Friday, 22 May 2015

The Problem with Math Education-Lack of Curiosity??

From Math Mojo Chronicles 3rd Feb 2009

Well, of course it’s not the problem, just one of many, but here it goes…

Somehow along the way, people got the feeling that math is supposed to always be right, and that math teachers are supposed to know all the answers.

Math has gotten the reputation of being an authoritarian science. I don’t think this is the fault of mathematicians, I think it is the fault of many math educators who have tried to turn mathematics from an art and science into a “subject.”

Math education is all too often about “standards” and “curricula” that students take “tests” about that they are “graded” on.

If Archimedes was to take a high-school math test today, he would be unfamiliar with the jargon, and would find little value in the trite little multiple-choice and partial credit nonsense that passes for assessment.

On the other hand, he could run rings around the math teachers with his knowledge of actual mathematics, and could twist their pedagogical dogma into moebius bands.

Trying to shove math into the education industry’s rubric is one of the worst educational crimes I can think of. School math seldom has anything to do with actual math, except for the very rare cases where an inspired person is doing the teaching. And when that happens, that person is invariably in trouble with the administration.

How do you know if your school is doing a really good job?

Easy - your school definitely is not doing a really good job. Even if the school representatives like to trot out some meaningless statistics saying how well their students score on this or that test.

The tests show nothing whatsoever about the essence of math. They are created by the same industry flunkies who sell the schools the textbooks and other curriculum material. It is the foxes guarding the henhouses.

Show me a school that can compete against the Russians and Chinese, and you might have a case. But you can’t .

The Germans have a great quote, which you will find yourself quoting frequently if you understand it. It’s - “Never trust any statistics that you haven’t falsified yourself.”

In other words, the education industry can manipulate their statistics to seem to “prove” anything it wants.

If you truly understand mathematics, you can understand why those statistics are worthless.

So what does matter in math education?

Here’s one thing that matters - Realize that education is not inculcation. It’s not about getting children to jump through hoops that somebody in the state capital thinks are important this week. It’s more about turning the mind on to enjoying and investigating a subject, and fostering a thirst for learning.

A Chinese acquaintance of mine said, “Curiosity is the best teacher.” I love that quote.

If you can get a child to be curious about a subject, all you then have to do is point him or her to the library where they can find out more about the subject, and they will learn more than all the textbooks in school closets have to offer.

They will also get more diverse input than from a “curriculum.” Curriculums, as far as I can see, are designed as much to limit knowledge as to teach. Maybe more.

School gives children the false sense that math is carved in stone, and all the answers are there, you just have to know the formulae. It teaches them how to answer questions that someone else has posed. It doesn’t teach them how to ask questions.

Math is about asking questions - asking how can you make and understand patterns of the things in your world. When was the last time you ever even heard about a teacher mentioning that in a classroom?

I’ll admit, it occasionally happens, but that is in spite of curricula, not because of them.

Curiosity ? ?                                     (Len Cooper)
It is suggested that there are two events that increase the activity of the
synapses in the brain.
One is:            Fear - Fight or flight 
The other:       Curiosity  
How much curiosity are we encouraging in our maths classrooms?
Questions to Nurture Student’s Curiosity
• Can you show me what you did?
• Where did you start?
• How did you decide that?
• Can you try that another way?
• What happens if you take part of it away?
• What would happen if. . .?
• Can you write about or tell me what you did first? second? third?
• What will you do next?
• Why do you think that happened?
• How would you describe what you saw (read)?
• Can you think of another way to do this?

Getting Your Math Skills Down Cold

From Math Mojo Chronicles 3rd Feb 2009

Getting your Math Skills Down Cold
There is a real problem in our society about what people think they know, and what they know.
What I mean is, so often I hear from students, and adults, that they, “know” the “math facts.”
Well, aside from the term “math facts” being counterproductive, most people can retrieve, say, basic multiplications from their memory, but they are not in their bones.
To illustrate, try this:
Relax, get in tune with yourself. Breathe easily. Start noticing your thinking.
Now, what is 7 x 8?
If you had to think, “Um, let’s see…”, or if you hesitated at all, you do know really “know” the answer. You can find it in your memory, but really knowing it is like knowing that “cat” spells “cat.” You don’t have to say, “um, let’s see, ‘c’ - ‘a’ -’t;’ that’s ‘cat!’” (At least I hope you don’t.)
If you don’t know your basic multiplications by second or third grade, someone has cheated you. Every seven-year old should be able to really master them. It’s just that our society makes wussie excuses, like, “Well, he has ADD, you know…”
Yeah, maybe he does. Glenn Cunningham had his legs burned so severely when he was eight years old, that the doctors suggested he have them amputated. His mother wouldn’t allow it.
Do you know who Glenn Cunningham was? He set a world record for the mile and indoor world records for the 1.500 meters and the mile. He was on the 1932 and 1936 Olympic teams .He was considered by many the greatest American miler of all time.
Did his mother use his burns as an excuse? Yes, she did. She used it as an excuse to help him excel against something much more horrific than ADD.
I am not trying to make it sound like ADD isn’t awful. I have it and it drives me nuts. But I’d really feel like a wuss if I said, “I can’t do this or that because I have ADD.”
I might say, “I can’t do this or that yet, because I haven’t worked hard enough to overcome my ADD to accomplish it, but I’m not giving up.”
That’s still pretty wussified, but at least it’s not blaming something outside myself.
There are some things that I have tried that have really helped, and recently I have started working on some of them again.
If you have ADD, you know that there are some things you don’t have symptoms about. I’ll bet you can surf the web for hours without interruption, or even food or drink.
You can get into that “trance” state when you play computer games, possibly. Many people with ADD can get into the “zone” when they do art, music, or sports. My wife wonders why I have a hard time getting my work at the desk done, yet can spend six hours in a row solving Sudoku puzzles. (I wonder, too. It’s not like my work isn’t interesting.)
So I’ve been trying some experiments to combat my short attention span. Lately I’ve been going to the gym and using the stationary bike and the elliptical machine - but with a twist. I bring something to learn or memorize on a small clip-board.
Let’s say I am memorizing a poem. It’s hard enough to do when you are in a quiet space and not distracted. But when your heart-rate is over 120 for more than a half-hour, and you’re sweating (and your a big, fat, out-of-shape middle-aged guy like me) it is really hard to concentrate.
It definitely takes me more time to memorize something when I am physically straining at something else. But you know what? I retain the stuff much better.
Later, when I am relaxed and trying to remember what I learned, it comes easier. I can’t explain why in scientific terms, but it seems like my body is saying, “If I can do it while panting for my breath, I can certainly do it now!”
It seems to work on the same principle as the Biathalon. Do you know what that is? It is one weird sport. It’s cross-country skiing combined with target shooting.
A guy (or girl) sprints long distances on cross-country skiis (that is a hell of a workout, let me tell you!) then has to shoot at a target with a very accurate rifle. Most people’s body would be shaking with exertion to the point of fainting, but these guys have to steady their hands and nerves, and shoot at a distant target. And they’re being timed! Now that’s pressure.
When I was a kid, I used to laugh at that sport. It seems so silly. Cross country ski and shoot? Why not sumo-wrestle and play ping-pong? But it really makes sense, and tests skills that other sports combinations cannot test as accurately.
So what am I getting at? You sit and home and look at multiplication tables, maybe look at flash-cards, or (God forbid) use some vacuous songs, rhymes or video games to memorize your “math facts.” Maybe you have the TV on at the same time, or are texting your friends.
What you are not doing is challenging yourself. It’s just so passive. You’re not engaged. You just have some passive distractions.
On the other hand, if you set a timer, and say, “I’m going to push myself for the next twenty minutes, ” and really exert some effort, you will be making an investment in yourself. And your subconscious will not let yourself be cheated out of your investment.
And if you can manage to do the same thing again the next day, but this time while taking a walk for 20 minutes, you’ll find that you can’t concentrate as well. But try it for another day, and another, until you can concentrate as well while walking as when you were in your room, then you have really made some progress.
The next time after that, when you try to study in your room, you will feel more empowered, and will not be as tempted to be distracted by the radio, your iPod, or that idiot that is texting you about some stupid YouTube vid.
Try it.


Anyone who has had their own children or taught young children will know that they go around asking questions.  The one most used of course is "Why?"

With my 3 year old grandchild, questions are a constant, often to the extent that her parents and grandparents get totally frustrated with them all.  BUT we know this is her way of learning and exploring the world she lives in.

Children NEVER lose the need to know why and question, but, often schooling does drum it out of them and the higher the level of education, we often see less chance of a learner asking questions.  

Questions are often replaced by what the Teachers says, or what will be in the exam/test.

If children learn through asking questions, why do we in Formal Education keep trying to prevent them?

Peter Duncan a retired New Zealand Educator wrote the following poem which has been published in a book of Poems (all written by Peter) "From The Space Between"

It really encapsulates the Education Systems and their views of Questions.


Five-year old enters school
with a thousand questions

In year four
the child's questions become 
less valued diversions
from the standard's curriculum

By year nine
no time to ask
no time to answer
or you will never get through
what has to be covered

At university
two questions remain

What do I need to get an A pass?
What's the minimum attendance required in this class?

The nine hundred and ninety eight other questions are
no longer relevant.

(posted with permission)