I Learned Mental Math In 40 Hours
ฝัง
- เผยแพร่เมื่อ 11 พ.ค. 2024
- Watch me put research-based learning principles to the test as I learn mental arithmetic. I use testing, lots of relevant, deliberate practice with feedback, spaced practice, interleaving, and review to learn to become as good at mental math as I can in 40 hours.
0:00 An introduction
0:20 The plan
1:08 How I apply the science of learning
3:29 My first diagnostic test
4:20 Reflections after ten hours
5:06 I'm noticing patterns
6:23 How to use practice tests to learn
8:47 Ten hour mark test
9:17 Next steps
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Here’s the link to the course I’m using: www.thegreatcourses.com/cours...
The link to the book I mentioned: bookshop.org/a/91541/97803073... (I'm a Bookshop.org affiliate, so get a commission if you purchase through this link).
REFERENCES:
For a readable introduction to interleaving in math from the teacher’s perspective, see: pdf.retrievalpractice.org/Inte....
For more background on interleaving (like so many of these principles, it get’s complicated), see: Firth, J., Rivers, I., & Boyle, J. (2021). A systematic review of interleaving as a concept learning strategy. Review of Education, 9(2), 642-684. bera-journals.onlinelibrary.w...
For more on spaced practice, see: Latimier, A., Peyre, H., & Ramus, F. (2021). A meta-analytic review of the benefit of spacing out retrieval practice episodes on retention. Educational Psychology Review, 33(3), 959-987. www.lscp.net/persons/ramus/doc...
For evidence supporting the “keep testing learned items” idea, see this classic: Karpicke, J. D., & Roediger III, H. L. (2008). The critical importance of retrieval for learning. science, 319(5865), 966-968. psychnet.wustl.edu/memory/wp-c...
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Combining your videos, Justin Sung's videos, Andrew Huberman's podcasts, and my own neuroscience and psychology knowledge of learning has helped me incredibly refine my own learning system, learning knowledge, and it's absolutely amazing. Thank you for doing what you do.
I hope some day you gain a massive reach. You are absolutely a hidden gem.
Thank you!
Absolutely! Dr. Keep is a national treasure lol
Quick question about Andrew Huberman's podcasts, which episodes did you find relevant to learning?
@@jimmyvo1667 Oh man, there's a lot. I have about 40 episodes in a list that I compiled, but I can't send that list here, so if I were to summarize my thought process in choosing which episodes relate to learning go with any mentions of learning, neuroplasticity, and the "Arrow Model of Focus" which is based in the neurochemicals: acetylcholine, dopamine and norepinephrine. Dr. Huberman has a playlist of all 132 episodes of his podcast available on his channel, so you can click on what podcast episodes has mentions of learning, neuroplasticity, and if any episode has mentions of the neurochemicals mentioned above, then it's worth checking out.
What is your system?
@@isaacp.m.305 My system is largely variable to be honest because it's going to be dependent on what it is I'm learning (skill, cognition heavy, varied combination of both), my motivation to learn it, and what amount of any relevant past information can I use to help my learning be better facilitated. However, if I were to try and list principles of my system it'd be this: I CREATE my BEST model of what the topic is about from what I already know/understand/can do, then from this model I punch out inaccurate bits of information by reading literature or other resources or by being corrected in the way I do something or correcting myself in the way I do something based on what I learned. During the bits I'm reformulating my understanding network/knowledge structure, I'm confused or I'm thinking really hard about how this information is important. In some moments I can't help but encounter isolated information, classic, common, stereotypical study tips are used. Now, this is really abstract and it's not really useful if you don't have specific things, so I think to help put this into a more practical perspective let me use an example.
Recently, I got interested in the general science of singing. What are the mechanisms of singing? What's the brain doing when a singer (or singers) sings/sing? Because I do sing myself, why do I get emotional when I sing certain genres? Here's the real question: why am I even curious about the science of singing in the first place? I answer these questions using my own personal experience with singing myself as well as what I already know about singing. "Well, mechanisms of singing obviously involve the throat and diaphragm because singing practice and singing improvement videos on TH-cam say these use them and are the most important... and my experience matches that too. Diaphragm is the part of the body that allows you to consciously direct your breathing which allows you to use your throat and voice" etc. Etc. And with these answers in my mind, I've already created a model, some kind of conceptualization of science of singing, that I can now refine and sharpen out the edges of by reading what many and ALL kinds of science papers or what MANY academics say and teach about singing. "OOOHHH So when a person wants to do metal screams or fry screams, the vestibular folds of the larynx is used. I knew I was going somewhere with the idea that singing involves my throat, but that's super interesting how the vestibular folds of the larynx is used in that way and it explains why it doesn't hurt to do metal screaming... I didn't know that the recurrent and superior laryngeal nerves are the nerves involved in singing and pitch change. In fact, they also portrude from the vagus nerve which can explain why singing can be very relaxing and emotionally freeing (i know some bits of what the vagus nerve does)! That's cool!" Lastly, the reason why all these findings are important to me is because I want to improve in singing myself which is why I'm looking into the science of singing in the first place... to USE it. I find that knowledge is much more relevant if you can use it, and even better if the way you can use that knowledge is exemplified in behavior, the literal movement of any kind of the many many muscles in your body. This is just only a TINY snippet of my system, and I hope that this answers your question of what my system is.
Sorry for the long winded reply, but if you want the TL;DR of everything: My past experiences allow me to think of a model of a topic which I can then refine using accurate resources as tools to make my model more accurate as well. It uses everything from encoding and retrieval practices, contextualizing information, Dr. Justin Sung's "HOTS (higher order thinking skills)", chunking, priming, cognitive architecture, neuroplasticity principles (I didn't even go into the biological side of my learning system), personalization and etc. It's a lot.
Bro i love this channel. Love this new form of content.
Great project! You should do something similar for a factual and conceptual knowledge based subject as well.
You got it. Just gotta factor in the usual delays, but it is on my list!
Thanks for the resources and great content!
I've been doing mental calculations since I first learned the addition tables, so it's been about 50 years. I can tell you that there's a HUGE difference between mentally working a problem that you can see on paper, and working a problem that you only hear but never see. The latter is far more difficult, and that's what I specialize in.
Long-term and short-term memory are both important, and there is no sharp division between them. I choose problems that take days, or sometimes weeks, to work, such as non-integer square roots up to forty digits or so. Not only do I have to calculate the correct answer, but I have to check it for accuracy without using a calculator.
As the years have passed, I find it easier to pick up on such problems exactly where I left off, even if hours or days have passed. When I was younger, I would generally have to start over at the beginning of the problem, though the parts I had already worked went quicker the second time because I recognized the work. It seems that my short-term memory and long-term memory have improved greatly, even as I passed age 30, where memory is supposed to begin a decline.
My memory is already supposed to be declining in my late 50s, but I've seen no evidence of that yet and in fact I continue to improve. I imagine that my calculating ability will level off and then decrease sometime soon.
Jeff, I've noticed something similar.. in a much smaller scale. Any suggestion for someone strating this practice? Thank you!
This is so helpful, thanks for sharing! :)
For learning multiple digits, the issue seems to be memorize vs. calculate.
For calculate, it is memory capacity (hold onto numbers for longer) or faster calculations.
Woah, my family bought that video course by Arthur t Benjamin when I was back in elementary and I loved it! What a throwback to a cool time
Fantastic video! Shake you for sharing your experience
Thank you. Perfect video
Your videos are great! ❤
Awesome video Ben! I can't wait for the next update. I've been thinking about learning mental math for a quite a while now, but never got to it, so this video came perfect! Love your videos, they've helped me so much. Greetings from Argentina
Saludos - thanks for watching!
Yess please do a similar video on conceptual knowledge (science). These really help to put the learning science into perspective so it's easier to implement them
You mean I gotta do the hard stuff too, huh? : ) Definitely plan on doing more in that direction. Glad it was helpful!
Using your content I've devised a sort of learning system for me to follow when learning new material in university. IT is divided into 3 categories (Pre-lecture, Lecture and post Lecture)
Pre Lecture
- Preview lecture
- Identify Main ideas
- Identify gaps in understanding
- create notes
- Create Goal for class
- Specific and measurable goals for class. (Identify core concepts, Learn Core Concepts, Answer gaps in understanding)
Lecture
- Active Learning
- Identify core concepts
- Elaboration - Connect what you are learning with previous knowledge
- come up with analogies
- In own words periodically summarize lecture
- ask questions
Post Lecture
- Active Recall
- Creation/Analysis/Evaluating (Engage in Higher order thinking)
- Feynman technique
- **Mind map from memory/Free Recall - explain relationships of ideas**
- Practice Questions (if available)
- creation questions based on notes
- Desirable Difficulties
- **Spaced Repetition**
- Interleaving
- Variation
Basically my question is this type of system missing anything? I've always wondered if adding more techniques would be chasing for marginal returns. Have you found an "endgame" system for yourself? If so that would be my video suggestion.
Nothing you wrote seems unreasonable. It's hard to answer questions like this in the abstract. I tend not to be wedded to particular learning systems. What you want to do depends on the goals you have in mind. I would let your own sense of what you know and can do (which is developed through practice/feedback cycles, self-testing, free recall, etc.) guide your next steps more than following any particular system.
Good job, this is what i was looking for , i wanted to see an application and a practice for the abstract ideas you explain in your videos, thank to you now i can see whether i'm doing well or not applying those theories about learning
at first the video title didn't attract me, but after watching the video i discovered that it wasn't about how to learn mental math but implicitly about how to learn , this is also taught me to not judge things before trying 'em
I'm working on more videos like this one (me, trying to learn something and talking about learning challenges along the way).
Thank you.
Excellent content!!. I would like you to talk about reading techniques to understand and retain more information.
Thanks - I've got a couple of videos coming up on those next month!
I should probably try that :)
I'm going to be a law student soon. I've searched all over and other influencers for best law school learning techniques. There's not much out there. Other than the IRAC method to understanding cases, and as a JD yourself, what can you recommend and would you please do videos on law school studying? Please and thanks!
I'm gonna be doing this
I responded to your answer in the last video. I am waiting for your response and don't worry take your time. Underrated channel.
I replied - thanks for waiting!
I can't seem to find the next video... :(
Mental math with inattentive adhd is just too difficult, I can calculate them as fast af on paper but once I only hear the number, they just dance in my head.
no Q&A?
I wish you could do this challenge for a foreign language, there is very little information on how to learn a language, is Krashen's comprehensible input the way to go ?
Great video!
Question: Will my input-output ratio look different If what I'm trying to learn involves a lot of reading textbooks and studies and trying to understand knowledge from them?
I don't have any hard and fast rule, but I think output should still be higher than input, or at least about on par with it. You need time to chew on the material (for lack of a better word). A lot of the learning is going on during "output".
Another way to think about it is, if you want to maximize what you get from the reading part (the input) you need to be doing some output. Because then you come back to the reading material with the right questions, with a better handle on the fundamentals, key concepts, and it all makes you more prepared to build on what you know.
What, exactly, this output looks like depends on the material. But routinely doing free recall after each chapter and, perhaps, a summary free recall would be a good thing to do. With science texts, addressing conceptual questions or solving problems with the material would be a good way of doing output. With history texts, writing about the material or explaining it to others is a good thing to do.
Whatever you do, I would flip-flop between reading the texts and doing output. If you read 10 chapters before you start doing any free recall or self-explanations, you've missed good opportunities to learn from the material.
@@benjaminkeep Thank you, your answer gives me reassurance. After watching nearly all of your videos I've been trying to change the process of how I study and learn things. I've noticed my INPUT(reading material) - OUTPUT(free recall, writing and doing mind maps without looking at the material - i.e. trying to figure stuff out on my own) ratio has drastically changed. Its probably close to 5-10% input and 90-95% output at this point and sometimes it still feels "wrong" to study like this, even though I actually feel like I'm learning things now and in many instances I figure stuff out before actually reading the material, ha... also studying this way actually feels enjoyable and rewarding!!
I'm so glad to hear it! One of the unexpected things when I first started doing free recall more regularly was how much I liked it. I'm excited to sit down and wrestle with things.
congrets for ur corage
Benjamin, do you think that practicing mental math could improve working memory?
Yes it can
What books or resources would you suggest for a college student that wants to improve their study system in general? Mainly I want to improve note taking, revision, and focus.
You might try "Make It Stick: The Science of Successful Learning". I also like "The ABCs of How We Learn," which will give you a much stronger background in the levers that you can play with to improve your studying practice.
Hey Benjamin!
Would you like to make a video about how to make a study routine effectively?
I'm getting problems with that, and I'm kind of lost. Lmaoo😂😂
Book suggestions about the science behind learning. Thanx
Two books that I frequently recommend are Make It Stick: The Science of Successful Learning and The ABCs of How We Learn. Both are written by experienced researchers and have plenty of examples. Make It Stick is probably more useful if you are a student; The ABCs is a more broad. Both are very readable.
The way I learn mental math in primary school was using an abacus and then imagine fiddling an abacus for the real mental calculations (the correct way) . I stopped learning it cuz i was actually forced by my parents to do so plus I've been memorising how different numbers add, subtract, mul, div together for the 4 years which according to my teacher is the wrong way of practice. Maybe you could try using an abacus and slowly your right brain can imagine an abacus and solve any arithmetic quickly. Not sure why this skill is popular in the Eastern world. Its called 珠心算 in Chinese. However Ive actually seen a mental math pro on the internet who can solve problems like 10digits multiple by another 10digits within 1 to 2 seconds.
Cool - not sure if anyone has compared the Vedic-style shortcuts that I'm using here to the abacus-style imagining. But I could buy that the abacus as a conceptual tool could speed things up, if you got good enough at it.
How to self study ?
Can you tell us how do you learn about these learning strategies ?what are the sources
I learned about them from going to grad school - "learning science" is a loosely connected field full of people who study how people learn.
I recommend checking out The ABCs of How We Learn (by Schwartz, Tsang, and Blair) and Make It Stick: The Science of Successful Learning (by Brown, Roediger, and McDaniel). Both summarize principles distilled from the past 50 years or so. The first one is a bit broader and more geared toward teachers, but does a nice job of contextualizing when a certain principle works and when it doesn't.
I do my best to keep up with the latest research, mostly through trawling Google Scholar. But there's a lot of new stuff out there and learning is a big field. I have other videos talking about how to read and understand this research in the works.
❤
How can these your method be applied (if it can) to math courses at university. University math would be more complex but it is still procedural knowledge.
The following principles apply:
Spaced practice - aim for problem-solving sessions spaced out over time.
Interleaved practice - don't solve problems in sets of similar problems; they need to be mixed up most of the time.
Testing - use tests/problem solving as the main thing you do during "study time"; don't re-read the text or re-watch until you've identified a specific problem or question. The general process should be: take a test or do a problem set, identify mistakes or issues, re-visit course material if necessary, do it again.
Keep the fundamentals around - it doesn't hurt to review some old stuff now and again. This is consistent with spaced practice.
Problem solving in math and science across the board shares certain features: there are problems and problem solving tools (in some cases these are algorithms, but also visualizations; in math there's proof techniques; abstract concepts like parity, etc.), and the goal is to leverage the tools to navigate through the problem space to reach the solution. So a lot of the learning that goes on is similar, too: learning which problems have a similar underlying structure (even if they look different) and which problems look the same but are actually fundamentally different; expanding your mental toolbox for solving the problems; expanding the contexts to where you can apply the tools. There's a fair amount of conceptual learning that goes on during problem solving, too - we don't instantly understand concepts from just reading or hearing about them - we have to see their limits, novel applications, etc. We deepen our understanding of concepts over time.
has the follow up for this video come out yet?
Not yet sadly. I am working on it!
where is the follow up video?
Er... uh... SPACED PRACTICE...and...uh....😅
Still working on it!
i cant even do basic math at work. cant understand numbers at all.
I hear you - still make a lot of mistakes with this stuff myself. A friend struggled with math until he had a handful of tutoring sessions as an adult. It helped him feel a lot more confident.
Personally, I always found visualizations of basic math to be helpful (like interpreting multiplication as area; exploring square and triangular numbers; seeing some of the relationships between adding and multiplying). Once you start seeing patterns, it gets more fun.
Like 3 * 3 = 9. Multiplying the numbers 1 below 3 and 1 above 3 we get: 2 * 4 = 8, one less than 9. Hmm...
4 * 4 is 16. Multiplying the numbers 1 below 4 and 1 above 4 we get: 3 * 5 = 15, one less than 16. Always true? It almost seems like we unlocked a secret.
Try jujitsu next, please. 🙂
I didnt understand what he was trying to say with contextual variation so here is what help me understand it: "Contextual variation is when learners are exposed to the same concept in two different contexts. When building in contextual variation the concept remains the same but the context is changed, making the original concept more salient to the learner."