This paper reports ongoing research investigating how students' experiences with the notion of tangent line in different lecture courses at a technical school are being integrated to the related mathematical concept. Focusing on a technical course case study, we examine how aspects of the notion of tangent line are related to features of the…

The definition-construction process is central to mathematics. The aim of this paper is to propose a few Situations of Definition-Construction (called SDC) and to study them. Our main objectives are to describe the definition-construction process and to design SDC for classroom. A SDC on "discrete straight line" and its mathematical and…

Recent publications continue to show that significant numbers of students in junior grades, while competent in basic ruler skills, seem not to have acquired important concepts about how rulers work and units of length. This paper reports on the results of a set of tasks completed by students from Grades 5 and 6. The results show that many students…

Tessellation is included in many mathematics curricula as one way of developing spatial ideas. If students do not understand tessellation in the intended ways, however, the development of other spatial ideas, such as properties of shapes and symmetry, may be compromised. Van Hiele levels were used as a basis for analysing the descriptions of eight…

"Function", as it is understood today, formulates one of the most important concepts of mathematics. Nevertheless, many students do not sufficiently understand the abstract but comprehensive meaning of function and problems concerning its didactical metaphor are often confronted. The present study examines the interpretation of the…

The paper provides a college mathematics student's concept maps, definitions, and essays to support the thesis that language-based prior knowledge can influence students' cognitive processes of mathematical concepts. A group of intermediate algebra students who displayed terms mainly from the spoken language on the first and the second concept…

This book introduces students to the types of problems and processes used throughout the "Reshaping Mathematics for Understanding" series. The problems in this unit deepen students' understanding of mathematics by encouraging them to clarify concepts and challenge their own assumptions. Additionally, by providing opportunities to give and follow…

Noting that current research on childrens mathematical development does not adequately detail how toddlers represent small numbers and the role that number words play in the development of number understanding, this study used a combination of methods to examine mathematical development in one toddler. Underlying the study was an Integrated Model…

In this paper the notion of "procept" (in the sense of Gray & Tall, 1994) is extended to advanced mathematics by considering mathematical proof as "formal procept". The statement of a theorem as a symbol may theoretically evoke the proof deduction as a process that may contain sequential procedures and require the synthesis…

In this paper part of the results obtained by a research project called "Primary Teachers' Thinking about the Concept of Volume and its Teaching", performed from 1997 to 2001, are reported. This paper focuses in one of the two main objectives of the aforementioned research: To describe the mental object volume of the participant…

The impact of prior learning on new learning is highlighted by the case of Dean, a Year 8 student who developed his own method to find the sum of the interior angles of a polygon without knowing why his method worked. Enriched transcripts and visual displays of the cognitive, social (Dreyfus, Hershkowitz, & Schwarz, 2001) and affective elements…

Saxon's primary mathematics series is a "hands-on," success-oriented program which emphasizes manipulatives and mental math. The series addresses the multisensory approach to teaching. Its use enables all children to develop a solid foundation in the language and basic concepts of mathematics. Concepts are presented in carefully…

This paper illustrates how to teach parallel perspective using Cabri software. Examples include how to move/present cubes, how to use symmetry to draw a star from triangles, how to modify tessellations, and how to present circles by Cabri software. (Author/KHR)

Discusses the importance of experiences with classification and seriation in aiding children to understand the concept of number. (GB)

The derivation of a method to drive the general term of a sequence is presented. The difference sequences and binomial coefficents are used in the derivation. An application of this method is made to solve Polya's problems concerned with dividing space in regions by a given number of planes. (JP)