CTK Insights

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 [...]

Some time early in the 20th century, a few math enthusiasts started a publishing house Mathesis in the then Russian city of Odessa. The purpose to publish books interesting and useful to young people and those responsible for their upbringing. The enterprise was around from 1904 through 1925 straddling the time of October revolution. More [...]

On Wednesday, June 4, 2008,  Rochester Democrat and Chronicle published an article by Latoya Manon. The article under the title Teachers cannot teach if students refuse to learn raised several very resaonable questions as to the validity of the comprehensive approach fostered by the NCLB program. Here are a few examples: # What would you [...]

How to divide evenly 5 apples between 6 boys if you are only permitted to cut an apple into not more than 4 pieces?  The answer is remarkably simple and the approach serves an excellent motivation for the process of adding two fractions.  First divide 3 apples into halves giving each boy a half, 1/2. Then divide [...]

Raymond Smullyan starts his What Is the Name of His Book with a story of how he was fooled by his older brother: (One) morning, my brother Emile (ten years my senior) came into my bedroom and said: "Well, Raymond, today is April's Fool Day, and I will foll you as you have never been [...]

A particular case of the Isoperimetric Theorem says that among all rectangles of a given perimeter, the square has the largest area. (This is of course equivalent to the claim that among all rectangles of a given area the square has the least perimeter.) This particular case of the general theorem is so simple that [...]