Thursday, May 3, 2012

Knowledge is Power - Thoughts on Math

Love2learn2day posted a video for thought, this afternoon...

...and it really did get me thinking.  In the short TED talk, math teacher John Bennett seeks to answer the question of whether higher level math classes should be required in middle and high school years, or not.

When asked the inevitable question by his students - "Why do we need to know this stuff anyway?"  Mr. Bennett moved through a progression of answers.

  • Math is all around us. Which is true, but doesn't necessarily answer the question.  Fibonacci numbers and golden ratios are cool, but useful?  Maybe not.
  • Math is helpful and necessary for technological advancements.  That's great if you want to be an engineer, but what about for the rest of us?
  •  You might need math in a future career.  How many people do you know, apart from math teachers, who actually use higher math in their work?  I know one - my nephew.  He's a rocket scientist (or something along that line).  Mind you, he was a high school drop out, too.  But, really the majority of working Americans do not need higher math to carry out the tasks of their employment.
  • You need math to do well on the SATs.  You need to do well on the SATs to get into a good university.  You need a university degree to land a high paying, fulfilling career.  The first two statements might be true, but the last one, especially in light of the recent economic turmoil, is open for debate.
Finally, Bennett settles on the fact, that higher math, algebra and beyond, teach inductive and deductive reasoning skills.  Skills, which Bennett feels could be learned through educational, strategy games.  He suggests then, making middle school and high school math classes elective courses, for those interested in math based careers, or with a general interest in math. 

I've gone through all the progressions above already, both in answering the question for myself, in debate with my husband (who is not a lover of math), and with my children, especially now that my oldest are moving into algebra, geometry and beyond.  Like Bennett I've come to the point that when the children ask when they are ever going to need the math they are learning, I answer - probably never.

So, why do I keep teaching it?  

That's the question I've been pondering all afternoon.  Strangely enough, as I considered the thought, my mind kept wandering to "The Feeling of Power", Isaac Asimov's short story about a future where people have lost the ability to perform even simple arithmetic without a computer. 

While the children were eating dinner, I found a copy of it online to read to them, and in the very last lines of the story, as Programmer Schuman considers his newly acquired ability to multiply sums, I found the answer for which I'd been grasping.

Nine times seven, thought Shuman with deep satisfaction, is sixty-three, and I don't need
a computer to tell me so. The computer is in my own head.

And it was amazing the feeling of power that gave him.

Why did I study algebra, geometry, trigonometry and calculus in high school and college, when I suspected I'd never use any of it?  Why do I insist my own children learn it, even though my suspicions have now been confirmed?

Because, it's knowledge, and knowledge is power, right?  Francis Bacon said it, or if he didn't, every teacher I ever had, did.  In fact, if I remember right, that phrase was usually used along with a patriotic speech, about it being our duty as good citizens to become educated, because knowledge is power, and an educated population means a powerful nation.

Of course, those same teachers also taught, usually during a Shakespeare unit, "power corrupts, and absolute power corrupts absolutely."

And, 1 Corinthians 8:1 warns knowledge puffs us up.

So then, if knowledge is power and power corrupts and knowledge makes us proud, an educated nation might be powerful, corrupt and proud.  Hmmm...that might be deductive reasoning, but I'm pretty sure it belongs more in freshman philosophy, than algebra II.

Don't get me wrong, I'm not ready to jump on the "ignorance is bliss" bandwagon.  I still think math is important.  I just think we've got to come up with some better reasons for teaching it, or maybe, just maybe, start using it.

It's great to be a homeschooler.


Lisa said...

I've had many similar thoughts. Not just about math, but about other subjects, too. I guess this is why there is a sect in the homeschool world called unschoolers. I don't fall under that category, but respect those who do because they are confident. At least they seem so.

Like you, I learned Calculus in high school. I tested out of math in college. For what reason? Never did I use that knowledge. And to be honest, I'm not even sure that it will return to me when the time comes for me to teach it, if I even choose to teach it.

Certain things are important for kids to learn, regardless of how they feel about it. My kids would love to sit at the dinner table and talk only about noisy bodily functions, but we teach them manners to be respectful. A general knowledge of history will hopefully help them to understand how we got to where we are and to build a good foundation.... and so on.

But it's all a catch 22. We know that some things we teach will never be useful in the lives of our children. And we know that a college degree does not guarantee a high-paid job in our current economy. (The Bible teaches that it's better to live in the middle anyway. But that's a whole other discussion.) Great SAT scores depend so much on, dare I say, some useless knowledge. So how do we know what to do?

I suppose that, for now, I will continue down the path that we started and take it one step at a time. And I'll continue trusting God to lead our way.

Jennifer said...

This video is going around! I wrote about math this week, too, but your take on it--with the Asimov story--is appreciated.


Kari said...

Your thoughts and observations are very wise. A very thought-provoking post......

Bailey said...

Part of my problem was how it was taught. Do to the memorization, drill and kill, I did struggle with it. However, the few teachers I had that taught it well helped me to apply it to thinking about other problems.

I remember sitting in a computer course with one of my brother's college friends when I was visting. I knew nothing about the language, but I kept poking the friend and telling him that the professor's math was wrong. This friend kept telling me to be quiet, but it annoyed me because while I couldn't understand a word of the rest of the class, the math was wrong. I got to it through algebra, not the formula the professor was using.

Sure enough as the lecture continued his program was failing and I kept pushing my friend to raise his hand and point out the math mistake. It took forever for the professor to get back to the math mistake.

The only reason I was able to do that is I had a decent math teacher who found a way to help me make sense of that portion of algebra. Geometry proofs helped me in debate classes years later. The only reason I got through the geometry class was the professor had a unique way of helping us "see" the geometry, not just memorizing it.

So, I can say you can't always understand how your brain can utilize the training it gets in other ways.

I also think it provides children with options. Certain classes are required for certain professions, etc. My sister struggled with math and science so she took the minimal classes she needed and sadly had poor teachers. When she wanted to be a nurse, her lack of math and science was a challenge. Another sister works in biotech and also had limited science and math which made going back to get her education very hard. In high school she focused on art because that was her interest. You can't predict what you will or won't need.

Phyllis said...

I have thought a lot about this myself, especially when my daughter with LD's would cry on a regular basis over math. I would ask myself why I was making her hate an otherwise beautiful subject? I have noticed, too, that over the years the emphasis on high and higher math. Back (in the old days) when I was in school the average was Algebra II, now it is Calculus. I asked my mother how much math she had. Business math. No algebra at all. I am guessing it is the technology, ironically, that is calling for the higher and higher math. Or, perhaps it is the fact that everyone is expected to go to college, so there is more competition there...and so there is some need to weed people out? All good food for thought, for sure.

Joyful Learner said...

Great summary and thoughts on this topic! Some people argue why everyone has to go to college. I think the question of needing higher math brings similar questions. When people are good at other things, shouldn't they study what they want to? Why not bring trade schools back? Isn't there value in that? While I agree on giving more freedom to choose, I am reluctant to let go of learning higher math. I just believe that if taught differently, more people would see the beauty and good in it. Just recently, I was asking my husband why we needed trig. He said he used it in his work in construction and architecture. I had no idea. It totally made sense. Then I went on Kahn Academy and learned that many other professions used trig. Go figure. I thought it was totally useless! I think the schools can do a better job of educating exactly why math is important. Without that, it's just another thing to memorize. That's just my 2 cents.

Jennifer said...

I like his idea of focusing on teaching logic and strategy instead of all the higher level maths. Thanks for sharing.

Bailey said...

My Mom was tracked in high school and chose a "business" program and thus had little in the way of science and math academics. Realistically she and her classmates weren't expected to work long. A few years as secretaries and they were expected to be raising families, which she did. Years later when the economy got bad and she did have to return to work, she did wish she had more math and English writing classes. Now that she is retired she wonders why she doesn't have the history knowledge that her children do who had a full academic load. She is on a campaign to read and learn what she missed.

Our local tech high schools have ramped up their math and science requirements because there is more required in the trades and technical fields than there was when kids in my generation graduated. In order to qualify for certificates in some fields the math, science, and computer requirements are much higher than ever before.

What has impressed me is HOW those teachers have risen to the challenge to teach their students the material in a way that the children understand. They utilize the interests and shops the students have chosen whenever they can to teach the material.

Our local high school was not amused when the tech school beat them on the standardized tests. It took them years to do it, but it was a result of finding methods to teach the children material in a way that made sense, not reteaching the same material that the child failed the first time. Instead of trying to apply the methods in their own system, they have tried every method to discredit what has been done.

An Almost Unschooling Mom said...

Bailey - That is interesting about the Tech school - I'm wondering if their success doesn't lay in the fact they are teaching students with purpose and a goal - much like elementary math. We know students will need to be able to add and subtract, so it makes sense to teach them in a real world fashion - but we're not as clear on how to use calculus - so we teach it abstractly. If the teachers knew how to use the math in the real world - they would teach it that way.

Raising a Happy Child said...

Well, why am I not surprised that math scores of American children are abysmal compared to the rest of the world? The prevalent notion here is that math is hard, and we don't want to make our precious children do hard things. God forbid they fail - it's bad for their self esteem. Better make it optional and source our intellect from other countries that are manically focused on math and science. Our children will be perfectly OK not going to college and serving food in MacDonald, right?

The Chipmans said...

I think you could make the same argument for any higher level subjects. Especially all those G.E.s we had to take in college that didn't pertain to our major. It's just good to understand the world around us. I'm pretty sure God probably used a lot of those complex math concepts when he created the world. There is a book you might enjoy reading that is along this same line of thinking. It is called the Number Devil by Hans Magnus Ensensberger. I really enjoyed reading it and it helped me appreciate math more and look at it in a more fun light.

Bailey said...

I think there are two reasons the tech school has seen success in their math and science programs. One is as you mentioned they see it in action. I think the other is something that should be considered by anyone teaching, finding a method that reaches the kids. Sure it isn't easy, but is always another way to teach it that may reach a student. That is one of the great benefits of homeschooling, you aren't tied to a specific curriculum. If it doesn't work, you do try another method. Schools often expect the child will adapt if they see the method often enough.

These teachers aren't afraid to use alternate teaching methods to find a way to reach the kids. If it means working with the shop teachers to find ways to help the kids "see" the math and science in action they do it. Just think about how much chemistry and physics goes on in those shops along with the math. You may not get the car driving problems in the text, but seeing an example in your shop that ties to a formula helps make the connection.

An Almost Unschooling Mom said...

Raising a Happy Child - My teachers would have loved you :)

Kathryn said...

I teach math (Algebra II and Pre-Algebra), so I hear, "When am I ever going to use this?" an awful lot. I've offered a lot of the reasons presented here at one time or another.

I'm realistic and understand that a large portion of the kids I teach don't want to have careers related to math and thus won't use many of the algorithms they learn in school. I do hope they latch onto the problem solving strategies I try to develop because those can serve them in any field.

I also frequently tell the story of my best friend who wanted to be a historian. She took the top math classes with me in high school, but certainly wasn't going to continue with them in college. After she spent a couple of semesters majoring in history, she realized it wasn't what she was looking for and she ended up majoring in math. I had a similar experience with French. I hated French classes in high school, but took them for a leg up on college applications. My college required one French course and it was so wonderful, I majored in French and went to work in France after college. None of those things would have happened if I'd walked away from the subject early on. I tell my students to make sure they leave all of their options open for a while in case their current passion doesn't last.

Pebblekeeper ~ Angie said...

Catching up on blog reading while the Northwest gets drizzly today. First, I want a cookie and an octopus roll. ;) I loved your questions/answers! I do think a trip to the beach is in order! Today, I am pondering math - I have a 6th grader next year. He's just not that into math yet.We did Jump Math 5 this year to make sure he had all the bases remembered/covered. Not sure if we should do TT 6 or Saxon 6/5 or ?? next year. Nate, the 14 year old LOVES math and Algebra has been simple for him this year. It is a daily discipline for us. Math scores give more opportunity for colleges, scholarships, military placement, etc. It's one thing that is hard, as an adult, to go back and learn incrementally. ;)

Anonymous said...

I think we should teach math because we like it and it's fun and the whole UniVERSE was designed mathematically! That's so amazing. I think if we teach math, we need to teach the wonder, and the sheer awesomeness of it. Rote memorization and drills, they can always be learned. But while the kids are young, teach them with awe and show them the beauty:). (This coming from someone who hated math in school and is only now discovering how fantastic it is with homeschooling my kids.)