Lift Up Your Hearts!

I can hardly count Perla Adams my friend, since we met online and I only visit her blog occasionally.  It's in my feedreader, but the posts and comments in Spanish get ignored.  I'm not proud of my monolingualism, but must deal with it.  Still, I'm not sure how to speak of her in this introduction.  "Internet acquaintance"?  "Fellow blogger?"  Nothing sounds quite right.  Anyway, this delightful person, of whatever label, recently wrote a post (in English) that provoked me to comment, and when I write that much I usually can’t resist sharing in more than one place, i.e. what I’ve written ends up here.  You can find Perla’s original post on her blog, The Classical Mommy.  (That's actually her main site, with all sorts of interesting things.  The post on math is here.)  My response, with a few modifications, is below.

Research on the Teaching of Math (one of the links Perla included in her post) is interesting; it is also disturbing, because some of the researchers seem to be amongst those who are afraid of mathematics themselves.

As you may or may not know from things I have posted, if I must give myself a label (which I usually don't), I'm closer to the "unschooler" side of the continuum, though I do believe in organization and discipline.  I also greatly respect Raymond and Dorothy Moore and agree wholeheartedly that children under the age of 10 should not be in school.  (Personally, I would extend that to at least 14.)  However, that doesn't mean I would withhold "formal" instruction from them, even workbooks.  There is a world of difference, which the researchers seem to have missed, between academics in a school setting and one-on-one, relaxed instruction at home that is sensitive to the child's needs, desires, and capacities.  In that context, a workbook is just a tool like any other, to be used or misused.

I am glad to see that some of the writers realize the importance of much immersion in mathematical language, even while recommending delay of mathematical study.  Because mathematics is a language, and as such much better grasped at an early age.  You certainly know much more about multi-lingualism than I do, but wouldn't you agree that those who learn second or third languages at a very early age learn them much, much better than those who wait till 10 or 12 to begin?  I've read studies (sorry I can't give a link) that show that language learning is physically different in the brain for early and late learners.  I strongly suspect that's also true for mathematics.

The question, I suppose, is then:  What is the equivalent in mathematics of making a two-year-old sit still for formal French grammar drills (which is not how they learn), and what is like surrounding the child with a linguistically rich, correct, and abundant exposure to the French language?  We must be careful not to give our children the equivalent in mathematics of a diet of French baby talk or street patois.

In everything we must be sensitive to our children.  Being a math major myself, I had no fear of the subject to pass on to my children, and they quickly came to understand that math and logic are delightful games.  (Better than me, in fact, since my initial mathematical experiences were those decried in the research you cited.  It wasn't until I discovered algebra that I realized math didn't have to be confusing and boring!  It wasn’t my age, but the subject matter that opened my eyes.  If I hadn’t been put into that advanced class in 8^th grade I’d have been miserable for yet another year.)

It's true that the one in our family who developed her mathematical skills the most was the one least exposed to stultifying school mathematics, but what I want to emphasize is this:  workbooks and worksheets were an important part of her preschool education—by her own choice.  She wanted "homework" like her older sister, and devoured every math workbook I could get my hands on (thanks to a helpful first grade teacher; there wasn't much available to the lay person in those days) and every worksheet I could invent for her.  Perhaps that did destroy her understanding of math, and we thus deprived the world of some brilliant mathematical discoveries, but somehow I doubt it.  Granted, her heart is in music, not math, but she “speaks” math and logic with ease, and she did get a math degree "along the way" in college whereas I had to struggle for mine.    As a young child she absorbed mathematics the way a Parisian child absorbs French, and workbooks were one of many contributors to her exposure.  They are not evil, nor are "formal" lessons, if one is sensitive to the individual child.