CTK Insights

Three ropes have been fastened to a horizontal plunk, tangled a little as if one tried to make a braid and, lastly, loosely attached to an auxiliary plank to keep them braided. Down below there is a third plank. The task is to attach three additional ropes to the first ones at one end and [...]

Denise of the superb blog Let’s Play Math has streamlined my online version of Euclid’s game. The game provides a playful practice for the divisibility, gcd and some counting. The game (more accurately, the Java applet) has been written more than a decade ago when I just began to learn the Java language. At the [...]

Valerie Strauss in the Answer Sheet blog tells us of the “most powerful learning experience” Arne Duncan, the US Secretary of Education, shared with author and educator Sam Chaltain. Arne Duncan’s Learning Story I grew up going to my mother’s afterschool tutoring program in a church basement on the South Side of Chicago. It is [...]

Here is a question: should students be given partial credit for incomplete solutions. I was still reading Andrei Toom’s online book to which I referred in the previous post when I was advised on twitter.com that New York City Council is in turmoil over a controversial policy that gives students partial credit for wrong answers [...]

I’ve been following the links the new edition of the Carnival of Mathematics sponsored by the Wild About Math! blog. This is an issue #66, and it appears that I have learned about this undertaking relatively late, of which I regret. It is a curious collection of online articles. The next submissions deadline is set [...]

As every one knows, the word problems supplied by textbooks that attempt to appear realistic are mostly artificial, silly, and elicit from students, if not disgust, then a heartfelt jeer. Teachers who are obligated to follow a curriculum and a prescribed text find themselves in a bind: they often share students’ perception of those problems. [...]

I have recently posted a simple result picked from a very early (1930s) Moscow Math Olympiad for the middle schoolers: In triangle ABC, AE and BD are the altitudes to sides BC and AC, respectively. M is the midpoint of AB. Prove that MD = ME. Vladimir Nikolin, an elementary school teacher from Serbia, noticed [...]

Another look at the perennial stumbling block of whether 0.999… = 1 and what it actually may mean, see http://www.cut-the-knot.org/WhatIs/Infinity/9999.shtml

Two material points are in equilibrium if their distances from the fulcrum are inversely proportional to their weights. This is known as the Law of the Lever. The law serves as an engaging exercise for finding the greatest common divisor of two integers. Its proof by Archimedes is a captivating example – accessible in middle [...]

This is a caption of a quiz my 6 grader son has recently taken. What can I say? Seeing this quiz I feel cheated. Do we really pay the taxes so that the kids in grade 6 learn the difference between inhalants and stimulants? Quite candidly, by sound of it, I could surmise the meaning [...]