The purpose of this article is to better understand how proof is introduced into the study of quadrilaterals and triangles in high school. To do this, we designed a grid to analyse mathematics textbooks in Cameroon francophone subsystems (7th Grade and 8th Grade). The Anthropological Theory of Didactics and the paradigms in geometry served as a…

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth…

In the monograph The Math Teacher (following the Third International Scientific Colloquium Mathematics and Children in 2011), the term "teacher" designates a person who teaches mathematics, and the context of each article reveals whether this implies the teacher at a pre-school institution, a school or a university instructor. In…

To discover a generalization from a pattern of data, students need to know how to analyze the data. This is a description of how high school students can find a formula to predict the number of spherical fruits in a piling by using differences. (JP)

Details of pupil exploration as to the largest number of sides that a polygon could have on a geoboard are presented. The problem is not seen as open-ended, but many different avenues of pursuit stem from it. (MP)

The problem of finding the area of a regular polygon is presented as a good example of a mathematical discovery that leads to a significant generalization. The problem of finding the number of sides which will maximize the area under certain conditions leads to several interesting results. (LS)

Outlines a guided discovery activity for ascertaining the conditions which allow for the correct tracing of networks. (JP)

A sample problem shows some pitfalls in approximating square roots when working with calculators or computers. (MP)

An activity-based unit on congruence and similarity is described. The themes underlying the unit are the usefulness of analogy in determining mathematical principles, and the notion that the number of conditions imposed on figures affects the number of factors which must be specified to insure congruence or similarity. (SD)

Numerous mathematical examples are presented which illustrate and raise questions about students' tendencies to overgeneralize. (BB)

Activities used with seventh and eighth grade students in Western Australia are described. The instructor guides pupils towards experimental solutions and encourages discovery of solutions for similar and more general problems. Investigations include study and construction of polygons, polyhedra, and one and two-sided surfaces. Commercial kits are…

Geometric construction problems are recommended as sources of stimulating exercises for mathematics classes. (MP)

A discussion of the reasons for the new design of international standard typing paper (AY) with dimensions of 210 mm by 297 mm leads to a discussion of the ratio of the sides and geometric concepts involving similar rectangles. (MP)