40 Hours to Learn Mental Math | The riveting conclusion?
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- เผยแพร่เมื่อ 22 พ.ค. 2024
- It can't be true! I finally published the update to my "learning mental math in 40 hours video"! How many eons have passed? First part is here: • I Learned Mental Math ...
00:00 Last time...
00:40 Is tracking my hours helpful?
01:08 Is the diagnostic test a good measure?
01:55 Speed vs accuracy
03:22 Interleaved vs deliberate practice
04:54 The importance of seeing progress
05:50 Midway diagnostic results
06:15 Practice and performance gains
07:08 Skill integration
09:33 What the test measures
10:12 Are your mistakes changing?
11:15 What I’m focusing on next
12:21 The major system
14:17 28 hours in
14:39 The development of intuition
16:29 35 hours in
18:38 The return of the major system
19:45 Lessons for learning something on your own
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The math course I was working from was: www.thegreatcourses.com/cours..., but Arthur Benjamin also has a book teaching the same things: bookshop.org/a/91541/97803073.... The bookshop link is an affiliate link so I get a buck or something if you buy it through this link (thanks, if you do!).
Some thoughts on interleaved practice: • Secrets of Interleaved...
Some thoughts on deliberate practice: • What People Get Wrong ... (tackling some myths about deliberate practice); • Is deliberate practice... (on criticisms of the deliberate practice model)
A quick intro to the novice to expert transition: • What happens when you ...
I am learning: speaking and understanding mandarin, penspinning/juggling, poker (estimating ranges, pot odds etc) - and I would like to learn pencil drawing, handwriting/caligraphy, skateboarding, abacus, slide rule, crochet. I love this channel, and you give me a lot to think about for the kinds of things that we choose to learn and what kinds of approaches to take. Thanks Ben!
Missed two important ingredients - image streaming and n-back
jeeez man get a life.
I commented on your first video, and I've been doing mental calculations for 50 years. It's all mental, and nothing on paper.
It seems to be helpful to focus on the basics while practicing. I do not take shortcuts while practicing. For example, if I were calculating 268x99, I'd think "200x90 is 18000, plus 60x90 is 23400, plus 8x90 is 24120," and so on.
If I were asked to calculate the problem by a friend, I'd calculate (268x100 - 268-1), because I'd be faster. In practice I don't like to use shortcuts, because different shortcuts are necessary in different situations. If I totally break a problem down, I can always do it the same way.
I've been waiting for this video since the first one. It's a great experiment and good to see some of the research applied! Thank you :D
"How could you have known unless you would have explored?" A good way to say you don't know unless you try. Many great tidbits on learning in this video. Look forward to videos like this where you use the science and test it out .
This format of following your journey while hearing an in-depth analysis from a first person pov - that is awesome and rare. please Benjamin do more videos like these. It gives us a unique pragmatic view of the actual application of theories.
Oh, and your channel is pure gold - the best of the best 👏🙏.
I'm not sure if you ever addressed this before, but can you sometime make a video about learning techniques or approaches which apply to kids/adolescent? I'm not sure if this is a special case - but it would be interesting to hear your thoughts about it.
Noticing your mistakes and using your experience to guide you to develop better in a skill blow my mind. I feel like I don't do this enough, before in high school it was easier to be on the "swallow" place of learning how to learn, but now in college I FEEL that I in fact did not know how to study to learn better.
It really got me in a sad place, I felt so frustrated that I was struggling with studying, but that's cuz I had no structure to face the materials. I am still learning what is best for me, like testing what techniques are better and trying not get anxious about studying (something I developed because I was not getting good results). Seeing your video made realize how wrong I was before when I saw learning as a black and white thing.
Now I see how complex it is and that you NEED to pay attention to YOUR performance and deal with your mistakes, in a compassionate way cuz trust me, being angry with yourself for making mistakes it's recipe for sadness.
I feel like I have to take a step back on "learning how to learn" videos, cuz I always try what's on the video and don't pay attention to my results, they feel like noise than help. But anyway I love your videos, they are so real and practical u know? Definitely watching more after I got in a better place with my learning experience 😁
Thanks for the kind words - and very happy to hear the videos have been helpful. It can be easy to get angry at yourself for making mistakes or under-performing, but agreed that it's almost always counter-productive.
YOU HAVE THE BEST TH-cam CHANNEL OF ALL TIME
I'm going deer hunting for the first time this week. Hopefully I can notice mistakes in my cache/bait placement, tracking, and stalking. Loved this video and your thoughts, thanks for sharing your experience :-)
I think of this as a kind of ancillary skill. You learn how to do it as a separate activity, but it is in itself not useful, so learning will be hindered if there is not a primary activity that utilizes it. And performance will best develop in the use of that primary activity. As a means of testing learning strategies in the abstract or for the purposes of making a video, I think it puts you at a disadvantage since those things aren't inherently linked to mental math the way that, perhaps, calculating interest rates regularly might make use of it. It's hard to learn things we don't have real purpose for.
Thank you for this video. You provide a lot of value with this and sharing your effort. I can personally say it's impactful, especially your lessons learned at the end.
I don't know if you're accepting suggestions, but if it's something that interests you, I'd love to see your approach to learning from a textbook. Something with concrete problems, such as Calculus, Physics, Chemistry, or Intro to Electricity. Just a thought.
Something in the science area is on my list! Thanks for the suggestion.
One day I hope you take up apiculture.
B. Keep - Bee Keeper.
Thank you for doing this videos, your delivery is wonderful and never seems waffling or padded for time.
I really enjoyed this video, I have learnt alot
Please can u make a video on high order learning
Nice to see your efforts have paid of! Did you applied any mindmap/grouping or any other Higher Order Learning technique during this Challenge? Or Which were the "Encoding Techniques" you used to help you on this challenge?
I took the same course you did years ago. Unfortunately I stopped at the intuition portion and thus didn’t fully solidify the knowledge. For the time I had it, it was incredible. The answer would just come to me (unless we are discussing very difficult problems) I’m starting up everything again and I’m really missing that ease with which the problems were solved.
Musicians have a saying, "If you can play it slowly, you can play it quickly".
Sounds similar to what you're describing concerning speed vs accuracy.
I ran into a similar saying in martial arts: "Slow is smooth and smooth is fast."
The first thing I though during the video speed vs accuracy part was gradual tempo acceleration 😆
I thought I wouldn't share any experience with "learning mental math", but I was wrong.
When I was watching your old videos, I did notice that conflict between interleaving and deliberate practice.
The way I thought about it or rather around it.. was actually integrating interleaving practice into deliberate practice.
To me the most important steps in deliberate practice were these 3: identifying key skills (to find right problems), self-evaluation and expert feedback.
I would interleave problems, apply self-evaluation + expert feedback after each problem (I would eventually come back to those problems because of spaced practice), and as I got good at the problems, I would move onto more challenging problems while still interleaving with other challenging problems.
I hope this isn't counter-effective, is it? I am using this method for practicing mathematical, technical problems.
Sounds reasonable to me.
Amazing.
You mentioned in the end of the video that what kept the learning interesting is that you started seeing things differently because you were developing new skills and vice versa.
Is there a way to make that a milestone in the learning journey?
Design a learning program with an adaptative assessment approach to keep things interesting and/or help the learner realize his perspective has changed.
It's an interesting thought - I think sometimes we don't realize how much has changed over time. A very low-tech way to do it, and something that I've considered doing in online courses, is having students answer a question (or solve a problem) in the beginning, before they've learned the material, then answer the same or a similar question at the end and show them their prior answer. Ideally, the question isn't just about the skill, but also illustrates some conceptual shift.
I also think that it's about the orientation of the learner, as well. If you enter into the experience with a certain mentality (i.e., "I'm going to look for patterns and observe things that no one explicitly tells me"), it's a little bit easier to have the feeling that you're seeing something a bit different.
I did 1/6+1/12=1/8 in today's quiz in a taylor series question. I do need this video.
I thought after the test I have been doing problems too quickly just to get them done even at cost of accuracy for my whole life.
1/4
in a real-world context, you're much less likely to accidentally do the wrong problem, because the problem itself is only part of a larger problem, and the wrong sub-problem would plainly not make sense.
It's absolutely amazing what someone can learn with such a small amount of hours put in, really makes me motivated to learn more.
So you believe you should focus on accuracy before speed? Would this also be true for more procedural skills such as playing the guitar or something like that?
Also, the tan looks good on you. 😁
I learned playing the guitar for 8 years and yes accuracy goes always before speed. Somtimes it is interesting to play as fast as you can but usually you should focus on accuracy. Get femiliar with the piece and get your muscelmemorie to kick in. Than go faster and faster over time.
There is this series of free audio courses for different languages called "Language transfer" that teach you how to construct sentences in a very methodical way. They emphasize the idea of prioritizing accuracy, tell you to slow down, and encourage you to think everything through carefully ("thinking method"). In my experience, speed was a by-product of this process. You will often hear the author say that "we want to think slowly to learn quickly". Now, I don't think you could get really proficient in a language through this type of analysis, but I feel like it taught me something deep about the way our minds work. Processing something deeply may feel slow, but in the end of the day, is far more time-efficient. I recommend everyone checks it out, even if you are not interested in learning languages.
@@jb_1971Think slowly to learn quickly.... Hmmm wow. That seems like something fundamental to a deep learning process. Thank you for writing that comment
I agree with the other commenters here that the answer is yes. I think it can be fun to try to play things very fast, and playing things at different speeds probably helps skill development in the long run. But prioritizing speed as a goal is usually unhelpful, IMO.
How well do you suspect you will retain these skills? Do you think that mental math is something ubiquitous enough in your life such that you will be practicing the skills regularly enough to retain your new abilities? Maybe a video in a few months discussing your skill retention could be instructive. Love the video, love your channel.
For reference, I am a graduate student mathematician. I like the discussion at the end of the "tricks". Oftentimes, mathematicians may disparage a particular useful mathematical manipulation as a "trick", simply because it seems to come out of the blue. I am of the opinion that it is better to think of these things as techniques that you yourself don't yet understand. Thinking of these things as tricks is problematic in my opinion for the sorts of reasons you discuss at the end here: if we disparage useful methods as mere "tricks", then how are we ever to understand the intuition behind them so that we might derive our own useful "tricks"?
@@OwenEkblad completely agree it is always best to truly know how the "tricks" works and what they could teach us. over time it clicks and the nuggets of insight we got make their way into our thought processes and enrichen it.
I've been on tenterhooks waiting for the thrilling reveal!
One question that popped up while you were talking about plateauing was about spaced retrieval/repetition for motor skills, in my case piano. I've noticed that if I leave a piece for a week (or three, let's be honest), a difficult part becomes suddenly easy / easier, or I solve a particularly sticky problem. So I'm wondering if it is better to "skip" the plateau then come back later, or is it better to keep practicing at regular intervals?
I need you to create a videos about how to find out relationship between concepts in a text , and a several example about what kind of relationship we could find out. And why do we have to comparison concepts to figure out what is similar and different and why it's beneficial for our learning. And about grouping ideal together and how we group them , can I group them by common Or by relationships . I take These ideas from Justin sung video about bloom taxonomy and mind map ( sorry for my poorly English 😅😅 ) and
After the second test, you didn't specifically call it that, but you talked (what i think is) the learning plateau.
I have question which might seem silly, but:
Do you "overcome" the learning plateau happen as time passes, or as you practice?
If the latter, does that mean you can speedrun your way through it by practicing more than usual?
And, if the learning plateau is caused by your brain/body struggling to integrate all the acquired tools/techniques with each other, does that ever get easier? As you reach expertise (or merely proficiency), does this process ever get faster, or nearly immediate/automatic? Or would that depend on the complexity of the technique you're trying to acquire and how well it integrates with your current "toolset" of techniques?
Hey Benjamin, could you analyze Ali Abdaal’s ‘3-Hour Studying Masterclass’ and share your thoughts on the quality of the course? I would appreciate it. Love your videos.
how do you get better at literature class, is it simply just doing lots of practice essays or should I do something different
Bro do a vid on mind mapping and chunking
Hey! I'm learning arithmetic word problems for my competition. What i wanted to ask is that can i learn the same concept that i learnt from one teacher from another teacher. I have tried it before but don't know why it confuses me and make me question my knowledge(and existence). Is that a good sign or should i stick to only one teacher.
Hi Benjamin, I study different subjects during my own study session, do you think that’s okay? For example, when I am studying Math then the moment i’m stuck, i pick up my geography textbook, once i don’t understand something again then i go back to my Math textbook, sometimes i can solve the problem because of switching my attention to the geography textbook for a while, but I don’t know if it works for the long term, Im doing it because i have only a week until my exam and i am just trying to make sense of all the materials within a short period of time, what do you think? Do you think it’s okay to do that?
That seems reasonable - focusing on something else for a little while is something I do too.
I looked into your degree, Stanford offers a masters in it. How did you get a PhD?
I am too bad at math, I'll be learning too, great video 😊
A lack of progress in basic mental calculation is more likely poor practice and technique rather than an integration problem.
Have you tried Justin Sung's iCanStudy course?
how is your face orange and your neck white?
I like watching you, I don't like this subject(boring)
Vedic math is better
Its great but its not a complete system unfortunately.
No offence meant, I can not tolerate the sound of Keep’s voice.