Learning mathematical thinking and reasoning is a main goal in mathematical education. Instructional tasks have an important role in fostering this learning. We introduce a learning sequence to approach the topic of integrals in secondary education to support students mathematical reasoning while participating in collaborative dialogue about the…

Inequalities are considered among the most useful tools of investigation in pure and applied mathematics; yet their didactical aspects have not received much attention in mathematics education research until recently. An important aspect of teaching problem solving at the secondary level deals with the notion of equivalence of algebraic…

Describes how the 16 permanent lists used by a first grade reading teacher (and mother of 6) to manage the household represents the whole range of documents covered in the 3 major types of documents: matrix documents, graphic documents, and locative documents. Suggests class activities to clarify students' understanding of the information in…

Teaches data interpretation using the example of world running records for men and women. Explains different ways of plotting data. (YDS)

Topics covered are: a game to provide drill with linear equations; the relationship between area and perimeter in a triangle; a new form for factoring polynomials; and a technique for graphing inverse functions. (MP)

A graphical representation is used to construct a line one centimetre in length. (MP)

An alternative approach is described for presenting the idea of the derivative through the use of chords of a graph. (MP)

This paper describes "The Migration Method," a new technique for graphing a quadratic function (one of the major foundations of undergraduate mathematics) and finding its zeroes. The method promotes a higher degree of conceptualization, reinforces the concept of symmetry, encourages mental visualization, and strengthens the ability to…

This discussion of ways to use spirolaterals in the classroom includes making conjectures, hypotheses testing, and proofs, as well as a number of examples. (MP)

Presents an approach that combines the discovery method with graphing skills and allows students to uncover scientific laws on their own. Attempts to make the discovery method more quantitative while still teaching students how to think scientifically. (JRH)

Emphasizes the commonalities among classes of polynomial functions. Provides exploratory activities for students as well as a teacher's guide. (KHR)

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

Explores strategies in the situation of a runner trying to evade a tackler on a football field. Enables the student to test intuitive strategies in a familiar situation using simple graphical and numerical methods or direct experimentation. (JRH)

Described is how the crumpling of paper balls exhibits the concept of a topological dimension similar to fractals. The mass of the crumpled paper ball is found to be proportional to its diameter raised to a nonintegral power. (KR)

An exercise which relates particle scattering and the calculation of cross-sections to answer the following question--"Do you get wetter by walking or running through the rain?"--is described. The calculations used to answer the question are provided. (KR)