How to LEARN effectively | Five evidence-based tips

[@aggualaqisaaqs3272]

Outstanding advice. I’ve found that 90% of the battle to mastering anything is just finding a way to intrinsically motivate yourself. It’s all downhill after that! Also, I’ve found that when it comes to intellectual activities like math, when people say something is “hard” or “challenging,” it really just means it requires more steps to complete than something that is deemed “easy,” but the individual steps are exactly the same (and equally basic) no matter what the perceived difficulty level. In other words, the real difference is simply that the “hard” problem takes more time. I think part of the problem is when we use words like “challenging” to describe math it brings to mind an analogy to physical activity, where some tasks actually are painful to complete and may be beyond the capabilities of some people. That mindset in itself can be a stumbling block.

[@user-ej7ss8ei2g]

It also takes forever and is often dry in contrast with whatever they may be used to doing.

[@mozzarellapasta1378]

I feel like the simplest counterpoint to this is mentioned in the video, what are the "individual steps" you would need to take to beat magnus carlsen at chest? Ultimately there can be a reason something is challenging or hard beyond the required steps, being dismissive of other peoples difficulties is a bit dismissive to genuine struggles that people can encounter, motived or not.

[@sankhanilnayek9345]

So, for the last couple of semesters, I've been procrastinating a lot, and I got through most of the exams by cramming stuff up like a madman 2 days before the exams. I did get satisfactory grades, but now that you talked about growth mindset, I realise that I actually did not learn anything well enough to actually be competent in any of it. I feel guilty, and I hope I can change that this semester. Thanks for the inspiration.

[@TheGuruNetOn]

Yet. 👍👍👍

[@sar6575]

Any student is just straight up blessed to have you as a teacher :) ! Keep spreading the magic !

[@jinwoo78]

I just discovered your channel today after searching for discrete math topics. I have a very big feeling that you're going to grow a larger base of viewers in the next few years! Thanks for making the content on your channel!

[@Shannxy]

I think the most important question here is... where did you get that wholesome tshirt?

[@DrTrefor]

haha my wife bought it for me!

[@aashsyed1277]

@@DrTrefor was it in a math t-shirt shop?

[@samanseraj326]

This tshirt is awesome

[@TheZMasterful]

Keep these kind of videos Trevor! Loving your ways of explaining things ♥️

[@onafets38]

so much work in your channel deserve a wider audience.. bravo!

[@newyorkguy158]

When learning new math concepts, a student can feel confused, lost and frustrated. It can feel as if there was a barrier to understanding, an impenetrable wall. It takes persistence to not give up and keep hammering away at that wall until it crumbles and the material becomes accessible to your understanding. This is something that students need to know. Keep at it, keep coming back to it, seek out alternative sources of understanding. I think a lot of students, as in calc 1, give up too quickly, because they haven't learned this important lesson.

[@DrTrefor]

Persistence is a big deal!

[@jeanyuan9852]

I can't agree more with Dr. Bazett. If you work hard on one math subject, say, calculus, you will (probably and likely) develop a mathematical mindset, the way how to deal with, to work on, and explore the mathematics. And this mindset will increase your chance to be successful in other math fields/subjects, algebra, probability, and statistics, to name just a few. Thanks for the show.

[@BoZhaoengineering]

I never thought I could learn math as much as I am doing. Partially it is my engineering motivation and the other reason is my curiosity in math and physics how the universe is. Thank you for the one of honest video in 2020 I have seen.

[@newyorkguy158]

I like your landscape photo Bo. I too am studying math and science and want to study engineering because I want to understand how the world works. I don't think anything is deeper than that.

[@TheGuruNetOn]

1) "A Mind for Numbers" by Barbara Oakley talks about cognitive science and methods that worked for many mathematicians, scientists and engineers. 2) Reinvent the wheel : Seeing a finished product is different from seeing it evolve. Learning the history of how Calculus came about across many attempts and refinements over centuries makes it a more human endeavour. More relatable and understandable. Math is basically about decoding/encoding the formula into a story with all kinds of context : history, applications, importance in daily life, getting involved in the puzzle aspects, thinking of the different approaches that one could take in problem solving/being a detective solving a whodunit. Moving from a fixed mindset to an explorative/creative mindset.

[@pedrovinicius7554]

Recently, on my Comp Sci course, I struggled with early concepts of Calculus because my "high school" (I'm from Brazil, so there is no exact equivalent of a high school here) barely touched pre-Calculus or learning things more close to this subject. I was even thinking that I choose the wrong grad course to do and was very nervous about my inability to learn it effectively. This video really helped me, not only on my academic life but also beyond it. Like for example at gym and being healthy. I think a good part of evolving your physical fitness at gyms and trainings is kinda similar to academic learning. I don't think if u agree w/ me on this last take, but I would just like to thank you for the vid.

[@RheaRevolver]

I've learned about all of these study strategies previously, but Dr. Bazett's explanations were clearer and contained more actionable advice than any other explanation I've come across. Thank-you!

[@albinashamanska4125]

Cool! Thank you!!!

[@j.o.5957]

Growth mindset, metacognition, explaining it simply, questions, intrinsic motivation. A note on explaining it simply: tying it to another important concept, namely active recollection, is a powerful combination. By doing this, you get two flies in on smack.

[@bnaalaa57]

Thanks so much for you ifrom Iraq and I love this chanal 💙💫

[@rizalpurnawan3796]

The Intrinsic Motivation is very important, and I have felt it. I have a bachelor degree in engineering, but now I love math a lot, not because math is practically useful, but because it is beautiful and extremely interesting. It makes me feel like studying math is more joyful than playing a video game. Now I feel bored with engineering and I want to spend my life with pure math.

[@DrTrefor]

Come to the dark side lol

[@rizalpurnawan3796]

@@DrTrefor Isn't there any solution to this professor? Haha Is there a chance I can get enrolled in math graduate study? I would be very thankful for your advice.

[@mubashartariq8076]

wow, what a gift this is. just amazing

[@Coolblueocean2001]

Summary: Growth Mindset, Metacognition, Simplify and Explain, Asking Questions, and Intrinsic Motivation

[@우진-o1v]

Thank you for motivating me Im Korea Univ. student major is IME all of your lectures are helpful thanks a lot Dr. Trefor

[@CR_07770]

1-Growth mindset 2-Metacognition 3- Simplify &explain 4-Questions Asking 5-Intrinsic Motivation

[@EvanMildenberger]

Trefor, I hope your channel blows up and you get more subscribers. I really like your content! One small suggestion from an audio perspective: if you position the mic to be more in front of your mouth, the audio quality will be a lot better as it’s possible to hear the reverb of your room which makes it seem lower production quality. The mic being a visual element of your background looks cool but audio quality is so important for conveyed quality. Cheers!

[@TheLethalDomain]

I think we can even extend upon the "yet" term added to the end of sentence. By letting "yet" occur after a comma instead of just ending the sentence with "can't learn this yet," we're intrinsically encouraging the mind to search for exceptions to the rule you assume about your potential. Doing this over and over, I imagine, "rewires" the brain to more efficiently do this process whenever a feeling of intellectual defeat occurs in the future. This allows you to add unknown variables to your own logic that allows for contradictions to the initial assumption to become more present when we actively try to solve the problem this way.

[@aashsyed1277]

Hey, if somebody says "I am good at math" well ..it's kinda bragging..... But saying that "I am good at math but make mistakes" well that's better ..... everybody makes mistakes......agreed with you. Fineman technique is a integration technique too! Game theory is my favorite!!

[@jimmyking8074]

You are Godsend mate, you deserve more subscribers. Been halfway through my 3rd semester as a math major and it's felt rather painful learning than enjoying it. Gonna try and do what you shared and hopefully things are better, keep doing what you're doing!

[@gian87lep3]

The greatest math teacher ever encountered. Period. The discrete math course is a kind of magic

[@DrTrefor]

Thank you so much!!

[@newyorkguy158]

@@DrTrefor even more important, you are a great person. -:)

[@linnkhantthwin5282]

A lot of the time the devil is the details. Universities are notorious for delivering a high level overview of concepts, reassuring the student that they will be fine on the final exam if they can simplify and explain to their peers, take good notes, etc. Only for students to find themselves in a exam that determines if they pass or fail regardless of how well they did on previous assesment that is now filled purposefully with convoluted wording, numerical tricks and riddle like questions. Alongside brutal conditions such as multiple correct choice questions that award no part marks unless all options are selected or 12 weeks worth of content crammed into a 2 hour slot. How can one prepare for a situation like that? You are a good Professor, Dr Bazzett, you care and so in your world these methods would definitely see students rising and achieving their full potential. Unfortunately, it cannot always be said for others. I have seen on multiple occasions, assesment that was disproportional to the level of support prior. Lecturers now having to bell curve entire cohorts to pass because the average score on a final was 30%

[@pantspooper9000]

Im an Electrical/Computer engineering major and immediately lost hope as classes switched to online. Finding this channel has been a life saver. Also I'm taking Discrete Math right now and all i can say its definitely the weirdest coarse ive ever taken lol but interesting though

[@ranulfocastillo5355]

Thank you for sharing!

[@lolitah8560]

I'm a Hispanic female who's been interested in getting into cloud computing which of course has advance level math I love the theory the cool and efficient things technology could do for society as a whole, but boy oh boy math is very intimidating I'm practicing so much math before taking steps in getting into IT

[@DrTrefor]

That's a smart move to focus on the math, as it will definitely help a lot in your IT Programs. Getting good at math is just about mastering each little detail and then moving on to the next, as time goes on the bigger connections form. Good luck!

[@anatolystrashkevich7621]

Thank You Dr.Trefor!

[@derickblacido2267]

Thanks for the information presented here Dr Trefor. You are an awesome teacher. With you and my textbooks for problems I get everything I need to get anywhere in maths. I´ve learnt quite a lot with this video. Aside, there is a similar book that tackles effectiveness in learning by PHd Barbara Oklay: How to learn math and sciences... It talks in-depth and with analogies how the brain works so with that foundations she goes on developing strategies that can work when studying. Highly recommended. Greetings from Peru Dr Bazzet. You inspire me a lot when I am in trouble. I just think on mathematics and the beautiful picture that comes from any equation. It´s not just a wall but a vivid image.

[@prolificEmmanuel]

Thank you sir!

[@penguinb4u]

I am pleasantly surprised to have seen you being bit by the chess bug. Cheers!

[@alanpturing3362]

Thank you .

[@KalmNKollected]

Its funny, Math is the only subject I apply the "Growth Mindset" to and it shows in grade comparison with my other classes; I have fun doing it and most concepts come easy. Although if something confuses me I tend to get scared and try to ignore the fact that I might not fully understand a concept, however, after watching this video I think I might start embracing those moments and jot down questions I have to later find the answers to. Hopefully, I have the motivation to apply these tips to my other classes :) ps miss your great Math 100 lectures!

[@mattl6886]

Amazing t-shirt. Great video too!

[@amadoudiallo9162]

Hey Trefor, I enjoy and understand your Math videos a lot. Can you please make a video on "Simplifying Combinational Circuit"?

[@normanhenderson7300]

Don’t youthink the concepts he explained might help you to do that?

[@bruces4515]

Look at dyscalculia. If you met somebody with a tangible disability, would you say the problem is just their confidence, or would you help to create a positive learning environment with tools and resources.

[@bojelotiroyakgosi]

I really enjoy your channel , you’re doing great work 👊🏾🔥💯

[@DrTrefor]

Thank you so much 🤗

[@SK-bu1yb]

Hi Professor! Thanks for the video. Very insightful. Currently, I am preparing for a competitive exam (containing significant Maths weightage) but, I have very limited time. I constantly find myself in situations where simply memorizing something is way simpler (and also, practical). Is there a way we can implement these ideas in my situation?

[@encapsulatio]

How would you design the "ultimate" course in "fundamentals of programing" that someone could go thru DIY style?Also this course absolutely needs to include "Pareto" math skill and tools that are transferable to your programming skills.

[@سلمةبنفارس]

If just all math professors were like you...

[@ajsworld77]

Let’s assume you are a recovering “fixed mindset” type of person, the former “memorization man” so to say. How can you go on a mathematical journey later in life with a growth mindset? How do you know when you’ve done “enough” when the yardstick “pass this test” is not relevant anymore? As an example: When trying to study probability again after 20 years, but this time from the ground up, I came across set theory first and then fell head first into induction proofs and when trying to clarify that each set really has 2^n subsets. But induction proofs are deep water and take time to really be mastered, so that took time, and I still feel I am barely scratching the surface. Thank you for the work you do, Trefor Bazett!

[@ajsworld77]

Trefor Bazett I appreciate your thoughts, they’ve put me back on a productive path that is not over analyzing. Thank you!

[@subramaniannk3364]

@@DrTrefor Thanks Trefor, even I was confused if i have "growth-mindset" or "fixed-mindset". For ex, I believe I can learn certain topics, but it cannot learned easily. It would take months or years to understand at an intuitive level

[@vinobajohn2393]

I saw your few days before my master's exam.. Really amazing every content..how i missed you all these days..

[@GabrielPohl]

Is easy to see you love what you do

[@DrTrefor]

That sure helps!

[@andrewpynch7732]

Why doesn't this channel get more views

[@youssephfofana9226]

Excellent, superbly and great video i love it...What's really exactly is METACOGNITION?? You did explain but still not clear...Is learning a subject without knowing the concept behind it???? Thanks...looking forward for the next video.

[@Brusselsprouts2023]

love your shirt.

[@nathanyao3525]

I'm pretty sure I have the same monitor

[@harlongbitimung4108]

I love your videos. They are very interesting.

[@brandonsarrasin5481]

One of the main problems I've had is trying to learn multiple things at once, especially as an engineering major. Before this semester I've really tried to go back to my previous courses and truly understand them rather than barely memorizing a few topics from them. However I've gotten into this trap where I feel that when I'm relearning basic calculus 3, I feel that I'm not spending enough time on linear algebra, or differential equations. How do you approach this feeling of not learning what's actually necessary?

[@pinklady7184]

I am mentally practising Gregg shorthand on you, while resisting pen and paper.

[@Youtube_Stole_My_Handle_Too]

What about you learning how to produce sound without echo?

[@ShahFahadKhan]

Nice

[@cocoarecords]

thanks alot

[@MsAora]

Will you do a course on PDEs anytime soon?

[@hvok99]

Genuine question, do you talk with your hands intentionally to help underscore and accent the meaning of your words?

[@vinnywong5808]

I love that t shirt. Where can I buy one?

[@DrTrefor]

Isn’t it awesome! Sadly my wife found it on Amazon so I don’t know the exact one:/

[@emilydedmon3288]

Hi Trefor! I have a question..what is the most effective way of learning multi-variable calculus. Is it going through pre-cal, cal 1, cal 2? or can you learn a different way. I am in data science and have been doing a deep learning course. but I am interested in doing an AI program which requires multi-cal before starting the program. Which way is the most effective way to learn this with, and how long might that take?

[@DrTrefor]

It really depends on where you are at. My personal multivariable calculus course on KZbin really presumes you have done Calc I/II. There are some textbooks out there that try to lightly do all three sort of concurrently at the same time which makes the minimal path.

[@emilydedmon3288]

@@DrTrefor Thank you

[@dhickey5919]

Intrinsic motivation maybe the cornerstone to higher math and science education. The "C's get degrees" students are often the same ones derailed by any setback or negative judgement they make on themselves. How's your 'Chess Growth Mindset' working one year on? What's next for resolutions?

[@suhailawm]

tnc sr

[@quadhd1121]

Hey any chance you could do differential geometry and vector algebra ....I'd really appreciate ,I suggest everyone else who wants the series join me and donate a small portion to the professor 😀

[@vivianna168]

@@DrTrefor oh my I would be over the moon if you did differential geometry!! I'm not there yet but I can't wait till my last year of my math degree:)

[@reservoirgeophysicist3013]

Bro, can u plz suggest introductory books for Complex Analysis.

[@kristinasecret1767]

is that a victoria (by paradox games) cup ??

[@DrTrefor]

Haha no university of Victoria:D

[@kristinasecret1767]

@@DrTrefor oh, okay :D thanks a lot for your videos. i am a math student in Germany...and yea.. always looking for tips

[@josephhajj1570]

By the way nice ideas

[@PasserbyP]

What do you do when you're trying to answer a difficult math question or assignment question and it's in the fringe of your capacity?

[@DrTrefor]

Sometimes it's a good idea to take a step back and work on the fundamentals of the topic before returning to the assignment. Often students are learning the basics in order to solve a particular homework problem, when it is usually best to learn those totally independently. After this, you might find the problem is now solidly inside your capacity

[@afuaamoako1061]

please where can i get some of T shirt

[@DrTrefor]

I actually have a link at my amazon store in the description, not quite the same one but pretty close.

[@dimitricondax9129]

this guy speaks fluent italian with his hand gestures

[@aggualaqisaaqs3272]

Another thing: we have this notion in our culture that only young people can truly go on to master certain things and that if you’re already of a certain age, it’s foolish to think you’ll be able to, say, become a chess grandmaster or learn to speak a foreign language fluently. I think this is patently false and if anything we become better and more efficient learners as we get older. I suspect that the “commonsense” perception that it seems to be true ultimately comes back negative growth mindset and the fact that in our society most adults, once settled into a career, stop learning new things altogether (and therefore practicing how to learn).

[@JoaoVitorBRgomes]

You're like Barbara Oakley with a beard! Cool

[@atreeinthewoods.9533]

How to learn effectively? watch Trefor Bazett calc videos.

[@abuzarrahmanmechanicalpesh3736]

plz talk in a slow mode being a mathematician

[@josephhajj1570]

Mister you should start with complex analysis

[@housamkak646]

Ill start this course on 22 this month

[@swojnowski453]

The video misses the point how to learn entirely. A total miss. What should it contain? Polya has already explained clearly. Draw your problem, if you can't draw it you do not understand what you're doing. If you have no picture of the object you're working with either in your mind, or more importantly in front of you, either as as drawing with multicolor pens or on a computer with vector graphics software, you are certain to be hurting your ability to learn more effectively. That's one. To, make sure all the variables and constants are on the drawing. Three, lets assume you have solved your problem based on the object you are working on. Do you understand it now? If you do, you should be able to program the concept using a programming language. If you are have understood how lines are built with vectors. You should be able to program this. That's was three. Let's move on to four, why would you want to program things? Also to make sure you do not repeat yourself while calculating with the objects you have just learnt to use. There are libraries etc. but can you be sure they are based on the same object you're thinking they are? If you can program your object, or concept. You should be able to use it, for example for building things. Moreover, you program so that you do not have to remember how things were built. Finally, once you have drawn your problem and build code that is based on it. Keep both the drawing and the code. They are two pieces of the whole. When you do not remember how code works, you go to the drawing. Code is there to save you time, the drawing to make you understand things quickly after some time. This is the way things should be learnt today. Try it, you will thank me later.

[@vansf3433]

Teachers' ignorance of the English language with ambiguous ways of explaining theorems and formulas can make simple mathematical statements complicated and confusing to people Calculus is not so difficult when it is explained in unambiguous ways . A lot of people find it difficult, because of ambiguous languages used by ignorant teacbers , but not because it is actually difficult

[@aminnima6145]

4 aliens disliked this video

[@shawcampbell7715]

Nice shirt lol

[@vansf3433]

All the curent methods of teaching and learning such subjects of natural science as maths, physics, chemistry and astronomy are not good when basically it iscall about copying theorems and formulas like a photocopying machines , instead of incouraging people to question the validity of such theorems and formulas until they can prove them to be correct by themselves to see whether there are any flaws and defective holes in such subjective interpretations by scientists of previous centuries , simply because there are only relative truths in human - created subjective reality , and human developments can make progress only when later human generations understand the same things in better ways which are closer to being parallel to objective reality than the ways how the previous human generations did

[@wjrasmussen666]

So someone might say, I haven't died of cancer yet.

[@ukranaut]

"Simplify and explain" i.e. - waste time to come up with a new name for the "divide and conquer". Sigh.

[@binabedin9823]

Professor , I'm pretty sure that you do play football XD