Thursday, January 9, 2014

Math problems of the week: 4th grade 1920s Math vs. Everyday Math

I. The first fractions problem set in the first 4th grade chapter of Hamilton's Essentials of Arithmetic, published in 1920, pp. 176-177 [click to enlarge]:



II. The final fractions problems in the "Fractions and Their Uses" chapter of the 4th grade Everyday Math Student Math Journal, published in 2002, pp. 226-228 [click to enlarge]:



III. Extra Credit

What did traditional math students miss out on in not being asked for their meta-cognitive reflections?

3 comments:

chinaphil said...

I think I know what you're trying to do with these comparisons, but honestly, this post just left me thinking how similar these problem sets are. How fascinating, that things have changed so little!
The big exception is the reflection questions. I thought the third one was too hard - I'd be very impressed if a 9(?) year old could answer that meaningfully. The first two seem helpful to me. Teaching what you know to someone else is a tried and tested way of checking your own knowledge. And question two exemplifies what the 1920s students missed out on: broader reflection on how numbers relate to their lives.
I'm not a teacher, and for me the proof of any teaching ideology/strategy must be in the practice: does this way of teaching work? (However working may be defined). If teachers tell me that the reform maths doesn't work, I'll listen and accept it. But you seem to be arguing that there is something inherently, conceptually wrong with it, and I don't really see this inherent flaw is.

Katharine Beals said...

Unless the two problem sets speak for themselves, it should be rather difficult for you to know what I'm trying to do with these comparisons. For example, perhaps I think it's sad that 1920s students missed out on broader reflection on how numbers relate to their lives.

To get a broader sense of what conceptual flaws these comparisons may or may not be highlighting, it would be a good idea to take a broader look, beyond the comparison of 1/9/2014.

Teachers are one source of information about whether Reform Math works. Other sources include students (including those with language impairments), SAT and AP scores, math professors who teach incoming college students, and... the actual curricula.

Hainish said...

"And question two exemplifies what the 1920s students missed out on: broader reflection on how numbers relate to their lives."

I think question 2 would have made me cry.