## Thursday, July 14, 2005

### PISA Math

Spiegel online has example problems for the Programme for International Student Assessment (PISA), the international study comparing the problem solving abilities of pubils in different countries in which Germany featured in the lower ranks amongst other develloping countries.

Today, the individual results for the German federal states are published, Bavaria comes out first and the city states (Hamburg, Berlin, Bremen, curiously all places where I was at the uni for some time...) came out last.

However, this might not only be due to superiour schools in conservative, rural federal states but also due to selection: If you are the child of a blue collar worker, your chances of attending high school are six times higher in the city states than in Bavaria. Plus, bad results in these tests can be traced to socially challenge areas with high unemployment and high percentage of immigrants. And those just happen to be more common in the cities than in rural areas.

But what I really wanted to talk about, is the first math problem (for the link in German). My translation is:

Walking
The picture shows the footprints of a walking man. The step length P corresponds to the distance between the two most rear points of two successive footprints. For men the formula n/P=140 expresses the approximate relation between n and P, where

n = number of steps per minute

P = step length in meters

This is followed by two questions asking to solve for P in one example, one asks for the walker's speed in m/s and km/h given P.

OK, these questions can be solved with simple algebra. But what I am worried about: n/P = 140 looks really suspicous! Not the the units are lacking (so it's like an astronomer's formula where you are told that you have to insert luminosity in magnitudes and distances in parsec and velocities by quater nautical miles per week), but if they had inserted units, they would see that 140 is actually 140 steps^2/s/m. What is this? They are suggesting that people who make longer steps have a higher frequency of steps?!? C'mon this is at least slightly against my intuition.

But this is a math rather than a natural sciences question, so as long as there are numbers, it's probably ok...

PS: The English version is on page 9 of this pdf.