This is a spin off of DadDude’s thread “The Theory Behind Encyclopedic Knowledge.” Rather than derail that thread even more, I figured I’d start a new one here.
So the question is, if Doman Math is legitimately possible, is it beneficial?
Aside from personal anecdotes of parents who have used Doman math successfully with their children, there are few studies that report this kind of learning is possible. This is an interesting study that suggests infants are able to differentiate to a certain extent depending on the numerosities and ratios shown.
Collectively, current and previous studies provide evidence that 6-month-old infants fail to discriminate between small numerosities, 1 vs. 2 and 2 vs. 4, but they succeed in discriminating large numerosities, 4 vs. 8, 8 vs. 16, and 16 vs. 32, when the ratio between the two numbers is held constant. These results are consistent with the hypothesis that two systems of representations are present early in infancy. One is an object-tracking system, and its signature property is the set size limit of 3 or 4 in adults and infants; the other is a number estimation system, and its signature property is the Weber fraction, i.e. the system accords with Weber’s Law – successful discrimination is determined by the ratio between two numbers, not the absolute difference.
http://babylab.berkeley.edu/XuArriaga.pdf
What I am unable to find are long-term studies specifically on Doman math. Parents on these forums are not showing their children math for a day for the purposes of completing a study, or even for a few weeks. These infants are being shown math daily, usually several times a day, for months or years on end. I would think the long term repeated exposure would greatly impact the level of math competency displayed when tested.
So this study suggests that it is possible for infants to learn to detect quantity at least to some degree. Combined with the claims of successful parents using Doman math, let’s suspend our disbelief for a moment and address the question–Assuming a baby can be taught math, is it beneficial?
Early Math Matters: Kindergarten Number Competence and Later Mathematics Outcomes
http://udel.edu/~njordan/Jordan_Developmental%20Psychology.pdf
According to this study, it seems as though what holds true for reading also holds true for math-- the kids who start ahead, stay ahead. This particular study only begins at the Kindergarten level, I assume because typically people do not begin math instruction before traditional school age. Similar to early reading, just because researchers are not studying infant/toddler level math and as a whole academia does not recognize it, does not make it any less valid. One would stand to reason that if the benefits of early number competencies are significant and predictive at the Kindergarten level, then they would be even more so at the infant/toddler level. Earlier acquisition of basic math concepts, just like reading, allows a child more time and a foundation on which to fully develop their skills in general. By Kindergarten, if a parent was consistent with Doman math, the child will have most likely progressed even further into traditional math and the gap will continue to to widen between the child and his or her peers, similar to the suggested Matthew affect in reading.
Just as the whole-word method makes reading accessible to very young infants, Doman style quantity exposure makes math accessible to infants. I can read the theories about early reading stimulating certain areas of the brain and so forth, but they are not proven and they are just that–theories. The brain stimulation and importance of learning to read during the language acquisition phase makes sense to me as an average layperson, but of course I cannot prove it one way or the other. Rather, what matters more to me are the end results which suggest that early readers make stronger readers. There are many examples of that here on these forums, as well as a small study of precocious readers at age 11 which supports this idea.
What Happens to Precocious Readers’ Performance by the Age of Eleven?
http://www.eric.ed.gov/ERICWebPortal/search/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=EJ686923&ERICExtSearch_SearchType_0=no&accno=EJ686923
Additionally, this paper claims that after analyzing 6 longitudinal studies on Kindergarten readiness and long-term academic achievement, the biggest three predictors of elementary academic success are school-entry math, reading, and attention skills.
http://eprints.ioe.ac.uk/5971/1/Duckworth2007SchoolReadiness1428.pdf
In essence, math is a language just like reading, speaking, and music are forms of language…representations of symbolic thinking with patterns and codes to be cracked. We know that there is a specific time frame for language acquisition in the early years and learning to read during this time period appears to be beneficial. Of course correlation does not equal causation, but whatever the real reason is and whatever theory holds true for reading, I would stand to venture it holds true for math as well. It’s a gamble I’m willing to take because if earlier is better in reading and foreign language, I would think for math (and music for that matter) it’s reasonable to assume the same. I could be completely incorrect, but according to the study cited above, early math pays off.
So yes, this is a bit of a leap but without any real research on the subject, that is all we can do. I recently read a quote comparing waiting around for studies on infant/toddler education to waiting around for the scientific community to agree on global warming. Your child will be grown and long gone before studies are ever done and a collective opinion is formed, so parents needs to follow their guts and form their own opinion regarding their child’s education.
So to me the short answer is: The point of doing Doman math is that it makes math accessible to a very young infant. Experience and common sense suggest that earlier is better in acquiring foreign language, reading skills, and that most likely holds true for learning math as well.
So, to Daddude, I say experiment with teaching your latest addition early math let us know how it worked out for you. 
