Posted in Teaching & Learning, Tips for Students

The Feynman Technique

The Feynman Technique

This old standby is a favorite of students everywhere: “I understand it, I just can’t explain it…”

Those of us with experience learning and teaching know, of course, that this is a contradiction in terms. If you can’t explain something, you don’t understand it!

The contrapositive of this gives rise to the Feynman Technique for mastering any material:

1. Study the material you want to learn until you feel you have some grasp of it

2. Re-communicate it in some form to someone who doesn’t already understand it, making it as simple yet as complete and accurate as you can; you can do this by writing as if you were explaining it to someone, or by actually explaining it to someone.

3. If you don’t understand a particular point or detail well enough to explain it in simple, clear terms to someone who doesn’t understand it, return and review the material until you can.

4. Repeat as necessary/desired.

Where the real magic of this technique comes in is that in the process of explaining the ideas you want to learn about, you will be organizing and contextualizing your thoughts as you articulate them, so the process of communication itself generates comprehension!

There are many ways to put this principle into practice in your own learning process. Of course you can just write about what you are learning on a piece of paper and keep it to yourself, but this is likely to seem dry and lifeless. An even better approach is to engage others in your learning process, by actually explaining what you are learning to interested friends and relatives, or other students in the same class. You can write articles and blog posts, answer questions and provide homework help online, or even tutor other students.

Whatever you do to put yourself into a situation where you are re-communicating what you are learning for someone else’s benefit, making it as simple and clear as possible, will cement your own comprehension. Just remember, you can’t say you understand something until you can explain it!

Posted in Tips for Students

Math Mistakes

A previous post looked at how to learn math, this post is about common mistakes that keep people from learning it.

1. Negative Self Talk

Telling yourself “This is hard”, “I hate this”, “I’m stupid”, or any of the many variations of these three main themes is wasted effort that both drains your mental resources and makes you miserable. You can just as easily talk yourself into learning math as you can talk yourself out of it, and increase your level of enjoyment at the same time, by training yourself to replace negative self talk with positive, or at least neutral, internal commentary.

2. Taking It Too Seriously

Allowing yourself to relax, go slow, be clumsy, and aimlessly explore is a crucial part of the learning process. Pressuring yourself to get it perfect right away will actually keep you from trying, leading you to fail before you even begin. Don’t worry about competing with anyone or solidifying your plans for the future. Just allow yourself to enjoy the process and learn at your own pace.

3. Not Taking It Seriously Enough

Learning math isn’t a life-or-death matter, but it does take practice and repetition, just like any other skill. You wouldn’t expect to sit out gym class by saying “I know how to do pushups.” Mere exposure to the material alone does not build mathematical skill; it takes practice and repetition to train your brain. The pay-off is that what seems hard at first becomes easy, and then automatic, allowing you to progress to greater levels of skill and understanding.

4. Cramming

Each day that you fall behind increases the proportional amount of work you have to do to get caught up, and decreases the chances that you ever will. In the extreme case, the chances that you will be able to fit several weeks or months worth of learning into a few days or hours are slim to none. And even if you do manage to successfully pass a test this way, the effort will be wasted in the long run because you will forget the material about as quickly as you learned it. Laying the foundation consistently is what provides the best short-term grades and long-term knowledge.

5. Not Getting Help

Not asking for help when you really need it can mean that you lose the opportunity to truly understand the material, or at the very least that you waste a lot of time following dead ends. You may waste three hours struggling to understand a concept that an experienced tutor or peer could explain to you in thirty minutes, allowing you to devote your time and energy to more productive pursuits. Don’t be afraid to ask for help when you need it, even if it is from an outside professional, because your time and the educational opportunities it represents is the most valuable thing you have.

Posted in Educational Reform, Math

A Mathematician’s Take On Standardized Exams

Theoretically, if a test is designed to measure what a student has learned, then there should be no such thing as “preparing” for the test. This is why I believe that the best “test prep” method is to focus on learning what is taught in school, and ignoring the test itself until the day of. This philosophy may go against the grain of the conventional wisdom perpetuated by test prep companies and anxious parents, but it got me a full-ride scholarship to the college of my choice based on my ACT score, so I know there is something to it.

In general, with the prevalence of test-prep courses, software, and services, what standardized tests really measure is not how effective a student’s overall education has been, but rather how well the student has prepared for the test. This goes to show that sometimes what you focus on doesn’t expand, it actually shrinks.

One of the most common complaints students have about learning math is, “I’ll never use this”, and, when it comes to math as it is usually taught and measured on standardized exams, they are right. Math professor Sanjoy Mahajan writes on the Freakonomics blog about how the math questions on standardized exams are unrealistic, and how they could be written to reflect the ways that people actually use math in real life. I especially enjoyed reading this article because Sanjoy’s methods reflect the ways that I teach students to think about computations: using their brains in natural, intuitive ways, rather than like a fleshy digital calculator.

Posted in Tips for Students, Tips for Teachers

Stop Taking Notes And Pay Attention

What’s one of the worst study habits that many students have which, if they stopped doing it, would drastically increase their retention and understanding and decrease their stress? Hint: it is a habit that many teachers and professors actually encourage!

It is amazing to me that the practice of note-taking in class is so widespread, given how ineffective it is. Chalk it up to tradition, I guess, a hold-over from the days when books were a scarce resource. We already know from studies of business environments that multi-tasking doesn’t work, so why should students be encouraged or even required to multi-task while they are trying to learn? If you are a student, it is best to focus on just one thing while you are in class: listening!

The philosophy of note-taking is patently absurd when you really think about it. The idea is that in class, the teacher verbally recites relevant facts, while students are supposed to split their attention between listening and writing them down, essentially taking dictation and creating a very low-fidelity personal copy of their textbook on the fly. Then the students are supposed to go home and re-learn (or learn for the first time) the information that the teacher gave them in class from this hastily constructed replica.

Isn’t it obvious that the best way to win this game, if you are a student, is to not play it? Isn’t it obvious that the best way to go about things is to read your professionally prepared and neatly organized textbook ahead of time, extract as much understanding from it as you can, and then go to class with a Zen mind, ready to be fully present, listen with your full attention, and ask questions if necessary to fill in the gaps in your understanding? Repetition is necessary for learning, and this way you get exposed to the material twice with your full attention. Unfortunately, if you try to take notes while you are listening, and then try to study from your notes later, you are receiving half-way exposure twice that doesn’t even add up to a whole.

You might object that in your particular subject, there is so much material to remember that taking notes is essential. But this is like saying that the more information there is, the more important it is to transmit it inefficiently. One of the worst subjects for note-taking dogma is organic chemistry, but here is the transcription of an irreverent and light-hearted lecture against lecturing written by a highly influential organic chemistry professor about the “Gutenberg method” of teaching, that makes the same case that taking notes, or expecting your students to, is a waste of time. An excerpt: “Now, if you can’t find a book that is even remotely acceptable to you, then you have to write your own. That’s how books get written. (Well, actually, it’s how books get started; they get finished because your third child is on the way, and you have no money to pay the rent.)” You can read about another professor’s experience with the Gutenberg method here.

You might also object that in this particular class, the teacher or professor teaches in such a way that you HAVE to take notes; that the material required for exams isn’t in the textbook, that you will be tested on information that is presented only once, in class, and nowhere else. While such incompetent teachers and professors may indeed exist, I think what is more relevant is the fact that note-taking is a self-perpetuating process. If you have spent your time in class trying to write things down rather than listening fully, of course you won’t remember what was said, and will feel later like you have to rely on your notes. So just try not taking notes and see what happens. Also remember the importance of pre-studying; read the relevant sections in the textbook ahead of time, so that when you see the material in class it will actually be your second exposure. Also don’t hesitate in asking questions in class; as soon as you feel that something is missing, speak up. As long as you keep up with what is being discussed, you will have no problem absorbing and understanding new material. It is when you start to fall behind in class and stop paying attention, a downward spiral that is enabled and exacerbated by note-taking, that problems start to pile up.

Posted in Educational Reform, Inspiration, Tips for Students

How to Maximize your Education, Part 2 of 6

This series of posts looks at six vital principles for getting the most value out of your education, regardless of how you go about pursuing it.

Principle # 2: Learn to learn from books.

Among reading, writing, and ‘rithmetic, reading is by far the most important, because if you can read then you can learn the other two skills and many more besides.  This principle may seem obvious, but if it were diligently put into practice it would drastically change the roles of both teacher and student.  Given that the majority of the world’s knowledge is stored in books, and that most of the rest is written about or otherwise available online, teachers have no business spoon feeding knowledge to students, but instead only need to endow the inspiration and skills to seek and acquire the knowledge they need.  If a focus on the ability to learn from books is maximized in the educational process, then practically all other aspects of it become obsolete.

This does not mean that there isn’t a role for teachers beyond teaching research and study skills, it just means that their role isn’t to impart knowledge.  Knowledge can be gained from books, but experience can only be gained by engaging with people and activities, and this is how a teachers’s experience can be of most value, by active engagement alongside students in DOING things.

Whether you are choosing to go through formal schooling or pursue your education independently, don’t fall into passive/receptive mode.  Learning is not like watching TV.  Actively engage your thought process with ideas that are interesting and important, and be proactive about acquiring the knowledge you are seeking.  Going through school at any level and just listening to the lectures is a massive waste of time and money.