CTK Insights

I am not sure who coined the term "The Star of David Theorem" to designate the identities discovered in the early 1970s. There are in fact two of them, both related to the "Star of David" configuration in Pascal triangle (The diagram is courtesy wikipedia.org.) The first result discovered by Hoggatt and Hansell in 1971 [...]

This is a small book written by one of my boys and illustrated by the other. The idea is along the lines discussed in my previous post. Any group of objects has an associated attribute that reflects on the size of the group. This attribute is called Number; its presence and uniqueness is what allows [...]

The Math Teachers at Play blog carnival had several articles that especially drew my attention. The visual for explaining and using Equivalent Fractions, Sue Downing found at the Wikiversity website is indeed wonderful. It requires hardly an explanation and beautifully applies to explain the division of fractions process: It is a pity the Wikiversity page [...]

Jay Mathews from the Washingtom Post wrote a follow up on a recent report by the Brookings Institution scholar Tom Loveless. Loveless is one of the nation's leading experts on PISA and TIMSS. He has been part of the cohorts of specialists who advise those programs. In his report he says the first international test [...]

Given two fractions a/b and c/d, the mediant of the two is defined as the fraction (a + c)/(b + d). Many would point to the mediant fraction as a dangerous concept that is bound to confuse students who often quite innocently produce it adding up to fractions. However, the mediant has its uses and [...]

I found a remarkable talk given by Robert Lang pointed to at the Math Frolic! blog. Dr. Robert J. Lang is an American physicist who is also one of the foremost origami artists and theorists in the world. Among other achievementsm he is known for having proved the completeness of Huzita–Hatori axioms and developing paper [...]

George G. Szpiro, author of Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present is a mathematician and journalist living in Switzerland. Numbers Rule focuses on key figures in the development of democracy and on the mathematics of voting, elections, and apportionment that they developed. Szpiro pays particular attention to the paradoxes [...]

This is a Math teachers at play carnival, issue # which I am going to reveal shortly. See if you can make it from what is known as a single image stereogram. Try focusing your eyes behind the screen. In this month issue: What is the number of this issue? Sad news Interesting and relevant [...]

How can be one so wrong? The common objection to the existence of trigonometric proofs of the Pythagorean theorem stems from the assertion that the most important trigonometric identity sin²α + cos²α = 1, being equivalent to the Pythagorean theorem, can;t be employed to proof the latter. However, as Jason Zimba has recently observed, that [...]

With the ever recurrent hoopla about forcing Algebra I courses on 9 and even 8 graders, I often recollect the expressed desire of an official math educator to have every student perform better than the average. Such semantic inconsistency does not necessarily strengthen the arguments either in favor or against making algebra a graduation requirement, but [...]