Teaching Math with Manipulatives

Notes re: Comparative Methods for CBC radio interview with Sheila Rogers, 2008

#1 Should we base our math teaching on the weakest mental skill children possess, or on the strongest?

Two quick questions: #1 Imagine the statue of Liberty. See the skyline of Manhattan? See her pointy crown and flowing robes? What is she holding in her right hand? What is tucked under her left arm? So, you can extract information from a visual image you didn't even study, fairly easily. Now.. #2 If I give you twenty ten-digit numbers, how long can you remember them? An hour? Ten Minutes? Long enough to write them down? Why would you base your teaching on children's weakest mental ability: short term memory, rather than say, imagination?

#2 The goal is to think creatively in problem solving, not the recitation of number facts.

Looking to the future: employers aren't interested in whether you can recite your times tables, they have computers to do that. They want people who can solve their problems and develop creative strategies to make them profitable.

#3 Rote memorization results in boredom not excitement, in de-motivation rather than motivation.

Your average ten-year-old boy would rather run outside and play baseball than memorize times tables, which has about as much meaning to him as reciting poetry in ancient Greek (think Homer).

#4 Understanding cannot arise naturally from mere memorization of abstract facts cf. John Searle, "Chinese Room"

A computer can exchange symbols rapidly in a literal translation of Chinese symbols into say, the Russian language. But it will never learn to speak Chinese this way, or Russian, for that matter.

#5 Concept formation results from relevant physical experiences appropriate to student's cognitive stage.

There is no logical way to reach understanding from the mere memorization of abstract symbols.

#6 After Jean Piaget, Swiss Psychologist, prior to age 14 approx., children need "tactile motor kinaesthetic" and "concrete operational" experiences, not practice in symbol manipulation.

#7 Without old school methods of discipline is memory training even possible?

How can you "make" children do anything they don't already want to do? At early ages, learning strategies must focus on "Play and Discover," acquiring experiences from which to generalize and form concepts.

#8 Motivation: What if we succeeded in coaxing, cajoling, training a student to math competency at Gr.12, but in so doing put them off pursuing math at a post-secondary level? Would it have been worth it?

Isn't that what is happening to a majority of students at present, with methods based on memorizing facts, rules, formulae and processes?

#9 National perspective: Math competence can be grown or it can be imported, but can Canada compete in the world economy without it?