Before class 1. Recall 2. Preview During class 3. Be active 4. Ask questions 5. Make annotations After class 6. Review 7. More questions 8. Practice 9. Concept maps
Making an attempt to understand the work before it is discussed in class is severely underestimated. Here’s how I look at it. Some of these people teaching these classes have been doing it for 30 years, yet I have yet to have one that doesn’t show up with notes, lists, and knowing exactly what they need to cover- even despite having taught that class over and over again. They probably could wing it and meet expectations- but they never chance it. They’re always prepared. What are your chances of succeeding on *brand new* material if you haven’t done that? You’re not getting paid either, you’re spending money. Are you going to gamble that money? Also, LaTex for notes was a huge headache at first but a lifesaver in the long run. Combine it with other languages such as python for iterative templates that can help you stay organized for the whole semester.
What a great video! I followed your advice closely last term. I got a 100% in a 4th year maths class and, as an undergraduate student, outperformed all graduate students in the same class! Thank you very much!
When I started to input my math notes in Notion using Latex, I noticed I retained the concepts better bc I was actively converting my math problems to “code”; similar to translating instructions to code in programming. I honestly need to do it more.
¡Qué notable..! Yo lo voy a probar para ver qué onda...gracias por compartir tu idea con los demás. Por cierto, me gusta mucho tu foto, es muy linda. Saludos desde Argentina.
I alsolutely feel that, since LaTeX kind of forces you to use mathematical signs very precisely so that you always want to give a lemma or something when using an implication. Love it, too. Have been doing my exercise sheets with LaTeX since my third semester and it boosted my understanding of maths a lot. Ultimately, my goal is to understand why something is so cool, e.g. galoistheory- very cool :)
Thanks! Very insightful video. My takeaways for anyone whom may like. 1. Pre-class Review. - Take 5 mins to recollect what you learnt previously. Saves from having to spend time and effort in class recalling. Just close your eyes and reflect on the previous class. Spaced retrieval is a great practice. 2. Preview. - For 10-15 mins, read through major concepts in your texts that will be covered in the class. Don’t read all the details; this is to create a rough scaffold that you can build upon in class. The foundation helps you be more attentive and understand more. 3. Be Present and Active. - Let’s make the already 30-40h per class each semester effective; leisure time must be had but it’d be better outside of class. Let’s not waste time being on our devices or thinking about other things (find time outside of class to reflect and worry instead). - Don’t be a stenographer. Understand as much as you can; if it’s going too fast and you’re forced to writing everything down, give feedback and try doing more reviews and previews. - Write down questions you have while taking notes, ponder over questions from the professor; learn actively. Tip: Annotate with symbols and lines to draw attention for you to understand what you were thinking when you look back on the notes. 4. Post-class Review. - Read notes made in class and check if you’re confident in understanding all you wrote. Get help with the questions you noted or wrestle with them yourself. Don’t let a class pass you by without you feeling that you understood it 100%. The review could take 10 mins if you’re confident, to perhaps the whole class time (but this helps you save time in the long run). - Come up with more questions as you review, perhaps three, and have one of them be a bigger-picture question which inquires how the concept relates to the others. Enmeshing this concept in a network with the rest is great for long-term retention. Concept maps can be drawn to help. 5. Practise. - The previous steps walked for this to run. This is where the bulk of your study time can be spent. Do the homework and extra practice questions to fully and deeply understand the concepts for you to remember them for the long-term.
Man, you and Professor Leonard are the two dudes that made me feel alright about upgrading math from a minor to a second major. Really appreciate this video, thank you!
Here’s one quote. “ learn effectively not harder “. We have to understand that we have to learn more effectively and not put more work onto ourselves by studying a long list of things that’s not related to a test tomorrow or to a assessment that needs to be done. What I usually do is focus or study dings that is related to my class tomorrow or to my test the following day but very good video overall.
The whole "rewriting your notes" thing is a fantastic tip. Take brief notes during classes, then at home/in the library try to fill in the gaps with either what you remember or by referring to slides/books. I almost pretend I'm writing lecture slides my future self. By far the best way I've found to actually learn concepts. Also means I write note physically (good for memory), but end up with digital copies (good for study). +1 for LaTeX as well.
Thank you so much I am a medical student who always struggled with how should I study I always wanted a clear routine which I would be doing on a daily basis And your video said everything👏🏻👏🏻
Before Class 1) Five minute review. Recollect what was brought up last class. 2) Previewing. Read up on what will be taught in the next class. Make a rough scaffold of the material so class will make more sense. During Class: 1) Be an active participant 2) Try to generate questions (write them down) 3) Annotate your notes After Class: 1) Quick Review of your notes. Go over everything until you feel confident you understand it. Don’t let a class go by where you don’t understand the material. 2) Generate Questions - at least three. Try to link concepts together 3) Practice Practice Practice! The more the better. 4) Make a Concept map, it will help with connections. (This was not in the Video but the book UltraLearning is really good)
Now this is a good way to start the new year 😁 I would always study ahead of the course back when I was in school, and I can say that's the best advice for any student.
You saved me last year with the Discrete Math videos. Online learning was hell. I was late in most classes not sleeping enough hours gave me zero energy for classes. But definitely l needed this more since l'm freaking out as the increase of Covid-19 cases in South Africa will mean we will be going back online.
Some things I've learnt to do while learning : 0) Annotating text with questions like "why?", "Did the author mean this OR this?" etc. 1) Generating questions by thinking like an investigative journalist : "who, what, when, where, why and how" 2) Making predictions based on what you learned ie the mental model you developed. 2) Teach : When one teaches, two learn.
I rarely comment on videos, but this was a fantastic video and I couldn’t help but thank you for taking the time to make this. I’m a university student studying single variable calc and loved the structure that you provided here; I’ll definitely be implementing the pre-reading technique starting tomorrow!
as a pre secondary school student, i find this exactly how i learn things. i am very good in physics and math, and the tips in videos were how i did it. i learned physics by myself one year b4 my first physics class, so i learned it better than anyone and i don't even have to revise b4 exam
I am an optometrist but I have a very strong passion for maths to the point where I wish I could go back in time and do a maths degree. I have always been enchanted with mathematics and have studied it in my own time to a pretty high level. I think it is the most beautiful subject. Am I an outlier or are there other people who feel the same about mathematics? Anyone else who majored in something else and wished they had got a maths degree instead? Love your channel Professor :)
@MadeOf Clay you surely are not alone! ) I can relate 100%. I also very much enjoy to study mathematics and physics. The only difference is that I did not get a chance to finish ANY degree before my mid thirties. But today I’m almost done with my physics degree. I’ve never regretted going back to school at 33 to study what I love. I also have a classmate, who got his Bachelor of Arts, and years later, went back to school for a degree in physics .^-^
Given a student who has met the prerequisites, it is IMPOSSIBLE for them to fail any class if they follow these techniques. As a teacher and lifelong student, I can attest these techniques are things good students consistently do, and that mediocre/poor students choose not to do or do consistently.
I didn’t realize the importance of pre class recollection until I was online and no longer had the time sitting in the class room before class to look at notes.
As a matter of fact, the points in this video are heavily supported by empirical evidence and research. I am taking a course called iCanStudy, which I absolutely recommend because it increased my understanding of the material by ~40% (which can be seen in my grades too) and I am studying 15% less than previously. Essentially the fundamental pillars of this iCanStudy course are mentioned here: 1, make a scaffolding before you go to class because it improves your understanding & improves long-term retention (if you are falling behind during class, then make sure to build a larger scaffolding) 2, Make "concept maps" during lecture instead of writing linear notes where you a, visually see the connections between topics and b, you are not taking linear notes which is detrimental for retention 3, revise after class by recreating the same mindmap from memory and 4, always ask yourself the question: How does this fit into the big picture?
Hi Trefor. You were my TA for linear algebra at UofT many, many years ago. I'm actually studying for my PhD comps in English literature. Although our disciplines are different, I will be using your studying techniques. Thank you!
Thank you for sharing these tips! As a student who's struggled to find a good way of learning new material, I'll definitely try this out. My main questions are how did you develop the discipline/motivation to continue doing this process especially if you aren't the fastest learner? Also, thanks for your linear algebra playlist, I would've been completely lost without your videos!
So glad the LA playlist helped:) I think it is totally ok and normal to not feel like the most disciplined or fastest learner, I think we all feel that way from time to time. I think the main thing is to be pausing somewhat regularly (maybe every two weeks?) and asking yourself what you've been doing that is effective, and what isn't as effective.
Very useful. I will assign this to students in my upcoming spring classes because I can't really say it better than this. One thing I always do as an instructor is do a short 10 minute review to connect back to the prior course. The class Wiki seems like a great idea, too.
Thank you! I actually used to do the ten minute review before class as well, because it’s so important for students to be caught up and present. However, I’ve now moved more to creating the supports before class so students have the resources and incentives to actually do this themselves, which gives me ten minutes more in class for active learning. But it only works if you can really get students invested otherwise some are just totally lost
Very good tips. I always looked at the syllabus and then tried to learn everything without the teacher and even if i didnt succeed it still make the class a lot easier. It is just a matter of searching up the topic on yt and then watching videos on it while playing video games.
It's remember me when I was studying English. I was learning a bit about the grammar (I still do a lot of mistakes) and I did 3 things when I read a grammar's book: 1. See all the book (it's like scanning) 2. Read the book and doing a lot of practice, all of those without ask myself. 3. Re-read the book and now like a criticism, I remember I asked myself questions like: Why, Where, How... do I need to use this, those? etc. I still have a lot of mistakes in English, but this kinds of videos have helped me a lot. Specially when I read and see videos and articles of science and math in English.
8:40 This is *so useful.* I'm used to things like this in the humanities, as discussing with and instructing others is really the best active learning method. Now I'm considering having another go with more STEM in uni, hopefully there's a possibility for some legit free form teamwork.
These are excellent tips for theoretical subjects. For experimental studies such as physical sciences and engineering, I would suggest to excel on experimentation, trial and error creative design and supporting your studies with internships.
I'll add that the only way a student can have a focused, organized, and consistent study routine is if the professor is running the class in a focused, organized, and consistent manner. No excuses, no victims, we are responsible for our own progress..but a professor with a schedule of some sort helps immensely.
I study mechanical engineering, and I have an other tactic. I think your way consumes a lot of energy and time, and most of us cannot keep up this routine along the semester, when we are on full of compulsory homeworks, exams/tests and we have so many classes. My way is to take the hardest exam problems, and sweat, even if your knowledge isn't enough. It forces you to check your notes/books, the information can be memorized better, because you need that particular solution, and the best part, is that you're facing the problems, you will actually get on the real exam. Worked in the most of the cases.
Trying to recollect: before class 1. review last class, 2. preview this class. During class: 3. active learning, 4. questions, 5. annotations After class: 6. review notes. Full understanding. 7. More questions. 8. Concept map Gonna try this in my classes, see how it goes
Other than the class preview which I should be doing and very lazy to do. All of the tips are actually tried and proven in my own study routine. Great video.
I mean that’s good tips but this is jot doable for everyone. In my case I have class from 8 AM to 18-19 PM and after that I need to go home I’m tired as hell and I still need to work like crazy to be well-ranked in my class. And I just cannot prepare what we will be covering during the next class, and it’s often not even possible cause we don’t know. We are all late on what we’re doing in class I mean that’s usual where I am, holidays are simply make to be on point for the next period but I will still try to apply some of the tips you gave. This was a really good video and even though it’s not the best for me, I’m pretty sure it’ll help a lot of students (Sorry if I did mistakes) Keep up the great work :)
I"m sorry to hear your schedule is so jammed packed, you are right if you can only ever do class+homework, then it is hard to gain the benefits from the types of tips I was talking about
Damn! I never went for preview or post-class reviews. Now, I know where I lost some of my grades during my undergrad studies. Thanks for this, will try to follow this strategy for my grad school.
It's if anything more important in grad school! If you're going to a seminar, its so easy to get lost in the firsts 5 minutes, but with a big of gaining familiarity with the basic concepts you can end up following the full hour
Hello professor I am a Moroccan math student and I am glad to find your channel it sounds interesting 💪. I finished my third year at university but I couldn't study a master this year for some circumstances but I am studying in my own .and I want to study number theory .yesterday I started by the book "introduction to modern number theory "please professor reccomend me some great books for number theory and algebraic topology as well professor Thanks infinitely
Most of the advice in this video requires you to spend more time working during the semester for courses without deadlines. Since you probably have enough deadlines on your plate already and don't have time to consistently maintain such a heavy routine, consider the following: Make a priority list of subjects ranked in terms of difficulty and apply these tips to the first few in the list.
While definitely true, it isn’t zero sum. As in, if you do some of these, likely your assignments happen faster as you go in with stronger content knowledge.
If MATH IS REALLY HARD, then whoever be the Professor, most students will tell it hard. But this is not the case. There are Professors, who make things interesting, and easy to understand. Their students are mostly satisfied and progress in a continued manner. Hence, the more important thing is ----- who is teaching the course, and how much effort and time you are putting in problem-solving.
haha I rarely highlight long passages of text, but I usually put a star next to something I think is important. I think it's funny how we chose that symbol.
My problem at school was that I was only mediocre at memorization. Therefore, my goal during my studies was to avoid memorizing. I think that made it possible for me to study physics very effectively. This should also apply to math studies.
Thank You, Dr for your efforts!!! It is a great routine to start within the new year. I learned a pile of new information in your Calculus III and Discrete Structures Courses :) (Starting with Calculus IV and Differential Equations after a little)
Attend the Professor's and Teaching Assistant's office hours. (1) In the real world, these technical professions are very social: you will need to talk with a lot of people to solve problems. (2) Few students show up for office hours. In addition to discussing lectures and homework, building a rapport with the faculty and staff is a critical networking activity. (3) Organize "Problem Set Parties" with a few classmates. Talk about lecture material, discuss approaches to homework solutions, and formulate qualitative solutions to develop an intuition about what a solution should look like.
One thing that i always wanted to ask that how to deal with the temptation that you get after the course progresses , "Oh i dont know the basics, once i know all those basics day by day, i will be in a position to understand this, then that one day never comes" so i want some tips, when you have missed a lot of points in the class before (genuinely) , then how to catch up with newer material , like should i understand as much as i can ,push myself a little bit while siimulatenously revising all the other ones. Any tips ?
I got this video suggested. I like how you explained everything well detailed. We have the same math book " Thomas". It is a well written book. I am studying computer engineer
Amazing as always. Thank you for your tireless efforts. Though I can't say for sure, the collection of courses (Calculus, Linear Algebra, Discrete Mathematics) on your channel seem to suggest you have some background in Computer Science. Anyways, so, where do we go from here? A full course on Differential Equations? on Probability & Statistics? on Real Analysis?
Indeed differential equations starts next week, and PROBABLY stats after that, but I might tak ea semester off and just make fun one-off cool math videos as opposed to a proper course
09:20 Yeah but if you study like this and your friends dont you still miss out on social interactions. The studying before class tipps also seem directed at someone who already knows how to study. its too general advice. Often being attentive for 90 minutes of University math was asking too much. If i looked at the script beforehand i could stay focused longer because i already grabbed the vague concepts. In total i had the best results in classes where i effectively read the entire script 3 times. And it didnt really matter if did everything just before the exam or continously throghout the semester. Just go through the thing 3 times. And make sure you have someone to ask if you get something terribly wrong.
Dr. Trefor, 1. What is the name and author of the calculus book you used briefly in this video ? 2. What is the name of that iPad software you were using for notes (I am a PC person) Thank you, Bob Wilmes P.S. Can you print those notes on printer ?
I never went to college :(. But one thing I always struggled with is how do you learn when you have to write so much from the teacher? I couldn't write as fast as my fellow students. So I sometimes missed things in writing and I certainly missed the point of the lessons because I had to be this fast. I have never understood this way of teaching. I didn't learn much in those lessons. That's why I am also am afraid of college. I am someone who needs lots of time to get concepts. It would be far better if you could film those lessons for you to learn from and participate in class when you are filming it. That way you could follow the class and interact and also learn afterward. Have a great New year by the way, from Belgium.
That totally happens to a lot of people, and it definitely sucks because if you are going to class and it’s too fast that just isn’t helpful. I usually try to help people find strategies before and after class so that the class time becomes understandable
@@DrTrefor Yeah that would have been great. My teachers were of the kind they didn't really cared. I love learning things. But I don't like to many distractions (I have Aspergers) or things that take away from learning like so much writing besidesusing it for the essential things and practice(I know many like to study that way, but that is not for me). Sadly writing is still so ingrained in school. I mean as a way to copy things that the teacher says.
I really like writing questions on the sides of my lecture notes as well! What do you do in a lecture when you are just completely lost? I know for the next class, you should do more previewing, but what do you do at that time? Also how many hours do you put between the class and reviewing your notes?
That's a great idea! I don't think the time gap matters SO much. Within a day or so? THe longer you wait the more effort it will be, but that isn't necessarily bad.
Before class
1. Recall
2. Preview
During class
3. Be active
4. Ask questions
5. Make annotations
After class
6. Review
7. More questions
8. Practice
9. Concept maps
Tysm for jotting down these points
Learning is an active process.
Making an attempt to understand the work before it is discussed in class is severely underestimated. Here’s how I look at it. Some of these people teaching these classes have been doing it for 30 years, yet I have yet to have one that doesn’t show up with notes, lists, and knowing exactly what they need to cover- even despite having taught that class over and over again. They probably could wing it and meet expectations- but they never chance it. They’re always prepared. What are your chances of succeeding on *brand new* material if you haven’t done that? You’re not getting paid either, you’re spending money. Are you going to gamble that money? Also, LaTex for notes was a huge headache at first but a lifesaver in the long run. Combine it with other languages such as python for iterative templates that can help you stay organized for the whole semester.
What a great video! I followed your advice closely last term.
I got a 100% in a 4th year maths class and, as an undergraduate student, outperformed all graduate students in the same class!
Thank you very much!
That’s amazing, congrats!
When I started to input my math notes in Notion using Latex, I noticed I retained the concepts better bc I was actively converting my math problems to “code”; similar to translating instructions to code in programming. I honestly need to do it more.
Great work
¡Qué notable..! Yo lo voy a probar para ver qué onda...gracias por compartir tu idea con los demás. Por cierto, me gusta mucho tu foto, es muy linda. Saludos desde Argentina.
@@walterretlaw4051 ¡Muchas gracias por tus amables palabras! Espero que te ayude en tu aprendizaje. :D
I alsolutely feel that, since LaTeX kind of forces you to use mathematical signs very precisely so that you always want to give a lemma or something when using an implication. Love it, too. Have been doing my exercise sheets with LaTeX since my third semester and it boosted my understanding of maths a lot. Ultimately, my goal is to understand why something is so cool, e.g. galoistheory- very cool :)
Pretty much do the same for I use LaTeX for Anki
Thanks! Very insightful video. My takeaways for anyone whom may like.
1. Pre-class Review.
- Take 5 mins to recollect what you learnt previously. Saves from having to spend time and effort in class recalling. Just close your eyes and reflect on the previous class. Spaced retrieval is a great practice.
2. Preview.
- For 10-15 mins, read through major concepts in your texts that will be covered in the class. Don’t read all the details; this is to create a rough scaffold that you can build upon in class. The foundation helps you be more attentive and understand more.
3. Be Present and Active.
- Let’s make the already 30-40h per class each semester effective; leisure time must be had but it’d be better outside of class. Let’s not waste time being on our devices or thinking about other things (find time outside of class to reflect and worry instead).
- Don’t be a stenographer. Understand as much as you can; if it’s going too fast and you’re forced to writing everything down, give feedback and try doing more reviews and previews.
- Write down questions you have while taking notes, ponder over questions from the professor; learn actively. Tip: Annotate with symbols and lines to draw attention for you to understand what you were thinking when you look back on the notes.
4. Post-class Review.
- Read notes made in class and check if you’re confident in understanding all you wrote. Get help with the questions you noted or wrestle with them yourself. Don’t let a class pass you by without you feeling that you understood it 100%. The review could take 10 mins if you’re confident, to perhaps the whole class time (but this helps you save time in the long run).
- Come up with more questions as you review, perhaps three, and have one of them be a bigger-picture question which inquires how the concept relates to the others. Enmeshing this concept in a network with the rest is great for long-term retention. Concept maps can be drawn to help.
5. Practise.
- The previous steps walked for this to run. This is where the bulk of your study time can be spent. Do the homework and extra practice questions to fully and deeply understand the concepts for you to remember them for the long-term.
Man, you and Professor Leonard are the two dudes that made me feel alright about upgrading math from a minor to a second major. Really appreciate this video, thank you!
That's so cool, always makes me happy that us math youtubers can inspire and help people out:)
Who do you think explains calculus the best? And what's your first major?
Here’s one quote. “ learn effectively not harder “.
We have to understand that we have to learn more effectively and not put more work onto ourselves by studying a long list of things that’s not related to a test tomorrow or to a assessment that needs to be done. What I usually do is focus or study dings that is related to my class tomorrow or to my test the following day but very good video overall.
I REALLY needed this video. Really interesting tips and brilliant insights! Thanks a LOT
Hope it helps!
Appreciate all your hard work man, the passion you put in this can be seen in your eyes.
Stay safe. Bless you!
Thank you so much!
The whole "rewriting your notes" thing is a fantastic tip. Take brief notes during classes, then at home/in the library try to fill in the gaps with either what you remember or by referring to slides/books. I almost pretend I'm writing lecture slides my future self. By far the best way I've found to actually learn concepts. Also means I write note physically (good for memory), but end up with digital copies (good for study). +1 for LaTeX as well.
Thank you so much
I am a medical student who always struggled with how should I study
I always wanted a clear routine which I would be doing on a daily basis
And your video said everything👏🏻👏🏻
Before Class
1) Five minute review. Recollect what was brought up last class.
2) Previewing. Read up on what will be taught in the next class. Make a rough scaffold of the material so class will make more sense.
During Class:
1) Be an active participant
2) Try to generate questions (write them down)
3) Annotate your notes
After Class:
1) Quick Review of your notes. Go over everything until you feel confident you understand it. Don’t let a class go by where you don’t understand the material.
2) Generate Questions - at least three. Try to link concepts together
3) Practice Practice Practice! The more the better.
4) Make a Concept map, it will help with connections.
(This was not in the Video but the book UltraLearning is really good)
That was helpful,thank you
Now this is a good way to start the new year 😁
I would always study ahead of the course back when I was in school, and I can say that's the best advice for any student.
It sounds so simple, but so few actually do it!
Maths as Concepts Maps ! Absolutely ! 👏🏽 Thank u so much sir, not only for ur precious advice but the contagious attitude u have as well !
You saved me last year with the Discrete Math videos. Online learning was hell. I was late in most classes not sleeping enough hours gave me zero energy for classes. But definitely l needed this more since l'm freaking out as the increase of Covid-19 cases in South Africa will mean we will be going back online.
Some things I've learnt to do while learning :
0) Annotating text with questions like "why?", "Did the author mean this OR this?" etc.
1) Generating questions by thinking like an investigative journalist : "who, what, when, where, why and how"
2) Making predictions based on what you learned ie the mental model you developed.
2) Teach : When one teaches, two learn.
Yay! First video of 2021 from your channel. Very excited if I could find content related to my math course in next trimester.
Yay! What course are you taking next semester?
@@DrTrefor series and matrices. Enjoyed vector calculus series btw.
I rarely comment on videos, but this was a fantastic video and I couldn’t help but thank you for taking the time to make this. I’m a university student studying single variable calc and loved the structure that you provided here; I’ll definitely be implementing the pre-reading technique starting tomorrow!
Thanks Will!! Also make sure to check out my calc playlists:)
as a pre secondary school student, i find this exactly how i learn things. i am very good in physics and math, and the tips in videos were how i did it. i learned physics by myself one year b4 my first physics class, so i learned it better than anyone and i don't even have to revise b4 exam
Cool, thanks for sharing!
nice on learning on your own before class!
I am an optometrist but I have a very strong passion for maths to the point where I wish I could go back in time and do a maths degree. I have always been enchanted with mathematics and have studied it in my own time to a pretty high level. I think it is the most beautiful subject.
Am I an outlier or are there other people who feel the same about mathematics? Anyone else who majored in something else and wished they had got a maths degree instead?
Love your channel Professor :)
You’re definitely not alone. While the majority of my viewers are in school still, there is a solid group who just loves maths and the beauty of it
@MadeOf Clay you surely are not alone! ) I can relate 100%. I also very much enjoy to study mathematics and physics. The only difference is that I did not get a chance to finish ANY degree before my mid thirties. But today I’m almost done with my physics degree. I’ve never regretted going back to school at 33 to study what I love. I also have a classmate, who got his Bachelor of Arts, and years later, went back to school for a degree in physics .^-^
I will recommend this video to everybody. We need more of these videos. Thanks Sir.
I really appreciate that!
Given a student who has met the prerequisites, it is IMPOSSIBLE for them to fail any class if they follow these techniques. As a teacher and lifelong student, I can attest these techniques are things good students consistently do, and that mediocre/poor students choose not to do or do consistently.
Thanks for this video Trefor! I am kinda jealous from your students, they are lucky to have such a great teacher like you.
thanks so much, i began some cool pure math courses and I needed to learn how to do real math. I got it!!
Thnks for the priceless Councilling
I wish you keep going forward this way to help us in our journey to master maths
I didn’t realize the importance of pre class recollection until I was online and no longer had the time sitting in the class room before class to look at notes.
That’s an interesting point actually, makes it more important to specifically carve out time for it.
As a matter of fact, the points in this video are heavily supported by empirical evidence and research. I am taking a course called iCanStudy, which I absolutely recommend because it increased my understanding of the material by ~40% (which can be seen in my grades too) and I am studying 15% less than previously. Essentially the fundamental pillars of this iCanStudy course are mentioned here: 1, make a scaffolding before you go to class because it improves your understanding & improves long-term retention (if you are falling behind during class, then make sure to build a larger scaffolding) 2, Make "concept maps" during lecture instead of writing linear notes where you a, visually see the connections between topics and b, you are not taking linear notes which is detrimental for retention 3, revise after class by recreating the same mindmap from memory and 4, always ask yourself the question: How does this fit into the big picture?
Hi Trefor. You were my TA for linear algebra at UofT many, many years ago. I'm actually studying for my PhD comps in English literature. Although our disciplines are different, I will be using your studying techniques. Thank you!
Very cool, thanks for the throw back!
I will most likely make this video a required watch for my students this semester. Thank you so much for making such great content!
Ha, I'm doing the same, thank you!
Thank you for sharing these tips! As a student who's struggled to find a good way of learning new material, I'll definitely try this out. My main questions are how did you develop the discipline/motivation to continue doing this process especially if you aren't the fastest learner? Also, thanks for your linear algebra playlist, I would've been completely lost without your videos!
So glad the LA playlist helped:) I think it is totally ok and normal to not feel like the most disciplined or fastest learner, I think we all feel that way from time to time. I think the main thing is to be pausing somewhat regularly (maybe every two weeks?) and asking yourself what you've been doing that is effective, and what isn't as effective.
@@DrTrefor Thank you, I'll definitely give it a try! I really appreciate the advice and the content that you share on this channel.
Commenting for the algorithm. You're saving people hours of work.
Very useful. I will assign this to students in my upcoming spring classes because I can't really say it better than this. One thing I always do as an instructor is do a short 10 minute review to connect back to the prior course. The class Wiki seems like a great idea, too.
Thank you! I actually used to do the ten minute review before class as well, because it’s so important for students to be caught up and present. However, I’ve now moved more to creating the supports before class so students have the resources and incentives to actually do this themselves, which gives me ten minutes more in class for active learning. But it only works if you can really get students invested otherwise some are just totally lost
The best way to study is what makes sense to students as individual learners.
Very good tips. I always looked at the syllabus and then tried to learn everything without the teacher and even if i didnt succeed it still make the class a lot easier. It is just a matter of searching up the topic on yt and then watching videos on it while playing video games.
This is just pure gold, thank you!
I am a high schooler and I watched all your calculus videos and learnt a lot.Thank you sir for your efforts
Nice! Always love to be able to help out people still in high school, I hope it will help so much for whatever comes next for you
Kind of reminds me of "Make It Stick"
By Henry L. Roediger III, Mark A. McDaniel, and Peter C Brown. Have you read it?
oh, I have! So many great ideas in that book:)
I loved :" a mind for numbers" by Barbara Oakley
And
"The science of learning"
Edition 2
By Doyle and Zakrajesk
Mybe i will review them in my channel
@@TALKmd please do
@@TALKmd
Yes, please can you do this review 😌
It's remember me when I was studying English. I was learning a bit about the grammar (I still do a lot of mistakes) and I did 3 things when I read a grammar's book:
1. See all the book (it's like scanning)
2. Read the book and doing a lot of practice, all of those without ask myself.
3. Re-read the book and now like a criticism, I remember I asked myself questions like: Why, Where, How... do I need to use this, those? etc.
I still have a lot of mistakes in English, but this kinds of videos have helped me a lot. Specially when I read and see videos and articles of science and math in English.
8:40 This is *so useful.* I'm used to things like this in the humanities, as discussing with and instructing others is really the best active learning method. Now I'm considering having another go with more STEM in uni, hopefully there's a possibility for some legit free form teamwork.
These are excellent tips for theoretical subjects. For experimental studies such as physical sciences and engineering, I would suggest to excel on experimentation, trial and error creative design and supporting your studies with internships.
True, these are definitely influenced by being math, I think some are true for different subjects but definitely not all
Absolutly right Sir♥️
I'll add that the only way a student can have a focused, organized, and consistent study routine is if the professor is running the class in a focused, organized, and consistent manner. No excuses, no victims, we are responsible for our own progress..but a professor with a schedule of some sort helps immensely.
Yup, heck some of tips don’t even work if have a disorganized prof who doesn’t have the students needs in mind
I study mechanical engineering, and I have an other tactic. I think your way consumes a lot of energy and time, and most of us cannot keep up this routine along the semester, when we are on full of compulsory homeworks, exams/tests and we have so many classes. My way is to take the hardest exam problems, and sweat, even if your knowledge isn't enough. It forces you to check your notes/books, the information can be memorized better, because you need that particular solution, and the best part, is that you're facing the problems, you will actually get on the real exam.
Worked in the most of the cases.
Hello I’d like to ask how your grades were using this method
Hello. In Hungary, the grades are from 1 to 5 (1 is worst (not pass), 5 is best). The last 2 semesters I had averages 4.2, 4.5.
Consider combinating the two methods, success guaranteed.
Okay boss... I will definitely try this. 😃
Trying to recollect: before class 1. review last class, 2. preview this class.
During class: 3. active learning, 4. questions, 5. annotations
After class: 6. review notes. Full understanding. 7. More questions. 8. Concept map
Gonna try this in my classes, see how it goes
Hope it helps!
I wish I saw this before the start of the semester.
Other than the class preview which I should be doing and very lazy to do. All of the tips are actually tried and proven in my own study routine. Great video.
haha laziness gets all of us! I do TRY to still do this any time I go to a colloquium or seminar but can't say I do it 100% of the time.
Best channel for learning math skills.
Glad you think so!
Wow thank you Prof! You are the best!
This was really interesting. Thanks for sharing
I mean that’s good tips but this is jot doable for everyone. In my case I have class from 8 AM to 18-19 PM and after that I need to go home I’m tired as hell and I still need to work like crazy to be well-ranked in my class. And I just cannot prepare what we will be covering during the next class, and it’s often not even possible cause we don’t know. We are all late on what we’re doing in class I mean that’s usual where I am, holidays are simply make to be on point for the next period but I will still try to apply some of the tips you gave.
This was a really good video and even though it’s not the best for me, I’m pretty sure it’ll help a lot of students
(Sorry if I did mistakes)
Keep up the great work :)
I"m sorry to hear your schedule is so jammed packed, you are right if you can only ever do class+homework, then it is hard to gain the benefits from the types of tips I was talking about
Damn! I never went for preview or post-class reviews. Now, I know where I lost some of my grades during my undergrad studies. Thanks for this, will try to follow this strategy for my grad school.
It's if anything more important in grad school! If you're going to a seminar, its so easy to get lost in the firsts 5 minutes, but with a big of gaining familiarity with the basic concepts you can end up following the full hour
@@DrTrefor thank you for this advice ❤️
Just mind blowing.
Wish to have such a brilliant Professor. ❤️👌
Thank you!!
So happy this video came up on my recommended page. Love your channel!
Thank you!!!
very good! i agree, but the thing is we don't have our books until 2-3 weeks before exams and we don't know what the teacher will teach
Hello professor I am a Moroccan math student and I am glad to find your channel it sounds interesting 💪.
I finished my third year at university but I couldn't study a master this year for some circumstances but I am studying in my own .and I want to study number theory .yesterday I started by the book "introduction to modern number theory "please professor reccomend me some great books for number theory and algebraic topology as well professor
Thanks infinitely
Brilliant techniques. I'll definitely try these in the upcoming spring term. (Already shared this video with my friends)
Thanks so much for sharing, and good luck this semester!
Love this video! Thank you for a reminder. Just in time before the new semester starts.
Thank you so much!
Great advice to start the new semester off right!
Hope your semester is great for you:)
Most of the advice in this video requires you to spend more time working during the semester for courses without deadlines. Since you probably have enough deadlines on your plate already and don't have time to consistently maintain such a heavy routine, consider the following: Make a priority list of subjects ranked in terms of difficulty and apply these tips to the first few in the list.
While definitely true, it isn’t zero sum. As in, if you do some of these, likely your assignments happen faster as you go in with stronger content knowledge.
Thank you sir...
it really solidified my thinkings about how really I should study.
hope it helps!
Thank you, I'll make sure to use these tips during this new semester!
Good luck!
Post class - defintely agree , this is great advice
Thank you!!
If MATH IS REALLY HARD, then whoever be the Professor, most students will tell it hard.
But this is not the case.
There are Professors, who make things interesting, and easy to understand.
Their students are mostly satisfied and progress in a continued manner.
Hence, the more important thing is ----- who is teaching the course, and how much effort and time you are putting in problem-solving.
thank you for this, sir XD one of my fav math channel ever!
You are most welcome, thank you!
You are a great teacher! I have seen all your videos on calculus.
Thank you so much!
It sucks I only saw this while cramming. So be it, I have to apply this for my future courses, Thank you!
haha I rarely highlight long passages of text, but I usually put a star next to something I think is important. I think it's funny how we chose that symbol.
Bang on as always. Happy New Year Trefor!
Thank you Steve, appreciate that:)
I need one of these for how to organize my PhD; great work!
That’s actually not a terrible idea except.....I was super disorganized in my PhD lol
I am trying to apply your tips to your calculs playlists ! Thanks so much professor
Good luck with Calc!
My problem at school was that I was only mediocre at memorization. Therefore, my goal during my studies was to avoid memorizing.
I think that made it possible for me to study physics very effectively. This should also apply to math studies.
Thank You, Dr for your efforts!!! It is a great routine to start within the new year. I learned a pile of new information in your Calculus III and Discrete Structures Courses :) (Starting with Calculus IV and Differential Equations after a little)
So glad my courses have been helping. Good luck this semester!
@@DrTrefor Thank You
very helpful tips...thank you sir..
and happy new year
watching at 1:19 am here 😁😁
Should add a new study tip: go to bed! Lol
@@DrTrefor 1:33 am here
@@DrTrefor 😂😂
Brilliant! Thank you for the tips
My pleasure!
thank you very much professor trefor , keep going
Attend the Professor's and Teaching Assistant's office hours.
(1) In the real world, these technical professions are very social: you will need to talk with a lot of people to solve problems.
(2) Few students show up for office hours. In addition to discussing lectures and homework, building a rapport with the faculty and staff is a critical networking activity.
(3) Organize "Problem Set Parties" with a few classmates. Talk about lecture material, discuss approaches to homework solutions, and formulate qualitative solutions to develop an intuition about what a solution should look like.
One thing that i always wanted to ask that how to deal with the temptation that you get after the course progresses , "Oh i dont know the basics, once i know all those basics day by day, i will be in a position to understand this, then that one day never comes" so i want some tips, when you have missed a lot of points in the class before (genuinely) , then how to catch up with newer material , like should i understand as much as i can ,push myself a little bit while siimulatenously revising all the other ones. Any tips ?
Bonne année = Happy New Year professor and colleagues 🎊🎊🎊🎊💕
Bonne annee to you too!
I got this video suggested. I like how you explained everything well detailed. We have the same math book " Thomas". It is a well written book. I am studying computer engineer
Love Thomas!
Aaaaaaawwwweeesomeeee tips, I'll start to practice those ones. Thanks so much teacher, greetings from Dominican Republic.
Amazing as always. Thank you for your tireless efforts. Though I can't say for sure, the collection of courses (Calculus, Linear Algebra, Discrete Mathematics) on your channel seem to suggest you have some background in Computer Science. Anyways, so, where do we go from here? A full course on Differential Equations? on Probability & Statistics? on Real Analysis?
Indeed differential equations starts next week, and PROBABLY stats after that, but I might tak ea semester off and just make fun one-off cool math videos as opposed to a proper course
Very cool video man, you are awesome!
Hey, thanks!
hats off to you
very few teachers/tutors/Profs are involved and teach with such enthusiasm
Will you do any statistics video?
Thank you! I mean to do a stats playlist, but not this semester:)
Ok UA-cam I'll watch this!
thumbnail is how actually this works ..... anyways Happy New Year.
Happy new year!
Thank you!
09:20 Yeah but if you study like this and your friends dont you still miss out on social interactions.
The studying before class tipps also seem directed at someone who already knows how to study. its too general advice.
Often being attentive for 90 minutes of University math was asking too much. If i looked at the script beforehand i could stay focused longer because i already grabbed the vague concepts.
In total i had the best results in classes where i effectively read the entire script 3 times. And it didnt really matter if did everything just before the exam or continously throghout the semester. Just go through the thing 3 times. And make sure you have someone to ask if you get something terribly wrong.
2:39 Great, you use (or at least have) the same book I'm reading
great video from a pedagogical perspective!
Props to your new microphone :) The sound is excellent now
Ha thank you, it’s much better!
Thank you very much for the video... could you also talk about how you approach your research problems ? Thanks in advance.
Great!
The best way to succeed in a class: to learn 90% if the material beforehand by self-study.
liked for the algorithm, and funny enough im procrastinating on my diff eq hw by watching this
Dr. Trefor,
1. What is the name and author of the calculus book you used briefly in this video ?
2. What is the name of that iPad software you were using for notes (I am a PC person)
Thank you, Bob Wilmes
P.S. Can you print those notes on printer ?
I think his notes were on OneNote, the Microsoft note program
Thank you so much. I am a 1st year bachelor's math major student.
I never went to college :(. But one thing I always struggled with is how do you learn when you have to write so much from the teacher? I couldn't write as fast as my fellow students. So I sometimes missed things in writing and I certainly missed the point of the lessons because I had to be this fast. I have never understood this way of teaching. I didn't learn much in those lessons. That's why I am also am afraid of college. I am someone who needs lots of time to get concepts. It would be far better if you could film those lessons for you to learn from and participate in class when you are filming it. That way you could follow the class and interact and also learn afterward. Have a great New year by the way, from Belgium.
That totally happens to a lot of people, and it definitely sucks because if you are going to class and it’s too fast that just isn’t helpful. I usually try to help people find strategies before and after class so that the class time becomes understandable
@@DrTrefor Yeah that would have been great. My teachers were of the kind they didn't really cared. I love learning things. But I don't like to many distractions (I have Aspergers) or things that take away from learning like so much writing besidesusing it for the essential things and practice(I know many like to study that way, but that is not for me). Sadly writing is still so ingrained in school. I mean as a way to copy things that the teacher says.
Thank you a lot.
You are most welcome!
I really like writing questions on the sides of my lecture notes as well! What do you do in a lecture when you are just completely lost? I know for the next class, you should do more previewing, but what do you do at that time?
Also how many hours do you put between the class and reviewing your notes?
That's a great idea! I don't think the time gap matters SO much. Within a day or so? THe longer you wait the more effort it will be, but that isn't necessarily bad.