South Africa has been battling with the poor performance of learners in Mathematics for a long time, with the Eastern Cape province being the worst-performing province. The Department of Education and other educational stakeholders have embarked on a journey of searching for solutions. Some of these include the use of Information communication…

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…

Background: The process of problem solving is difficult for students; thus, mathematics educators have made multiple attempts to seek ways of making this process more accessible to learners. The purpose of this study was to examine the effect size statistic of utilizing exploratory computerized environments (ECEs) to support the process of word…

This article presents an instructional approach to constructing discovery-oriented activities. The cornerstone of the approach is a systematically asked question "If a mathematical statement under consideration is plausible, but wrong anyway, how can one fix it?" or, in brief, "If not, what yes?" The approach is illustrated with examples from…

In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed…

A situation is presented that is intended to lead to open-ended mathematical discussions that allow students to conjecture, discover, and prove mathematical statements. (MP)

Discussed are generalizations and problem solving, unsound uses of generalizations, generalization as data, and student discovery of generalizations. (CT)

The idea of "complete permutations" of n distinct objects is explored in order to investigate an application of the concept that arises in Rex Stout's mystery novel, Too Many Cooks. (MN)

An exploratory problem is presented which involves the identification of all the ways a unit fraction with prime denominator can be written as a sum of two unit fractions. (MN)

A problem concerning the generation of an array of numbers is posed. The author examines the use of this problem in several secondary-school and college classes. (SD)

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)

A discussion on the general equation of a line shows how students can be lead to discover mathematical properties, find how one discovery leads to another, see how different branches of mathematics can lead to a solution, and be provided with a starting point for studying special mathematical topics. (MP)