As I was teaching my 6-9 year grandsons and their friends some basic algebra for our Sunday Academics Hour recently, they sometimes reached wrong answers because their arithmetic facts are a bit iffy. I still praised them when their methodology was sound.
Using this specific example, what does multiplication mean? For starters I have the kids draw 3 rows and 4 columns of smiley faces and count them to get twelve smiley faces. But if the toddler is too young to draw the smiley faces in neat rows and columns, they might inadvertently miss one and get eleven. I would still praise the process and urge the kid to be more careful about lining up his rows and columns for future computations.
This curriculum person is 100% right -- process is much more important than the rote memorization of arithmetic facts. Because our schools have put so much emphasis on rote arithmetic (and rote geometry, algebra, trig, and calculus), we have created generations of math-phobic students who never see the beauty and logic of math.
They will all eventually use arithmetic facts often enough to get to accurate answers (and billion dollar structural calculations are seldom wrong since they are always checked by multiple people and have built in safety factors for each structural member) but, in the meantime, teaching them the logic and processes of mathematics will give them a better foundation for tackling differential equations, statics, non-Euclidean geometries, and physics that are so important to science and technology professionals.
And this is not a matter of installing false self-esteem in kids -- it is simply giving them confidence that they can tackle math. One needs to tell them both what they have done correctly and what they did not do correctly.
Lee Nason, Engineer
New Bedford, Massachusetts