Friday, March 14, 2014

Math problems of the week: math exams a century ago and now

I. The math portion of the 1912 8th Grade Examination for Bullitt County Kentucky Schools, courtesy Catherine Johnson [click to enlarge; you'll also find typos]:

II. Word problems from a sample test for the new Pennsylvania Keystone Algebra I exam, also taken by 8th graders (as well as by 9th-11th graders who either failed it or are only now taking Algebra I) [click to enlarge]:

III. Extra Credit:

There are a bunch of things that bug me about the sample Keystone questions, not all of which I can articulate. What do other people think?


TerriW said...

I feel like I'm supposed to think, "Hey, look, modern kids are doing ALGEBRA and those old timers were still stuck in arithmetic."

TerriW said...

(To be clear, not that *you* were trying to give that impression.)

Auntie Ann said...

1) They're wordy.
2) They give you far more information than necessary. If kids really are supposed to understand this stuff, why does almost every problem write out the equation for the student? Why not have them generate it themselves? Shows a lack of faith that the kids *have* actually learned what to do.

Barry Garelick said...

From the old test, one of the problems was "A school enrolled 120 pupils and the number of boys was 2/3 the number of girls. How many of each sex were enrolled?"

This can be solved algebraically. But probably in those days it was solved arithmetically, just as Singapore shows how to do this (using bar modeling). And in a recent paper by Liping Ma, she talks about how mastery of arithmetic used to be standard in education. The thorough grounding in arithmetic led to better results in algebra. Her article on this is here.