Mind-Manual

Why You Have/Had to Learn Math

If you asked someone when you were growing up why you had to learn math, they probably told you something like, “You’ll use it someday”. That’s mostly a lie. For example, I still do use the algebra I learned back in grade 9 and 10. But much of the other stuff I learned I haven’t used, at least not yet. In fact, if it came up, I probably wouldn’t remember how to find the angle of a triangle using sine.

But, what they didn’t tell you is that the facts and knowledge about math is not what you’re really learning. What you’re doing is improving certain skills and thus improving your production capacity. Thus, you’re learning how to solve problems better and improving your spatial skills, as well as your general mathematical skills.

This point really struck home back in my first year economics class. The professor said that even though we wouldn’t be using anything beyond grade 10 math (graphs and simple line equations, etc), people who had taken calculus in university would do better. “That’s weird,” I thought, and it has to do with the problem solving abilities that are stimulated in both math and economics.

So, learn your maths, it’ll make you smarter and better at solving problems, even if the math itself you may never use.

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I (Heart) The Teaching Company

As many of you know, I love learning in all its forms. I have at least 200-300 books in my room. I have a number of audio books for listening to while on the subway on my iPod, and I also have a number of video tutorials on a number of things.  Another thing I like to do is track down good professors or interesting courses and just attend the classes without being enrolled in them. I love learning but I’m not a fan of the “course work”. I understand its reason d’etre (reason to be), but I just find it tedious, usually.

There are also a number of subjects I’m interested in knowing but the actual process of learning them seems tedious to me. Certain maths, statistics and probabilities fall in this category. I like to know them, but not to actually have to learn them. Books are useless to me here because I have yet to find a book that explains these subjects in a very entertaining or interesting way (perhaps through the use of stories), but audio programs or video programs are great because all I have to do is pay attention and that’s great for this sort of thing.

Another thing I like to do is have some idea of the course material for the courses I’m taking. I find it really cuts down the amount of time I need to study and improves my grade. Watching a ten hour series of lectures may reduce my studying/homework by five times that over the duration of a course, and I’ll get better grades because I have first brush familiarity with the ideas.

That’s how we learn, see, complex ideas are learned best by being introduced to them in passes. The first pass, you get a shallow understanding of the key terms. The next pass is a little deeper and you start to get an understanding of the parts. And so on. I like to reserve some time to step back and make sure all the big parts link together. Its easy to simply think of each class or chapter as a discrete unit when you’re studying in a course, but everything is actually connected together and its important to understand this connection.

That all brings me to The Teaching Company. They seek out nationally-recognized professors (and I can tell you, its really worth it. The difference in learning and enjoyment from a good prof versus a great prof is very noticeable) and have them teach courses and record them on video and audio. They cover a very wide range of topics and have been in operation for many years. Here’s a list of the courses they offer. Truly an excellent business.

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A Very Important Idea

A very important idea/mental model in life is the idea of production and production capacity. I first got this idea from Stephen Covey’s audiobook of 7 Habits of Highly Effective People. He used the story of the goose that laid the golden eggs (the production capacity) and the golden eggs it laid (the production), but I’ll simplify it using another common adage:

Give a man a fish and he eats for a day. Teach a man to fish and he eats for a lifetime.

The desired result/production is for the man to be fed. In the first case, he is fed but you have to do it. So you get the production/result that you want. In the second case, the man learns to fish for himself, and you have improved his production capacity/result-creating capacity.

More examples (because examples help you understand things):

• Say you have a child and you want a clean child’s room. You could do it yourself, but then the production capacity would be unaffected. The key is to get the child to clean the room, and you could bug the child until it does it just so you’ll stop bugging it, and you produce the result you want, but the child will not voluntarily clean the room, except out of fear. You have to find some way to get the child to happily clean the room.
• I want to keep track of my finances. I could do it manually by keeping track of my receipts and my cash-in-pocket and just do the whole thing on paper. Or, I could make a slight improvement to my production capacity and upgrade to using a digital financial software, like Quicken, and then it can do a lot of this stuff automatically. I try to pay for as many things by debit as I can and carry as little cash with me as possible so that Quicken can simply download my transactions from my bank and automatically figure out a lot of where my money is coming and going.
• Steve Pavlina spends a lot of time working on the production capacity that produces money for him, which is his blog.
• I’ve been making back-end changes to the way this blog is run so that its easier for me to write posts or what have you. So, I improve my production capacity to produce blogs faster and easier.
• When you are involved in personal development, you are usually engaged in a process of improving production capacity, unless you make growth the goal itself (as Steve Pavlina’s done).

Main Point:

• Give a man a fish and he eats for a day. Teach a man to fish and he eats for a lifetime. When the desired production is for the man to be fed, you can gain the same production by giving him a fish every day, or by improving his ability to feed himself, which improves the production capacity.

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4 Stages of How You Learn!

A very powerful model for measuring your stages of learning is the Four Stages of Competence model. Strictly speaking, this model is used to understand the stages of learning a skill, but I find it generally applicable to all sorts of learning, especially learning new mental models.

1. Unconscious Incompetence: You don’t know that you don’t know. Say you’re a child and you don’t know that you don’t how to ride a bike. The thought of riding a bike hasn’t even entered your mind.

2. Conscious Incompetence: You know that you don’t know. You might have figured out that you want to ride a bike but you don’t quite know how to go about doing it.

3. Conscious Competence: You can do it but you have to have conscious attention on it. You can ride a bike, but it requires all your concentration to make sure you are balanced, pedaling at the right speed, making sure the handle bars are straight, and so forth.

4. Unconscious Competence: You’re so good that it’s entirely automatic. How many of you need to focus on riding a bike now? You just do it. Unfortunately, if someone asked you to help with riding a bike, you couldn’t put it into words. This is one of the reasons if you want to learn something from someone else, not only does the other person have to be good at what you want to learn about–they have to be a good explainer, too. This is one of the reasons there are teachers who just can’t understand how you can’t understand what they’re trying to teach you.

How would you apply this model to learning how to drive? It’ll help you integrate this model into your mind if you do.

Resources:

Wikipedia: Four Stages of Competence

Businessballs: conscious competence learning model

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