Open Thread -- Are Teachers Losing Their Marbles?

In a story published on Friday, April 25 by REUTERS, writer Julie Steenhuysen informs us of a study by Ohio State University research scientists that recently appeared in the journal Science:


The findings cast doubt on the widely used practice among elementary and middle schools in the United States and elsewhere of using friendly, concrete examples to teach abstract math concepts.

The study found that students who learned math concepts using abstract symbols first fared better than those who learned the concepts using real-world examples,1 and that the abstract-first students were better able to apply the concepts to a variety of situations.

Researcher Jennifer Kaminski stated that this doesn't mean real-world examples or story problems should just go away, however. According to Kaminski, story problems provide a a method for testing whether a student has mastered the abstract concept.

This is an Open Thread.



  1. Real-world examples described in the article included using marbles for discussing probability or "story problems" ('a train leaves Chicago at 3:00...') to teach other abstract concepts.
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This stuff was hot on the left, in 1968 when I was teaching in a Manhattan High school. At that time radicals were framing lesson plans around problems to do with redistributing plantations to the poor--ie what math would you need to divy up the farms. I thought then that it was pretty weird stuff.

What was the killer when I was teaching was the new math, which was organized around too much use of fancy language. Like the 1/3 and 3 are "multiplicative inverses." and given the problem 2x =6, find the "solution set" for x. In my simple example it would be the number 3. That sort of thing.

The geometry currciulum then was a simplified version of Euclid, with a bit too much emphasis, I thought, on elaborating the reasons for a statement. ie angle a and b are right angles, all right angles are equal, therefore angle a = angle b. But IMO it was a lot better than present geometry texts I have seen which have eliminated the whole idea of a proof structure, which was the joy of studying Euclid.

I have never gotten on top of the computer learning applications for math which I think are probably pretty exciting. For example being able to map three dimensional objects and then shift them in space, and show who two such might intersect to produce interesting surfaces.

Some of the new material I was teaching in the 'sixties and 'seventies were taken from symbolic logic and was a kind of thinking that has an important place in software programming, but that implication was not clear to me at all at the time.

How kids use abstraction in mathematics as well as reading must relate to the kind of home environment they come from, and the verbal facility they gain from interactions within the family.

Very interesting subject I think.


teachers in general think/feel, as it pertains directly to what they would have witnessed or experienced in the classroom itself?

All I know is I liked math and in particular, loved trigonometry. I always had trouble with Limits though. I just never quite grasped the concept.

Going to the limit--in math not sports--implies looking at a developing series as a process and conceptualizing the whole, rather than sticking with the endless and then, and then, and yet again as the terms approach the limit.

What I found really fun was to determine which series approach a limit and which do not. For example compare the series 1+1/2+1/3... Does it approach a definite sum as the terms get smaller. What about 1+1/4+10=1/18.

Interesting to me was that the first series keeps growing without limit and the second series does not.