> As an undergraduate student, I found that writing a summary of everything I had learned in a class was one of the best ways to study for an exam. I would just sit down with a blank piece of paper and try to summarize everything as precisely as possible. Ultimately, writing your own textbook would be a very effective way to learn the material.
Amen.
Back when I was tutoring a lot, I used to ask the students to keep a "master formula sheet" and continuously add formulas to it. In the final review session, I asked them to explain each math formula in plain English, e.g F=ma --> forces cause acceleration (and the acceleration produced by a force is inversely proportional to the mass of the object). I could immediately tell who understood the material and who was trying to get by on memorization.
Another useful exercise is to pretend you forgot your "formula sheet" and try to reproduce it from scratch. If you can't it means you're not solving enough problems---after solving 5-10 problems using a given formula, you start to remember it, and not as a string, but as an idea. You can forget a string; you can't forget an idea.
I used a similar technique. In undergrad and grad school my studying consisted of typing up the notes from class and summarizing the book chapters. I was always amused when people would ask me for the notes without realizing that the act of creating them was the study part. I rarely looked at them after the fact.
That's right. You train to recall, by recalling. This was a big revelation for me when I studied mnemonics.
Information can flow in two directions: into your brain, and out from your brain. It is the act of repeatedly retrieving the info from your brain that strengthens your memory of that info, not the repeated input of that info into the brain.
In college, I returned a textbook before I opened the shrink wrap when I realized the student next to me was highlighting verbatim from the textbook what the professor was talking about. Writing everything down saved me >$100 and earned me an easy A.
I seem to mostly remember them as strings orthogonally to the idea. One particular example was "x equals negative b plus or minus square root b squared minus four a c all over two a" set to "pop goes the weasel" in high school. After knowing that for a while I came across a visual diagram of what the quadratic formula and completing the square actually mean and it wasn't until then that I understood them. Some formula formats I recognize more by shape/appearance such as the g = G m1m2 / r^2 form that applies to some contactless forces.
I was briefly a college professor. The thing I took away from the experience was - if you really want to learn something as well as possible, teach it to a class of 60.
There is a coursera course called "Learning How to Learn"[1] by Barbara Oakley that is starting soon. I took the previous session and it was very interesting. I liked the science[2] behind each part of the course (procrastination, memory, modes of thinking etc). The weekly interviews were certainly a big plus (however they were usually long at ~40 minutes).
It's a fun four week course with very little work and I recommend it.
If I were to pick one part of that course to share it would be the explanation of how long term memories are formed through practice (1-6 Introduction to Memory).
Knowing how something actually works, and knowing precisely how my actions achieve the desired result is important to me. I'm very skeptical of study techniques, and more interested in the underlying physiology that I am trying to manipulate.
Long-term potentiation (LTP) "is widely considered one of the major cellular mechanisms that underlies learning and memory."[1]
Spaced Repetition[2] and Spaced Learning[3] at techniques directly designed around LTP.
The course content is locked, but there is a fantastic paper that gives a thorough overview of what we know about the behavior of memory[4], as well as a video series by the principle author[5] linked below.
This is kind of my thing. Please let me know if you are interested in learning more, or if you know of additional sources you'd recommend I check out.
I have found Part II of Luc Beaudoin's book "Cognitive Productivity"[1] to be very interesting. It presents a theory of learning using a "mindware" model in which learning is the purposeful instilling of mindware[2]. His core strategies for "instilling mindware" include deliberate practice and repetition. I'm no expert in this field, but I've found Beaudoin's model to be helpful in understanding why deliberate practice works--it helps develop the "monitors" we need to recognize when knowledge is applicable, the "motivators" to push us to do something about it, and the knowledge itself. I don't know how widely accepted his theories are, or if there are other accessible sources, but I've found the book to be very useful in thinking about how I learn.
Other sources commonly cited by Beaudoin include Carl Bereiter, K. Anders Ericsson, Keith Stanovich, Phillip Ackerman, and Aaron Sloman. I hope this provides as much fodder for you as it has for me :).
Actually, you can view both previous sessions. I am not sure if you can do it without previously registering for the course since I registered for both previous sessions. I am sure though that you have to login to view the content. Here are the urls:
What a great reference! Awhile back I wrote down "learning to learn" as one of my outside-work goals and didn't really know how to approach it. It seems like a force-multiplier for everything you can do - I look forward to the course!
Thank you. I am embarking on a course of independent study which I expect to last for a year to four, and I have a feeling that this course will pay for itself in both time, effort, and increased understanding.
I like this article in large, but sometimes it really is appropriate to blame the instructor/textbook if you feel confused.
Everyone wants to believe that the harder and more painful an experience is, the more you got out of it, but that's not the case.
Imagine if you took a math textbook and then removed every fifth sentence. It'd be way more confusing, way harder, and require much more struggle, and that struggle would be a waste of time.
Struggle matters, but you need to struggle on the right things.
You intuitively know a bad teacher from a good one.
When I learned programming both my teachers left me confused.
But I rapidly understood that the first was hard to understand because he was a sort of genius and you had to get to speed if you wanted to follow him, the other was just an incompetent lazy bastard that was there just for the pay (I remember asking him once a simple question on his domain specialty, he just resorted to Google and didn't even find the answer !).
You're absolutely right, but I think it's wrong to say that most people think a harder and more painful experience is better. The sad truth is that school is no longer set up to be challenging in any way, and that is in fact a bigger problem than the more subtle issue you point out.
I would absolutely recommend the book that's mentioned at the end of the article:
"Make It Stick: The Science of Successful Learning by Peter C. Brown et al."
It's a great read for anybody who wants to continue learning new material. I'm one of the people who had very poor studying practices beforehand...
Marked to read, thanks for the recommendation! Moonwalking With Einstein is also a good read, albeit more for pleasure and insight into our brains than any practical applications.
The Learning Style theory is junk with the flimsiest evidence, but tell that to any teaching institute in this arena so obsessed with constructivist ideals. The reason I did not continue on to teach physics was partially due to an insistence that it was teachers who needed to expend more effort to make classes "fit" a student's preferences so that their learning would be a gradual climb. You learn material by flailing, not by floating.
I am a dyed-in-the-wool constructivist and I think the theory of "Learning Styles" as it's used today is rubbish. It's a mistake to think they're attached at the hip.
By "the theory of Learning Styles", I specifically mean the idea that some people are "auditory learners", "visual learners", "kinesthetic learners", etc. and that part of a teacher's job is to figure out which "learning style" best fits a given student and present them material in a manner consistent with that style.
I'll add that in the "literature" these things are called "learning modalities" and "learning style" refers to something else, but I've never heard someone use "learning style" and not mean learning modality.
It's also ironic that you use the phrase "constructivist ideals."
Constructivism has deep roots in the American philosophical tradition of Pragmatism[1]. C.S. Peirce coined the term "pragmatism" to contrast _specifically_ with the Kant's transcendental idealism. One of it's core epistemological tenets is that the only thing we can be sure of is that certainty is impossible.
In _The Quest for Certainty_[2], JohnDewey himself called out the "fallacy" of philosophers in taking abstract categories (e.g., "Visual Learners") for granted and not seeing them as conceptual tools invented to solve specific problems in a specific context.
Like you, I find it frustrating that many educational thinkers take these concepts for granted and deploy them in a classroom environment as if it would be absurd to ever do anything else. However, if you read any early Pragmatist thinkers like Oliver Wendell Holmes, Jr., C.S. Peirce, William James, or John Dewey, it's clear that rejection of this maneuver is one of the central themes in everything they write.
Perhaps I should clarify. I am not claiming that there is a superior educational philosophy. I am only claiming that in most modern educational institutions, constructivism is the practiced philosophy of education and is taught to all teachers. These institutes often also hold a belief in the idea of learning modalities and, contrary to the foundations of constructivism, preach these ideas quite blindly without regard to their flimsy evidence or poor performance when put into practice.
I was agreeing with you while simultaneously pointing out that you, like the folks you're criticizing, are conflating a constructivist model of learning with a handful of specific approach to teaching derived (mistakenly, IMO) from that model.
Just don't throw the constructivist baby out with the bathwater. :)
As a counterpoint, the Logo programming language[1] is an example of a well-executed pedagogical approach informed by constructivist thinking.
Yes, exactly. One can criticize a consequence of a thing without criticizing the thing itself. I did not actually criticize constructivism anywhere. One might criticize, for instance, certain aspects of US economic practice which are derived from capitalism without actually criticizing the economic theory of capitalism. It is possible (probable) that educational institutes, like governments, are merely misusing theory. I don't know why there needs to be any counterpoints, I did not criticize constructivism.
"The reason I did not continue on to teach physics was partially due to an insistence that it was teachers who needed to expend more effort to make classes "fit" a student's preferences so that their learning would be a gradual climb."
What's wrong with that?
"You learn material by flailing, not by floating."
Because in practice it's impossible to do what is being asked. Maybe if your class size was six students, but that's the case basically nowhere. I believe that learning is best achieved when people struggle greatly. If someone is cautiously guided through every problem in life, or in education, they will possess a sense that they know how to do something because they have seen it done by others and they were guided through it a few times. However, when it comes time to actually do the thing they often do not recall it. It's what the article is about. Did you read it?
When I studied physics in college I learned at a much faster rate than I had in the past because I had to often teach myself. I have heard this from others as well. Coddling students and handing them information, letting them climb without falling, seems to yield pretty pathetic results.
>I believe that learning is best achieved when people struggle greatly.
I personally find "a bit of struggle" is probably the best way to learn.
There are a few things I have trried to learn, and made it more difficult than need be (Trying to learn JavaScript and Angular together, Spanish classes that were too advanced for my level). I feel like I learned more when I went back and did some more basic JavaScript, and classes that were at the appropriate level for me, rather than taking on too much, and just being overwhelmed.
"It's what the article is about. Did you read it?"
Arranging a course so that your students never struggle with the material is one thing. Never bending to your students' needs, as a teacher, is another. A teacher can provide a lot of opportunities for the students to struggle with the material. But I think it's ridiculous (and lazy) to teach without any regard for pedagogy, especially with high school students.
I know exactly what the point of the article is. Thanks for asking.
By the way, "cautiously [guiding them] through every problem in life, or in education" communicates a very different thing from "[putting in] more effort to make classes "fit" a student's preferences".
"More" implies that some is already being done, for the most part. I don't want to get into an Internet argument with someone about pedagogy because obviously there's no objectively correct answer. But you can believe what you want to believe and go become a teacher if you'd like. Administrators often want your students to never struggle. This is pushed upon teachers, especially new ones, even in their learning. I was lucky enough not to just have a degree in education so I left pretty quickly, but while I was teaching I was pushed to dumb down my material so that every student could achieve an A. I was told to fit my student's every preference so that they might get an A in the class. Not everyone should get an A in the class.
I'm one of those people who failed as an undergraduate. You know what's not pleasant? Being under constant stress to perform and "progress". Maybe, just maybe, that has something to do with learning in school. By the way, that's entirely a product of the academic system.
"The opposite is true: a good course is one where you always feel that you will barely make it."
Because making people stress necessarily means they're learning more? How do we know that? My experience suggests the opposite.
"It might not be a pleasant course, but it is one where you are learning. It is by struggling that we learn."
I guess the author agrees with me in another one of his articles (so maybe I just misinterpreted):
"There is no trace of evidence that you can get the best out of people at high-level tasks through pressure and competition. The opposite is true. Worried people get dumber. They may be faster at carrying rocks… but they do not get smarter.
Stressing out academics, students, engineers or any modern-day worker… makes them less effective. If we had any sense, we would minimize competition to optimize our performance."
Upvoted this. I have many students who face the challenge of mathematics with relish and they learn a lot by struggling. I have others who look at math, think "I'm not the kind of person who does/can do this" (for a variety of reasons), and fade out. Struggling with the material only happens if you are relaxed enough, in some sense, to engage with the material. A good part of my job with some populations was persuading them that they could fruitfully struggle with the material. The fear of mathematics is surprisingly pervasive in the US, as is the fear of struggle and the fear of not "performing".
"Drive" by Dan Pink sort of talks about that. Your purpose should be something that you provide, not external factors, like grades and fears from what comes from them.
It's entirely possible to be internally driven and to still not function well in a school. (Unless you think the only purpose students should pursue is "succeeding in school".)
I think my story is a decent anecdote to support your statement. I spent half of college on academic probation with the main contribution to my terrible GPA being default failing status from skipping too much class.
I dropped out of school, got a job that was supposed to teach me something. It turned into answering the phone, but I used that time and title to land a Jr. software dev position and within just a few months I was being assigned solo projects and completing them ahead of schedule because I actually enjoyed learning the material outside of a structured environment.
I'm not a genius. I'd bet I'm not even that special. I think many people are just too conditioned to follow the wide beaten path, that even when they see a more appealing path they are scared to take it, and no one is actually encouraging them to take that path.
I'm in the same boat. I struggled through college because I had to in order to keep my parents' health insurance (!), but my heart wasn't in it. Eventually I learned to do the minimum and coast through, but I had other things going on in my life that were so much more interesting and I just couldn't muster the motivation to "study".
Enter the real world, and guess what? Critical thinking skills and a tenacity to solve real problems are in tremendously short supply. You've got high-GPA graduates galore who can't tie their own bloody shoes. Motivation is everything.
> Interleaved practice feels much harder (e.g., “you feel confused”), and it feels discouraging because progress appears to be slow. However, this confusion you feel… that is your brain learning.
I'm sorry to be a grouch, but is this based on any scientific evidence or just the OP's opinion?
Most of the techniques mentioned in this article relate directly to the way our brain makes associations and forms memory. Learning something is a two step process: retaining the new information in the brain and then forming association between that and the things that we already know.
I have observed that trying to recall something that I have learnt ensures I retain the information instead of simply getting the illusion of learning something.
Mixing topics essentially allows you to create new associations in the brain about the topic. The stronger the association about a topic, the more you retain the information. Another technique that works really well is trying to apply a new topic to your own life. By relating new information to things you already remember, you create the pathways to remember and retrieve certain information.
Edit: link - how long term memory works:
http://education.purduecal.edu/Vockell/EdPsyBook/Edpsy6/edps...
Something my high school Computer Science teacher told me was that I wasn't learning effectively if I didn't have to try to understand something at least three times before it clicked.
Roughly 15 years later, I've found his advice to at least smell true.
Stated more generally, learning is to some significant extent about gaining understanding[1]. When you don't understand something, it is confusing.
In my experience, if you are not experiencing confusion -- more specifically the removal of confusion through effort of some sort --the "learning" you are participating in would more accurately be called memorization..
I like the essence of this blog post. I have applied similar strategies and although I am not a 100% sure about them being the 'right thing' to do, I am fairly convinced that they are a 'way to go' about learning new things. One thing is clear though (like Malkiel says in his book 'Random Walk Down the Wall Street' -- you become rich slowly, you only become poor fast), you have to learn to be patient -- you are going to get better at things only gradually.
Sometimes however, you need a more direct feedback if you are 'making progress'. I have seen that maintaining a blog or two is very effective in getting that feedback in two different ways. Making video lectures of your own is also an attractive option, but requires more effort. If you just write down something you think you understand as succinctly as you can, it helps to solidify your understanding. And if your (understanding of the matter and hence) writing is any good (of course, you should actively promote it), the magic of Internet will make your writing visible to many. People will flock to your blog and will ask you all kinds of questions, sometimes they will point out your mistakes and then you learn more what you thought you had already learned.
I think it's wrong to think of "learning how to program" as "learning a specific programming language." This is difficult to see as a beginner, if not impossible.
IMO it's better to think of each particular programming language as a stage and your goal is to practice acting.
Learning multiple programming languages at once is more like trying to learn Spanish and Portuguese simultaneously. It's not impossible, but you'll find yourself doing "double duty" because your brain has yet to develop clear lines between the two languages.
I've directly taught hundreds of people how to code and have seen this first hand. Take a beginning programmer who knows a little Python (or Java or C or anything), teach them some basic Ruby syntax, and ask them to write a Ruby program, they'll write in a creole of Ruby/Python, Ruby/Java, Ruby/C, etc. (cf. http://en.wikipedia.org/wiki/Creole_language)
I'm not kidding. You'll see things like this from C or Java programmers
def Fixnum add(Fixnum x, Fixnum y)
return x + y
end
It's remarkably consistent and they never once saw an example of code that looked like that. They mashed together ideas from Ruby and C and honest-to-goodness expected it to work.
Untangling those false connections just adds overhead to the learning process and (IMO) are best avoided until you have a clearer mental distinction between programming _per se_ and programming in a specific language.
My current quest is to take something from the business domain I work in and implement the bizarre math stuff (which I don't get all of) in a backend in F# with a frontend in Javascript (I'm fluent in neither).
I've tried it before (with different technologies), and although it didn't make me an expert in either field, I've found it neatly ties most things together.
Oh, and it's usually fun, especially if you put somewhat bizarre obstacles in your way (remember, it's a learning experience, not production code). It could be something elaborate like http://www.xpteam.com/jeff/writings/objectcalisthenics.rtf or just a concious decision to implement a part of the design in a part of the system where it isn't most obviously at home.
If your goal is to learn those two languages, I'd instead pick a problem/domain you understand very well and then express the various aspects of that problem in both F# and JavaScript rather than implementing some aspects in F# and some aspects in JavaScript.
This will help you develop a better sense of how F# and JavaScript differ as languages, what ideas are natural in one but unnatural in another, the conventions and idioms around tackling certain problems, and so on.
I once worked with an engineer who implemented the card game hearts in every language he learned. After the first implementation, you don't have to spend so much time thinking about the problem domain and can focus on finding the most idiomatic solution in the new language. The other benefit is that the project always has a clear endpoint.
I enjoyed this essay and he makes some good points. There is this feeling though so much isn't said about context and results. The audience seems to be college students.
I have been an avid learner since I left high school but my college experience was more understanding closed systems of teacher/professor goals and requirements (3.8 computer science graduate). I really didn't learn anything except to be exposed to ideas. The real learning always starts after school. What I find is we as human beings are incredible learning machines and learn efficiently already. What the OP seems to really be saying is a watered down approach to making another person happy with what they think you need to learn. AKA, express results within that system.
Goals, curiosity and discovery are tools to learning.
Thanks for the awesome piece, I never knew about these stuff, but I have always realized that when I'm a little confused that means am almost learning about the topic.
Also! I can say I agree about the school part %100!
My professor who use to make us feel like we are failing the course every quiz, taught us the best of Web Protocols and advanced topics, however %3 passed the class. Literally me and 2 other students out of 10, so I guess it's just the matter of who really wants learn and whom just going in to get a degree.
I was very lucky, from an early age, to be told that I should focus on learning how I learnt. I figured out how I learnt best in high school and never looked back. Now I have no problems learning any skill becase I know how my brain learns things and thus can cater specifically to it.
Unfortunately there is no catch-all method to learning and it is something you have to discover for yourself through exploration and good old trial-and-error.
This is why I always make an active effort to participate in my classes. It generally all sticks better in my brain if there's something I can remember with it - I'll remember the four stages of the 30 Years' War if I can remember my teacher lecturing and me asking questions and my classmates joking around. It has worked so far, so I guess there's something to that.
For people still in school, I have found that nothing beats flash cards for learning. It takes a bit of time, effort and discipline to write and use them, but in the long run, it's going to be easier and faster to study for exams.
I never found flash cards effective. The card became a visual trigger and the answer was tied to the appearance of the card, not the question on it. I found that, for me, regurgitating _all_ the card's questions (and subsequent answers with reasoning) in my head, with a reference sheet nearby to glance at to spur my recollection of all the questions, was most effective.
I should have mentioned: you have to say the questions out loud, and give out the answers out loud. And yes, your answers should be elaborate (e.g. explain how to do row elimination in a matrix).
I've found that the things I taught to others are the things that I learned the most completely. Not sure if it is the most efficient way but having to explain it to someone else always seemed to crystalize the details for me.
There is a joke about that: geometry teacher in the teaching room complains, how dumb her class was: "I explain it once—they do not understand. I explain it second time: they do not understand. I explain it third time: I myself understood, they still don't."
Reading this, I couldn't help but draw the parallel with body building. The pain means new muscle is filling the micro-tears made during effort, and you train an other group the next day while the one you did today recovers.
Pain is a terrible word to use when describing that it's much too intense/broad of a word.
Soreness is acceptable (most likely not ideal either though, if your work to soreness let alone DOMS you will need extra recovery time that could slow your overall progress), but pain should never be tolerated.
Body sense is one of the most important things beginners have trouble learning. Whats' the differences between discomfort, soreness, pain, etc? Body position part of that difficult for beginners, what's it feel like to have a straight back?
Day 1: Raw DOM manipulation with jQuery to fill it with micro-tears.
Day 2: D3.js/Socket.io to work the untouched parts of the DOM with different micro-tears.
Day 3: Profit.
I like the idea that whether you're creating product, solving problem or acquiring skill, the underlying dynamics are very much the same.
Perseverance, reaching positive failure and resilience.
For example, the parallel between muscle building and learning (as well, creativity and problem solving).
In the context of muscle growth, you're looking to balance two states - anabolic (protein synthesis) and catabolic (protein breakdown). During your exercises, you're training your [1] nervous system, which is responsible for signalling and transmission of impulses to your muscles, triggering hormonal responses and adaptations. The load you try to lift is proportional to the stress you place on your nervous system. Accordingly, [2] hypertrophy (from Greek, excess + nourishment) occurs post-workout during your resting periods and muscle tissue is [3] formed when you're not weight training.
Protein synthesis > Protein breakdown = Muscle mass increases
Protein synthesis = Protein breakdown = No change in muscle mass
Protein synthesis < Protein breakdown = Muscle mass decreases
On the other hand, your [4] neurocognitive functioning and [5] mental resources are no different. You're looking to balance state of intense conscious efforts with unconscious state of incubation. During your conscious efforts, you're collecting data and confronting with the elements of the problem. The effort you put into solving the problem is proportional to the decline of your cognitive capacity, leading to a decision to put the problem aside. The unconscious incubation state takes place (ex. sleep, mindfulness, meditation), where the memory is being repaired, information is consolidated and new associations are formed, accordingly leading to creative insights and problem solving.
1. Conscious, intense and focused state of confrontation w/ the problem;
2. Decision to put the problem aside;
3. Unconscious incubation state;
The quality of your recovery is crucial and directly correlative to the amount of your output.
Amen.
Back when I was tutoring a lot, I used to ask the students to keep a "master formula sheet" and continuously add formulas to it. In the final review session, I asked them to explain each math formula in plain English, e.g F=ma --> forces cause acceleration (and the acceleration produced by a force is inversely proportional to the mass of the object). I could immediately tell who understood the material and who was trying to get by on memorization.
Another useful exercise is to pretend you forgot your "formula sheet" and try to reproduce it from scratch. If you can't it means you're not solving enough problems---after solving 5-10 problems using a given formula, you start to remember it, and not as a string, but as an idea. You can forget a string; you can't forget an idea.