Digital cameras are now commonplace in many classrooms and in the lives of many children in early childhood centres and primary schools. They are regularly used by adults and teachers for "saving special moments and documenting experiences." The use of previously expensive photographic and recording equipment has often remained in the…

This article describes a particular activity, the Motorized Toy unit, which supports science, technology, engineering, and mathematics (STEM) goals and teaches students the basic concept of ratio. The unit addresses both mathematics and science standards and is part of a team-teaching activity. The unit comes from a curriculum titled A World In…

When solving problems involving proportions, students may intuitively draw on strategies that connect to their understanding of fractions, decimals, and percents. These two statements--"Instruction in solving proportions should include methods that have a strong intuitive basis" and "Teachers should begin instruction with more intuitive…

Teachers often find it difficult to integrate writing and mathematics while honoring the integrity of both disciplines. In this article, the authors present two levels of integration that teachers may use as a starting point. The first level, writing without revision, can be worked into mathematics instruction quickly and readily. The second…

Tasks that ask students to label rational number points on a number line are common not only in curricula in the upper elementary school grades but also on state assessments. Such tasks target foundational rational number concepts: A fraction (or a decimal) is more than a shaded part of an area, a part of a pizza, or a representation using…

Computer graphics and animation experts have been using the Catmull-Rom smooth curve interpolation equations since 1974, but the vector and matrix equations can be derived and simplified using basic algebra, resulting in a simple set of linear equations with constant coefficients. A variety of uses of Catmull-Rom interpolation are demonstrated,…

The formulae for the convergents of continued fractions are always given recursively rather than in explicit form. This article derives explicit formulae for the convergents of the continued fraction expansions for square roots.

The study of trigonometry suffers from a basic dichotomy that presents a serious obstacle to many students. On the one hand, there is triangle trigonometry, in which angles are commonly measured in degrees and trigonometric functions are defined as ratios of sides of a right-angled triangle. On the other hand, there is circle trigonometry, in…

This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…

How are we to understand the power of certain literary metaphors? The author argues that the apprehension of good metaphors is importantly similar to the apprehension of fruitful mathematical analogies: both involve a structural realignment of vision. The author then explores consequences of this claim, drawing conceptually significant parallels…

Statistical adjustments to accommodate multiple comparisons are routinely covered in introductory statistical courses. The fundamental rationale for such adjustments, however, may not be readily understood. This article presents a simple illustration to help remedy this.

Asterisks should not be used to indicate if the result of a hypothesis test is significant.

"Proofs and refutations: the logic of mathematical discovery" by Imre Lakatos was published posthumously in 1976. This is a fascinating, if somewhat hard to access, book which calls into question many of the assumptions that people make about proof--one may start reading with a clear sense of what mathematical proof is, but almost certainly will…

A remarkable feature of the set of papers in this issue is the consistent pattern of tending to deal with non-linear situations as if they are linear that is shown by students widely differing in age and educational systems, and studying various topics within mathematics. Methodological issues about the difficulty of interpretation of student…

In recent years, there has been a demand to teach engineering in high schools, particularly using a challenge-based curriculum. Many of these programs have the dual goals of teaching students the engineering design process (EDP), and teaching to deepen their understanding and ability to apply science and math concepts. Using both quantitative and…