Here are the timestamps. Please check out our sponsors to support this podcast. 0:00 - Introduction & sponsor mentions: - Truebill: truebill.com/lex - Fundrise: fundrise.com/lex - ExpressVPN: expressvpn.com/lexpod and use code LexPod to get 3 months free - Indeed: indeed.com/lex to get $75 credit - Stamps.com: stamps.com and use code LEX to get free postage & scale 0:23 - What is beautiful about mathematics? 9:12 - How difficult should math really be? 17:31 - Students giving up on math 28:52 - Improving math education in schools 38:49 - Inspiring mathematical creativity 56:35 - youcubed 1:00:55 - Best methods for studying math 1:21:29 - Advice for young people
Thank you ..I for one needed to hear this. I so wanted to know math but couldnt bec I had math teachrrs. Unlike this lady. I need visuals I guess and words to understand . Thc 🤗🤗❤️
I often think back to being in class in middle school, all the way to the back, trying to understand Mrs. "Smith". She pause after explaining something and i thought to myself, how come? She said right after that "i bet none of you would think, how come". I wonder how many others thought the same but like me, didn't say anything. I like math cause math is like the only empirical absolute truth. It's as if it were Gawd. True everywhere, all the time, 0 🧢 all 📤 fax lol
I had a teacher in grade 11 that was surprised I was staying on the normal math path instead of transferring to the remedial one. I ended up with a finance degree, data analytics certificates.
I had a midle school teacher who flunked me in maths in 10th grade, high school second grade. I had a different teacher next year. I ended up as a financial analyst...
The most important message I learned is, some people cannot do math. And that is ok. They (we) are no less valuable than a person who cannot play basketball, or paint, or fix automobiles. People who love math think it is way more important than it is. :) To each their own.
I’m in my 70’s now and felt pretty much lost in math by age 10. I got through high school and undergrad years well enough, got two masters degrees, and then worked on big bank financial systems. But always felt I was bluffing my way through anything computational, even basic algebra. I sure wish this approach to mathematics and visualization had been used way back when I was in elementary school. But hey, it’s never too late to learn! Thank you for another wonderful discussion!
Been doing a self study maths, stats and econometrics from zero. Used to feel miserable when getting stuck. Nowadays I feel blessed getting stuck. It confirms I need to do more work, like a free counselling.
Spot on. I was told very early that I was dumb & couldn’t do math. It wasn’t until I found a practical use, electricity, that things clicked. Once I told myself “If someone else is doing it, I can do it”. The belief I’m myself helped me develop a career in the electrical industry & today there isn’t a day that I’m not doing math! Believe that anything is possible & it will be. Thank you for this.
- Recognize mathematics as a creative and visual discipline (0:23) - Explore multiple methods and solutions to enhance understanding (0:41) - Utilize visual approaches to activate brain pathways for deeper learning (2:17) - Encourage connected thinking by integrating different perspectives on problems (3:00) - Foster intuition as a key component in mathematical problem-solving (4:45) - Emphasize the importance of struggle and challenge for brain development (5:58) - Create a multi-dimensional learning experience to cater to diverse thinking styles (11:08) - Strive for excellence while understanding the importance of supportive teaching (14:15) - Engage deeply with concepts rather than skimming through material (1:01:50)
Very nice conversation. One thing I was missing in math classes was "why do I have to learn this" and "what can it be used for". I wish teachers can give more examples of why something is important and how it can be applied so the students get more interested and engaged. With so many references to books and websites you guys will keep me busy! Keep 'em coming Lex!
Thank you.. Please do more conversations about our direct relationship to learning, understanding & exploring how to make sense of the world. So that the bad habits many of us carry from school, can be challenged with a counterweight through perspectives. This conversation was truly brilliant, and after this vid, I already view mathematics in a completely different light. Part of it is excitement about the mentality of learning.. Cheers
A teacher in Serbia from a high school I taught at used to say "math is learned by writing", meaning when you keep doing it and it becomes automatic you start seeing patterns you haven't noticed before... Some similarity with around 1:01:22. Giving yourself problems to work on and keep practicing.
I know what you mean. I tend to go for the difficult problem solving aspect, put in a lot of time there. Others are better at working endless problems. But if I am familiar with an area I then switch to doing all the problems, probably because there isn't much new to learn. I think it's to do with the neural reward system somehow.
@@jarne5581 yeah I gave up on math when my junior year high school teacher called me an idiot in front of the whole class. It’s unfortunate that most teachers are crap and only a very few take their jobs seriously.
@@weignerleigner3037 I was a idiot and did not care much for school and got the complete opposite, my only A Class and exam. He was a amazing at dragging effort out of me with humour. I usually spent my time drawing in class before that, filling out the least amount of words possible to answer and just writing one word solution or just the correct addition without showing, showing the entire calculation seemed like the dumbest thing in the world to me if i thought i had the solution. Math to me was nerd, not cool. "Gonna be a DJ" ridiculous at 15. But ended up the best class i had in school. That's really something, not my experience but that teacher. If he did 1 or more student that favour each year, he has helped 20+ idiots get a grade in math. Think that is the only teacher i respected in school in 14years. My dad always said teachers where after him in school too, showing a disrespect i kinda brought with my lunch i guess. I hope its was a "me" problem and not all the teachers. lol upto 49ish useless teachers and one good. It dont really seem plausible. One just said to me early semester, if you just sit still and shut up you get a D. That really sparked the further inquire of interest. What a bitch, she knew that.
@@mirroredname3389 I grew up in a small town and our schools were atrocious we lost teachers every year to budget cuts. In summers they would call off school because we had no a/c and it got too hot in the classrooms. I don’t blame my teachers they probably weren’t having much fun doing their jobs but it’s unfortunate for the students because we didn’t really get a great education.
I've always grouped and sought patterns in things. I was considered an advanced math student but got put off in grade 5 by a particular teacher who was obsessed with using high pressure competitive games in class. It stressed me out and I shut down. I didn't mind competition in sports, but I craved freedom in academic pursuits, so this didn't work for me. I kept exploring and took more math classes than any other by the time I finished 12th grade. It wasn't until I got to Uni where I found a teacher who absolutely loved teaching calculus and my love for math shone (I got a perfect score on my final exam and it felt amazing). At the same Uni I found another teacher who was able to answer all my questions around particular algorithms, who created them and why, and also what were the real world applications inherent in them. It seems to have taken a lifetime to get the context I was craving since ~ grade 3 or 4. It thrills me to hear a transition toward big ideas and connections is afoot. This could be a game changer.
It's quite true how the number of questions asked decreases in education with age. It's as though education is stifling exploration and rather just learning to conform to the tests.
I had a fellow maths teacher use Boalers methods to teaching her algebra class, it took her a couple years to curate her lessons. Once she started she quickly found out that she could only make it through one section of a unit in about a week because of the level of deeper thinking and productive struggle necessary for applications. Its very interesting and i think important to deeper understanding, but unfortunately schools are not structure at the primary/secondary level for this type of method. I do blame “the state test” for hijacking maths instruction leaving little time for true maths exploration.
So pleased to hear you mention Richard Feynman. His lectures should be a high school requirement. Sadly I stumbled upon him but then I binge watched everything he had recorded.
Feynman, just the name brings a smile, what a man! The talk about collapsing reality onto it self into a micro verse or how he meant it to avoid a planet killer comet, wow. That far out and also so down to earth. He so unique. I am pleased you mention they mentioning it.
Stay inspired! Remember that curiosity and playful exploration is more long term important than immediate results. And people inspire each other, so expose your kids to people you think are a good influence.
Look forward to listening to this in full. Maths is a subject often so poorly taught and subsequently difficult to grasp as part of the wider system of its application.
Totally agree. We teach our children math, in exact way and environment and structure the way we teach them social science or English. Its plain sad to be honest.
good interview. Needed this. University classes start again soon and am taking Intro to Discrete Mathematics, Calculus 2, and Physics 2 in tandem. Am very overwhelmed and self-doubt is certainty there. Will do my best, have high-expectations and will not/can not settle for less than an A in all 3.
The recent news on her influence destroying math curricula in public schools while sending her children to private schools casts this in a different light now.
I would “talk math” with my children when ever we were driving in the car from the time they could talk and count. All the way through high school. I’ve had to re teach myself advanced math through the years, and my children are great at math. One of them is a senior in high school and planning on being an engineer. I did similar things with English writing, science experiments, music and history.
I enjoy your channel/podcast SO much - your polite, logical, professional style and presentation is something I greatly admire. I always come away from one of your shows a more inspired and knowledgeable person than I was before. In fact, you have inspired me to start my own channel, which I'm in the process of putting together. I also play electric guitar, and I always enjoy your tasteful performance. Thanks so much for everything you do!
It is interesting that much of what is being said here about the importance of encouraging pupils / students, through emphasizing collaboration, asking questions and so on, and the positive effects those kinds of things have on building resilience, and creating 'success', are the very things that have been known and worked with in what are sometimes called the 'soft' sciences for many years. As a retired psychotherapist, who did most of his work with adolescents, I kept on having the reaction when watching this video that most of what was being talked about here as new or novel approaches to maths education, was familiar to me in terms of being the ways in which my colleagues and I worked with adolescents in addressing their problems in life - much of this work was influenced, and taught to us by our clients. This has made me conscious, yet again, of the tragedy of how various fields separate themselves from others to the detriment of (in this case) students.
One of the hardest challenges in math instruction is that it has so far been virtually impossible to create lessons/practice that serve both students who will excel in math no matter what and those who will need more help. Every time I see someone talking about revolutions in math instruction, I ask myself if this new system will address both. Often, it is focused heavily on one at the expense of the other. I don't know about Jo's work in particular, but hope springs eternal.
I just started watching this, but I did poke over to to youcubed and watched the intro video there. Wow! I went to Montessori school from preschool to grade 3. The first thing we learned about math was using beads on metal wires. Single beads, 10 beads in a line, 100 beads in a square, 1,000 beads in a cube. The first time I ever actually wrote down an equation on paper was in second grade (7 or 8 years old) after I had visualized what I wanted to describe and could write down exponents to describe it. It was an exhilarating victory; I remember it to this day (I'm 59 now). After that, algebra was cake to me. I realized that equations are the result of a lot of work distilling down the complexity of a visual panorama, like eating a lavish meal and then dropping a turd and proclaiming "Look at what I did!" That's the problem. You can't work backwards from the turd to understand the meal. You have to work the problem the other way around.
My child had a visual issue called convergence insufficiency. The ability to memorize verbally was huge and she was very good at it. So, the 2-minute memorization of times tables was easy and could do it the first time but the struggle with mathematics, especially geometry, was huge due to a struggle to visualize. Vision therapy helped but her eye communication to the "brain wiring" as you mentioned was impaired. As a result, she was learning entirely by hearing. This is an area that neuro-science, teachers, eye doctors, etc. need to better understand. Both my husband and I are extremely well-educated and spent quite a bit of time trying to figure out what the issue was (which we finally figured out when she was 10) and the school system was not helpful. Lots of math would have made her life miserable but a different way of teaching someone with her issues would have been huge.
My daughter is actually a teacher now at the k-3 level. She teaches ILT. Her personal experience makes her much more aware of the issue snd others like it. We lived in what was considered a wonderful school district but the administration refused to have her tested. Their response was that she was an average child in a high performing district. Not sure many teachers would be educated to understand or test for what was actually going on.
I am a math teacher from a school obsessed with Jo Boaler. She is a hack. Specifically: I was told over and over how useless and unimportant (and actually "oppressive") making kids memorize times tables is.
@@PJ-qx5yt my daughter is now in her twenties. I would say that learning multiplication tables didn’t harm her in any way and that it helped us as her parents hone in on what was actually going on with her vision. As with all things, there are many paths to find answers and to helping children learn. Unfortunately, the world and school systems tend to focus on a few avenues that help the most students or the latest “in vogue” methods. This leads at times to a lack of learning. I also think that it’s leading to the trend of more home schooling as I recognize that teachers do not have the bandwidth to address every need. It also speaks to the need for parents to be involved and attuned to what’s being taught and how that curriculum is being taught to their own children.
Im in my 2nd year of a maths degree and have almost never been shown visual representations of what we are meant to be learning. I feel like the whole point is to "see" what the numbers are really telling us.
Lex, I am with you on textbooks!!! I loved, loved, loved my calc textbook. By the end of the year, it was tattered and torn from over use. And there is nothing like the sound of a mechanical pencil.
1:19:00 I can't believe I've only just now heard this idea. Amazing and so powerful. It's like I've heard said before about teaching, that we think everyone else already knows what we know so we don't think about what the learner may really know at that point. Thank you Jo and Lex.
No one is a visual learner. The point is what memory trick that works to activate your connection pathways. The best is a word and a visual combined for whatever dimension works to have a concept stick.
Amazing show, as a young kid I was always very artistic, but I had a numerical mind as well. I never further explored math because of how it was presented to me, in sort of in a dry repetitive fashion that would make me question why I was learning this? Now I find myself drawn to math more than ever to articulate thoughts or ideas or concepts in a creative way through the medium called math, so the distinction between visualization, creativity and mathematics for me was profound!
A key element not discussed directly in this video is how kids are taught to handle frustration. Learning anything new can be frustrating; how you manage that frustration largely determines if you stick with something or quit. We typically learn this by example from our parents. Do they curse and throw things or have a calmer and more measured approach? You can unlearn the more negative approach but having the tools to handle frustration early on almost guarantees a more positive outcome.
Despite my lack of talent with math, I enjoy it and because of encouragement by some teachers, I continued where others had stopped and I have ended up more proficient than many other nonprofessional math people.
You might want to soundproof that table. Everytime someone bumps on it (you or the guest), the deep sounds gets picked up way too well by the mic. Maybe the mics should be on their own stand and not connected to the table at all. Example 1:04:25 .. you barely touch the table and it's a massive boom on proper speakers. As a quick fix .. a bit of yoga-mat material between clamp and table might help too.
Wow, I was always told I was not a math person. My parents said they were not math people so don’t worry that I couldn’t understand it, just get through it with a passing grade. I then told that to my children, and now over the years I so regret it. My youngest who is 19 is wanting to major in astronomy or geology. He is very determined and always tries to figure something out. My husband said to me, why would he want to go into those majors he’s not that great in math?. I said, just let him try, you never know what can happen. In middle school my son would be crying over algebra and in high school he had straight A’s in it. It was because of his determination to figure it out that pushed him forward and gave him confidence, don’t squash it. A very good friend of ours asked what my son wanted to major in, I told him and also added that he isn’t a whiz in math, he said, don’t let that stop him keep going . I thought that was such great response. I told my son and he smiled. I have told my son I am so very proud of him for pushing forward and having the determination to figure math out, to not let it make him scared and pass up a major he is truly interested in. When I was young and in grade school I came up with this special way of adding and subtracting, I remember my parent’s quizzing me and were in amazement how how my way of doing math worked. But, when I would go to school they told me it was wrong and to do it the way they were teaching me. I stopped and can not remember how I did it. I am so saddened by that, how many kids has that happened to over the years. I was imaginative and I was told I was wrong. I am so glad people are realizing there are different ways to look at problems and it’s okay to be creative. Thank you for your wonderful work.
Thank you for making this available to us as a resource, Lex. Half the people at the EmTech conference have been a guest on your show, and they're charging $800+ to view. You're helping so many
Emphatically yes, I agree that our systems are set up to eschew the slower, deeper, perhaps more creative thinkers. I guess the only saving grace is that this type of learner is apt to keep at in life and possibly emerge later as successful in their pursuits.
39:00 1)How well you groupitize predicts how well you will do in maths 2) Questioning is an important skill 3) Reflect your struggle 4) Solve more problems & Reflect the concept 5) Best way to learn is teach
Joe's opening statement absolutely beautiful and unfortunately the problem with schools in America because they don't teach creativity in math they teach an absolute way so kids don't learn that there are other options to solve the same problems actually have to go to college to even broach the idea
I think many dont connect it to real use at all, its just a routine, trained. No touch or feel for it inside, its correct but no one notice it is fake. A trick if you like. Because its important is a lousy answer to students asking why oh why we have to learn this? and further why? pay attention, you are disturbing class.
I don't think this is an American problem only. The reason Asian countries are good at math in general and is because of repetition and rigorous formula memorization. I see a lot of people including myself who find it difficult to be creative with maths. But you hear people here and there that are incredibly creative but you realise that they are usually one in the millions. Which tells me that they developed the intuition naturally and not by training
ugh i just want to cry right now...my life has been stunted because i could do math the way they tried to help me, i am super visual huge creative mind.Seriously nothing hurt me more than people telling me it was so easy and me in my head knowing i couldn't make any sense of what was in front of me. when i got pregnant the only thing i prayed for was for them to be good at math. i got geometry but not algebra, a statistic teacher tried three classes to help me said it was mind boggling how i could sit in class drift off while everyone participated in filling in the blanks, when the class got stumped id notice the silence look up and blurt out a symbol or number, the class would laugh at me knowing i wasn't paying attention and the teacher would just shake his head and ask while writing what i said into the equation, how the hell do you do that;;;i would just see it floating in my head;;;yes so weird for me. turns out i have a problem remembering a sequence of order
I'm adhd and struggle to listen to lessons. I've been realizing lately that I need to drill extra problems with solutions nearby so I can see where I went wrong, I'm a doer when it comes to math. It's not very forgiving because the current math school system punishes my type for going through their learning process.
when I was a sophomore in high school I almost failed math and at the end of the year my teacher shook my hand and went, "you didnt have a fun year... but I did :)"
I think of intuition as being subconscious understanding, both learned and innate. Not all connections our minds are able to make are always available to our consciousness.
@@hypno5690 How helpful would be a deep discussion about idealist metaphysics and theology? From Brouwer's solipsism and Heyting's more "objective" idealism to Ramanujan's Goddess, etc.? Could it be more helpful to refer to a fairly common phenomenal example, "receiving" ideas in the zone between sleep and awake, trying to remember but mostly failing? Or simply geometric imagination? Knowing and experience by experience is intuitive...
17:59 Losing interest in math in 5th grade! Having grown up in Moscow, I remember being bored to hell with it since my third grade, and the system forces you to endure it for SEVEN MORE YEARS (11th grade allows for some slack due to local state exams).
Math is one of the most complex and intense courses in university, and I'm in basic College Algebra. Every other class is like child's play. The amount of things you have to memorize is insane.
I'm 37, Math was always my friend, the education system not so much. At least I'm allowed to experience the beauty of genious text courses. *now playing: Outnumbered* Well on the other Hand I can be sure there will be a lot of surprises still ahead in the mathmatical literature for me.
This conversation is encouraging to me, as an adult who struggled immensely with math, but have keen spatial and pattern awareness, I finally recognized that I have Discalculia. number symbols mean absolutely nothing to my brain. If I had had a single teacher who could have said the following: math is a language, and it can be done entirely visually.... a whole different world would open up. I am still open to learning. I went to the youcubed website, but it seems really geared for k-12 students, and teachers. where do I go to find a tutor who can teach visual mathematics to an adult learner with very little background math education that made sense. I need to ask questions 1-1, not so much follow a program. The other thing I want to emphasize is that there is a huge difference between a visual or geometric math object,and a symbolic pictorial image describing a math concept. The symbolic visuals, which are not numerically precise, are actually more confusing than helpful. it is where the visuals/colors/shapes/sounds ARE the math, not a representation of the math, that is when it actually makes sense as a language, to me.
I START TO LIKE MATH IN GRADE 5 WHEN I GOT THE BOOK Mathematical recreations BY BORIS KORDEMSKY. I RECOMAND IT VERY MUCH.I HAD A OLDER COUSIN WHICH SOLVE ONE OF THE PUZZLES USING ALGEBRA AND THAT MESMERIZED ME AND I WHISHED TO LEARNE IT. AND THAT PROBLEM WAS AN EXEMPLE OF HOW TO GO FROM RETORIC ALGEBRA TO SYMBOLIC ALGEBRA.And later in life i discovery two elementary proofs of Fermat Last theorem. fROM CONCRET TO ABSTRACT AND BACK.That is the secret for the first years of arithmetic learning and that is why is not good for on line learning.
As a math teacher of 22 years, I highly recommend Barbara Oakley's approach to help students find success and satisfaction in Math. Algebra matters. Quality direct instruction matters. Systematic practice matters.
My wife did a linear algebra class (was a teacher, needed to take a class each year) and the text book was terrible and dry so she was left wondering "Why?" Matrices manipulate space. Determinant represents how they change the volume of finite space (so 0 means it collapses space in one or more dimensions), eigenvectors tell you the lines that stay on the line, and eigenvalues tell you how those lines change (stretch/squash and/or reflected about the origin). None of that explained, instead just a definition.
I took linear Algebra last semester and I enjoyed it until we got to vector spaces, eigenvectors, etc. Class average was in the 60s. I barely passed. Sucks because as a CS major, Linear Algebra was a class I was really looking forward to, but looking back, it was an exercise in futility. Lol.
Having Linear Algebra II exam in a few weeks, my university approach of teaching it was throwing 800 pages of books at you and give you 5 exam examples at the end of the semester. Lecturer reads same book out loud and that's it. 3blue1brown can only get you so far, it was helpful in LA1, but now Jordan forms went almost completely over my head. At least they give really good problems for homework, but sometimes they are too good, takes too much time to solve when you only presented with a large assortment of theorems without good explanations.
I would love to watch an interview about the best ways to lean math as an adult. I, as well as some non natural gifted that i know, struggle with it and it would be really enlightening to know if it's possible and what is realistic goal to a non-gifted person to achieve in his/her learning. *Unfortunately, at least in my personal experience, the more the teacher or the reasercher that is trying to teach math is naturally gifted the less (s)he understand how is not to be gifted.
I advice you, to take the "learn how to learn" course on coursera it's free, It was made by a electrical engineer professor who had a problem with maths but really wanted to be an engineer, she started learning maths at 26 years old, in fact you'll learn a lot about the brain how you can learn anything not only math, good luck!
Fav joke is 4/3 of adults have trouble with fractions! as a youth i hated math and failed and not just failed but record setting for worst marks ever. It took a goal that used and needed math in my twenties, but even then the algebra was killer. I had to find cheats that worked. Only thing i grasped was geometry and trig followed . Now i love the Hopf vibration Fibonacci and Mandel brot set / julia set too. I watch you and "numberphile" Dr Holly Krieger and i am very impressed with Scot Manley orbital math skills. i was lucky IBM or zerox brought a card reading machine and an intro to boolean and hex to my high school and those seemed so easy. But i really think fast food cash machines should delete cash return function and force learning arithmetic
I've seen many college freshmen give up on Calculus because they do not understand that they need to keep at the concepts. As she said, it's deep learning. They need to work on mastering the concepts and do extra problem sets, work in groups, take turns teaching each other and explaining the equations. I've seen students who were very smart give up....because they said they didn't want to work 'so hard'. And I saw D/F students keep pushing and slowly their grades improved and they were successful in more rigorous math, science, engineering and CS classes...and Graduate!
2:34 The most difficult aspect of a visualized math curriculum is ensuring that it meets accessibility constraints. eg. describe a normal distribution without the jargon to a blind person. Literacy, expertise, and time are necessary to ensure brevity(optimize) and intuitive precision. Failure to do so implies legal action/censure. Another reason teaching is treacherous, and why we need a Noam Chomsky slash Dr Seuss in every department.
This was good chat for me. I have often thought, children in today’s world spend more time with teachers and school than with any other group. Including friends and parents. I could expand on how I see it. But it gets the point across.
I think what a lot of this discussion reveals is how succinctly education has for the most part simply been a tool for selecting out those with high IQ, and dismissing any who showed a lack of high IQ. It's only now that we have even begun the task of attempting to actually educate people.
Great video, great links to information. Absolutely, if you feel the possibility to get inspired, just go and follow the links to the classes and go ahead and do the kids stuff too. This video is a great launching point. I'm surprised by the slightly low number of views, this may be Lex's most underrated video of the year.
Jo Boaler isn't just a math educator but someone who has had a huge impact on getting education as a whole to start shifting from a fixed mindset to a growth mindset. I start my classes with her growth mindset activities every semester.
@@peterfireflylundrecent research has shown that while "growth mindset" is important (believing you can do it leading to internal motivation), literally every other way of motivating kids in high school works better. Telling kids "you can do it" doesn't magically make them get at it. Growth mindset only accounts for about 5-8% of the increase in math test scores internationally. This woman is a fucking hack.
@@PJ-qx5yt I tried to post links to real research that debunked her crazy ideas. They got deleted. I tried to post references that people could Google themselves. They also got deleted. The above comment was just about all I was allowed to post!
@@peterfireflylund my favorite is her wildly suspicious study of her methods at Berkeley High School. When her (male) colleague at Stanford in the Mathematics department requested she reveal the raw data and she refused, he publicly called on her to reveal the data and wrote a paper debunking the study. So she publicly called his requests for transparency "sexist" and "harassment".
As documented in a recent article in the Chronicle of Higher Education, as well as a website by Brian Conrad (Stanford professor of math -- actual math), Boaler has a pattern of misrepresenting data and published studies. She'll claim that "according to neuroscience, your brain grows when you make a mistake," and the actual neuroscientist she cites will say "our study didn't say that, and we didn't even try to study that question." And she doesn't back down or apologize for repeated misunderstandings and misrepresentations like this. Sad to see.
Another possible reason teenagers don't ask questions, at least in my time in high school, is that it was considered "uncool" to do so. Trying hard in school was considered "lame". Eventually we start adopting the same mentality. It wasn't until college where I stopped thinking this way. Pretty sad.
Learning new math is like meeting a stranger for the first time. You shake hands with the new acquaintance and there's nothing to lead you to suspect what's beneath the surface, good or bad; so you accept everything at face value. Then later you meet the same person under entirely different circumstances and you start seeing a different side, maybe even a contradictory side. Still the picture is incomplete, till you meet the same person again and again under different degrees of separation. On then does the whole person begin to come through. After meeting the same person under the most diverse circumstances, you start getting some insight. YOu realize that insight, not rigorous proof, is what gives you that "oceanic" feeling or an all-seeing eye. You've arrived at the Langland's Program.
When I was in junior high school, even though I had never been good in math, I took Algebra 1. I made, probably a C. I kind of liked it though. I connected with the teacher. The next semester, I wanted to take Algebra 2, but I couldn't. There was another class I had to take first. It was Geometry. I didn't understand it, and I thought it was just drawing and talking about a bunch of triangles. Kind of kindergarten stuff. I didn't connect with the teacher either. I pass the class, but I learned very little, and had acquired a much lower opinion of my mathematical abilities. I signed up for that Algebra 2 class. I went to the first day of class. The teacher, the same teacher I had liked and connected with before, told us all how difficult this class was going to be. He said he would let anyone who wanted withdraw right then would be allowed to, but after that, he wouldn't allow it. He wouldn't let you withdraw from the class no matter how badly you were doing. That was enough to prompt me to withdraw from that class. I took more math classes later, and studies on my own. I do feel like I could have gone much further in math, and in my career, if I had had better teachers back then.
Here Is how i, a guy Who hated math Is now doing computer science with perfect score on all the math subjects. I studied all math over from aritmetics to integrals, and did every exercises of the books. I Also created a sort of note book of all the themes with all the formula, so i can look It up when needed. Math Is like a Building, if you are weak on floor 3 you Will have problem going on floor 4 or 5 dice you dont fully understand or Remember floor 3. To Remember math what you have ti do Is practice. When you are studying the theory you only get to know the big picture. To get good you have to solve a lot of problems, only this way you Will get to see cool tricks One problem May have. Math Is like going to the gym. Be consistent, progressive overload = harder problems, frequency. Hope It helped.
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0:00 - Introduction & sponsor mentions:
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0:23 - What is beautiful about mathematics?
9:12 - How difficult should math really be?
17:31 - Students giving up on math
28:52 - Improving math education in schools
38:49 - Inspiring mathematical creativity
56:35 - youcubed
1:00:55 - Best methods for studying math
1:21:29 - Advice for young people
Thanks!
Thank you ..I for one needed to hear this. I so wanted to know math but couldnt bec I had math teachrrs. Unlike this lady. I need visuals I guess and words to understand . Thc 🤗🤗❤️
infinite...
thanks lex,it really inspired me to revisit maths i gave up 6 years ago
Major missed opportunity to ask Jo about the CA math curriculum reform.
I remember a 7th grade teacher who told me I wasn't cut out for mathematics. I ended up getting a B.S. and M.S. in Mathematics.
I love this^^ that’s bad ass.
I can relate to the struggle a bit brother. In HS and University I failed my algebra classes. Now I'm in the middle of learning Stochastic Calculus!
I often think back to being in class in middle school, all the way to the back, trying to understand Mrs. "Smith". She pause after explaining something and i thought to myself, how come? She said right after that "i bet none of you would think, how come". I wonder how many others thought the same but like me, didn't say anything. I like math cause math is like the only empirical absolute truth. It's as if it were Gawd. True everywhere, all the time, 0 🧢 all 📤 fax lol
I had a teacher in grade 11 that was surprised I was staying on the normal math path instead of transferring to the remedial one. I ended up with a finance degree, data analytics certificates.
I had a midle school teacher who flunked me in maths in 10th grade, high school second grade. I had a different teacher next year. I ended up as a financial analyst...
The three important messages I learned while teaching math:
1. This is important.
2. You can do it.
3. I won't give up on you.
I wish someone said that to me as a kid. 😎🤓🥸
The most important message I learned is, some people cannot do math. And that is ok. They (we) are no less valuable than a person who cannot play basketball, or paint, or fix automobiles. People who love math think it is way more important than it is. :) To each their own.
Again self-esteem without hard work. stop this propaganda Sir.
@@eriklarson9137 coping hard
@@eriklarson9137 Everyone can do math. If i could learn math anyone can. ( I was told in school i couldn't do math)
I’m in my 70’s now and felt pretty much lost in math by age 10. I got through high school and undergrad years well enough, got two masters degrees, and then worked on big bank financial systems. But always felt I was bluffing my way through anything computational, even basic algebra. I sure wish this approach to mathematics and visualization had been used way back when I was in elementary school. But hey, it’s never too late to learn!
Thank you for another wonderful discussion!
Been doing a self study maths, stats and econometrics from zero. Used to feel miserable when getting stuck. Nowadays I feel blessed getting stuck. It confirms I need to do more work, like a free counselling.
Spot on. I was told very early that I was dumb & couldn’t do math. It wasn’t until I found a practical use, electricity, that things clicked. Once I told myself “If someone else is doing it, I can do it”. The belief I’m myself helped me develop a career in the electrical industry & today there isn’t a day that I’m not doing math!
Believe that anything is possible & it will be.
Thank you for this.
Lex has been cranking out bangers with CONSISTENCY lately, I’m here for it
Yea, lately being past 3 years
@@atti1120 time flies :D
- Recognize mathematics as a creative and visual discipline (0:23)
- Explore multiple methods and solutions to enhance understanding (0:41)
- Utilize visual approaches to activate brain pathways for deeper learning (2:17)
- Encourage connected thinking by integrating different perspectives on problems (3:00)
- Foster intuition as a key component in mathematical problem-solving (4:45)
- Emphasize the importance of struggle and challenge for brain development (5:58)
- Create a multi-dimensional learning experience to cater to diverse thinking styles (11:08)
- Strive for excellence while understanding the importance of supportive teaching (14:15)
- Engage deeply with concepts rather than skimming through material (1:01:50)
Thank you
Very nice conversation. One thing I was missing in math classes was "why do I have to learn this" and "what can it be used for". I wish teachers can give more examples of why something is important and how it can be applied so the students get more interested and engaged.
With so many references to books and websites you guys will keep me busy! Keep 'em coming Lex!
I think this is key, to most it just seems like exercise to make those less wired to math feel inadequate,
I think of it like art.. I was never looking for it’s utility.. it was just beautiful in and of itself
This may be my favorite interview so far. Teachers and mentors are so, so important.
Thank you..
Please do more conversations about our direct relationship to learning, understanding & exploring how to make sense of the world. So that the bad habits many of us carry from school, can be challenged with a counterweight through perspectives.
This conversation was truly brilliant, and after this vid, I already view mathematics in a completely different light. Part of it is excitement about the mentality of learning..
Cheers
A teacher in Serbia from a high school I taught at used to say "math is learned by writing", meaning when you keep doing it and it becomes automatic you start seeing patterns you haven't noticed before... Some similarity with around 1:01:22. Giving yourself problems to work on and keep practicing.
I know what you mean. I tend to go for the difficult problem solving aspect, put in a lot of time there. Others are better at working endless problems. But if I am familiar with an area I then switch to doing all the problems, probably because there isn't much new to learn. I think it's to do with the neural reward system somehow.
As a 1st year HS Geometry teacher, I am incredibly excited to experience this. Thank you both.
Good luck, having an inspiring math teacher is extremly important.
@@jarne5581 yeah I gave up on math when my junior year high school teacher called me an idiot in front of the whole class. It’s unfortunate that most teachers are crap and only a very few take their jobs seriously.
You are and will be great!
@@weignerleigner3037 I was a idiot and did not care much for school and got the complete opposite, my only A Class and exam. He was a amazing at dragging effort out of me with humour. I usually spent my time drawing in class before that, filling out the least amount of words possible to answer and just writing one word solution or just the correct addition without showing, showing the entire calculation seemed like the dumbest thing in the world to me if i thought i had the solution. Math to me was nerd, not cool. "Gonna be a DJ" ridiculous at 15. But ended up the best class i had in school. That's really something, not my experience but that teacher. If he did 1 or more student that favour each year, he has helped 20+ idiots get a grade in math. Think that is the only teacher i respected in school in 14years. My dad always said teachers where after him in school too, showing a disrespect i kinda brought with my lunch i guess. I hope its was a "me" problem and not all the teachers. lol upto 49ish useless teachers and one good. It dont really seem plausible. One just said to me early semester, if you just sit still and shut up you get a D. That really sparked the further inquire of interest. What a bitch, she knew that.
@@mirroredname3389 I grew up in a small town and our schools were atrocious we lost teachers every year to budget cuts. In summers they would call off school because we had no a/c and it got too hot in the classrooms. I don’t blame my teachers they probably weren’t having much fun doing their jobs but it’s unfortunate for the students because we didn’t really get a great education.
I've always grouped and sought patterns in things. I was considered an advanced math student but got put off in grade 5 by a particular teacher who was obsessed with using high pressure competitive games in class. It stressed me out and I shut down. I didn't mind competition in sports, but I craved freedom in academic pursuits, so this didn't work for me. I kept exploring and took more math classes than any other by the time I finished 12th grade. It wasn't until I got to Uni where I found a teacher who absolutely loved teaching calculus and my love for math shone (I got a perfect score on my final exam and it felt amazing). At the same Uni I found another teacher who was able to answer all my questions around particular algorithms, who created them and why, and also what were the real world applications inherent in them. It seems to have taken a lifetime to get the context I was craving since ~ grade 3 or 4. It thrills me to hear a transition toward big ideas and connections is afoot. This could be a game changer.
It's quite true how the number of questions asked decreases in education with age. It's as though education is stifling exploration and rather just learning to conform to the tests.
I hated math my whole life...after listening to this I am thinking to learn again. Thanks @Lex and Joel.
I had a fellow maths teacher use Boalers methods to teaching her algebra class, it took her a couple years to curate her lessons. Once she started she quickly found out that she could only make it through one section of a unit in about a week because of the level of deeper thinking and productive struggle necessary for applications. Its very interesting and i think important to deeper understanding, but unfortunately schools are not structure at the primary/secondary level for this type of method. I do blame “the state test” for hijacking maths instruction leaving little time for true maths exploration.
The dot grouping exercise would be pretty hard on people with dyscalculia tbh. That's how you test for it actually.
So pleased to hear you mention Richard Feynman. His lectures should be a high school requirement. Sadly I stumbled upon him but then I binge watched everything he had recorded.
Feynman, just the name brings a smile, what a man! The talk about collapsing reality onto it self into a micro verse or how he meant it to avoid a planet killer comet, wow. That far out and also so down to earth. He so unique. I am pleased you mention they mentioning it.
Thank you! I'm a mother to 6&8 year old boys and this was great information.
Stay inspired! Remember that curiosity and playful exploration is more long term important than immediate results. And people inspire each other, so expose your kids to people you think are a good influence.
Loving textbooks is one of the most Lex things I can imagine.
Look forward to listening to this in full. Maths is a subject often so poorly taught and subsequently difficult to grasp as part of the wider system of its application.
@DSUMNo doubt. Sadly the case in so many subjects.
@DSUM it's a ton of teachers fault too, let's not defend teachers for the sake of it, there should be meritocracy among them too
@DSUM If formal education didn't exist and we'd have to implement it from scratch today, it would look entirely different.
Totally agree. We teach our children math, in exact way and environment and structure the way we teach them social science or English. Its plain sad to be honest.
Lookings forward to it also
good interview. Needed this. University classes start again soon and am taking Intro to Discrete Mathematics, Calculus 2, and Physics 2 in tandem. Am very overwhelmed and self-doubt is certainty there. Will do my best, have high-expectations and will not/can not settle for less than an A in all 3.
That it's been an year, how's it been going ?
@@bikramjeet6536 I forgot about this comment, didn’t get that A in E&M thanks for reminding me :(
The recent news on her influence destroying math curricula in public schools while sending her children to private schools casts this in a different light now.
Got sources?
This is exactly my thoughts based on the course I'm reading right now that's based in her work.
I would “talk math” with my children when ever we were driving in the car from the time they could talk and count. All the way through high school. I’ve had to re teach myself advanced math through the years, and my children are great at math. One of them is a senior in high school and planning on being an engineer.
I did similar things with English writing, science experiments, music and history.
I enjoy your channel/podcast SO much - your polite, logical, professional style and presentation is something I greatly admire. I always come away from one of your shows a more inspired and knowledgeable person than I was before. In fact, you have inspired me to start my own channel, which I'm in the process of putting together. I also play electric guitar, and I always enjoy your tasteful performance. Thanks so much for everything you do!
You should have on Barbara Oakley. She directly refutes some of Jo Boaler's research and is an expert in the space of teaching and learning.
It is interesting that much of what is being said here about the importance of encouraging pupils / students, through emphasizing collaboration, asking questions and so on, and the positive effects those kinds of things have on building resilience, and creating 'success', are the very things that have been known and worked with in what are sometimes called the 'soft' sciences for many years.
As a retired psychotherapist, who did most of his work with adolescents, I kept on having the reaction when watching this video that most of what was being talked about here as new or novel approaches to maths education, was familiar to me in terms of being the ways in which my colleagues and I worked with adolescents in addressing their problems in life - much of this work was influenced, and taught to us by our clients.
This has made me conscious, yet again, of the tragedy of how various fields separate themselves from others to the detriment of (in this case) students.
One of the hardest challenges in math instruction is that it has so far been virtually impossible to create lessons/practice that serve both students who will excel in math no matter what and those who will need more help. Every time I see someone talking about revolutions in math instruction, I ask myself if this new system will address both. Often, it is focused heavily on one at the expense of the other. I don't know about Jo's work in particular, but hope springs eternal.
Adding a small extra restriction or making the problem more generalised should help the more advanced students challenge themselves.
I just started watching this, but I did poke over to to youcubed and watched the intro video there. Wow! I went to Montessori school from preschool to grade 3. The first thing we learned about math was using beads on metal wires. Single beads, 10 beads in a line, 100 beads in a square, 1,000 beads in a cube. The first time I ever actually wrote down an equation on paper was in second grade (7 or 8 years old) after I had visualized what I wanted to describe and could write down exponents to describe it. It was an exhilarating victory; I remember it to this day (I'm 59 now). After that, algebra was cake to me. I realized that equations are the result of a lot of work distilling down the complexity of a visual panorama, like eating a lavish meal and then dropping a turd and proclaiming "Look at what I did!" That's the problem. You can't work backwards from the turd to understand the meal. You have to work the problem the other way around.
My child had a visual issue called convergence insufficiency. The ability to memorize verbally was huge and she was very good at it. So, the 2-minute memorization of times tables was easy and could do it the first time but the struggle with mathematics, especially geometry, was huge due to a struggle to visualize. Vision therapy helped but her eye communication to the "brain wiring" as you mentioned was impaired. As a result, she was learning entirely by hearing. This is an area that neuro-science, teachers, eye doctors, etc. need to better understand. Both my husband and I are extremely well-educated and spent quite a bit of time trying to figure out what the issue was (which we finally figured out when she was 10) and the school system was not helpful. Lots of math would have made her life miserable but a different way of teaching someone with her issues would have been huge.
You'd be asking too much of schoolteachers to actually do their job.
❤
My daughter is actually a teacher now at the k-3 level. She teaches ILT. Her personal experience makes her much more aware of the issue snd others like it. We lived in what was considered a wonderful school district but the administration refused to have her tested. Their response was that she was an average child in a high performing district. Not sure many teachers would be educated to understand or test for what was actually going on.
I am a math teacher from a school obsessed with Jo Boaler. She is a hack. Specifically: I was told over and over how useless and unimportant (and actually "oppressive") making kids memorize times tables is.
@@PJ-qx5yt my daughter is now in her twenties. I would say that learning multiplication tables didn’t harm her in any way and that it helped us as her parents hone in on what was actually going on with her vision. As with all things, there are many paths to find answers and to helping children learn. Unfortunately, the world and school systems tend to focus on a few avenues that help the most students or the latest “in vogue” methods. This leads at times to a lack of learning. I also think that it’s leading to the trend of more home schooling as I recognize that teachers do not have the bandwidth to address every need. It also speaks to the need for parents to be involved and attuned to what’s being taught and how that curriculum is being taught to their own children.
Intuition changed my math life. After some time I was able to see that math really is beautiful.
Thanks Joe rogan for introducing me to Lex
Im in my 2nd year of a maths degree and have almost never been shown visual representations of what we are meant to be learning. I feel like the whole point is to "see" what the numbers are really telling us.
Lex, I am with you on textbooks!!! I loved, loved, loved my calc textbook. By the end of the year, it was tattered and torn from over use. And there is nothing like the sound of a mechanical pencil.
1:19:00 I can't believe I've only just now heard this idea. Amazing and so powerful. It's like I've heard said before about teaching, that we think everyone else already knows what we know so we don't think about what the learner may really know at that point. Thank you Jo and Lex.
No one is a visual learner. The point is what memory trick that works to activate your connection pathways. The best is a word and a visual combined for whatever dimension works to have a concept stick.
Very good conversation. Thanks Jo and Lex.
Thank you for bringing her to your podcast. I just bought her book.
This lady has an absolutely wonderful voice.. 👍🏼
Amazing show, as a young kid I was always very artistic, but I had a numerical mind as well. I never further explored math because of how it was presented to me, in sort of in a dry repetitive fashion that would make me question why I was learning this? Now I find myself drawn to math more than ever to articulate thoughts or ideas or concepts in a creative way through the medium called math, so the distinction between visualization, creativity and mathematics for me was profound!
A key element not discussed directly in this video is how kids are taught to handle frustration. Learning anything new can be frustrating; how you manage that frustration largely determines if you stick with something or quit. We typically learn this by example from our parents. Do they curse and throw things or have a calmer and more measured approach? You can unlearn the more negative approach but having the tools to handle frustration early on almost guarantees a more positive outcome.
I love Lex, you sir are an amazing human!
Despite my lack of talent with math, I enjoy it and because of encouragement by some teachers, I continued where others had stopped and I have ended up more proficient than many other nonprofessional math people.
You might want to soundproof that table. Everytime someone bumps on it (you or the guest), the deep sounds gets picked up way too well by the mic. Maybe the mics should be on their own stand and not connected to the table at all. Example 1:04:25 .. you barely touch the table and it's a massive boom on proper speakers.
As a quick fix .. a bit of yoga-mat material between clamp and table might help too.
Nice. Always good to listen to kindred thinkers.
I used to think I hated maths until I realized I hated copying numbers from textbooks and whiteboards.
Wow, I was always told I was not a math person. My parents said they were not math people so don’t worry that I couldn’t understand it, just get through it with a passing grade. I then told that to my children, and now over the years I so regret it. My youngest who is 19 is wanting to major in astronomy or geology. He is very determined and always tries to figure something out. My husband said to me, why would he want to go into those majors he’s not that great in math?. I said, just let him try, you never know what can happen. In middle school my son would be crying over algebra and in high school he had straight A’s in it. It was because of his determination to figure it out that pushed him forward and gave him confidence, don’t squash it. A very good friend of ours asked what my son wanted to major in, I told him and also added that he isn’t a whiz in math, he said, don’t let that stop him keep going . I thought that was such great response. I told my son and he smiled. I have told my son I am so very proud of him for pushing forward and having the determination to figure math out, to not let it make him scared and pass up a major he is truly interested in.
When I was young and in grade school I came up with this special way of adding and subtracting, I remember my parent’s quizzing me and were in amazement how how my way of doing math worked. But, when I would go to school they told me it was wrong and to do it the way they were teaching me. I stopped and can not remember how I did it. I am so saddened by that, how many kids has that happened to over the years. I was imaginative and I was told I was wrong. I am so glad people are realizing there are different ways to look at problems and it’s okay to be creative. Thank you for your wonderful work.
Thank you for making this available to us as a resource, Lex. Half the people at the EmTech conference have been a guest on your show, and they're charging $800+ to view. You're helping so many
Emphatically yes, I agree that our systems are set up to eschew the slower, deeper, perhaps more creative thinkers. I guess the only saving grace is that this type of learner is apt to keep at in life and possibly emerge later as successful in their pursuits.
As a father of 4th graders starting out on more complex maths, I appreciated this so much, Lex. Thank you.
39:00
1)How well you groupitize predicts
how well you will do in maths
2) Questioning is an important skill
3) Reflect your struggle
4) Solve more problems & Reflect the concept
5) Best way to learn is teach
Joe's opening statement absolutely beautiful and unfortunately the problem with schools in America because they don't teach creativity in math they teach an absolute way so kids don't learn that there are other options to solve the same problems actually have to go to college to even broach the idea
I think many dont connect it to real use at all, its just a routine, trained. No touch or feel for it inside, its correct but no one notice it is fake. A trick if you like. Because its important is a lousy answer to students asking why oh why we have to learn this? and further why? pay attention, you are disturbing class.
I don't think this is an American problem only. The reason Asian countries are good at math in general and is because of repetition and rigorous formula memorization.
I see a lot of people including myself who find it difficult to be creative with maths. But you hear people here and there that are incredibly creative but you realise that they are usually one in the millions. Which tells me that they developed the intuition naturally and not by training
ugh i just want to cry right now...my life has been stunted because i could do math the way they tried to help me, i am super visual huge creative mind.Seriously nothing hurt me more than people telling me it was so easy and me in my head knowing i couldn't make any sense of what was in front of me. when i got pregnant the only thing i prayed for was for them to be good at math. i got geometry but not algebra, a statistic teacher tried three classes to help me said it was mind boggling how i could sit in class drift off while everyone participated in filling in the blanks, when the class got stumped id notice the silence look up and blurt out a symbol or number, the class would laugh at me knowing i wasn't paying attention and the teacher would just shake his head and ask while writing what i said into the equation, how the hell do you do that;;;i would just see it floating in my head;;;yes so weird for me. turns out i have a problem remembering a sequence of order
Lex Fridman, Now we want Derek Muller from UA-cam Channel Veritasium. He is great science communicator
I'm adhd and struggle to listen to lessons. I've been realizing lately that I need to drill extra problems with solutions nearby so I can see where I went wrong, I'm a doer when it comes to math. It's not very forgiving because the current math school system punishes my type for going through their learning process.
I feel this
when I was a sophomore in high school I almost failed math and at the end of the year my teacher shook my hand and went, "you didnt have a fun year... but I did :)"
Beautiful interview!
Mathologer doesn't get enough love, but he's got some great things going on in his youtube channel.
But we must clarify the usage of the term “intuition “
The meaning of 'intuition' is intuitive. :)
I think of intuition as being subconscious understanding, both learned and innate. Not all connections our minds are able to make are always available to our consciousness.
@@hypno5690 How helpful would be a deep discussion about idealist metaphysics and theology? From Brouwer's solipsism and Heyting's more "objective" idealism to Ramanujan's Goddess, etc.?
Could it be more helpful to refer to a fairly common phenomenal example, "receiving" ideas in the zone between sleep and awake, trying to remember but mostly failing? Or simply geometric imagination? Knowing and experience by experience is intuitive...
Love the idea of learning through collaboration.
17:59 Losing interest in math in 5th grade! Having grown up in Moscow, I remember being bored to hell with it since my third grade, and the system forces you to endure it for SEVEN MORE YEARS (11th grade allows for some slack due to local state exams).
This is still my favourite episode after two years❤
Math is one of the most complex and intense courses in university, and I'm in basic College Algebra. Every other class is like child's play. The amount of things you have to memorize is insane.
I'm 37, Math was always my friend, the education system not so much. At least I'm allowed to experience the beauty of genious text courses. *now playing: Outnumbered* Well on the other Hand I can be sure there will be a lot of surprises still ahead in the mathmatical literature for me.
This conversation is encouraging to me, as an adult who struggled immensely with math, but have keen spatial and pattern awareness, I finally recognized that I have Discalculia. number symbols mean absolutely nothing to my brain. If I had had a single teacher who could have said the following: math is a language, and it can be done entirely visually.... a whole different world would open up. I am still open to learning. I went to the youcubed website, but it seems really geared for k-12 students, and teachers. where do I go to find a tutor who can teach visual mathematics to an adult learner with very little background math education that made sense. I need to ask questions 1-1, not so much follow a program. The other thing I want to emphasize is that there is a huge difference between a visual or geometric math object,and a symbolic pictorial image describing a math concept. The symbolic visuals, which are not numerically precise, are actually more confusing than helpful. it is where the visuals/colors/shapes/sounds ARE the math, not a representation of the math, that is when it actually makes sense as a language, to me.
I START TO LIKE MATH IN GRADE 5 WHEN I GOT THE BOOK Mathematical recreations BY BORIS KORDEMSKY.
I RECOMAND IT VERY MUCH.I HAD A OLDER COUSIN WHICH SOLVE ONE OF THE PUZZLES USING ALGEBRA AND THAT
MESMERIZED ME AND I WHISHED TO LEARNE IT. AND THAT PROBLEM WAS AN EXEMPLE OF HOW TO GO FROM RETORIC ALGEBRA TO SYMBOLIC ALGEBRA.And later in life i discovery two elementary proofs of Fermat Last theorem. fROM CONCRET TO ABSTRACT AND BACK.That is the secret for the first years of arithmetic learning and that is why is not good for on line learning.
As a math teacher of 22 years, I highly recommend Barbara Oakley's approach to help students find success and satisfaction in Math. Algebra matters. Quality direct instruction matters. Systematic practice matters.
Struggling to learn linear algebra right now. So good timing.
My wife did a linear algebra class (was a teacher, needed to take a class each year) and the text book was terrible and dry so she was left wondering "Why?" Matrices manipulate space. Determinant represents how they change the volume of finite space (so 0 means it collapses space in one or more dimensions), eigenvectors tell you the lines that stay on the line, and eigenvalues tell you how those lines change (stretch/squash and/or reflected about the origin). None of that explained, instead just a definition.
I took linear Algebra last semester and I enjoyed it until we got to vector spaces, eigenvectors, etc. Class average was in the 60s. I barely passed. Sucks because as a CS major, Linear Algebra was a class I was really looking forward to, but looking back, it was an exercise in futility. Lol.
Having Linear Algebra II exam in a few weeks, my university approach of teaching it was throwing 800 pages of books at you and give you 5 exam examples at the end of the semester. Lecturer reads same book out loud and that's it. 3blue1brown can only get you so far, it was helpful in LA1, but now Jordan forms went almost completely over my head. At least they give really good problems for homework, but sometimes they are too good, takes too much time to solve when you only presented with a large assortment of theorems without good explanations.
I didn't know that Lex discusses Math as well. Nice. :)
This content is underrated
I would love to watch an interview about the best ways to lean math as an adult. I, as well as some non natural gifted that i know, struggle with it and it would be really enlightening to know if it's possible and what is realistic goal to a non-gifted person to achieve in his/her learning.
*Unfortunately, at least in my personal experience, the more the teacher or the reasercher that is trying to teach math is naturally gifted the less (s)he understand how is not to be gifted.
I advice you, to take the "learn how to learn" course on coursera it's free, It was made by a electrical engineer professor who had a problem with maths but really wanted to be an engineer, she started learning maths at 26 years old, in fact you'll learn a lot about the brain how you can learn anything not only math, good luck!
That's another kind of perspective. I love seeing things in so many perspectives and what is said in the podcast is helpful in that way.
Fav joke is 4/3 of adults have trouble with fractions!
as a youth i hated math and failed and not just failed but record setting for worst marks ever. It took a goal that used and needed math in my twenties, but even then the algebra was killer. I had to find cheats that worked. Only thing i grasped was geometry and trig followed . Now i love the Hopf vibration Fibonacci and Mandel brot set / julia set too. I watch you and "numberphile" Dr Holly Krieger and i am very impressed with Scot Manley orbital math skills. i was lucky IBM or zerox brought a card reading machine and an intro to boolean and hex to my high school and those seemed so easy. But i really think fast food cash machines should delete cash return function and force learning arithmetic
Some of the classes I made the worst grades in , I learned the most!
That is a beautiful definition of math and reminds me of Andrew Yang’s slogan,MATH, Make America Think Harder.
I've seen many college freshmen give up on Calculus because they do not understand that they need to keep at the concepts. As she said, it's deep learning. They need to work on mastering the concepts and do extra problem sets, work in groups, take turns teaching each other and explaining the equations. I've seen students who were very smart give up....because they said they didn't want to work 'so hard'. And I saw D/F students keep pushing and slowly their grades improved and they were successful in more rigorous math, science, engineering and CS classes...and Graduate!
2:34 The most difficult aspect of a visualized math curriculum is ensuring that it meets accessibility constraints. eg. describe a normal distribution without the jargon to a blind person. Literacy, expertise, and time are necessary to ensure brevity(optimize) and intuitive precision. Failure to do so implies legal action/censure. Another reason teaching is treacherous, and why we need a Noam Chomsky slash Dr Seuss in every department.
This was good chat for me. I have often thought, children in today’s world spend more time with teachers and school than with any other group. Including friends and parents. I could expand on how I see it. But it gets the point across.
I think what a lot of this discussion reveals is how succinctly education has for the most part simply been a tool for selecting out those with high IQ, and dismissing any who showed a lack of high IQ. It's only now that we have even begun the task of attempting to actually educate people.
Great video, great links to information. Absolutely, if you feel the possibility to get inspired, just go and follow the links to the classes and go ahead and do the kids stuff too. This video is a great launching point.
I'm surprised by the slightly low number of views, this may be Lex's most underrated video of the year.
Jo Boaler isn't just a math educator but someone who has had a huge impact on getting education as a whole to start shifting from a fixed mindset to a growth mindset. I start my classes with her growth mindset activities every semester.
"Growth mindset" doesn't replicate. I'm sure it's comforting to talk about but it doesn't actually work.
@@peterfireflylundrecent research has shown that while "growth mindset" is important (believing you can do it leading to internal motivation), literally every other way of motivating kids in high school works better.
Telling kids "you can do it" doesn't magically make them get at it. Growth mindset only accounts for about 5-8% of the increase in math test scores internationally.
This woman is a fucking hack.
@@PJ-qx5yt I tried to post links to real research that debunked her crazy ideas. They got deleted. I tried to post references that people could Google themselves. They also got deleted. The above comment was just about all I was allowed to post!
@@peterfireflylund my favorite is her wildly suspicious study of her methods at Berkeley High School. When her (male) colleague at Stanford in the Mathematics department requested she reveal the raw data and she refused, he publicly called on her to reveal the data and wrote a paper debunking the study. So she publicly called his requests for transparency "sexist" and "harassment".
Headphones please! Talk into the mic… love you lex :*
This is really great insight 🙌🏼
Thanks! ❤️🍃
So excited to learn about Math. 🇺🇸🇺🇸🇺🇸
As documented in a recent article in the Chronicle of Higher Education, as well as a website by Brian Conrad (Stanford professor of math -- actual math), Boaler has a pattern of misrepresenting data and published studies. She'll claim that "according to neuroscience, your brain grows when you make a mistake," and the actual neuroscientist she cites will say "our study didn't say that, and we didn't even try to study that question." And she doesn't back down or apologize for repeated misunderstandings and misrepresentations like this. Sad to see.
Conclude in general, we've to work hard swallow struggle and find good mentor
Another possible reason teenagers don't ask questions, at least in my time in high school, is that it was considered "uncool" to do so. Trying hard in school was considered "lame". Eventually we start adopting the same mentality. It wasn't until college where I stopped thinking this way. Pretty sad.
I suck at math but this was good
53:12 Ah, the age-old question...
Thank you
Man does it feel like American high schools hate letting student lean into intuition when working with math
Learning new math is like meeting a stranger for the first time. You shake hands with the new acquaintance and there's nothing to lead you to suspect what's beneath the surface, good or bad; so you accept everything at face value. Then later you meet the same person under entirely different circumstances and you start seeing a different side, maybe even a contradictory side. Still the picture is incomplete, till you meet the same person again and again under different degrees of separation. On then does the whole person begin to come through. After meeting the same person under the most diverse circumstances, you start getting some insight. YOu realize that insight, not rigorous proof, is what gives you that "oceanic" feeling or an all-seeing eye. You've arrived at the Langland's Program.
When I was in junior high school, even though I had never been good in math, I took Algebra 1. I made, probably a C. I kind of liked it though. I connected with the teacher. The next semester, I wanted to take Algebra 2, but I couldn't. There was another class I had to take first. It was Geometry. I didn't understand it, and I thought it was just drawing and talking about a bunch of triangles. Kind of kindergarten stuff. I didn't connect with the teacher either. I pass the class, but I learned very little, and had acquired a much lower opinion of my mathematical abilities. I signed up for that Algebra 2 class. I went to the first day of class. The teacher, the same teacher I had liked and connected with before, told us all how difficult this class was going to be. He said he would let anyone who wanted withdraw right then would be allowed to, but after that, he wouldn't allow it. He wouldn't let you withdraw from the class no matter how badly you were doing. That was enough to prompt me to withdraw from that class. I took more math classes later, and studies on my own. I do feel like I could have gone much further in math, and in my career, if I had had better teachers back then.
@11:00 multiple ways of learning
I also like the Joe speaks of maths plural
actually that’s how they say it in england.
My text books had no colors
Here Is how i, a guy Who hated math Is now doing computer science with perfect score on all the math subjects. I studied all math over from aritmetics to integrals, and did every exercises of the books. I Also created a sort of note book of all the themes with all the formula, so i can look It up when needed.
Math Is like a Building, if you are weak on floor 3 you Will have problem going on floor 4 or 5 dice you dont fully understand or Remember floor 3.
To Remember math what you have ti do Is practice. When you are studying the theory you only get to know the big picture. To get good you have to solve a lot of problems, only this way you Will get to see cool tricks One problem May have.
Math Is like going to the gym. Be consistent, progressive overload = harder problems, frequency.
Hope It helped.
I wonder how different life would have been if I had better teachers, and didn't have parents that didn't punish wrong answers with pain.