Five Principles of Extraordinary Math Teaching | Dan Finkel | TEDxRainier 

"Not knowing is not failure, it's the first step to understanding" BEST QUOTE EVER

Summary: 1. Start with a question 2. Give students time to struggle 3. You are not the answer key.. try to figure stuff out WITH them. 4. Say yes to students' ideas and questions: take their ideas and go to conclusions. 5. Have a play mindset

"When we're not comfortable with math, we don't question the authority of numbers."

I had a math teacher last year who was not just teaching lessons on the board, but bringing them to life. And despite the fact that I had a lot of trouble understanding math at first, I started to have real fun going to Math class. A pleasure that I had never experienced before since I sincerely began to like a subject in high school. This teacher, by bringing his lessons to life with a pedagogy that I have not encountered to date, opened my eyes to mathematics. I no longer considered this as a simple matter, but as a world apart, I realized the magic that stood behind mathematics, all the paths that could be walked in this area and all the geniuses that made it possible to advance our vision of the world thanks to mathematics. I also realized, thanks to this teacher that everything is mathematical, and that even in everyday objects to which we do not take any consideration, there are incredible mathematical principles hiding. So today, I'm still "in love" with this subject thanks to my teacher. So if I were to conclude this insignificant comment on the assumption that I address myself to people who do not like mathematics, I would advise them to try to be interested in this subject, and to read stories on mathematics or on mathematicians. One film that I highly recommend is "The Man who Knew Infinity". Thank you very much for reading me and good day to you!

"I know if I rush to an answer, I would have robbed you of the opportunity to learn" what a beautiful quote. This is exactly what I tell my students. "Figure it out. You can do it." Always give the question, you'll be really surprised with the answers the kids come up with :) Learned a lot of new techniques this way - even from 4th graders. Wonderful wonderful presentation. It’s like you took all the words from my mouth and put it in the most beautiful way - something that I would never have been able to do! Like someone here said - this is the "I have a dream" speech of mathematics

As a math teacher myself, this is the kind of thing they should be showing us in our Teaching degrees. Phenomenal. Dan - if you ever read this - please know that I'm trying my darnedest to work your philosophies into my teaching (and RU-vid videos!). I hope all math teachers can live up to your approach.

I am a math teacher. I do exactly what he said. I never give my students an answer when they ask me a question. Discuss about it and find out how much they understood so I can suggest what could happen next. But most parents are not happy about it. They want their kids get answers immediately. A few parents are very happy because their kids develop how to study by themselves.

Principles: 1. Start with a question. 2. Thinking happens only when we have time to struggle. 3. You are not the answer key. 4. Say yes to your students ideas. 5. Play!

As a Mathematics teacher, I am 100% agree with your thoughts. You have explained five principles very well and every Mathematics teacher must have to follow them. Thanks, Dan for the video.

Brilliant! Einstein once said, "If you cannot explain it simply you don't understand it well enough". Dan certainly doesn't fall in this category. I have recently started teaching Mathematics to my 12-year old daughter and her friends on weekends. And I am doing quite what he is doing. I am doing something similar and the kids are now discovering (not learning) that fractions, decimals, ratios, proportions, percentages and probability are just different dishes with the same main ingredient.

This teaching method applies to any subject by dealing with your students with respect. Great to see there are truly inspiring teachers out there. Loved it!

I paused the screen when the circles with the colors were showing and I asked my little brother (who is in 4th grade) if he could figure out what any of it meant. At first, he just said, " I don't know," and he didn't want to make an effort to try. However, after reassuring him to try, he was able to figure out what all of the colors and patterns meant within ten minutes . All I did was sat there and watched, and when he asked me if he was right on a part of its meaning, I would just ask him to explain why he came to that conclusion. In doing so, he would reassure himself of his own findings, and accomplished understanding the tasks all by himself. It was very accomplishing to watch him struggle and then figure it out through his own means. Thank you!

This video is so important. I'm really disappointed with the state of math education right now when it's so easy to show how amazing it is!

This brought tears to my eyes. My 9yr old came home from school and said I'm sad I am asked him why and he said I have math homework and I can't do it. I sat him down and said son you can do it. If some kids in your class can do it. So can you. I taught him and taught him. Since that day wev'e been working math together everyday. Last week he came home with a test sheet and he scored 100%. I was like I know you can do it. I could not be more happier and him too. He is always happy when he gets a question right.

I am a teacher and I was jumping around when I found the answer of the connection in those colors. I am just visualising how students will behave when I show them in the class and most important when they get the answer 😍😍😍😍😍😍😍😍 😱 Mind Boggling session 🤩🤩

Outstanding presentation! It has frustrated me so to have experienced math education reduced to a set of rules. Many textbooks have been fillled with formulaic, "cookbook" type content. Math should be challenging, but fun and playful at the same time. We need to empower students with the power of mathematical thinking and reasoning, not beat them down with rules and procedures. Thank you!

Rule number 6 -Be careful not to confuse. Be sure to summarize at the end what was correct and what wasn't and more important why.

Thank you so much. Tomorrow my kids are going to spend a whole lesson with one fraction each and they are going to have to draw it and then place themselves on a number line. They are going to have to reason as to why they are in that place on the number line. We have spent 2 weeks struggling with fractions and I think playing like this, they might finally get it! I'm really excited to teach :D

4:00 Those colours indicates the factors of the number, most of the prime number has same colour some 2,3,5,7 has different colours and non prime numbers has colour of it's factor, for example, 4 is 2×2 which is indicated by using 2's colour two times and 20 is 2×2×5 which is indicated by three segments of colours two 2's colour and one 5's colour, 49 is 7×7 so two 7's colour, 44 is 2×2×11 two 2's colour segment and one 11's colour segment, 60 is 2×2×3×5 thus two 2's colour segment one 3's colour segment one 5's colour segment.

At 4:03 this is prime factorisation of a number...... That's why prime numbers are in single colour.. 6=2x3 that's why 6 is coloured with half of colour 2 and half of colour 3..... That's a great creative play

I am a average math student, but I love love the power of math to discover new things like Q-R code using probability, finding patterns. And I knew one day I would become a great mathematician. ..........................

This is the "I have a dream" speech of mathematicians. You read it here first :)

This is addressed to people who understand maths, not to those, like me,who don't, and who feel a physical sense of horror at the very thought of maths.

I found it satisfying to be able to memorize facts and steps as a little kid, that was how I figured out patterns all by myself. I remember realizing how it all made sense *after* I had *already* mastered basic facts.

I think we all would agree that Dan's philosophies are where we should all aspire. It is difficult, however, because we're all caught in this bind of trying to both do problems like this to stoke students' interest while finding enough time to give students exposure and practice for all of the "required topics". Even after 27 years teaching high school math, I'm still trying to find the right balance. But watching these inspirational videos remind me what the goal should be - to first and foremost get students to buy in...

I'm currently doing my masters of teaching and I've always thought that there were several important things to be being a good teacher, 1. Life experience. I never liked those who immediately went into teaching after high school because you have nothing but high school to give back to your students. 2. Passion. If you are not passionate about the topic, why would you expect your students to be? 3. Strategy. Students all learn differently. Students all react differently to teaching styles. For maths specifically, I've always seen it as the true and unbiased representation of the natural world. In a religious school you could describe this as the true language of God. Otherwise it would be akin to a magical language that holds all the secrets of the universe. Math is no less magical than I have described yet it is rarely seen as such. Many things in science struggle to be expressed purely mathematically but it is still essential. As a new microbiologist, I was consulted by my manager who had a masters in accounting about mathematical principles relating to micriobiology because she simply didn't understand it as well. Biology is the least mathematical of the main highschool sciences and yet it's still relevant. If you go to university for science, you'll no doubt see a lot of scientific studies. What you may or may not see is that much of that statistical analysis is done by a statistician because the scientists themselves do not understand it. But that in itself presents a flaw in the process. Statistical analysis is open to interpretation and if the statistician doesn't understand the subject he won't understand how to properly represent the data.

when ever i feel like math is not for me i watch beautiful mind and then i feel like it is the coolest thing ever.

I agree, respect and have a passion for what you have expressed. Now, if we can all work together to allow this to happen in a classroom, it would be beautiful. People not directly involved in education and seeing what is happening are shoveling more onto our already overfilling plates. Sadly, many teachers are spoon feeding students in order to meet the requirements. Breaks my heart. Everyone deserves to find a love for learning through struggles and successes.

I love the idea of starting a math class with a question. Allowing students to think creatively in an open ended math problem, gives them independence and confidence in their learning. I love the steps, they make a lot of sense!

One word can change the tone of everything. Posing questions is a less threatening beginning to lessons. And tellikng them I don't know. You tell me. Creates laughter giggles and "noise". Absolutely agree.

Incredible presentation! If only Dan could be cloned and placed in every learning institution all over the world!!

Tremendously inspiring, enjoyable, and easy to understand. As a future teacher, I'm delighted to have found this video. Thank you, Dan Finkel!

it's sad that we live in a society where there is the need for extra, or, out of the, ordinary teaching when it should be the ordinary to have good teaching in math

"When we're not comfortable with math we don't question the authority of numbers", According to Decartes "what is a thinking thing: it is a thing that doubts, understands, conceives, that affirms and denies, wills and refuses, that imagines also and perceives" THIS IS THE TYPE OF THINKING WE NEED IN EVERY MATH CLASS EVERY DAY.

This opened my eyes- I'm about to tutor some kids struggling in mathematics, this will help us both!

This is the most interesting speech I ever heard on Math Teaching. Really very useful for aspirant math teachers. You have explained five principles very well and every Mathematics teacher must have to follow them.

This was actually AMAZING! I am studying mathematics for secondary education and I think this is a really neat approach to math.

I just realized that what he said, is unconsciously were my POV in Math, without my teachers ever taught me. In my sight, since I like to play, Math is like a mystery game that is not to solve. Thank you for the insight

Love the following the what if and ending up modular!

Great ! What is more impressive is the authors' own conviction in giving space, time and scaffolding questions that cultiates mathematicians. Thank YOU Dan for your enlightenment.

Most of the time there is undue pressure, time constraints and irrelevant administrative procedures for teachers that are given more weight than teaching. Teachers also deal with large classes with a wide spectrum of student abilities. This makes it very hard to generalise teaching techniques. This is a great video, but must also be questioned, depending on context.

As a math teacher who tries desperately to get her students to think about bigger questions and more beautiful connections I fully relate to the, "I don't consider myself a mean person but I have no problem denying you what you want," comment. Love it.

After watching till 8:52 I found the logic.. it shows the prime factorisation. Like 1 = white 2 = orange 3 = green 5 = blue 7 = violet Number of times the colour appear is the power of corresponding prime factor.

I was, and still am, quite happy to absorb the techniques devised by very smart people over the centuries without having to rediscover them, even in a small way. What I really like is being able to do useful stuff with mathematics - and I can. That started with applied maths problems at school but the rest I've had to learn for myself from real problems in life. I wish that, at school, the skills for developing notation and developing models in new areas had been taught systematically, with guidelines and techniques. That would have made it easier for me to do what I have now done.

Great presentation! As a math teacher, couldn't agree more. I have a student returning to education after nearly a decade and half. With barely any memory of math, she came in with a lot of apprehension about learning and doing math. Today she looks forward to our math classes! Nothing can be more satisfying than that!!

common multiples I saw it instantly and had a mathgasm-one poisonous high school math teacher robbed me of something I loved and I left my my love for decades. I rediscovered it as a middle-aged adult and have risen higher and explored deeper than I ever thought possible for myself. Salman Khan believes anyone can learn anything and based on my own Calculus journey I believe it too be true. If I can do it yourself can too!!

How refreshing -- and inspiring! I have a learning center and am going to offer $1 to each of my students (they are still young enough to appreciate $1) who watches this and brings me a list of these five principals. Then, I'll ask them how we should try to incorporate them into our program. Thanks Dan.

This is some of the best advice I have ever seen on how to teach maths at school. I would also add that all multiple choice answer math exams should be banned. Solving a maths problem is a journey and students should have the chance of showing what paths they took on their journey. As Dan Finkel points out major progress in maths entails taking new and unusual paths. Very little of real maths is about doing calculations or repeating rote memorized formulars.

Start with questions - but what if the students are not interested in questions/answers (this is the case at least sometimes). Students need time to struggle - in my experience most people, not just students, want to avoid struggle as much as possible. Teacher is not the answer key - as I mentioned before some students are not interested in answers or lack thereof. Say yes to your students' ideas - the example 2 + 2 = 12 is a nice one but a student who has problems with regular addition will have very little chance of understanding 'number circle'. that example is appropriate only for the best of students which usually like math already. Play - whoever is able to consistently persuade 5 out of 10 students to set aside their phone and play with math deserves a teaching degree, the one who can do it with 7 out of 10 students deserves a doctorate, and the one who can do it with 90% must be some sort of god.

I had watched this once and remembered all but still couldn't help watching the whole thing again! As someone teaching math at university level I feel so bad that there is just not much room (space, time, money, etc.) to PLAY in a math class. Syllabus must be covered, exams given, and grades assigned -- all by deadlines. Despite this I have indeed taken the adventure and I have witnessed firsthand the magic that happens when you as a math teacher keep your mouth shut and become invisible for 20 minutes. The ice is broken and dialogue begins!

Oh, wow. This is an educational gold mine. I’m starting uni next year doing a bachelor en route to a primary teaching degree and EVERYTHING said in here is going to be amazing for my assignments. It doesn’t just apply to maths, either. All of the information could apply to all aspects of learning and teaching particularly for children, as they learn predominantly through play.

I would give this talk at least a 1000 Thumbs Up. One of the best talks on mathematical education!

I am so amazed by the moment he brought modular from the riduculous equation, full of joy and intellectual

This is probably the best Ted Talk I’ve ever watched!

I like this point "The teacher is not the answer key." Growing up, I always thought the teacher knew everything, so they must know the answer to my question. This makes sense to let the student prove his point to see if they can back up their answer.

Beautiful advice. I think the key is having the right mindset about learning. Its bigger than just attaining knowledge

Beautifully crafted talk that says so succinctly what matters in math education. The key is the last point: experience math as play. That's exactly why I love math. And when I get together with other mathematicians, that's what we do: play.

My number 1 issue with this IS time. The school year is too short and so are my classes. By the time students really get thinking the bell rings. Doesn't mean we can't do this stuff but the journey needs to happen on a treadmill to keep the pace.

"Thinking happens only, when we have time to struggle" Dan Finkel

These talks are changing my life and keen my brain challenged and growing

This is the most interesting speech I heard on Math Teaching. It is only if we enjoy "playing" with math than we become really good at it. Love it! Thanks for sharing!

Such great ideas on how to get students to ponder questions and find solutions on their own and as a group. That's the path to getting them to love math.

Not knowing-not failure love it. I wish I knew this 20 years ago when studying certain topics in real analysis

As a teacher of 4th grade I love this. However, I wonder what the thought is about, and I believe he mentioned it, learning basic facts before 6th grade. I see the biggest struggle with students being able to play and have fun with math is that they can not easily manipulate numbers and patterns on paper or mentally with ease. We have been told by our district many times that learning basic facts is not necessary and timed tests are bad. Not I am as playful with math facts as possible and am fairly flexible with the time but I find again that students flounder when they can't manipulate numbers so they can feel comfortable taking risks and playing. Thoughts?

"What matters in math isn't if their answer is right, but if they have the understanding and logical arguments to that its right. After all, when they solve the Riemann Hypothesis, nobody is going to be able to say 'that's wrong, try again', they will be checking their reasoning. If the reasoning is faulty, that's when we know they're wrong." -Me.

As a preschooler it was my greatest hobby to play with maths... until elementary school killed it. I was fortunate enough to find my way back to it later on, though.

blue is 5 , yellow is 2, green is 3, red is prime , purple is 7. Just write multiplicative factors and there you have it :)

I'm an English teacher in China but I found this very helpful for what I do, thanks for uploading!

Every parent involved in Classical Conversations should watch this video!

"I learn to understand, not to remember." - George Chavez(a.k.a Me)

Dan Finkel both inspired and enlightened me. He speaks clearly and presents ideas logically. Is his penchant for math exploration the source of his creativity in improv comedy?

Why did you stop!!!! Come back and keep enriching us. The best ever i have heard.

The circular representation is a type of graph which can be used to depict octal bases and, as such, there is an error: have a look at the second ring where 14 is listed twice. [14 base 10 is 16 base 8]

I couldn't keep silent when watching this. You echo my thoughts. Absolutely amazing presentation. We need many more math teachers like you.

AS a math teacher I try to develop interest in students towards mathematics.

I study maths and tutor highschoolers/collage freshmen, when you said what if 2+2 ?= 12 I knew that if you define (+) operand int he vector space right 2 (+) 2 = 12 is legit, I know that RSA method is based on modular arithmetics etc... But I could not come up with ideas like your or with that speech. I mean of course abstract algebra is extremely useful but I never thought of "throwing" it at younger kids/teenagers not attempting to just tell them the theory but discover it with them... That´s awesome

How love for math (or comfort with it) gets developed is a very mysterious thing. There is no fixed rule. What works for one kid may not work for other kids. In fact, it can potentially be counter productive. I think it is because math is connected so deeply with us that different people perceive its manifestations at different level in different forms. It doesn't click it when it is presented at some other level or form. Real love/fun starts once it 'clicks' that difference is only in the level/form but not in the core concept. Until then it is a tough road for everyone.

such a simple, easy , beautiful and elegant question. Although easy to solve it was very satisfying.

G. K. Chesterton, in one of his short stories (I forget the title, but it is the one in which (spoiler-alert) a hard-of-hearing man is deliberately shot in the leg in order to save his life) explicitly, via commentary of a teacher to a visitor, makes the connection between play and teaching mathematics ("the only way").

Every math teacher should see this! Too often we teach math the way we were taught. The only way to get kids to love math is to change the way instruction is delivered by following Dan’s five rules

every teacher on earth should see this and use this method in there class so many do not and a lot of very intelligent students just get bored and give up because of it when curiosity is shunned by a teacher it has a horrible and lasting impact on a students education and view of the education system as a whole

That was completely AWESOME. I have a 4-year-old granddaughter and I don't want her to "hate math" the way I was taught to hate it. This talk will help me discover fun ways to help her be more comfortable with math than I ever was. Thank you, thank you, thank you.

Hits differently now that I am watching this as a teacher compared when I was still a College Student. :D A VERY GOOD TEACHING STRATEGY INDEED.

As an aspiring middle school math teacher, I found this very empowering.

I am a math teacher and it was so helpful !!!

Just watched this video having today been talking to my Primary Education students about mathematical thinking. I will be suggesting that they watch it too. I find it reassuring that there are like-minded people out there and that I'm not making this stuff up! Thank you Dan, I can continue doing what I'm doing with confidence.

I'll tell you the truth, I love math, and always wanted to teach it, but when I got the opportunity to tutor 2 cognitively disabled adults in basic maths, I realized it's really, really, really hard to get someone to figure out WHY something is true, disheartened, I decide to revisit this video, right now I'm planning in my head the question needed to trigger the thinking that leads to understanding basic division. If this goes well, then your video has made an amazing impact on the life of not 1, but 2 (and counting me, 3) disabled people. So thank you

I am working towards a math teaching credential to instill confidence in students to accept the relevance of math in everyday life.

The colour thing in the beginning represent the decomposition of all numbers into powers and product of prime numbers, each prime number has a specific colour forming a full circle of this unique colour, sometimes the portions of circles in non prime numbers are differentiated, like 11 and 17 in the numbers 33 and 34 perhaps because the colours are too similar or to give an hint, the number of portions of circles of the same colour represent the power of the associated prime number and when we do the product of all portions of the circle we get the number we're looking for, for exemple, 60 has two orange portions of circles representing 2x2=2² and one green portion of circle representing 3¹ so 3,and the last blue one represent 5¹ so five, u take the product of them so 2²x5x3=60, u can do the same with each number, btw, the number 1 has a white circle, representing the fact it is a multiple of all numbers as white contains all colours, but at the same time it does not have its own colours, because it is not a prime number.

Question of time: I think the answer is that each color is defined by 1 2 3 5 and since 4 = 2 * 2 means two colors of the same color... And so 6 = 3 * 2 means the color of 3 and 2... And there are the initial numbers that are known as orange colors...

This is a great approach, well-described. It takes a lot of self-confidence and trust to say "I don't know" or "let's see where that leads". I like it!

11:52 Very important words start here. You need much courage to ask such question as "What if there IS a number that, after squaring, gives negative one?" and to bring the humanity to the new mathematical world.

Indeed, it is time to love the beauty in math.

Competitive time-bound exams are necessary evils, but maths teachers have to teach kids to spend time with maths without deadlines. Like every other subject, lazy curiosity and creative thinking make you understand how things are really interconnected, even in maths. This way the kid might not be able to solve more test papers in less time, but he has a good chance of writing a paper that discovers or invents something new. Quality over competitive scores.

A simple but valuable math game. Get a blank piece of paper and write 0 x 0 = 0, 1 x 1 = 1, 2 X 2 = 4, keep going, and go up as high as you feel like going. Draw a line connecting the squares, starting with 0, 1, and 4. Look for patterns. Try to explain any patterns you see.

Of course I agree, though I'm constantly faced with students, parents, or colleagues who say: students should just learn the rules of math, pass the exam and get higher grades. That's all, we want degrees to look for a college or a job. What do you *actually* do when the teaching and school environment is (almost) all against the 5 principles? Thanks for suggestions! Congratulations mr. Dan.

You made my day, i really love math. I dont know it but i love studying it. I love the ‘why’ of things, it is the ‘why’ that stars it all, the thinking the ideas, the struggling…im just a nobody but i think that everything is physics and that you can never understand or conclude something without mathematics. To all the science lovers (especially math and physics lovers) i recommend you to listen to Richard Feynmans way of thinking and Walter Lewins way of proving things.

Love of resonance comes naturally in this resonance Totality and the Universe is Mathematical Singularity positioning integration here-now-forever continuous creation QM-TIME condensation connection. Don't fight it.

I am so grateful for you kind sir. There's hope.

I agree with you sir being a teacher we have syllabus completion responsibility and we just end up messing up with the whole idea of participative learning....