Information Age Education Blog

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:

Two chapters from the book Mind, Brain, & Education: Neuroscience Implications for the Classroom (Sousa, 2010) focus on reading. As you know, a major goal in education is to help students learn to read well enough so they can learn in other curricular areas by reading. It is a major landmark in a child’s education when reading skills develop to a level that learning by reading begins to dominate other aids in formal schooling.

Chapter 6, "The Reading Brain," is written by John Gabrieli, Joanna A. Christodoulou, Tricia O'Loughli and Marianna D. Eddy (2010). Quoting from this chapter:

A September 2010 state-by-state report on funding levels for education is available at http://schoolfundingfairness.org/index.htm.

I enjoy browsing such reports, but I am always troubled by the very large differences among the states. Quoting from the report, here are some general data: