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…

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…

In this article, the author comments on the article "Solid geometry in the works of an iron artisan,'" Castro, 23(3). The author finds it interesting to read about the implicit mathematical knowledge of ironworkers, weavers, tailors and other practitioners as they undertake their various crafts and professions. In the article, Fernando…

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

In assessing the quality of science teaching for an effort such as the National Assessment of Educational Progress (NAEP), it is important to understand what is meant by scientific thinking--the search for explanations. Instruction should involve higher-order cognitive skill development, but it is difficult to measure reasoning and understanding…

Makes the analogy between Wilfred Bion's theory of mental processes involving preconception and mathematical problem solving. (MDH)

The author arranges 26 current states of mathematical knowledge (in relation to solving a problem) in an informal taxonomy and comments on them. (MNS)

The relationship between logic and mathematics is examined. Four basic concepts inherent in symbolic logic that are typically included in ninth- and tenth-grade mathematics programs are reviewed. Symbolic logic is advocated for all students who will study algebra and/or geometry. (MP)

While John Dewey and Bertrand Russell share certain fundamental similarities in thought on many major social issues, it is in their educational thought that the disparity is most evident. (JN)

A simple enumeration problem from some research on problem solving is used to illustrate the contention that conjecture and proof have a central place in mathematics teaching. (Author/TG)

The need for incorporating algorithmics into mathematics instruction is presented. The proliferation of computers is seen to have made the designing of algorithms an essential skill. Examples are given, and the view that mathematics will lose much prestige and importance if algorithmics is not integrated into it is presented. (MP)

The concept and use of proof in mathematics are examined. Uses and purposes of proofs are listed and described. (MP)

Compares two approaches to the teaching of mathematics, rote versus reasoning. Discusses the way to teach mathematics as reasoning in elementary classroom as stated in the NCTM Standards. (YP)

Rhetoric and mathematics have much in common that can help explain the composing process. Common elements of rhetoric and mathematics important to the teaching of writing are (1) relationships between syntax and semantics, (2) practices of representation, and (3) focus on problem solving. Recent emphasis on "repair processes" in mathematics is…

This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…