a representation of the learner's thinking, strategies, and misconceptions. The Cognitive Tutor curricula typically speed up learning and yield greater learning as compared to traditional math curricula (Morgan & Ritter, 2002; Sarkis, 2004; Koedinger,…

"Focus in Grade 1: Teaching with Curriculum Focal Points" describes and illustrates learning paths for the mathematical concepts and skills of each grade 1 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate…

This book describes and illustrates learning paths for the mathematical concepts and skills of each grade 8 Focal Point as presented in Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. It includes representational supports for teaching and learning that can facilitate understanding, stimulate productive discussions about…

Describes an episode involving conditional statements and the notion of logical equivalence that occurred in a 10th-grade college-preparatory geometry class. Illustrates some of the confusion that can arise in connection with this topic, for both students and teachers. (ASK)

Described are inconsistencies, definitions, and examples and their complex relationship which can be used to interpret students' reactions to the geometric tasks used to investigate inconsistencies in student thinking. Discusses the nature of definitions, the value of precise vocabulary, the use and limitations of prototypes, and the power of…

This is a record of the proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia (MERGA). The theme of the conference is "Mathematics: Essential research, essential practice." The theme draws attention to the importance of developing and maintaining links between research and practice and…