I read the original article about this experiment a while back. It seems that two things were going on with the kids in question. First, they did do a lot of practical measuring and were thus able to detect nonsensical answers that involved confusion of units (3000 yards vs. 3000 miles, etc.) Second they worked a lot on language skills, oral and listening skills in particular, with and emphasis on precise expression (again learning to avoid nonsense). Once the students in the study picked up arithmetic facts they had a huge jump on other students in interpreting and solving word problems.

Math is not the only thing taught poorly in elementary schools, unfortunately. From my reading specialist friends I've head stories about new movements in teaching reading that are about as far removed from teaching children to read and enjoy good books as a lot of elementary math is removed from teaching children to solve and enjoy math problems.

I took the point of the original article (from the 1920's) to be, not that math shouldn't be taught to young children, but that language skills are fundamental to all other subjects. I completely agree with this actually. I wonder if the differences between the wealthier white and less wealthy African-American students mentioned in the article you cite was due not so much to surreptitious homeschooling in math per se as to the generally higher level of language skills the wealthier group -- more books read aloud, more conversations with adults, etc., some of which might incidentally involve math. I know that there have been recent movements in both African-American and Latino communities to greatly increase the amount and level of reading-aloud that parents and other adults do for children as a way of jump-starting language development and improving academic achievement in all areas.

Sorry I can't cite a study now but one African-American professor in Georgia looked at what was distinctive about the highest-scoring African American students on aptitude tests and found that they typically came from homes where they were exposed to rich language through reading and being read to from a variety of "difficult" books. Granted there are reasons, including a vastly unequal educational system and denial of access to public libraries in the segregated South, why African-American culture evolved strong oral tradition but a relatively weak emphasis on literary learning. I suspect there are analogous stories to be told about other academically "underachieving" groups -- rural Appalachians, some Latino-Americans. And these groups are often low-scoring on both math and language aptitude and achievement tests. On the other hand I suspect that most groups of people who are high-achieving in math also come from cultures that have a strong history of valuing literacy (even when in the case of recent immigrants their grasp of English may be incomplete).

I'd worry that if "elementary math specialist" became a defined high-paying position in this country, it would be made a graduate-level education specialty. I fear that instead of a practical focus on teaching kids to do and understand basic math there would be a proliferation of gimmickry that would mainly benefit textbook publishers and academic careers rather than children.

I suspect that it would be possible to train elementary math specialists and not really have to pay them a lot more than other teachers, if candidates were identified early in their college career as having an interest in both math and elementary teaching and allowed to skip a lot of stuff that usual elementary ed programs require. Elementary math is truly not rocket science -- in the past China has done well training people with essentially a 9th grade education to teach elementary math in a few years of normal school. Li-Ping Ma has written about this. On her account prospective elementary math teachers study only math at the normal schools and only teach math once they're out. They practice the same problems they give the children and they also focus on the kinds of misunderstandings that lead school children to make mistakes, so they're prepared to lead their students back on to the right path when they get confused. I think a lot of kids get lost with math somewhere along the way and since no one helps them get back on track, they give up on math forever. At least I've heard this kind of story enough to think it happens frequently. (Then there are the really kids who give up on math because its so easy it's boring, but now they have AoPS . . . .)

I strongly agree that language skills are essential. When I speak to parent groups and am asked about what to do with younger children to develop problem solving skills, I give tell them, "1. Read. 2. Play."

As for the math specialist, I just think it would be hard to get people with an interest in math to want to teach in elementary school, but maybe I'm wrong about that... I'd be very happy to be proved wrong on a large scale about that.

Mr. Rusczyk,

I'm curious if you think a program like New Math (the post-Sputnik-era program) is what should be taught in elementary schools. My most memorable formative mathematical experience was when I was taught number bases in the seventh grade, and since then, I've always wished that I had been introduced to such a convention-breaking experience earlier on. I know New Math taught the basic tenants of abstract mathematics in primary schools, and I've always suspected that one reason most parents and teachers disliked New Math was because they didn't understand it themselves and assumed that, since teachers and parents are smarter than their students, the students could not possibly understand it, either. Do you think New Math is what primary schools need, and do you think the presence of teachers who understand abstract mathematics would make it possible to teach a New Math-like curriculum more successfully?

I think you misinterpret the study. The point was that they didn't teach any of the algorithms of arithmetic until 6th grade. As I understand it, they still read lots of stories involving math, talked about sizes of things, did projects with budgets (fundraisers for a class field trip), built scale models of things, and so on. That is, they did lots of math, but only in context of something else, not as a separate isolated topic, and with no teaching of formal algorithms.

I think this ties in to the story I often tell about 6th graders doing worse than 1st graders on some tests. For instance, "three ships left Boston for New York at the same time. One took 11 hours, one took 13 hours, and one took 14 hours to get to the destination. How long does it take for all three ships to arrive?" Kids with more training in "math" are more likely to give 11+13+14 as the answer, while younger kids are more likely to get it right.

I suppose what this all boils down to is whether the teaching of algorithms is likely to be done poorly with young kids, and whether teaching math in context is more likely to give them a meaningful experience with mathematics and problem solving. I think this study points to a "yes" answer to both questions.

Good point -- I think that fits the idea of "teaching math better" rather than not teaching math at all.

As for "New Math", I don't know much about it, so I can't really say. I suspect it's probably a lot like the current fad of Everyday Math -- if it's in the hands of a highly trained teacher, it can be amazing, but if it's in the hands of an untrained, or lightly trained, teacher, it's a disaster.