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.
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.
It's a fun four week course with very little work and I recommend it.
 After each lecture there was a list of references to check out for more info.
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."
Spaced Repetition and Spaced Learning 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, as well as a video series by the principle author 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.
 a term coined by David Perkins, who provides some of the foundation upon which Beaudoin builds his theories: http://www.gse.harvard.edu/faculty/david-perkins (see also http://amzn.com/089859863X)
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:
Session 2: https://class.coursera.org/learning-002
Session 1: https://class.coursera.org/learning-001
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.
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 !).
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...
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. 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_, 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.
Just don't throw the constructivist baby out with the bathwater. :)
As a counterpoint, the Logo programming language is an example of a well-executed pedagogical approach informed by constructivist thinking.
What's wrong with that?
"You learn material by flailing, not by floating."
Why do you believe that?
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 personally find "a bit of struggle" is probably the best way to learn.
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".
"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."
Yes: struggling with the material.
"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."
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.
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.
I'm sorry to be a grouch, but is this based on any scientific evidence or just the OP's opinion?
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:
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. 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..
 at least in this context
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.
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
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.
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.
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.
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.
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.
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?
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  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,  hypertrophy (from Greek, excess + nourishment) occurs post-workout during your resting periods and muscle tissue is  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  neurocognitive functioning and  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.
 - https://www.youtube.com/watch?v=3V77oaboEmY&feature=youtu.be...
 - http://en.wikipedia.org/wiki/Muscle_hypertrophy
 - http://www.ncbi.nlm.nih.gov/pubmed/11255140
 - http://www.med.upenn.edu/uep/user_documents/VanDongen_etal_S...
 - http://www.ncbi.nlm.nih.gov/pubmed/25275517