# CTK Insights

• ## Pages

24 Feb

### Does Triangle Have Area?

TweetFollowing the appearance of three videos by James Tanton a question was raised on twitter.com, Why does a triangle have an area?. The discussion was summarized at the Republic of Math blog. I gave several relevant definitions at my site. Generally speaking, area is a non-negative function defined for some plane sets that is supposed […]

18 Feb

### Math Teachers at Play - a Blog Carnival, February 2011

TweetThe 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 […]

16 Feb

### Area of a Circle

TweetEuclid did not know yet that the same constant () appears in the formula for the circumference and the area of a circle. Archimedes did, athough his method of approximating either by exausting the circle with regular polygons does not make this quite obvious. In the 16th century, Leonardo da Vinci, and in the 17th […]

13 Feb

### The myth of declining U.S. schools: another sane voice.

TweetJay 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 […]

10 Feb

### Debunking Education Myths: America's Never Been Number One in Math

TweetThis is a quote from an article by Liz Dwyer from the Good Education website. Has America really fallen behind the rest of the world in academic achievement? According to a new report from the nonprofit Brookings Institution, all the doom-and-gloom commentary suggesting that we've fallen from the top spot simply isn't true. And, even […]

06 Feb

### Mediant Fractions and Simpson's Paradox

TweetGiven 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 […]

04 Feb

### Integration or Geometry:a Problem for College Students

TweetThe Ariel University Center in Samaria (Israel) runs an online mathematical olympiad for college students. Last year there were several beautiful problems, one of which might appear harder for college students than for younger mathematicians: The point P = P(a, b) is located in the first quadrant. Consider a circle centered at the point P […]