Letting Life Lead
Let’s face it. If you are reading this, you are probably old. That’s not a bad thing. We are experienced and wise in the ways of the world. Experience is often a boon when we are learning new things. However, that same experience can sometimes impede learning. For example, take a look at the Japanese characters in Hiragana and Katakana. A bunch of squiggles and crazy lines to you likely. However, there are a few of them that remind us English speakers of something else. Take the Hiragana “ra” pictured above. To English speakers it looks like a five especially when the strokes are more of a cursive, connected style as shown. I can’t NOT see the five. It sometimes feels like a brain zap because that series of strokes to me is not a sound “ra”, it’s a number. If you want to confuse a person fluent in Japanese and English type something in this font. When you see a child learning mathematics or writing and working hard on something you find easy to do your way, I want you to remember that you are going in with prejudice. That “new math” they are coming home with does look strange. Hang on to the end to see something pretty awesome.
Anything new we learn is going to seem difficult at first. It’s not a reflection of how smart we are, it’s just new. We need practice.
The way children are being taught mathematics in school now (which encompasses the whys and the hows rather than just steps), may be as unfamiliar to you as it was to your grandparents or great-grandparents who were dumbfounded why their kids and grandkids were only adding numbers backwards rather than left to right.
First, I am going to simulate for you what it is like to learn something completely new without your comfort and experiences to back you up. Sometimes we get set in our ways, say how easy our way is, and we forget how hard it was to learn it in the first place.
Below are Braille numbers 1- 9 and 0 in the Nemeth system (don’t click the link yet) invented specifically for mathematics. In Braille, there is a special dot symbol to indicate that these are numbers, but I left it out for now.
The image starts at 1 and ends at 0. The first two you might think, “Piece of cake!” And then you get to the rest and you start to give me the stink eye because it make no sense to you. Perfect! Exactly what I was going for. The next image will help you out.
Okay. Ready to do some math?
Oh, right. There are some “extra” things in there to indicate that you are doing mathematics. Much like the horizontal line and symbols we use when we write addition or subtraction in the vertical format.
There, is that better? The first box with the four dots that looks like a revers “L” is the symbol for number (#). It just indicates that the next series of dots are numbers. So every time you see it, remember that it is the pound sign/hashtag. The next box with the three dots is the plus sign (+). Whenever you see that, it means addition. The third box that looks like the four side of a dice is the equal (=) sign. Everything unboxed is a number. Okay, now use the number chart to identify the numbers and do the arithmetic.
Hover over the image or highlight here –> #17 + #12 = #29 for the answer.
What do you think? Was that hard for you? Had to think about it even though you know perfectly well how to add? I had a hard time for sure.
In the beginning, it’s a bunch of gobbeldy-gook. Then we get used to it and after a while we forget how hard it was at first. And because we forget how hard it is, we tend to shy away from learning a new way because our way works just fine thank you.
By the way, why don’t Braille numbers look like a dice? Well, that’s because the letters in Braille came first. They follow a pattern in a six grid box. Louis Braille was French, so the English “W” breaks the pattern. Oops! Anyway, the numbers are based upon the first ten Braille letters with the dot # symbol added. That works just fine until you start getting into Algebra.
How do you indicate 3a + 5y without getting the numbers mixed up with letters!? Well, Abraham Nemeth took those numbers and adjusted their vertical position slightly and the problem was solved. When we want to indicate an exponent when typing without a superscript, we use the ^ symbol. Nemeth used a new set of dots that didn’t interfere with the existing numbers. If that’s not an example of the brilliance of our flexible intelligence, I don’t know what is.
We are perfectly capable of learning Braille numbers. We use a six-sided dice with no problem, so the issue isn’t the dots. The issue is our lack of experience with the dots representing the numbers in a way we aren’t used to. We are hard-wired from birth to do basic mathematics (adding to, grouping, taking away, dividing). The written/symbolic notation, however, is not hardwired. If it was, all languages would be the same whether spoken, written with strokes, in Braille, or Sign Language.
We are no more hard-wired to see the random lines “5” as the number five than we are to see it as “ra”. That part is flexible.
Sometimes that “new math” that looks odd that our children come home with is going to be a skill we already have, but we might not recognize it right away.
I promised to show you something pretty awesome.
I read the World Book Encyclopedia a lot as a kid. (Don’t judge me.) And in it were the origins of the letters at the beginning of each volume. It went from Egyptian to our present day letter formations. I was fascinated. How interesting! I forgot about it, but the other day I started to think about it again. Numbers had similar origins.
Why do we have more than one way to write numbers? We have the very straight, no nonsense four and it’s fancier sibling. Nine sometimes has a straight back and sometimes curvy. Eight can be two perfect circles or some fancy infinity squiggle. Seven sometimes is a fashion beast with its frou-frou collar.
Why is that?
Well, when the numbers we are using now were first invented, each angle was the count of that number. Oooo! I thought.
I bet you have no trouble recognizing those angular numbers. It looks like some fancy font. You should be able to see the hints of the numbers we write with curvy strokes and how we also write numbers with more angles or a mish-mosh of the two styles. But why were they written without curves?
Because the angles — or lack thereof — meant something.
Look at the dots on the angles. Zero has zero angles. One has one. Two has two… so on and so forth. Even though you have memorized the values of those strokes, this is still fascinating. It gives meaning to the strokes. We have turned something abstract into something visual, tactile, logical, and relatable. Imagine how cool that is to a kid just learning the numbers. Imagine, too, how helpful it is to someone who has extreme difficulty remembering what the strokes mean. Tell them to touch the angles (or dots) and count, and the doors to understanding fling open. You can make your own manipulatives.
Though we may not have realized it, every time we write numbers we practiced this recognition. The “new math” will often be in disguise like that. We will know it, but not realize it.
The how and why benefits everyone. It might be the long way around the barn, but if you are only going through the barn what are you missing on the outside?
Did you know the origins of number strokes? What did you think about the Braille example?
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