What To Do If Your Child Struggles With Math
I teach high school mathematics. I’ve done so for nearly ten years. I’ve taught everything from algebra to calculus to computer science. In other words I’ve got a lot of experience watching kids struggle with learning mathematics. I’ve come to the conclusion that there are only two reasons why kids don’t do well with math.
I know you want to know what the reasons are, and I’ll tell you in just a moment. First, however, I need to explain and defend myself.
I suspect there is no discipline so rife with buzz words and impotent panaceas as public education–unless it’s witchcraft. Over the past ten years, I’ve been through more education fads than Madonna has boyfriends. Every year, we hear of another sure fire fix. Every year, the quick fix does not work. Check out this excellent post about education-speak.
Parents look at their children and wonder why they can’t read or do simple mathematics. All that is really asked of us is to teach the basics, which are roughly reading, writing, and arithmetic. Yet, as we push more and more children into the stratospheres of calculus and AP chemistry, we have more and more children incapable of these basics.
Almost without fail, the children whom I have taught who struggle in mathematics have not mastered two things. One, their multiplication tables. Two, arithmetic with fractions.
There! That’s it! That really is all there is to it.
I’m completely convinced that if your kids really learn their multiplication tables and then learn to do arithmetic with fractions, the rest of high school math will be much easier, even fairly simple.
You see, algebra is nothing more than arithmetic with letters. Trigonometry is merely a simple extension of algebra. Calculus only adds a couple of concepts on top of all of this.
So, the gateway to excellence in math is not found in the smoke and mirrors fad of the year. The gateway is merely learning the multiplication tables and fractions.
To be completely clear, let me define what I mean by “learning” the multiplication tables.
The way multiplication is taught in elementary school is this. Children explore multiplication. They do things like line up four columns of bunny rabbits and then put five bunny rabbits in each column. Then they count the bunny rabbits. Well, four by five, that’s twenty! There! They just multiplied four by five.
There is a misunderstood and therefore pernicious concept going around called “child-centered” learning. The idea is that children, through their innate curiosity, need to lead the education process.
At base, this is a great idea! I learn a lot just due to application of my own curiosity.
The problem is roughly this. A child’s curiosity generally leads to a cursory understanding of subjects. It’s a unique child who is so curious and so driven that she will stay with a subject to the point of mastery.
Yet, schools tout child-centered learning as a way out of the education morass we’re in. In the Stalinist world of public education, by the time a good idea is implemented, it’s usually only the shell of the idea that’s left. The function, the meaning, is all but lost. Most of our directives make about as much sense as ritualistic dances of the Cargo Cult.
You see, here’s what happens. Your child learns to place bunnies in rows and columns and count them. The teacher doesn’t really understand that counting bunnies is a sham substitute for mastery of multiplication. Yet, since your child can count bunnies proficiently, the teacher assumes that the child has “learned” the multiplication tables.
Of course, something so shallowly learned is quickly forgotten.
Exploration has great merit. However, once a topic is explored, to whet the appetite, mastery normally comes through rote memorization, especially at the more basic levels.
Multiplication tables must be memorized! Grammar must be memorized! I remember in elementary school when I was a kid the whole class chanted the multiplication tables over and over again. It seemed horribly boring. I was horribly boring! Please note: I’m now a mathematics teacher. I know my multiplication tables.
After a child has mastered multiplication, he must master fractions. I can’t tell you how many smart students I teach who really struggle with new concepts in math because they can’t add 2/5 to 9/7. Even in my honors classes, a lot of students (maybe most) confuse the rules for multiplying fractions and those for adding fractions.
Invariably, even my honors students reach for the calculator and try to convert everything into a decimal. That will work if you’re only adding numbers, but when you need to add complex algebraic fractions…well, the calculator is not longer your friend.
How did these kids get convinced that you can do all math by turning everything into a decimal? By some mathematically challenged elementary school teacher/idiot. Probably the same one who thought teaching multiplication was all about lining up bunnies.
Your kids must master (memorize) the rules for arithmetic with fractions. If they do, then high school math should be a no-brainer. If they don’t, well hopefully they’re good at English…or sports.
What children really need to learn through high school is not that hard. What’s lacking is proper foundations, because in elementary school “fun” was substituted for real learning. Don’t even get me started on middle school. Let me just say that my opinion of middle school is that it’s something like “Lord of the Flies” meets “Clockwork Orange”.
Public school is not necessarily going to teach your kids what they need to know about basic math (mastery of multiplication and fractions). You as a parent must take complete responsibility for the education of your children.
You have to teach your kids this stuff yourself. If you don’t really know your multiplication tables that well, make a chart and drill your kid using the chart. By the time they know them, you will too. Same goes for fractions.
Simple solutions requiring some hard work. Oh well, time to roll up the sleeves.
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May 2nd, 2007 at 2:25 pm
Agree completely. I did know my multiplication tables, but fractions were not completely explained to me until high school chemistry (stoichiometry). Only then did I understand that they are the same as division. Then the whole PEMDAS thing made sense. Algebra was unfortunately a mystery until I was forced to learn it for college Calculus. Fractions taught properly and learned well would have made my school life so very different.
May 2nd, 2007 at 3:57 pm
Daisy, Thanks. Actually, fractions even more than multiplication is where we’re missing. A good student can learn their multiplication tables either by osmosis or other means, but it’s much more difficult for that student to learn arithmetic with fractions.
May 2nd, 2007 at 6:55 pm
Lee,
I agree on rote memorization of multiplication tables, but I disagree about grammar.
Memorizing multiplication tables through 12 is a foundational math skill. There is nowhere to go without it.
That just isn’t the case with grammar. You can learn perfect English by osmosis. The problem is you must be surrounded by people that speak and write proper English. I work with a man who immigrated from Germany shortly after the 2nd World War and didn’t know a word of English. He speaks and writes better English than I do and hasn’t been taught ANY English grammar. Teaching grammar at the Elementary and Secondary school level distracts kids from learning and understanding the proper applied use of the language. The problem for many of these public school kids is that teachers are the only people they communicate with that speak and write proper English.
Anyway…
My opinion.
May 2nd, 2007 at 8:00 pm
Steve, Thanks! I might modify my stance somewhat on grammar, but not much. You would have to know how much German grammar your German friend knew before he came here. If he was educated in Germany before WWII, I would suspect he knew quite a bit. When you know the grammar of one langauge, it’s a lot easier to learn the grammar of a foreign language.
I completely agree with you that kids need to learn applied use of language, by which I’m guessing you mean how to write an essay and how to speak properly. My problem is this: a lot of the kids I teach know so little grammar that I can’t even begin to talk to them about what they need to change. When I have kids write essays (we call that writing across the curriculum), some of them have such trouble with the mechanics of their language they can’t even begin to express themselves.
One more thing. I’ve never taught reading, but I suspect it’s a lot more difficult in some cases than teaching mathematics. One of the huge influences on children is what they’ve heard at home before they even come to kindergarten. Both my wife and I have college degrees. We speak like educated people even when we’re just discussing what we want to eat for lunch. A kid from a background like ours has at least twice the vocabulary that a kid from a lower socioeconomic family has. Math’s different. In math kids start out on a more even footing.
Anyway, fabulous comment!