Basic Fact Mastery. How did that happen? (Chapter 10)

Chapter 10 is all about helping students to get their 'basic facts' straight. By the term 'basic facts', the authors mean the ability to give a quick response (in 3 seconds) to an equation without having to resort to inefficient means to calculate the solution, e.g. counting by ones. When a child is savvy with basic facts, he can more easily do mental calculations through numerical reasoning in his head. He is not reliant on calculators or inefficient working-methods to do simple computations. 

Try this out for fun:

*Basic facts for addition and multiplication are the number combination where both addends or both factors < 10.
*Basic facts for division and subtraction are the corresponding combinations, e.g. 15-8=7; 40/5=8.

This is an interesting topic. Come to think about it, when and how did you and I ever get to the point of just simply knowing that 5x6=30 or that 8+6=14, without needing to count or to even think about it? It's a curious thing. I can't seem to pinpoint a specific time when it happened to me; it seemed to be a cumulative, gradual experience borne of consistent exposure to these combinations and practice in computing such sums.
(My timing for the above exercise is 26secs, FYI.)

Apparently, there are 3 phases to development of basic fact mastery, according to Baroody, a mathematician who researches basic fact mastery (Pg 172 of the text):

Phase 1- Counting strategies (using fingers or objects to count verbally to get the answer)

Phase 2- Reasoning strategies (using known information to logically determine an unknown combination)

Phase 3- Mastery (producing answers efficiently, quickly, and accurately)

My husband told me that when he was little, his dad would often create exercises like this for the kids to work on; the goal, he said, was to beat each other's timings and to train their brains to be able to answer these simple sums instantly by recognition of/familiarity with the combinations of numbers. I wonder how productive such 'drills' are.

Well, I've just found my answer to that and I'm going to just quote and unquote it in a chunk:
"You may be tempted to respond that you learned your facts in this manner, as did many other students. However, studies...concluded that students develop a variety of different thought processes or strategies for basic facts in spite of the amount of isolated drill they experience. Unfortunately, drill does not encourage or support the refinement of these strategies...this approach to basic fact instructions works against the development of...mathematics proficiency..." (pg 173 of the text; italics added for emphasis)

It is so true, the fact the memorization is but a quick fix to Math problems . But what happens when memory fails you? Memorization leaves you with zilch strategies to resolve the difficulty- it fails you too (memorizing isolated facts without a basis or context is worse). It is unfortunate that I am a product of such drills. I could have been very successful at using strategies if only I'd been taught them when my brain was still young and quick; not so sluggish and set in its stubborn old ways as it is now. However, I am hopeful about re-learning my fundamentals in mathematics as I teach it to my children. It's never too late!


Chapter 10 is an amazing collection of methods that educators can use to guide children in strategy development in addition, subtraction, multiplication and division- towards attaining basic fact mastery. If you want your child to attain mathematics proficiency and have a happier time while learning and doing math, please take note of this chapter?


References:
Van de Walle, J. Elementary and middle school mathematics: Teaching developmentally (8th Edition). New York: Longman.