I read Amy and David Mantell's comments about unschooling math with piqued interest since math has always been a sensitive subject in our house.  Both of my husband's parents were college professors of math/physics so math education was highly prioritized by them.  Although they were always very supportive of our homeschooling in general, we knew they never really agreed with our inconsistent, laid back, child-directed learning methods when it came to their specialty and love, mathematics.

It was always their contention that a certain amount of drill, repetition and rote learning was necessary to truly "get" a solid mathematical foundation. Without strong math footings, they believed, our kids would be unable to build up a knowledge of higher mathematical concepts like algebra, calculus and trigonometry.  They were concerned that their grandchildren would be handicapped in later years if they wanted to go to college and didn't have the required math knowledge to get good SAT's scores.

In reading the Mantell's comments I agree that young children can very easily learn basic arithmetic concepts through everyday play.  My 8 year old son, Toby, does multiplication and division when he isn't even aware he is doing a math problem.  The arithmetic is simply a byproduct of cards or some game he is playing, but I wonder if he, who is not being pressured in any way to "do" math, is getting enough of a foundation to support him in his later years.

Unlike I did with his 3 older siblings, I never pressure Toby to do math.  We don't have enforced flashcard sessions nor does he tolerate being "quizzed" on math facts when we are driving or just hanging around, but on his own he has learned how to add, subtract, multiply and divide simple numbers.  He even learned about fractions, long division and multi-digit multiplication because he wanted to work his way through a Math Blaster computer game that required doing such traditional procedures in order to progress through the game.  But he is by no means a math natural, i.e. someone who innately is drawn to numbers and number problems and wants to play with number patterns for their sake alone nor do I see him playing with numbers like he plays with words when he's making rhymes, creating puns, unscrambling word puzzles or enjoying games like scrabble.

I feel torn by the whole math issue. I'm no longer willing to don the Math Enforcer helmet and be the schoolwork heavy in our house like I was periodically with my 3 older kids when they were Toby's age. And yet I tend now to think my in-laws were right that without a solid math foundation it is extremely difficult for a non-math kid to get a satisfactory result on a major test like the SATs.

My oldest daughter, Amber. wanted to go to college very much and she studied hard to be able to take the SAT's and jump through all the required college admission hoops.  Although her results on the English section of the tests were extremely high (she has always been a voracious reader) her math scores were relatively low.  Those low scores combined with her limited advanced math course work, required by certain state universities, made her ineligible for a number of colleges right off the bat.  She did get accepted to 3 of the 4 colleges she applied to and begins school in the fall but Amber feels her lack of math proficiency handicapped her and made her admission process much harder than it could have been.  She tells us now that she wishes we had pushed her more when she was younger, despite her strong resistance at the time, and that she had become more proficient at math.

In some ways I do feel like we let her down.  It's not that I regret refusing to insist she do schoolwork when she rebelled against it.  I'm glad I stopped doing that, but I  wish I'd found more creative ways to make learning math something that she wanted to do.  I could have tried harder to find mentors for her, some other person who might have inspired her with their own love of math (too bad her grandparents lived so far away).  At the very least, I could have been much better informed about what colleges required for admission so I could have given her guidance that would have helped instead of hindered her efforts for an easier college admission process.

I have a lot of trouble, as a homeschooled parent, being put in the role of task-master by my kids.  I really don't like having to stand over my children and make them do something that they don't want to do and that's how it often was with math when my three oldest children were younger.  We would alternate between regular math lessons out of books to very free form, indirect math learning with games and play.

Over the years I came to entirely reject the role of task-master.  What I really wanted for my children was for them to learn to direct themselves, motivate themselves to learn what they wanted and felt they needed to learn. But a problem can arise out of that philosophy too. If, as a homeschooling parent, you take a more child-directed, non-didactic approach to learning, how do you help your non-math loving kids achieve that solid rock foundation of basic math facts so they will have it should they need it when they get older and possibly want to go to college or pursue a career that requires many advanced math courses?

Theoretically, the answer is that a child who really wanted those things would be motivated to learn all the math they would need to know to pursue such a career or go to such a school.  But in reality, how many of our kids or us, as adults, for that matter, are that self-disciplined?  Deciding you need to become proficient at algebra II and calculus when you are a teenager and then learning it without a basic math comfort zone already in place is, as my in-laws always suggested, a very difficult thing to do.

During the high school curriculum stage of my older kid's homeschooling, they struggled through math textbooks, often rebelling against doing the required work.  It was a long, drawn out, not fun process to complete algebra I and geometry.  None of them ever chose to take algebra II or any other more advanced electives although they were available had they wanted to.  (Note: the American School college-track high school degree program did not require any math above algebra I and we took that to mean that more advanced course work was unnecessary to meet most college requirements.  Unfortunately, we later realized that that is not true for state universities in Florida or NC, two of the states where our daughter wished to attend schools. Both states required at least one other advanced math course in addition to algebra I.)

I doubt that I will follow a correspondence curriculum for Toby like I did with his siblings unless he really wants to.  Although I still feel going the curriculum route has merits, it also has drawbacks.  Perhaps the main disadvantage to buying a pre-packaged program has been that most of the required courses were not subjects the kids were ever really interested in learning at the time.  Some were, of course, and other subjects surprised them by exposing them to interesting concepts and ideas they might not otherwise have happened upon until later but, for the most part, I don't think they enjoyed the overall experience.

Believing that learning should be fun and that people should follow their hearts to study that which interests them is at odds with the philosophy that certain core knowledge is necessary in order to develop a well-rounded foundation that will enable people to move easily toward whatever directions they later wish to focus on.  After 12 years of homeschooling I am still unresolved about that conflict between two seemingly opposing perspectives on learning.