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Oct 21
2010
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The math brain: Keith Devlin’s chapter in the book “Mind, Brain, and Education.”Posted by: Dave Moursund Tagged in: Improving Education
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Click here to learn about Dave Moursund's free book on science and technology education for teaches and parents of K-8 children.
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Keith Devlin is a world-class researcher and writer in the combined areas of cognitive neuroscience and math education. His short chapter in the book Mind, Brain, and Education edited by David Sousa is packed with information that underlies current progress in the Science of Teaching and Learning (SoTL) math.
A human brain has some innate ability to deal with:
- Very small quantities in the range of one to three.
- Distinguishing between larger qualities, when the ratio of the larger to the smaller quantity is sufficiently large.
Learning math involves:
- A bottom-up approach, constructing new counting and arithmetic knowledge and skills based on innate number sense. It is important to understand that there is considerable abstraction in number words, number symbols, cardinality, and ordinality. All of these ideas “stretch” the brain’s capabilities.
- A top-down approach based on learning to deal with the types of abstraction such as those introduced in algebra. Teaching and learning of these abstractions is a challenge to teachers and students.
Two ideas that I surmised from Devlin’s chapter are:
- Learning math is a greater challenge than learning to read. Even though the human brain has some innate math ability, it is small relative to the language ability and its contribution to learning to read.
- We are further along in research, fundamental understanding, and SoTL for the reading brain than we are for the math brain.
What You Can Do
You know that the message sent is not necessarily the message received. You, for example, have “constructed” a personal meaning to my message given above. My overall intent is to provide you with some information and ideas that you will act upon in a manner that leads to improving our informal and formal education system.
So, pause for a few seconds and think about the meaning you have constructed from my message and some possible action that you might take based on the meaning you have constructed. What occurs to you that you, personally, will try out in your quest to improve our education system?
As a personal example, when talking to people who are preparing to teach math at the precollege level or who do teach math at this level. I ask them the question of when they learned to learn math by reading a math book. (Note that my "sample" includes elementary school teachers, since most of them teach math as part of their overall teaching.) My conclusion is that while most people are capable of learning to learn math by reading, few achieve this before encountering calculus in college. This is an area of special interest to me.
Final Remarks
Spend a bit of time reflecting on what you have just read. How does the information fit in with your current knowledge, beliefs, and activities? How can you make use of the information to help improve our informal and formal educational systems? Who do you know that might benefit from reading the IAE Blog entry?
If the IAE blog entries are useful to you, then consider signing up for a Free Subscription. (See the menu on the left side of the page). You will automatically receive email about new postings to the blog. Typically, there are about three new postings per week.
Links to Related IAE Documents
Being "Proficient" with 50 Percent Correct Answers. Math competence and math maturity. IAE Newsletter - Issue 23, August 2009.
Gaining expertise in reading, writing, arithmetic and in other areas. IAE Newsletter - Issue 11, February, 2009.
Cognitive development and IQ. IAE Newsletter - Issue 20, June 2009.
Communicating in the Language of Mathematics.
Five brains are better than one.
Some things brain science research tells us about learning and doing arithmetic.
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1. Number sense.
2. Numerical ability.
3. Spatial-reasoning ability.
4. A sense of cause and effect.
5. The ability to construct and follow a chain a chain of facts or events.
6. Algorithmic ability.
7. The ability to handle abstraction.
8. Logical-reasoning ability.
9. Relational-reasoning ability.
Many of these takes years to develop to a level that meets contemporary standards, and many are important in both math and other disciplines.