The Magic Numbers: A New Way to Teach Math
Asking a child to memorize the times tables is like asking them to memorize the meaning of each hieroglyphics on a cave wall.
It's the look that's somewhere between constipation and a fear of public speaking. Though it's slightly different for each kid that struggles in math, the feeling is undoubtedly there. It's the sick, sinking feeling of being asked something you don't know and have no way of figuring it out. A set of abstract lines and shapes in the form of numbers from the times tables. For some, this feeling comes every day at the same time; math class.
Imagine a student that has never been taught the right way to do math. When a basic facts question comes up in one of the units, like geometry, fractions, or algebra it not only brings up these feelings, but while they are trying in vain to answer it, they can't focus on what is being taught. When asked what 6x7 is, a great deal of time and energy is spent counting up by sixes or seventh until they think they have the right answer. While the focus is on counting sets, the teacher has explained all the details of how to solve the question. Not only are they doing a lot of extra work mentally, they developing bad habits that often never get broken.
A good way to look at this is to imagine two students working out side in a garden. Asking the first student what 6 × 7 when they can answer it quickly is like asking them to carry one load of dirt. Asking a student what 6 × 7 is when they can't answer without counting six sets of seven or seven sets of six is like asking them to take seven loads of dirt. At the end of the day the second student will have done six or seven times more mental work than the first. Not only will they be tired and exhausted but based on our great wisdom, the solution is to give that student more work after the school day is done in the form of remedial homework. It's no wonder some kids learn to hate math.
At this point, when a child doesn't know the answer they have three options. The first is to contemplate going to the bathroom, a great way to get out of a tough situation and to be quite honest, a quite natural reaction. The second is to rummage through their mind hoping for a strategy that might work even though nothing in the four years prior to this moment has. It's kind of like a frazzled grandmother rummaging through her purse at a car accident hoping to find a stethoscope to help the man with a broken arm. It's hopeless. The third option is to stand and look as awkward and pathetic as possible hoping a classmate will whisper in answer to them. Why do we put kids through this?
The problem is, most children minds aren't designed to remember abstract lines or shapes. We are not asking them to remember something concrete, just a bunch of random curved lines. The number eight as it's represented with lines means nothing to them. If it were that easy, everybody would be able to memorize the Mandarin language of symbols in the same way. Somehow their brain is supposed to remember that the number of reindeer pulling the sled is the same as two circles stacked on top of each other. Sounds crazy, but we ask very young children do some very abstract things.
Here's a perfect example of how our mind works. When was the last time you read the story The Three Little Pigs. I bet it was at least a year (if not years) ago. You probably have not read a book like this since you were a kid, unless you have young children yourself. In which case, you don't read it every night, at most maybe once in the past year. But even though it was a long time ago I bet you still remember who blew the houses down in the story. You probably also remember the name of the girl who ate the porridge in 'The Three Bears" or what kind of animal "Mary" had.
Now let's try some abstract lines. Most people use a computer keyboard at least once a week, if not on a daily basis. Now if you're one of those people, try to answer this question. What symbol is above the number is on top of the number 7 key on the keyboard? Is it an *, %, or $? Your mind probably looks like a very long curse word but you probably still didn't come up with the right answer. Chances are, even if you did guess right, you're still not sure if it's the right answer. Some things are easy to remember and some things aren't. Asking children to remember the times tables is asking them to do something very difficult.
Looking had a child trying to figure out what 6 × 7 is, when they never been able to do it fluently, is like watching a car accident. It's horrible and you can feel their pain, but you can't look away. I'm guessing it's the same look I had when my daughter asked me were all the purple color went after she drink grape juice then went to the bathroom. It's a horrible, sick feeling when you don't know the answer. I wanted to explain it to her using biology and chemistry concepts and make a simple but understandable analogy using marbles as molecules, but the truth is, I don't know the answer. The only solace for children stuck in a class they are not good at or simply hate is they only have to spend two thousands hours of math class during their elementary school career.
These questions, or basic facts, without question are the most important thing to learn in math. The basic facts in math are adding, subtracting, multiplying, and dividing using two numbers no bigger than 9. That means questions like 6 × 7, 8 + 5, 13 - 4, and 24 ÷ 8. If the child is struggling with math, chances are they don't know these basic facts, or they don't know them well enough. The basic facts are included in everything in math. In geometry, trying to find the area of a rectangle, a child will have to multiply the width and height. When studying equal fractions, whether you cross multiply or use a different strategy, students will need to be able to multiply two numbers together. When doing algebra you need to be able to add subtract or multiply to find out the answer for each letter. Basic facts in math are like snowflakes in Canadian winters. We can pretend they're not there, but the reality is, they are everywhere.
The expectation of a child should be to know the basic facts with one hundred percent accuracy and to do each one in no less than three seconds. Research shows that three seconds for each question is a benchmark for how well a child will do that math. Though answering a question in less than one second is ideal, if it's any slower than that, they are going to struggle. Simply put, a child who was listening to instructions from the teacher will be lost when it comes to numbers that he has to count on his fingers or count sets of. While doing this mental calculation, the rest of the lesson is lost. They are spending all of their time in their head counting.
Many kids have learned math in an untraditional and unconventional way.
Imagine girls and boys as young as six and seven years old sitting in a circle listening to stories. With giggles and gasps of excitement, they listen to Munsch style stories that including them or their friends. They hear how their mom lost it and broke the kitchen when a spider scared her or how two of their friends made a tower of books that toppled over and smashed into their teacher's car or how their brother or sister crashes a tricycle into a fire hydrant causing their grandmother to get soaked while carrying her groceries home. You watch as this cute and friendly, but slightly delusional substitute teacher wastes your child precious math time by telling stories for no other reason than to get cheap laughs.
Then he starts to explain how these stories can help them remember math. With simple, easy to understand words he explains how they just learned how to multiply numbers, something they are not supposed to learn until grade four or five. Now they are even more excited and are hooked. They now listen as the objects turn into numbers, numbers that will be almost impossible forget. A spider become the number 8 since it's body shaped like an 8 and has 8 legs. He also points out that every number has a color, something he says will help them later. He says, "Can you think of something that has handlebars shaped like a 3, 3 wheels and is called a 3-wheeler? I'll give you a hint. It's red." Every hand goes up. (He'll help them with that later... )
Now this is something adults have trouble with, especially teachers. I am a teacher and can tell you there is something deep inside of us that tells us that that we should know everything before we teach it to children. We convince ourselves that we are experts on the Fur Trade because we read a chapter in a textbook written in the 1980's... twice. We for some reason think that we can stay ahead of children, even though we still haven't set the time on our VCR. It's really sad that we still have a VCR. The reality is at this point, we may not be able to keep with their learning.
Here's how it works. One story is about Sarah's mom freaking out about a giant spider that crawls into the kitchen. She grabs a golf club and starts swinging at the spider knocking over everything in the kitchen like the flour jar and vase. The spider crawls onto the curtains of the house. She cries out like a wild banshee, swings and misses the spider, but smashes the window. Now for those are now uptight at the level of violence taught to our young minds, please send your concerns to Bill Nye. After telling this crazy and slightly violent story the substitute teacher begins questioning the children.
Teacher: We're going to figure out 8 x 9. Can anyone tell me something that is shaped like an 8, has eight legs and is black?
Jamie: A spider?
Teacher: Nice job. What's shaped like a 9, comes in sets of 9 and is called a 9-iron?
Jesse: A golf club?
Teacher: Wow! Good job. Now does anyone remember a story with a golf club and a spider?
Anna: Yeah. Sarah's mom was chasing a spider around the house and (blah, blah, blah). It's not that she's boring, but with her first few words I know that she's remembered the story. And yes, I am the geeky substitute teacher).
Teacher: And what get's broken? (Here's where it gets cool.)
Graham: The window of the house.
(The teacher get the group to make a 'roof' shape with their hand, turn it sideways and asks them what number it looks like.)
Teacher: 7. Right. It the bigger picture so we'll say 70. And how many curtains are there? 2 right. So eight (spider) times nine (golf club) is seventy (house) two (window).
It seems surreal so he goes through the story again and the kids are engaged. Go ahead. Read through it again. Pretty cool, right?
Now this is one of six stories he tells for their first sit down. Question after question the kids are able to answer and seem excited about them. It's almost like they know they can't get the answers wrong. It is the first time they see connections and start to see numbers in a different way. It's like they're not in the math class that they remember. Now math is fun, fast and easy.
Now this teacher who seems like a cross between Christopher Lloyd from back to the Future and Bill Nye the Science Guy seems to have stumbled upon something pretty cool. I guess stumbled might not be the right word. This way of thinking actually has a pretty fascinating history. This book is too short to go through the entire history, here's a quick explanation.
This technique of using mnemonics, strategies for remembering things, goes way back even to the time of Ancient Greece. A simple example of a pneumonic is the word 'HOMES' for remembering the Great Lakes of North America. Each letter stands for one of the five Great Lakes; Huron, Ontario, Michigan, Erie and Superior. Another is using the phrase 'Every Good Boy Deserves Fudge to remember the notes on a musical staff or the name ROY G BIV to remember the colors in the spectrum. There are different types of mnemonic devices, though some are more effective than the others. You can connect information either using logic, like the spider is a number eight because it's shaped like an eight and has eight legs, or using the opposite of logic like a crazy story about Sarah's mom freaking out in the kitchen. Both ends of the spectrum work well.
These math stories use mnemonics that work with kids. Because they include them, friends or family, they are wild and crazy, out of this world or magical, they trigger emotions or their senses and they are just plain fun, kids will remember them for a lifetime. Most people can't remember what they had for breakfast three weeks ago, but if they heard a story about an African elephant crashing through the wall of the kindergarten class, picking up the small blonde haired girl and carrying her off to a spray park, they would remember that story forever.
By putting numbers into very specific stories with very specific mnemonics, children as young as 5 years old can memorize the entire multiplication facts in a few hours. Consider it takes most children spend years trying to learn them with a very low success rate (less than one in three). Suddenly math becomes fast, fun and easy.
By Darren Michalczuk