Five Principles of Extraordinary Math Teaching | Dan Finkel | TEDxRainier
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- Опубликовано: 14 май 2024
- In this perspective-expanding and enjoyable talk, Dan Finkel invites us to approach learning and teaching math with courage, curiosity, and a sense of play.
Dan Finkel wants everyone to have fun with math. After completing his Ph.D. in algebraic geometry at the University of Washington, he decided that teaching math was the most important contribution he could make to the world. He has devoted much of his life to understanding and teaching the motivation, history, aesthetics, and deep structure of mathematics.
Dan is the Founder and Director of Operations of Math for Love, a Seattle-based organization devoted to transforming how math is taught and learned. A teacher of teachers and students, Dan works with schools, develops curriculum, leads teacher workshops, and gives talks on mathematics and education throughout the Pacific Northwest and beyond.
Dan is one of the creators of Prime Climb, the beautiful, colorful, mathematical board game. He contributes regularly to the New York Times Numberplay blog and hosts Seattle’s Julia Robinson Math Festival annually. In his spare time he performs improv comedy in Seattle.
This talk was given at a TEDx event using the TED conference format but independently organized by a local community. Learn more at ted.com/tedx
"Not knowing is not failure, it's the first step to understanding" BEST QUOTE EVER
Vic7or you cannot fill a cup that is already filled
Socrates taught that well over 2k years ago, but alright
Vic7or I agree
I actually stopped the video and wrote it down, and I'm going to make it a poster for my classroom!
Vic7or no its not- Einstein lol jk but lol
"When we're not comfortable with math, we don't question the authority of numbers."
Math has no authority, nor do numbers only magic does and that there are no rules. You create the rules you are the only authority.
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
The real MVP
Thank you!
Thanks man!
5 simple steps. I'm not sure if I want to be a teacher or not as a career, but I do want to be able to give genuine lectures at some point. And I believe this is the five fundamental steps that my best teachers used in the math classes that I enjoyed the most.
Great tip for teaching Math.❤
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!
Incredible story mate
Thank you for sharing this encouraging experience. Your teacher was amazing, no doubt, but well done for having an open mind to what he/she presented. When that partnership is in play in a Math classroom... The possibilities are endless. Thank you for sharing your story. 👍
Can u plz xplain,what magic he used to do in his class??
👏👏
Respect for math teachers!
Hey there! I want am actually a teacher trainee and want to become a maths teacher, could you give me an example of what your teacher did? I really want to make maths fun and interesting for my students
"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
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
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 RUclips videos!). I hope all math teachers can live up to your approach.
I am not sure what grade level you teach, but Illustrative Mathematics lends itself very well to this type of philosophy.
But to what end can you play? After all they are going to have exams. What if you are welcoming their ideas but will it not take all the time you have to drive them to the answer? After all they have to pass. They must know the rigjt solution to put it on the paper. I am helplessly writing this because of all the system we are bound to.
@@waseelmusic I believe the thought is that from the learning that happens through exploration and play, the teacher can help students express their understanding in a number of traditional ways. This is an idea impressed on me by Jo Boaler.
@@waseelmusic it's just the initial struggle most of my students start performing within a month or even week of starting a new concept...give the Cues...help them arrive at their own conclusions...they won't forget it or ever get confused.
So how are you doing today with your intentions?
This is the "I have a dream" speech of mathematicians.
You read it here first :)
And hopefully I won't read it again.
lmao so accurate
If you don't have anything clever to comment, don't comment at all.
@You Tube it's been 2 years, did anything change?
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.
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!
It’s not easy at all to show that. It depends on the moment to moment patience of each teacher
@@tpstrat14 If you are interested in maths videos try my ICT enabled one I am sure that you will ask me about the software used construct figures like this this is geogebra a magical software to teach maths so students will easily understand call me if you have any doubt in its construction
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!
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.
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.
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.
Hello I’m going to become a math teacher In bad at math
But I want to be a math teacher
I don’t know how to teach math only how to do the problems could you give me some advice
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 🤩🤩
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 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!
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
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.
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.
This does not help people who are color blind but may help find out the students who are color blind.
@@owenprince4823 😂
@@46prakashs22 I attempted to take a class in electronics. They gave me a test first to see if I could see the different color of the wires and I failed the test. They would not let me take the class. I told them it was not a fair test as they did not let me study for it (LOL)
If you are interested in maths videos try my ICT enabled one I am sure that you will ask me about the software used construct figures like this this is geogebra a magical software to teach maths so students will easily understand call me if you have any doubt in its construction
@@owenprince4823 If you are interested in maths videos try my ICT enabled one I am sure that you will ask me about the software used construct figures like this this is geogebra a magical software to teach maths so students will easily understand call me if you have any doubt in its construction
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.
Learning math is truly not about memorizing facts. It is impossible to take things to the next step if you only memorize. The old ways brought us to being forced to get qualified people out of the USA to work in STEM jobs.
Memorizing may be necessary but not sufficient for understanding and appreciating mathematics
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!
exactly
If you are interested in maths videos try my ICT enabled one I am sure that you will ask me about the software used construct figures like this this is geogebra a magical software to teach maths so students will easily understand call me if you have any doubt in its construction
If you are interested in maths videos try my ICT enabled one I am sure that you will ask me about the software used construct figures like this this is geogebra a magical software to teach maths so students will easily understand call me if you have any doubt in its construction
Tremendously inspiring, enjoyable, and easy to understand. As a future teacher, I'm delighted to have found this video. Thank you, Dan Finkel!
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.
It is the mind set believe in your, work hard and you will make it
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.
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. ..........................
I believe you will be a great mathematician
Yes you will
Excellent don't turn back. Just go forward
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.
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.
This was actually AMAZING! I am studying mathematics for secondary education and I think this is a really neat approach to math.
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!
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.
this was my first time watching anything like this. I've struggled with certain areas in maths, I can relate to what you have said. I enjoyed this and will defiantly watch again. thank you, keep inspiring
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.
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!!
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...
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!
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
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.
Watched this again, while in search of a motivating send- off for a professional development period....perfect! Thank you.
Love the following the what if and ending up modular!
+John Golden Yes, that was a great twist, and made the point about saying yes so well!
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!
such a simple, easy , beautiful and elegant question. Although easy to solve it was very satisfying.
Beautiful advice. I think the key is having the right mindset about learning. Its bigger than just attaining knowledge
"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.
I am so amazed by the moment he brought modular from the riduculous equation, full of joy and intellectual
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.
This opened my eyes- I'm about to tutor some kids struggling in mathematics, this will help us both!
Indeed, it is time to love the beauty in math.
Incredible presentation! If only Dan could be cloned and placed in every learning institution all over the world!!
I am in love! Thank you!
Every parent involved in Classical Conversations should watch this video!
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.
What a great talk! Thank you!
Indeed extraordinary ! Great talk . Thank you, bless you. All your dreams come true.
These talks are changing my life and keen my brain challenged and growing
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.
I'm an English teacher in China but I found this very helpful for what I do, thanks for uploading!
Not knowing-not failure love it. I wish I knew this 20 years ago when studying certain topics in real analysis
What a beautiful way to discuss the prime factorization!
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
yea and how that is gonna happen with low salary and less to no privileges ?
Why did you stop!!!! Come back and keep enriching us. The best ever i have heard.
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 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.
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.
I am so grateful for you kind sir. There's hope.
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!
Simply amazing !!!
"I learn to understand, not to remember." - George Chavez(a.k.a Me)
learn to understand and then memorize. as memory is also a part of intelligence
OP's comment reminds me of a.a
Lewis, the euphoric atheist "quote-maker"
Read. Understand. Remember. Apply.
well i forget my own understanding sometimes so memorizing is helpful
love this. students need more time to explore and play.
omg. thank u so much for this absolutely inspiring presentation. I think I have the right arguments now to convince my colleagues that this is the kind of math we should be teaching
I would give this talk at least a 1000 Thumbs Up. One of the best talks on mathematical education!
As an aspiring middle school math teacher, I found this very empowering.
AMAZING!! love the video!
Excellent. It changed my perspective ! Sincere thanks.
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.
You're right, it says so right in the title. It's about teaching math. Teaching it in a way that allows the next generation to love math, instead of experiencing a physical sense of horror at the very thought of math. I encourage you to not give up, you can improve, and build tenacity at the same time, one place to start is Khan academy, work a little every day and soon you could be less horrified by the thought of math.
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.
Sir.. can I ask questions..
wow, i'm quite impressed. thanks for sharing this!
What a great speech. Thank you
Very good talk on the subject; it's wonderful he remembers Descartes and his discovery of the thinking subject, to see math as a thinking activity rather than a calculating task; the principles can vary: NCTM in 1980 gave a valuable document title An agenda for action that pretty much have been ignore by math teachers.
I couldn't keep silent when watching this. You echo my thoughts. Absolutely amazing presentation.
We need many more math teachers like you.
So glad I incorporate finger use during classroom instruction with my UPK groups. Base Ten in the palms of both hands.
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.
This is probably the best Ted Talk I’ve ever watched!
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?
Thank you! Great advice. Seriously, thank you!
Ow! I loved! thanks a lot for this!
Somehow this video helped me finally figure out the math problem I’ve been fighting with lol I always get my friend’s help and realized I can do this all on my own with some reverse thinking with my equations
Absolutely brilliant!
Brilliant! all teachers should listen to this and apply it, thanks!
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!!
David DeMar it was easy to see the pattern. All that stuff you're saying makes you sound like some kind of flakey nut.
Hi David...I am in the same boat as you..loved math when i was young, but the teachers made me memorize things and use it instead of teaching how to apply them in real world..i am reading mathematics on my own now...how did you progress in your calculus journey? Which books or materials did you use to learn Algebra, Trigonometry and Calculus? Thank you for your help
David DeMar - Knew my 24x24 tables in 2nd grade with ease. Lost interest in middle school. Came back curious before my 30s ;)
no it's breaking the numbers down to the prime number multiples
Max Carson actually it's more than just multiples, it's reflecting the fundamental theorem of arithmetic, that is writing the numbers as products of prime powers. The number of equally colored segments reflects the power. Primes bases up to 7 have their own color, higher prime factors are red.
Beautiful. Thank you.
I like it very much !
Thanks for the principles.
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.
Very moving inspiring talk!
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?
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]
Math is so beautiful indeed! I love it too.
Cheers
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.
The every word came out from his mouth is to be quoted 👏
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.