CTK Insights

Archive for June, 2012

29 Jun

Word Problems with Percents for the Summer Break

Would not it be nice if the kids never forgot what they were taught? The beginning of the summer break endows this question with the sense of extra urgency. I know what I am talking about: my all-around-honors kid will in the Fall start high school, but a few days after the end of the school year he is already having a difficulty recollecting what it was that he learned at the junior high.

27 Jun

Bags, Coins, and Questions

There are 31 bags placed in a row with 100 identical coins each. One bag is selected and one coin is moved from the selected bag to every bag to the right of it. A question can be asked for a total number of coins in any group of bags. How many questions are needed to determine the chosen bag?

19 Jun

Children, parents and puzzles

I wonder whether the girl in the story was naturally scared of mental exercises, disliked puzzles or math, or, perhaps, her mom's injunction played a role in setting the girl into a wrong mood. I had a very clever classmate who - likely for that very reason - felt under pressure to perform well at examinations, but never had.

18 Jun

The Euclid Debate from 1869

TweetI am reading Lewis Carroll in Numberland by Robin Wilson that I reported buying earlier. The book is an extended professional - so to speak - biography of Charles Dodgson, better known as Lewis Carroll. Here's a passage from the book (pp 89-90) that adds another pair of quotes to the two I posted not […]

16 Jun

Weakly Refuted Story of Queen Victoria

TweetI like buying books, especially serendipitously. For the past year this was mostly by simply browsing the amazon.com Kindle store. Today after a long hiatus I bought a book in a bookstore of old ("conventional" may not be the right word anymore.) I've been taking a walk with my sister-in-law - a full-time Israeli, and […]

15 Jun

Two quotes on math education

TweetThere is a firmly held belief that study of mathematics has a benevolent effect on brain development. I am not aware of any research that supports this thesis. The evidence is mostly anecdotal, like that expressed in the following quote: To those of us who have not pursued the study of mathematics since college days […]

10 Jun

Dominoes and Chessboard Activities

Tiling a chessboard with dominoes is uniquely suitable as an entertaining and edifying activity even for young children. Both implements are widely available, while experimentation with them leads to a good number of problems. Some of the problems admit simple (albeit ingenious) proofs that I would classify as the "very first," in the sense that they require minimal (if any) knowledge of mathematics.

09 Jun

Archimedes' Law of Buoyancy

Every body has a shape. Bodies may have the same or different shapes. We visualize a shape as separate from any connection to any physical body. Shapes have volume.

There are various forces that act on a physical body: gravity, air pressure, surface tension, forces due to the possible interaction of the surface of the body with the surrounding environment. For a derivation of Archimedes' law, we make an assumption that, excluding the weight, the force total that acts on a body in a given environment depends solely on the shape of the body. This is a reasonable assumption, especially because we shall be only interested in the bodies of the same shape that occupy a fixed volume, i.e., the bodies that may occupy the same physical space.

08 Jun

Serendipity and Luck

Although the role of serendipity is familiar, what's not so well appreciated is how different serendipity is from luck. Serendipity is not just an apparent aptitude for making fortunate discoveries accidentally, as my dictionary defines it. Serendipitous discoveries are always made by people in a particular frame of mind, people who are focused and alert because they're searching for something. They just happen to find something else.

07 Jun

A Kindergarten Activity As a Problem for Adolescents

TweetTwelve kids stand in a circle, a kid per one of twelve marked spots. Every now and then one moves clockwise, another counterclockwise to an adjacent position (which may be occupied by more than one kid or be empty.) Is it possible that after a while all of them stand at the same spot? The […]

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