Math: organization and frustration

Sometimes the learning skills have nothing to do with memory or speedreading. They can involve creativity and analytical skills, but this is not the point here. The point is simple: without proper organization, you will not progress! This is especially true for math. Read alternative math teaching ideas here and here.

How to learn basic math faster

There are several levels of math. Each level feeds the others. Honestly, following the basic rules and learning the formulas is not a strain on intelligence.

On the basic level, kids memorize. There are summation tables and multiplication tables. They need to be memorized, overlearned, and used automatically. Mnemonic devices may be used as a backup, but they will be too slow to be effective. Older kids also remember squares, geometric formulas, basic equations, and series formulas. Students further memorize common integrals and differentials, known solutions for differential equations, the convergence of series, frequency transforms, probability formulas. PhD students obviously remember even more specific formulas.

Next children learn definitions. The definitions have strange names and the stream of definitions never stops. Usually, the basic story technique is good enough, only the story needs to be damn good. For all those strange words that come from Latin and Greek get ever stranger. Take for example “hypotenuse” etymologically meaning stretched under and “cathetus” etymologically meaning perpendicular. “Two square cats equal a square hypo in use”. I created the phrase on the spot. Kids love this stuff. Can get harder, like try to describe Jacobian from the name of a Prussian professor, and its friend Hessian loosely meaning first and second order of partial derivatives.

Then the kids learn a set of basic instructions solving various kinds of challenges. When they see a new challenge, they need to classify it within a group of solutions they know and apply the instructions.  Basically, this means solving a lot of similar examples, until a new example looks like a familiar face. The main challenge is making zero mistakes following a long set of complex instructions. You need to solve like 20 examples of each category until the brain learns to recognize the category. Then solve a set with a random selection of examples from different categories, say 20 categories, to train classification better.

How to learn mathematical thinking

Math is computation-heavy. Stupid people cannot handle the math. Not because they cannot follow a long set of instructions. But because what comes next.

Understanding the problem is the hardest part. A few days ago my son saw a list of math and started to cry. “This exam is too hard! What they need me to do!”. I checked. He got a list of formulas, did not understand it and tried to prove each and every formula on the list. That could get hard.

The next issue is not fearing the challenges. There are many examples of a novice mathematician solving an open problem, simply because he does not know that the problem was not yet solved. This situation is uncommon. Some of these mathematicians become very famous like Gauss and arithmetic progression. Others are hardly known as Lisa Piccirillo and the knot.

Then there are computational problems. Like doing long divisions and multiplication preferably in one’s head. There are mental math tricks that can help. Search this blog for some of them if you want. More advanced students constantly run computer simulations to test every hypothesis they might have.

Abstract math can get very complex subject. It is more of music in numbers. Like various solutions for prime numbers, np-hard problems, or geometrical maniflolds. Even something relatively simple, like Maxwell’s equations, is pretty hard to imagine with various solutions and their meaning. Fortunately, this abstract math is a second-degree material.  By that time your mathematical intuition is rock-solid.

My kids and their math issues

Before COVID19 my boys had a perfect track record in math, and my girl was somewhat lagging. Now the situation reversed. Why? Girls are on average more organized than boys, especially when working without supervision.

I stopped here to check that my science is right. Actually, just found the link and love the article. The correct word is self-regulation. Girls follow instructions better than boys. Basic math is a set of instructions that need to be executed in a certain order, and girls ace that.

Why do grown-up men get on average better math scores than women? Possibly because men have slightly more neurons, and use those neurons for visual processing. Ladies get better results for example in languages, where the extra neurons are not required.

Self-discipline

Now, learning from home, my kids need to do all the learning. And once they finish, they can play video games and watch TV. This task is particularly hard for boys, who really prefer to cut corners and not do the instructions properly.

Cutting corners, especially not copying properly and understanding the details of the description of each problem, the boys start the impossible tasks. Even if they get the description right, home is a distracting environment. Messing up with a small minus destroys the entire exercise.

The boys try to jump several boring steps. They kind of do this with a real staircase, so they also do it with math. This works fine with simpler exercises and fails with more complex questions. A teacher when in the room can stop this behavior, but he cannot stop this behavior via zoom. The parents are busy with their own things. So what can we do?

Why I paid 20USD to a kid to watch my 14 years old

With COVID19 the teachers and educators went remote. At the same time, Anna and I had more tasks. The kids had more homework but less patience. It was brutal.

We tried several solutions. Sitting with the kids was very emotional for them. After all, we are their parents. They are used to discuss with us various projects, but not used to us teaching them. Every time they make a mistake they feel embarrassed, as our opinion is very important. Yet they do not really value our time since we are always there.

Next, we tried gradma zoom. We set the boys with their grandparents watching and trying to help over skype. This way, they had to work and could not play games. Unfortunately, the grandparents watching were also micromanaging. The internal motivation we built for years was destroyed in a couple of months. Now what?

We matched our kids with a boy one year older than them, a boy they did not know. He watched them work. Somehow teenagers have more affinity to their peers, and suddenly they started to work.

Back to organization

My son learns in a prestigious math program, where they get many tasks and he fails quite often. I tried to analyze his failures.

60% of the failures he did not copy numbers correctly or misplaced the sign

30% of the failures he did not understand the question

10% of the failures are real, like not knowing how to reduce a new challenge to a simpler challenge previously solved.

Simply being more organized and systematic would solve 90% of my kid’s problems! And this is a smart kid who reads 600wpm at 14 years old…

When the questions got boring he tried to solve it faster, using brute force and assumptions like “from here it is easy to see”. The result was disastrous.

Learning to read and write very fast is only a part of the issue. Thinking equally fast can be hard. We may actually need to slow down. Also, math uses our visual cortex, and we should not speedread math unless the math is way below our level.

Bottom line

I had the best math teacher a kid can wish for. During my first years, he asked me to slow down and write everything beautifully, to enjoy the esthetics of beautiful formulas. So I did not make mistakes, and my PhD is highly mathematical.

Want to learn math faster? Do not focus on tricks. Be organized!

The image below is a mess! Organize it 🙂