The editors of Mathematics Teacher appreciate the interest of readers and value the views of those who write in with comments. The editors ask that name and affiliation including email address be provided at the end of their letters. This September 2016 Reader Reflections, provides reader comments on the following articles: (1) "Innocent…

I am a volunteer reader at the Princeton unit of "Learning Ally" (formerly "Recording for the Blind & Dyslexic") and I recently discovered that high school students are introduced to the concept of quantization well before they take chemistry and physics. For the past few months I have been reading onto computer files a…

In this webinar, Dr. William Schmidt of Michigan State University discussed helpful instructional tools for promoting the higher order conceptual thinking found in the Common Core Standards. The PowerPoint presentation and webinar recording are also available.

This article first describes some of the basic skills and knowledge that a solid elementary school mathematics foundation requires. It then elaborates on several points germane to these practices. These are then followed with a discussion and conclude with final comments and suggestions for future research. The article sets out the five…

Flexible knowledge, knowing multiple approaches for solving problems, is a hallmark of expertise in mathematics. Frequently, the author writes, students memorize only one method of solving a certain kind of problem, without understanding what they are doing, why a given strategy works, and whether there are alternative solution methods. Comparison…

In this paper we put forward a theoretical position that, in cognitive terms, a differentiation should be made between a correspondence and a function. Important in understanding this difference is the role of an assignation rule; the correspondence acts as a way to identify a rule in context, whilst the function accommodates the rule in a more…

The concept of symmetry is fundamental to mathematics. Arguments and proofs based on symmetry are often aesthetically pleasing because they are subtle and succinct and non-standard. This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical…

Open-ended tasks for developing numeracy skills reflect the fact that real-life math problems are seldom closed or have a single right answer. The "giving a party" problem shows how different math concepts and problem-solving skills can be brought out in open-ended tasks. (SK)

The fundamental opposition of two types of discourse, mathematical proof and argumentation to the problem of validation in mathematics is explored. The naturalistic study of interaction in classrooms suggests the possibility of a mathematical argumentation to which students have access by the practice of discussions ruled by socio-mathematical…

The concept of proof is discussed from a "human" viewpoint. The author concludes that "a good proof is one which makes us wiser." (MP)

An attempt is made to detail the nature of mathematics as perceived by mathematicians. Mathematics is viewed here as both abstract and an experimental science. The typical working mathematician is described as proceeding through problems with an attitude of discovery and examples of such an approach are given. (MP)

A traditional question is whether or not computers shall ever think like humans. This question is redirected to a discussion of whether computers shall ever be truly creative. Creativity is defined and a program is described that is designed to complete creatively a series problem in mathematics. (MP)

An attempt is made to link the domain of mathematics and the natures and abilities of mathematicians to that which is perceptual, presentational, and implicit. (MP)

University students' answers to a "Minds on Physics" problem revealed six distinct approaches to the solution. Discusses implications for teaching and assessment. (Author/WRM)

Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend to blend conceptual physics with mathematical symbolism in a way that profoundly affects the way equations are…