Continuing with this month’s theme of digging into how unschooling is different than school, and with reading and writing under our belts, let’s tackle math. Because unschoolers don’t slice the world into different subjects, we see a broader picture of the myriad of ways math is intrinsically tangled with the world. We see math as much more than just arithmetic, the branch of math concerned with numerical computation, which is the main focus of school’s math curriculum, certainly in the earlier years.
I was recently asked to sum up my experience with unschooling math and here’s what I wrote:
“As an unschooling parent for over ten years I’ve seen how resolutely my kids pursue their interests and goals. Their persistence when they are curious and motivated seems inexhaustible, even through frustration and disappointment. But, as unschooling parents realize, real learning is minimal when a person is disinterested. When they need math is when they learn math. My kids encountered everyday arithmetic living and learning in the world around them: counting toys; playing board games; calculating hit points; baking delicious food; making store purchases; measuring distance; balancing their bank account. The reasons for performing these tasks are clear, and the computational skills are picked up unobtrusively along the way—without developing the usual curriculum-induced aversion to math. And many adults living active and joyful lives have no need for more advanced skills.
Yet in the real world, mathematics is so much bigger than arithmetic and through years of exploring the world, analyzing situations, and making choices, my kids have developed solid critical thinking, reasoning, and logic skills. It’s that strong foundation of mathematical thinking, along with their everyday computational skills, that I’m comfortable will continue to support them in whatever direction they choose to pursue. If at any point the interest or need to learn more advanced mathematical skills presents itself, that’s when they can be picked up. The time conventional students have spent learning what they know, (say, a high school math curriculum) my kids have spent learning other things that make up their knowledge base. With a lifelong view of learning there is no value in comparing the particular ages at which people learn things. It’s not a competition; there’s no behind or ahead. Time is not lost, just used at their preference.”
There are a few ideas in there that I’d like to expand upon now that I have the space. 🙂
“without developing the usual curriculum-induced aversion to math”
This is a big one, just google math anxiety or phobia. There are a couple of ways that school’s math curriculum contribute to this phenomenon. First, with the early focus on arithmetic, math quickly boils down to right or wrong. And who wants to be wrong? Soon, many kids would rather avoid it altogether.
Second, with the focus on “show your work” for full marks, children aren’t encouraged to think and play with numbers. Class time is focused on preparing kids to do well on the next test so there isn’t time to explore other ways to get the answer, or why some approaches that seem logical at first can lead you astray, or to try to understand a student’s intuition when there’s a right answer and little written work to back it up; they are expected to memorize a process to get to the answer and repeat it ad nauseum. And on that test, you had better use that same method the teacher taught to get to your answer. This is often because grade school teachers aren’t themselves fluent in math so they only understand the one typical method through a math question. And that’s not meant as a slight on the teachers—that’s the way the system is designed.
I still remember, more than once, sitting around the kitchen table choking back tears because my well-intentioned Dad was showing me how to work through some math problem using a different method. I knew that wouldn’t be acceptable. I kept saying “but that’s not how the teacher wants us to do it!!” And I wasn’t math phobic at all. I ended up taking math all through university for my engineering physics degree. But the environment created through school was such that I just wanted to learn the method they wanted me to use and get on with it.
“many adults living active and joyful lives have no need for more advanced skills.”
So, having taken countless math courses over my school career, was it worth it? I liked math and I enjoyed wrestling numbers for that right answer—it was a game, a puzzle. And I imagine some of those advanced math skills would be useful for many practicing engineers, though in my own ten-year career I didn’t use them. And I certainly couldn’t use them now, though I’m pretty sure I could relearn them, if I had a need.
“But they need to know about calculus!”
Just because unschooling kids don’t follow a math curriculum doesn’t mean they will never know that advanced mathematical topics and skills exist; not teaching something is a far cry from actively shutting kids away from it. If they have an interest or passion in something that extends into more complex math (say, for example, computer programming or complex origami or game theory or astronomy), they may become interested in learning more. If they love playing with numbers, they may encounter it that way, as they explore deeper and deeper. The need for some people to understand and use higher mathematics exists in the world for real reasons. And it’s through those reasons that interested unschooling kids will find it.
Yet there aren’t a lot of careers that require advanced math skills. Many adults living active and joyful lives have no need for them—myself included. One of the advantages to unschooling is that the children don’t spend time learning stuff they might need to know some day; they spend time learning what they need or want to know *now*. With the corollary being when they need or want to know something, they learn it.
“strong foundation of mathematical thinking, along with their everyday computational skills”
I was surfing around the web while writing this, brushing up on the reasons being bandied about for why students should learn advanced math. This quote is representative of what I found: “Many jobs and hobbies will require a quick mind that is logical and able to creatively solve problems. Each of those skills can be perfected by studying math. It may not seem like you will use the things you learn, but they will improve your mind and your ability to be flexible with what you want to do in life.” (This one happens to be taken from http://www.freemathhelp.com/math-real-world.html)
I understand the reasoning. Solving higher math problems often demands logical thinking and analysis to parse out the applicable method. But there are other paths to developing those skills beyond a math curriculum. Instead, unschooling kids gain logical thinking and reasoning skills through their experiences with analyzing situations and making choices on a day-to-day basis. Unschooling parents work hard to give their children the time, space, and support to gain lots of experience with those critical thinking skills that enable them to evaluate, compare, analyze, critique, and synthesize information, regardless of topic. Unschooling encourages that in spades. As the quote above suggests, and I agree, it’s not really about the math.
“Time is not lost, just used at their preference”
Along those lines, during the time kids in school spend learning that math curriculum, unschooling kids aren’t sitting around learning nothing; it’s not a void created in their lives. They are living and learning other things that have meaning for them. They know lots of other things useful to their lives that schooled kids don’t. The point is, it’s not a competition. Time is not lost, just used at their preference. If learning more formal computational arithmetic and advanced math becomes a need or interest, they can pursue it then, regardless of their age.
So here’s what math looks like from my unschooling perspective. Arithmetic is useful because it’s basic stuff that we use in our day-to-day lives—unschooling kids learn these computational skills by encountering the need for them as they live in the world. Critical thinking skills are beneficial to contributing to society and achieving our personal goals—unschooling kids gain these skills through gathering, analyzing, and critiquing information, making choices, and feeding the resulting experiences back into that loop as they follow their interests and passions.
And in my experience, that’s a great foundation for living an active and joyful life.
Glenda Sikes says
This is a beautifully-written post, Pam, one I happen to agree with 100% =).
Pam Laricchia says
Thanks, Glenda. 🙂
Beatrice Mantovani says
I’ve translated this one into French too: http://apprendreenliberte.wordpress.com/2013/04/05/les-maths-ne-se-resument-pas-qua-larithmetique/
Dave Crigger says
While I understand what you’re trying to say with the post, and basically agree, I completely disagree with the title. All math is arithmetic. I’ve used this approach to help math-phobes get past their fear of higher mathematics by showing how even calculus is just complicated arithmetic. Math is learning to do the next iteration of what you already learned, and it’s all based on addition.
Pam Laricchia says
I understand your point, Dave. And describing higher-level math as just complicated arithmetic can be a helpful way to help people move through their fear and intimidation of higher-level calculations.
What I was trying to say is that math is so much bigger than the calculations themselves. It encompasses logic, patterns, and critical thinking. For example, I’ve been re-watching some episodes of Numb3rs lately and the “breakthroughs” in the math side of the case are often about the logic, about how to look at the data available creatively and figure out what kind of analysis might answer the question at hand. And then they crunch the numbers, i.e. do the arithmetic/calculations.
So when someone figures out ways to approach putting a puzzle together, that’s math. When they play with the logic of the Monty Hall problem, that’s math. When they play a game of checkers or Clue, even though there are no numbers or calculations involved specifically, they are full of analytical thinking. Math thinking. But not arithmetic. By saying “math is more than arithmetic” I’m not trying to say that math is more complicated than arithmetic, but wider-reaching.
An expanded view of math can help some people feel less intimidated by math itself. It can be another way to help a parent ease past their worry that without calculation worksheets their children “aren’t doing any math.” 🙂