The way math should be taught

Second channel: @tibees2

Book link is an Amazon affiliate link.

Editing by Noor Hanania

[ferdievanschalkwyk]

Classical math teaching, is both abstract and prescriptive. This approach gets rid of the prescriptive portion, but the abstract portion is still there. That is the portion many people struggle with.

Maths only really "clicked" for me, when it was taught the way it was discovered. First starting with ways to approximate with fair accuracy and then learning more sophisticated methods as increased accuracy is required.

Even now, in computing, we use approximations to a large degree for greater efficiency, so that computational power can be expended on more important tasks.

[StephenBoothUK]

The problem I’ve found with how Maths is taught, and to a lesser extent other STEM subjects, is fundamental to how Maths is structured. In Maths each topic builds on the ones that came before. You need to understand counting before you can understand addition and subtraction, you need to understand addition before you can understand multiplication, you need to understand multiplication before you can understand division, you need to understand all 4 of those basic operations before you can understand geometry and algebra, you need to understand geometry and algebra to understand trigonometry, you need to understand trigonometry to understand calculus &c. You don’t find that to the same degree in most other subjects. You don’t need a thorough understanding of the 100 years war to understand Tudor England, whilst a decent understanding of Tudor England may help understanding of the English Civil war you can get by without it. In Geography knowledge of how glaciers shaped Northern European isn’t needed to understand the principle exports of South Africa or what the different sorts of clouds are.

Maths is like a wall built of bricks whilst many other subjects are similar bricks scattered about. In Maths if you are missing a brick (maybe you missed that class due to illness or changing schools) or is damaged (maybe your teacher didn’t explain something in a way that clicked with you and didn’t give proper feedback when you got answers wrong in tests/homework, then had barrelled on to the next topic) then every brick (topic) that relies on that is weaker. At first you can get by, but as the damaged bricks and holes accumulate you find it harder and harder to understand each topic. A common experience for people who struggle with maths is that it all made sense up to a point, then it stopped making sense. That point often correlates to a life change such as changing school of a period of sickness.

[umarus]

Once, I covered an art class and saw how students interact. The students even invited me to join them. Although my artistic skills are almost non-existent, I painted a piece of paper motivated by their encouragement. Since then I have been considering implementing this approach (I believe this was the case in Ancient Greece and the Middle East.). However, one of the biggest obstacles to enjoying mathematics classes is the amount of content and limited time

[jakobklug]

i had an excellent math teacher.... he started explaining that most math won't be necessary in most of our futures - but that it helps train complex logical patterns

[themsdosnerd]

"In art class there are no right answers."

Unfortunately that's not how most schools teach art. In most art schools there are right and wrong answers. What's right and what's wrong is decided by the teacher, not by the book.

[jorgetorresramos]

Beautiful video. The shorter side of the rectangle is the one that should be labeled flower minus one, and the longer one flower.

[mnmlst]

I literally had the exact same conversation about that yesterday.
This is so true. Too unfortunate the majority of global educational system is developed to be a bore.

[scottguitar]

It's been a while since I have been in a math class but if I remember correctly it seemed that in the very basic math, most students could see the value of learning this. It was only when we got away from numbers and into variables that the number one question was "what am I going to use this for?". The teachers often did not have any good answers, nor anything to spark interest in learning higher math. Many kids had problems with the question of why, when it came to the rules of higher math where the typical response from teachers is just accept those rules and move on.

I had a natural interest in math and could just accept the rules and move on. It was my pursuit of an engineering degree that I finally reached the level in math that answered all those questions of why and gave me that huge a-ha moment of understanding math to be a beautiful language. I don't think most math teachers have that comprehension, which is why they never had good answers for their students as to why. Math is very apparent with things like measurements and keeping track of finances, but it is found in art and music, which is less obvious.

[brianlhughes]

one of my favorites is how to draw a perfect equilateral triangle inside a circle. I was a DJ and we did an AA (alcoholics anonymous) dance and I wanted to put a huge AA symbol, a circle with a triangle inside it, on the wall with twinkle lights. I put the circle up no problem using a length of string as a radius but I couldn't figure out how to do the triangle! I happened to post about my old dilemma on YT and someone said, just tape the string to the top of the circle and mark the spot where it intersects, tape the string to that spot and do it again to mark the bottom of the triangle, repeat it for the other side and there you are! I tested it out with a compass and found it quite interesting that the radius of the circle can be used to divide a circle into 6 parts. Are there any other fun secrets shared between a circle and it's radius?

[LifeLikeSage]

The problem is that those who are smart enough don't need to go through the negative experience of making mistakes in mathematics; They can experience the creative flow in maths, because they already understand the rules.
In order to get to this state, it takes most people a lot of training, and a lot of failure (being wrong). This negative experience, naturally pushes people away into things they are good at (things they don't get as much negative feedback from).

[vivekpujaravp]

Phenomenal presentation and book recommendation. Please do more like this.

[aniksamiurrahman]

No matter what you do, learning math will always take a lot of elbow grease.

[FirstNameLastName-wtto]

You lose the average student at the rectangle because you didn’t explain why a rectangle. That’s pulled out of thin air. The average student will not be able to catch up after this because they’ll get stuck at “where the heck did she get the rectangle from?” That’s when they check out. This is why students start to bow out of math in high school. Not because it’s boring or hard. But because the why is not being satisfied by teachers who don’t see the steps they are skipping.

[carolinedelisle]

I hated art classes in school. This wouldn’t have worked for me. I guess the morale of the story is that not all people learn the same way.

[trayne]

I remember taking calculus in high school, my teacher sent us out around the school to create and solve a problem using calculus. I did a problem of the tip of a persons shadow as they run towards, under, and past a streetlight. Using some calculus and trig an assuming a constant pace for the runner, I was able to find an equation to represent the tip of the shadow throughout that process. I loved that class.

I'm the opposite to most people (in my social groups) in math though, it didn't make full sense to me until I took my first geometry course with proofs. Most people I talk to started having a hard time when the curriculum got to geometry, but I found it began clicking with me when I got to that point.

[JohnDanielBryant]

Paul Lockhart is GOATed. Guy works independently for years, submits his research to Columbia University, and they give him a PhD in math. He says math is taught all wrong in schools, and he's completely right.

[duncanhill]

My kids are probably a bit young for this, but the way I'm teaching my kids at the moment is through exploration. Giving them a nudge to find things like Kaprekar's constant by themselves, all the time practising the basic skills (who wants to do a massive sheet of practising subtraction, when you can find if some other 4 digit number has the same result, or if the first one they picked is somehow special). This definitely looks like a book I need to invest in for them though.

[airsicklowlander]

I struggled with memorizing multiplication tables as an eight-year-old. My teacher had a poster in the back of the classroom with all of the kids’ names on it. Whenever someone got 100% on our weekly multiplication tests, they’d get a sticker next to their name. By the end of the year everyone had like 10-15ish stickers next to their name except for me who maybe had 1 or 2. It was humiliating. It was an always-present public shaming. I distinctly remember one day when some older kids came into our classroom and started laughing at how that one kid with no stickers must be stupid. It gave me life-long self-esteem issues that I didn’t identify and start to address until my late 20’s. Math permanently traumatized me.

[neutronenstern.]

and then there are actual teachers that deny 63 on the question:
" Write down a two digit number, where the tens place is double the one place". Why you ask?
Because the sample solution suggested 21.

[me]

"There are no wrong answers, but there are bad answers" -a my former Math professor of mine. His attitude to math was, "You can tell me 2+2=5. You just have to prove it."

I really liked his approach.