Information Age Education Blog

The free Information Age Education Newsletter recently published a sequence of seven issues comparing and contrasting our educational system with our medical care system. This “apples and oranges” comparison provides interesting and useful insights into these two important aspects of life in our society. You can read these newsletters at http://iae-pedia.org/IAE_Newsletter.

A recent article in my local newspaper reported that vaccinations for meningitis were not remaining effective for as many years as expected, and discussed teenagers needing a booster shot that costs $100. The article reported data on how many deaths per year are prevented by the initial shot and indicated that a second shot would save 24 deaths per year in the United States. Unfortunately, the article did not indicate how many people would need to be vaccinated per year to save this many lives.

A kindergartener I know—let's call him Jack—is a bundle of energy and “smart as a whip.” He is gluten intolerant, and so has to exercise considerable care in his diet. He had some eye problems and wears relatively thick corrective lenses. He had speech problems with several of his sounds, and had the help of a speech therapist to overcome these problems. Our health care system has contributed greatly to his quality of current and future life.

Jack has also had the advantage of very well-educated parents and grandparents. He is getting a very good informal and formal education.

Many years ago I heard the statement that a computer is a solution looking for a problem. This statement has stuck in my head, and it still seems relevant.

The history of computing devices is usually traced back many thousands of years ago to the abacus and still earlier aids to counting and keeping track of quantities. An abacus is an excellent and easy-to-learn aid to adding and subtracting integers.

This IAE Blog entry is based on “The Calculating Brain,” written by Stanislas Dehaene (2010). It is chapter 9 in Brain, Mind, and Education (Sousa, 2010). Dehaene has long been a world leader in research on the brain science of children developing arithmetic knowledge and skills.The following are some of the ideas discussed in Dehaene's chapter.

• An undamaged infant’s brain has innate ability to distinguish between 1, 2, and 3 objects. This level of exactness serves as a starting point for eventually learning the math language and  notation for dealing with larger quantities and with a number line of evenly spaced numbers.
• The infant’s brain also has innate ability to deal with approximations. Humans and some other animals can tell when one group of objects is larger than another. For example, a small pride of lions that encounters a much larger pride of lions will retreat to avoid a confrontation. A human toddler can distinguish a difference when the ratio of objects in two sets is two to one (such as eight objects versus four objects). This ability improves as a brain matures, so that a typical adult is able to distinguish a difference when one set of objects is about 1.15 times as large as another set.

Math education builds on these two innate abilities. It takes a lot of education to bring these innate skills to the contemporary standards we expect in arithmetic.

Keith Devlin (2010) is a world-class researcher and writer in the combined areas of cognitive neuroscience and math education. His chapter, "The Mathematical Brain," is in Mind, Brain, and Education edited by David Sousa (2010). It is packed with information that underlies current progress in the Science of Teaching and Learning (SoTL) in math.

A human brain has some innate ability to deal with: