How to Learn Math

You maybe unfortunate and classrooms that offer math is a drive not in a subject or you maybe fortunate and in classrooms for math is shown as a living breathing subject with lots of ways to access it. But whichever you’re in this course will help you as it’ll show you the real nature of math not the boring drivers and often presented in textbooks but living breathing math that it’s all around us in the world, the math there you have a positive relationship with.

Mindset

Research see that the students with a growth mindset are on this positive upward learning path. The reason is people with the growth mindst also engage in a set of really useful behaviors:

• They try harder and longer because they don’t think that trying hard means they’re not smart.
• when they make a mistake they don’t think it means they can’t do math, they see it as a learning opportunity, it makes them determined to do better.
• they persist and don’t give up when something is hard.

In one research study found that when:

• Parents told their children to help them: “I didn’t do well in math at school either, so don’t worry”. The children’s achievement went down in the same term.
• Teachers gave student feedback on an essay and they attach this note for half of their students:“I am giving you this feedback because I believe in you”. Students who got that note achieved at significantly higher levels at the end of school years.

People used to think that learning was just about getting knowledge but now we know that the messages you carry around in your head and ideas you have about yourself are really important. Never let anyone say you cannot do something if you get ideas from school or elsewhere but suggest you you can’t do something keep telling yourself that you can as that maybe more important than anything, never let anyone who says anything negative to you stop you from thinking that you can achieve at the highest levels.

Mistakes

I’ve learned in recent years that shocks most people I meet is this:

• When you make mistake in math, your brain grows synapse is fire in your brain, in fact your brain grows when you make a mistake, but when you get work right no brain growth happens.
• Synapses to fire that is because struggle in hard thinking at times when your brain grows the most.

This is what we known that: “Genius is 1% inspiration and 99% perspiration”.

Mistakes and life

Expert studied that the difference between successful and unsuccessful business people they found that successful do more of these important things:

• Try seemingly pop wild ideas, feel comfortable being wrong and open to different experience.
• Play with ideas without judging them.
• Keep going through difficulties are willing to go against traditional ideas.

Michael Jordan said: “I’ve missed more than 9000 shots in my career, I’ve lost almost 300 games, 26 times I’ve been trusted to take the game winning shot and missed. I’ve failed over and over again in my life. And that is why I succeed.”

The most successful students are not those who don’t mess up, they are the ones who mess up and learn from it and continue on.

Math and Speed

Lawrence Schwartz struggled in school because his school valued speed and here’s one of the slowest math thinkers in his class, after he became very successful he wrote an autobiography and this is how he describes his school days: “I was always deeply uncertain about my own intellectual capacity I thought I was unintelligent. And it is true that I was, and still am, rather slow. I need time to seize things because I always need to understand them fully.

Towards the end of the eleventh grade, I secretly thought of myself as stupid. I worried about this for a long time. I’m still just as slow. At the end of eleventh grade, I took the measure of the situatin, and come to the conclusion that rapidity doesn’t have a precise relation to intelligence what is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn’t really relevant.”

Some good questions that make you think more deeply:

• Why does this work
• How is this method connected to other methods
• What would a drawing of this situation look like

Strategy

Number Flexibility

One of reasons many people dislike math and don’t do well is the messages they have in their heads, the other is that they’re not introduced to math in the right way, and they get the idea that math is something it’s not and this turns out to be very important for learning.

Many people have been led to believe that math is:

• A lot of methods and rules that have to be remembered.
• An individual subject, best learned alone with a book or teacher, all about right + wrong answers, not interpretation.
• Has no opportunity for creativity is about being fast with numbers.

Different strategy to calculate 18x5

when you learn math in school, if a teacher shows you a method think to yourself what the other ways of solving this, there are always others and discuss them with your teacher or your friends or parents this will help you learn deeply.

Talking and discuss

A mathematician called Uri Treisman found that large groups of students were failing Berkeley calculus and leaving the University, he studied the students who are failing and those are his results:

• did not relevant if have higher grades coming in
• did not relevant if know more math
• did not relevant if comes from more wealthy backgrounds

The only difference between unsuccessful and successful is that successful student talked about math.

Talking gives access to understanding it’s really helpful for understanding math, but it also does something else when you talk you do something really important in math which is called reasoning. Reasoning is when you talk through your methods and give reasons for your choices, this is really the essence of what mathematics is.

When you work on a math problem if you can think about the pathways you’re taking and tell someone else and then discuss the choice of pathways you’re doing something really important. This is what mathematicians do for their job.

They discuss their reasons for the pathways they take with other mathematicians and often breakthroughs are made in maths, because someone gives the result and even through their result was wrong they formed a pathway that others then use to make great breakthroughs.

Reasoning is also super important for working in today’s technological world. In most famous high-tech companies everyone uses math, but they use it by having an idea mapping out a pathway and talking to others about it they connect with each other’s thinking to create things, the math is totally collaborative and usually very creative.

Mathematical Connections

It turns out that people who do well in math are those who make connections and see math as a connected subject. People who don’t do well are the people who see math as a lot of isolated methods.

A tour of mathematical connections

This section best advice to see the original video.

Every 4 years the PISA teams conducts international surveys and tests to find out how students think about math and how well they achieve in math, in the last survey they found this:

• The lowest achieving students were those who used to memorization strategy when they approached math, the lower achieving students try to remember lots of methods when they study for a test they tried to memorize methods by heart.
• The highest achieving students were those who approach in math by thinking about big ideas, thinking about what they knew and didn’t know and thinking about how math related to the world(mathematical connections).

Make Sense

You need to know that it’s your job to make sense of math, and one way to do this is to ask questions to yourself or your friends, your questions such as:

• Why does this make sense
• How does this work
• How is this connected to other methods or areas of math.

Intuition

Other methods or areas of math part of making sense in math is using intuition. Everyone has the natural ability to use intuition when they approach math. Using intuition means looking at a math problem in thinking: I have a general sense of this ever feeling about what works here.

Intuition is really important in math every time you see a math problem it is useful to stop and think intuitively what do I think is going on here.

Sebastian Thrun talking about intuition and math and life.

We want to show you what we need by the difference between approaching math with sense making an intuition and thinking about the big idea as opposed to thinking only about one set method. We will first show you by asking you to have a goal at this question, if it seems hard, don’t worry just give it a try and remember that struggling means your brain is growing.

Drawing and Representing

When mathematicians work in math problems they are presenting physical things with drawings or with other representations.

Drawing like talking gives access to understanding. I always sketch any ideas that I get when faced with the math problem it really helps me, so here are some examples of people using diagrams to help them solve problems.

Looking for Big Ideas

We saw in the piece of data the successfully students were those who didn’t try to remember, they were people who thought what is the big idea and other questions like what do I need to know and what do I know now.

Math and Patterns

We’ve told that math is all about finding a general idea, another way to think about that is that math is really all about finding patterns, so when you look at a new area of math is always a pattern to see.

Math is a way of making sense of the world and math is everywhere in the world if you get in the habit of seeing math in the world and thinking about the patterns you see it can be really helpful and put you on a great learning path.