This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3-5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modeled by multiplication have an element that represents the scalar and an element that…

Al-Kashi's 1427 "Key to Arithmetic" had important use over several hundred years in mathematics teaching in Medieval Islam throughout the time of the Ottoman Empire. Its pedagogical features have never been studied before. In this dissertation I have made a close pedagogical analysis of these features and discovered several teaching…

This study aims to examine the effect of instructional materials developed on the basis of 4 stage constructivist model on the success of 6th grade students in the subject of decimal fractions. For this purpose, a worksheet on decimal fractions, a conceptual change text and an anology map were developed. These instructional materials were…

This study examined opportunities provided for students to conceptualize linear relationships, as reflected in five United States mathematics textbooks. Texts represented a broad spectrum of types: commercial, so-called "back to basics", and NSF funded. Analysis of allocation, topic choice, presentation, context, and cognitive level was…

Much research on early measurement learning is small-scale and dependent on the items used. While such research is helpful for indicating the key aspects of learning length, it does not give teachers a clear indication of the expectations for student learning of them. This paper presents substantial data from a large project that used individual…

This study examined how preservice elementary teachers think about situations involving probability. Twenty-four preservice elementary teachers who had not yet studied probability as part of their preservice elementary mathematics coursework were interviewed using a task-based interview. The participants' responses showed a wide variety of…

In deciding whether to choose a real event from which to develop children's mathematical understanding, it is crucial to have a clear appreciation of what mathematics pupils need to learn. In this article, the author looks at the issue of "context"--the positives, and negatives for the learner. He describes a project in which the context…

The author states her belief that mathematics is a human construct based on axiomatic systems, and that these constructs are both personal and social. She argues that to succeed in mathematics, learners' personal constructs need to be aligned with formal globally agreed mathematical conventions. Put more simply, she informs her students that…

It is common to see, in the books on calculus, primitives of functions (some authors use the word "antiderivative" instead of primitive). However, the majority of authors pay scant attention to the domains over which the primitives are valid, which could lead to errors in the evaluation of definite integrals. In the teaching of calculus, in…

Calculators and computers make new modes of instruction possible; yet, at the same time they pose hardships for school districts and mathematics educators trying to incorporate technology with limited monetary resources. In the "Standards," a recommended classroom is one in which calculators, computers, courseware, and manipulative materials are…

Using modern technology to examine classical mathematics problems at the high school level can reduce difficult computations and encourage generalizations. When teachers combine historical context with access to technology, they challenge advanced students to think deeply, spark interest in students whose primary interest is not mathematics, and…

The semiotic approach to mathematics education introduces the notion of "semiotic system" as a tool to describe mathematical activity. The semiotic system is formed by the set of signs, the production rules of signs and the underlying meaning structures. In this paper, we present the notions of system of practices and configuration of objects and…

This study investigates how students understand and apply the area under the curve concept and the integral-area relation in solving introductory physics problems. We interviewed 20 students in the first semester and 15 students from the same cohort in the second semester of a calculus-based physics course sequence on several problems involving…

This study investigates Chinese and U.S. teachers' construction and use of pedagogical representations surrounding implementation of mathematical tasks. It does this by analyzing video-taped lessons from the Learner's Perspective Study, involving 15 Chinese and 10 U.S. consecutive lessons on the topic of linear equations/linear relations. We…

Trigonometry is an integral part of the draft for the Senior Secondary Australian National Curriculum for Mathematics, as it is a topic in Unit 2 of both Specialist Mathematics and Mathematics Methods, and a reviewing topic in Unit 1, Topic 3: Measurement and Geometry of General Mathematics. However, learning trigonometric ideas is difficult for…