Use of the computer program "Integrate Using Definition" can help students develop understanding of integral. Several applications of the program are discussed. (MNS)

Criticizes current methods of mathematics instruction and math textbooks for lacking review, repetition, and logical sequencing. Advocates a combination of old and new math that will ensure learning of fundamentals as well as understanding of underlying concepts. (SK)

Suggest several math activities using the simple technique of tapping a sugar maple tree for sap. Information and activities presented are useful in tapping one or two trees on school property, helping students who tap trees at home, or leading a field trip to a nearby maple sugaring site. (ERB)

Explores meanings of "generic" and "generality" as they are found both in everyday language and as they confront mathematics students. Considers everyday occurrences of the idea of generic (leading to the notion of a generic example of a class) and some ramifications in elementary algebra. (JN)

Various approaches to curriculum design and issues related to constructing course syllabi are discussed. (SD)

This article shows that the recognition of the dualities in equality (operator-equivalent) of the minus sign (unary-binary) and the zero (nullity-totality) during the transitional process from arithmetic to algebra by 12-13 year-old students constitutes a possible way to achieve the extension of the natural number domain to the integers. (Contains…

School students' intuitive concepts of infinity are gained from personal experiences and in many cases the tacit models built up by them are inconsistent. The paper describes and analyses a series of tasks which were developed to enable the researchers to look into the mental processes used by students when they are thinking about infinity and to…

In this paper we study how a student begins to acquire the concept of the derivative, what kind of representations he acquires and how he connects these representations. A teaching period, in which different perceptual and symbolic representation were emphasized, was carried out and task based interviews conducted to five students. The students…

The aim of this research is to advance understanding of how mathematical knowledge functions in the proving in geometry. We focus on the rules whose mobilization is due rather to the mathematical knowledge at stake than to the proof. We observed students who are asked to solve construction problem and proving problem. The problems require to…

This paper describes aspects of 13 year-olds activity in mathematics as emerged during the implementation of proportional geometric tasks in the classroom. Pupils were working in pairs using a piece of software specially designed for multiple representation (symbolic and graphical) of the variation in parametric procedures with dynamic…

This paper is based on the preparatory study of a doctoral study in which we learned to consider defining in the realm of organizing. In particular, having engaged students in a situation based on "equivalence relations" (from an expert point of view), we report two different ways of organizing the given situation. One of them results in a "new"…

This is a step-by-step guidebook that is designed to help students on the quantitative section of the SAT. This guidebook produces an understanding of key mathematical concepts as the various topics are covered by the text, and, unlike other SAT guides, lists skills and capabilities, that if mastered will result in well-prepared students. More…

This study investigates student understanding of the part-whole concept in mathematics at an independent two-year post-secondary institution in New Mexico. The mathematics portion of the Tests of Adult Basic Education (TABE) Summary Form was used as the evaluative instrument. Evidence for a lack of part-whole concept understanding as a hidden…

Based on an individual interest theory as a sensitising theory, empirical data are used to gain social interest concepts, as there are situated collective interest and interest-dense situation. These concepts serve as a basis for a social extension of a psychological interest theory. Its construction combines social interactions, the dynamic of…

In this study, we explore six students' conceptions of Z[subscript n] in an effort to understand students' conceptions of quotient groups in general. We discovered that there were three different ways our students thought about Z[subscript n], namely as infinite sets, element-set combinations, and representative elements. We explore how…