I used to worry about teaching my children math. See, I’m not great at math. It all started when I was taught to add and subtract with “touch-math” in first and second grade (OMG, they still use that method somewhere? It’s so addictive I STILL use it to balance my checkbook in the absence of a calculator *SIGH*) and was compounded when I was handed a sheet of multiplaction facts to learn, but wasn’t told that I should ask my parents to help me memorize them. I told my mom when she saw that I had no stars on the chart indicating who in the class had mastered the multiplation tables (don’t even get me STARTED on the problems with that), “everyone just KNOWS them and I don’t know how they do it. I don’t know them.”
Sometime in middle school I decided that I would just work my ass off and DO IT, even if I didn’t GET IT. I tested into early algebra in 8th grade and had some of the biggest homework battles ever with my mother that year. I couldn’t understand what she was saying, and when I did, she was telling me to do it differerently than the teacher told me, which would mean even if I got the answer right, I wouldn’t get credit because I’d used the wrong process to get the right answer (if you come up with the right answer, how can the process be wrong?!). I decided to stop asking her for help and muddled my way through the rest of my math classes with a B- or C+ average (this was hard because up until this point, I had been a STRAIGHT A student). Since I took early algebra, I was in the “college track” in high school and took more math than required, all the way up to trigonometry in my junior year and calculus in my senior year. I knew as I was working my way through this process that I had a string of REALLY BAD math teachers (and this is true…just because you can DO it doesn’t mean you can TEACH it). As a matter of fact, I quit calculus after three weeks and joined the school’s newspaper staff in third period because calculus wasn’t something I needed, my GPA certainly didn’t need to reflect my efforts at calculus (isn’t that ironic: I decided to stop learning higher math because I feared what it would do to my GPA and thus my college prospects), and because the teacher was so bad that our soon-t0-be valedictorian was teaching the class behind her back (incidentally, he was the son of missionaries and homeschooled until 8th grade when he joined our closed-minded little learning institution). Don’t get me wrong, we all loved our teacher. She was great fun, sweet, her son was in our graduating class, but man…she couldn’t bring her mind down to a level that would allow her to communicate in a way that our brains could understand!
Interestingly enough, my struggle with math was one of the reasons I started to consider homeschooling. I remember sitting in my weekly talented-and-gifted class in third grade looking around the classroom and thinking “when will I learn to do math with letters? and how on Earth can you add letters?” The class met in a freshman algebra classroom and there were always algebraic equations all over the board during our weekly sessions. At the point when I figured out that a letter simply represents an unknown (about 2/3 of the way through my first year of algebra…seriously, the first 2/3 of the year I was still trying to figure out how you do math with letters!), I realized that someone could have saved me a lot of time by teaching me this concept when I was much younger and homeschooling became a thought in my head and eventually that thought became a reality. Still, I wasn’t sure that I was competent enough to teach my children math. Sure, I managed to muddle through and grasp a lot of concepts that other people don’t (Jason often calls me from work for help with geometry, partly because I’m near a computer and can google formulas for things like the volume of a cylinder, but also because I can do things like figure out the angles of a right triangle using just the measurements of the sides: Hello, Trigonometry!), but I am still haunted by the notion that I’m “bad” at math.
The other day I realized that rather than a hindrance to my teaching efforts, my struggle with math is an advantage. A friend was asking me about doing homework with her second grade daughter, who is in public school. The math homework was simple addition and math facts and her mother was frustrated after doing it with her because the daughter didn’t grasp the concepts (ie doesn’t naturally think mathematically…this sounds very familiar to me!). For example, she didn’t understand that addition is commutative so 5+3 and 3+5 are always going to equal the same number. Her mom kept saying to me (and, I suspect, to her), “her thinking doesn’t make any sense.” As an example, she said that the daughter, in trying to figure out what 6+6 equals expressed her reasoning this way: “since 6+7 equals 14, 6+6 equals 14.” And here’s a secret: I’m so “bad” at math that I didn’t realize that both of those statements are wrong for at least a few moments!
I tried really hard to explain to this mama, who obviously thinks more mathematically than either or daughter or me, what might be going through her daughter’s head here. First of all, none of this makes any sense to her at all. Her reasoning illustrates that she is feeling the way I felt with the multiplation tables: everyone else just KNOWS this and I don’t. She is guessing, hoping that she’ll get it right and get let off of the hook. To say that her thinking doesn’t make sense doesn’t help her because to her none of it makes sense! There’s no rhyme, reason or order to it (as indicated by her belief that both 6+6 and 6+7 equal 14). She doesn’t understand that there’s a process behind it. While many people have tried to explain the process to her (I know her mom has, she was talking to me about what she was doing to teach this concept and it was very reasonable, sensible stuff), no one has managed to explain it in a way that resonates with her. I tried to explain all of this, but was worried that I was coming off as critical of her daughter or of my friend’s teaching methods. I guess I was critical of her teaching methods (though again, they were perfectly sensible to someone who already knows the concepts or who thinks mathematically) because as we talked about it, I was taken back to first and second grade and realized that her daughter was probably feeling just as confused, hurt, stupid, and attacked as I did every time someone tried (and failed) to explain the math concepts to me yet again. I love her daughter and don’t wish anything like my math struggle on her, so I tried to explain to her mama that unless she approaches this very gently, her daugher will decide that she’s just “bad” at math and shut down, even at this early age!
Today I was reading John Holt’s Learning All the Time and I had to call my friend because John Holt says all of this so much better than I said it to her the other day. I told her that she MUST read his chapter on math before she does another homework assignment with her daughter: it’s THAT good!
A few excerpts:
“Nothing makes school more mysterious, meaningless, baffling and terrifying to a child than to constantly hear adults tell him things as if they were simple, self-evident, natural and logical, when in fact they are quite the reverse–arbitrary, contradictory, obscure, and often absurd, flying directly in the face of a child’s common sense.”
“It occurred to me then…that children could get a very strange notion about numbers. They might see them as a procession of little creatures, the first one named One, the second named Two, the third Three and so on. Later on these tiny creatures would seem to do mysterious and meaningless dances about which people would say things like ‘two and two make four.’ It seemed likely that any child with such a notion of numbers could get into serious trouble before long…For this reason when…little children frist meet numbers they should always meet them as adjectives, not nouns. It should not at first be ‘three’ or ’seven’ all by itself, but always ‘two coins’ or ‘three matches’ or ‘four spoons.’”
He goes on to discuss addition and subtraction and the teaching of “math facts” like “3+2=5″ and “2+3=5″ and the fact that they are taught separately. About this, he says the fact that a group of five things can be divided into a group of two things and a group of three things “is not a fact of arithmetic, but a fact of nature. It did not become true only when human beings invented arithmetic. It has nothing to do with human beings…an infant playing with blocks or a dog pawing at sticks might do that operation, though probably neither of them would notice that he had done it; for them, the difference …would be a difference that didn’t make any difference. Arithmetic began…when human beings began to notice and think about this and other numerical facts of nature…Once we get it clear in our minds that [this] is a fact of nature, we can see that…whether we put these in symbols or in words…they are simply four different ways of looking at and talking about one original fact…In short, all of the number facts that children are now given, and then asked to memorize, they could discover and write down for themselves. The advantage of the latter is that our minds are much more powerful when discovering than memorizing, not least of all because discovering is more fun. Another advantage is that so much of arithmetic (and by extension mathematics) that now seems mysterious and full of coincidences and contradictions would be seen to be perfectly sensible.” (bold emphasis mine, all other emphasis his)
Now, chew on THAT! You mean, children can be allowed to discover mathematical principles on their own and in the process LEARN to think mathematically?! Sure, some people are more mathematically minded than others (my long-time friend Robin is a great example of this…she has always thought mathematically, much to my amazement, especially when we were sitting in 8th grade algebra together!), but I realize now that people who think mathematically after a typical elementary school math education do not think mathematically because of the way they were taught, but IN SPITE of the way they were taught. However, it is possible to teach (0r more appropriately, to allow children to learn) math in such a way that those who don’t naturally think mathematically can learn to think mathematically, which is a very important skill in any society, but particularly in our society, which rewards technology and innovation more highly than it rewards creativity and art.
I fantasize often about going back to college and taking the courses that I avoided because I was “bad” at math: calculus, organic and inorganic chemistry, statistics, microbiology and so on. Incidentally, these are all prereqs for a career path I would love to follow: medicine (specifically obstetrics). So far, though, my fear of all things mathematical has prevented me from taking that path. I’m slowly learning to think more mathematically and to reframe my math struggle to realize that someone who successfully learned trigonometry and precalculus in high school is not “bad” at math! I hope that someday I’ll be able to choose that path or at least to say that I chose not to take that path for reasons besides fear of math!