Some amazing research results were presented at the Conference on World Affairs by Dr. Sanjoy Mahajan of MIT, an internationally known expert on the mechanisms that allow humans to do mathematics. His work has shown that some people who suffer a loss of speech due to brain injury also lose their ability to do simple multiplication. They can still do addition and subtraction with ease. Only multiplication skill seems to be effected. Moreover, this loss is seen mostly in older people who have been educated in the American school system.
The reason for this is astounding. Our American public school system arose during the 1840s and 1850s as a response to the coming industrial revolution. Children growing up on rural farms needed to be trained to adapt to the requirements of factory jobs jobs which were regimented under authoritarian supervision. The schools of the time also reflected that same regimentation, and one of the ways this manifested itself was in the memorization of multiplication tables. For the last 150 years, students have memorized that 6 times 3 is 18, and this knowledge seems to be stored in the brain as a verbal statement rather than a mathematical concept. When speaking ability is lost, memories of verbal statements are lost too, and simple multiplication skill goes away. In other cultures where multiplication skill is taught as a mathematical concept, brain injury has no effect on this skill.
To demonstrate how “multiplication by memory” shortchanges American students, a large group of high school graduates was tested (all of whom were proficient in reciting their multiplication tables) and they were asked to multiply 3.147 by 5.0842. They had to do it quickly in their head, without paper and pencil, and they answered by selecting one of four multiple choice responses A-1, B-16, C-160, or D-1600. Only 18% of them answered correctly, B-16. Statistical random selection would have predicted that 25% would have chosen correctly if they had simply guessed at the answer, but such was not the case. Ignoring the decimal points, most of them thought they were multiplying very large numbers, and the most common response was the most absurd choice, D-1600.
For Dr. Mahajan, work like this helps him explain why Americans are so poor at numerical estimation and conceptualization. If a disease effects 3% of the population, and a certain health-adverse behavior is said to increase the risk of that disease by 30%, then the overall chance of getting the disease is still less than 4%, even for those who indulge in the bad behavior. Less than 10% of the adult American public can understand this concept, and there are hundreds of similar examples to show that we just don’t, “get it,” when it comes to even the most basic arithmetic.
America has eliminated almost all of its factories. Maybe it’s time to change our factory schools.