# PISA and V.I. Arnold questions from twitter

Yesterday Fawn Ngyuen posted a link to some sample questions used by PISA.  Here’s the website:

http://www.oecd.org/pisa/test/

I was pretty surprised by the Level 6 question for 15 year olds and the fact that only 2% of US students performed at or above Level 6.  When I got home from work yesterday, I gave the Level 6 sample question to my older son:

He had a little difficult working through it, but did manage to get to the right answer.   The biggest struggle was finding a way to check his answer.  That particular struggle made me happy since one of the things that we’ve been working on is slowing down and double checking his work.

Overall, I like the question, but I’m still struggling to understand how only about 1 in 50 US 15 year olds are able to work through this problem correctly.

While I was publishing the video least night, Steven Strogatz put a link to Tanya Khovanova’s blog on twitter:

http://blog.tanyakhovanova.com/?p=131

This blog post discusses the following problem from V. I. Arnold’s book “Problems for Kids from 5 to 15″ :

(From an American standardized test) A hypotenuse of a right triangle is 10 inches, and the altitude having the hypotenuse as its base is 6 inches. Find the area of the triangle. American students solved this problem successfully for 10 years, by providing the “correct” answer: 30 inches squared. However, when Russian students from Moscow tried to solve it, none of them “succeeded”. Why?

According to Khovanova’s blog post, Arnold expected kids under age 10 to be able to solve this problem.  Wow.  I’d be pretty surprised if 1 in 50 10 year olds could solve this one, but it is a very interesting problem.  Since we were in the middle of studying quadratics anyway, I took a break from our Algebra book today and used this problem as a jumping off point to talk about the arithmetic mean / geometric mean inequality.  Definitely fun:

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Definitely a fun and educational day for me on twitter yesterday.