Archive for the ‘Math Education’ Category.
18th February 2009, 01:20 pm
I bought the book “Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail“ by Danica McKellar because I couldn’t resist the title. Sometimes this book reads like a fashion magazine for girls: celebrities, shopping, diet, love, shoes, boyfriends. At the same time it covers elementary math: fractions, percents and word problems.
You can apply math to anything in life. Certainly you can apply it to fashion and shoes. I liked the parallel between shoes and fractions that Danica used. She compared improper fractions to tennis shoes and mixed numbers to high heels. It is much easier to work with improper fractions, but mixed numbers are far more presentable.
Danica is trying to break the stereotype that girls are not good at math by feeding all the other stereotypes about girls. If you are a typical American girl who hates math and missed some math basics, this book is for you. If you want to discover whether the stars are on your side when you are learning math, the book even includes a math horoscope.
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13th January 2009, 05:52 pm
I ran an experiment. I copied multiple choices from the 2007 AMC 8 into a file and asked my son Sergei to try to guess the answers, looking only at the choices. I allowed him to keep several choices. The score I assigned depended on the number of leftover choices. If the leftover choices didn’t contain the right answer, the score for the problem was zero. Otherwise, it was scaled according to the number of choices he left. For example, if he had four choices left and the right answer was among them he got 1/4 of a point. Here are the choices:
- 9, 10, 11, 12, 13.
- 2/5, 1/2, 5/4, 5/3, 5/2.
- 2, 5, 7, 10, 12.
- 12, 15, 18, 30, 36.
- 24, 25, 26, 27, 28.
- 7, 17, 34, 41, 80.
- 25, 26, 29, 33, 36.
- 3, 4.5, 6, 9, 18.
- 1, 2, 3, 4, cannot be determined.
- 13, 20, 24, 28, 30.
- Choose picture: I, II, III, IV, cannot be determined.
- 1:1, 6:5, 3:2, 2:1, 3:1.
- 503, 1006, 1504, 1507, 1510.
- 5, 8, 13, 14, 18.
- a+c < b, ab < c, a+b < c, ac < b, b/c = a.
- Choose picture: 1, 2, 3, 4, 5.
- 25, 35, 40, 45, 50.
- 2, 5, 6, 8, 10.
- 2, 64, 79, 96, 131.
- 48, 50, 53, 54, 60.
- 2/7, 3/8, 1/2, 4/7, 5/8.
- 2, 4.5, 5, 6.2, 7.
- 4, 6, 8, 10, 12.
- 1/4, 1/3, 1/2, 2/3, 3/4.
- 17/36, 35/72, 1/2, 37/72, 19/36.
It is clear that if you keep all choices, your score will be 5, which is the expected score for AMC if you are randomly guessing the answers. Sergei’s total score was 7.77, which is noticeably better than the expected 5.
There were two questions where Sergei felt that he knew the answer exactly. First was question number two with choices: 2/5, 1/2, 5/4, 5/3, 5/2. All but one of the choices has a 5 in it, so 1/2 must be wrong. Numbers 2/5 and 5/2 are inverses of each other, so if organizers expect you to make a mistake by inverting the right answer, then one of these choices must be the right answer. But 5/4 and 5/3 are better suited as a miscalculation of 5/2, than of 2/5. His choice was 5/2, and it was correct. The second question for which he was sure of the answer was question 19, with his answer 79. I still do not have a clue why.
Sergei’s result wasn’t too much better than just guessing. That means that AMC 8 organizers do a reasonably good job of hiding the real answer. You can try it at home and see if you can improve on Sergei’s result. I will publish the right answers as a comment to this essay in a week or so.
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