Posted in Teaching & Learning, Tips for Students

How To Learn Math (Or Anything Else) Faster

I always say it’s better to play keep-up than catch-up, which means staying a little ahead of the progression of concepts in a class, rather than a little (or a lot) behind.  This means that you have to proceed at the rate the class progresses.  But what can you do if you feel like a class is progressing faster than your ability keep up?

Logically, there are only three things you can do to increase your rate of learning:

  1. Spend more time studying than you already do. If you are currently spending two hours per day, spend three, for example. Note that this approach has diminishing returns.
  2. Improve your process by learning how to study more efficiently. This requires that you invest time in learning how to learn faster. There are various resources and approaches for this, such as Scott Young’s Ultralearning.
  3. Hire a guide. Working with a tutor can increase the overall rate at which you learn by roughly a factor of three while reducing the stress you experience, and a tutor who is also a good academic coach will help you improve your process so that you can learn more efficiently on your own as well.
Posted in Math, Teaching & Learning, Tips for Students

How To Learn Math (Or Anything Else)

As the title of this post indicates, the process I am about to describe is actually the natural learning process for anything, not just math.

First, Get Curious

Learning has to start with curiosity. You can be curious about math as a means to an end (say, if you want to be a financial analyst or engineer, for example), or you can be curious about math for its own sake (if you want to be a mathematician, this will probably apply to you).

Remember, curiosity is an emotion, and emotions are generated in part by what we focus on and what we tell ourselves. So, if you want to learn something but don’t have any curiosity about it, generate some! Curiosity is the glue that makes new knowledge stick.


Once you get started, let your curiosity lead you into new and interesting territory. Venture forth into the material with an agenda of pure discovery. Let this be an open-ended, non-directive process, with no particular goal in mind, the same way that you would read a novel or watch a movie.

Think of the last new movie that you saw. Can you remember the setting? The plot? The characters? Were you trying to memorize any of those things? That should be proof enough to you that this method works.


In math, practice could take the form of performing calculations, solving problems, or writing proofs. In other subjects, it could take the form of answering practice questions or re-communicating what you have learned, either by writing or speaking. It is a Law of Learning that the harder you work for a particular piece of knowledge the better you will retain it, so don’t shirk on effort here. Just like with working out, the more you sweat, the more you get!

Get Help

Once you have put in sufficient practice, you are in an ideal position to ask for and receive help. Asking for help from a teacher, tutor, or mentor at this point will help you fill in any gaps that you have identified in your understanding, uncover any blind spots you may have and improve your process. This is how you go from proficient to efficient. Having first put in the effort to understand the material yourself will prepare you to appreciate and receive what is being offered.

Posted in Books, Educational Reform, Teaching & Learning, Tips for Students, Tips for Teachers

The Role of Neural Associations in Learning

Excerpted from Triggers, by Stanley Mann:

“Multisensory imagination is the world’s finest teaching machine, and we all possess it.  We simply need to learn how to use it.”

I just came across this great quote in a book I’m reading. The book is about using triggers, or neural associations, to direct one’s attention in constructive ways. The quote comes from a chapter on using triggers to enhance learning ability. It resonates with me on a number of levels.

First of all, the idea of multisensory imagination is a little-known but extremely powerful learning enhancement tool, and is the sort of thing that we should be teaching kids about in school instead of pumping them full of facts and figures. To truly learn anything you have to make it real in your mind, fully engaging with it in your imagination with as many sensory channels as possible; both sight and sound at the very least, and ideally touch, smell, and taste if possible. Conversely, teaching can’t work unless it engages the imagination and the emotions through multiple sensory channels. Educators and curriculum designers need to be mindful of this principle in order to be effective.

Secondly, triggers in general, and learning triggers in particular, rely on the principle of association. Our brains are constantly making associations among various environments, stimuli, and emotional states based on our experience. Neurons that fire together wire together, so when two experiences are repeatedly juxtaposed, they tend to become linked. This means that to optimize your learning process, you need to create a positive physical and mental learning environment for yourself, so that you are comfortable and feeling good while you are learning. Conversely, if the learning environment is physically or mentally uncomfortable, such as by feeling coercive and emotionally unsafe, then the negative feelings it evokes will come to be associated with the process of learning itself, causing them to be re-experienced whenever future learning endeavors are undertaken. This is another principle of human psychology that educators and legislators need to take heed of.

Posted in Inspiration, Tips for Parents, Tips for Students

Catch Up or Keep Up?

Something that I often find myself reminding students and parents alike is that “it’s easier to play keep up than catch up”. In other words, it requires less time, energy, and attention to stay current with your responsibilities than it does to get caught up when you are behind.

What it really comes down to is being proactive. Playing keep up means being proactive in your life, which corresponds to ease and and a positive sense of control. Playing catch-up means being reactive, which corresponds to feelings of helplessness and overwhelm.

If you’re a student, whether you’re constantly working a week ahead of your classes or a week behind, you have to maintain the same pace, but one position gives rise to a lot more stress than the other!

This is also why I counsel parents to have a conversation with their kids at the beginning of each semester where they look at their upcoming classes and consider whether the student is likely to need the help of a tutor in any of them, and be proactive about the hiring decision, rather than waiting until the student is struggling and lost before taking action.

Is “playing keep up, rather than catch up” something that you can relate to from your own experience? If so, let me know how in the comments!

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 Educational Reform, Gamification, Inspiration

Gamification: The Coming Wave Of Education

Tech blogger and serial entrepreneur Peter Diamandis, famous for opening up the space frontier with the original Ansari X-Prize for commercialized spaceflight, recently wrote

“In the traditional education system, you start at an ‘A,’ and every time you get something wrong, your score gets lower and lower. At best it’s demotivating, and at worst it has nothing to do with the world you occupy as an adult. In the gaming world (e.g. Angry Birds), it’s just the opposite. You start with zero and every time you come up with something right, your score gets higher and higher.”

This quote gets to the heart of why I think gamification is the coming wave of education. Gamified learning is not only more relevant and efficient than traditional learning, it is inherently exciting and motivating. Long recognized as a powerful productivity tool in the business and sales realms, gamification is just now starting to make headway in education. One of the most popular language-learning apps, Duolingo, gamifies the process of learning a new language. Even more exciting, to my mind, is that what started as a commercial app like any other is now making its way into classrooms, helping to transform the school experience into something more fun and empowering.

The implications of this to me seem staggering. Imagine a world where “education” and “school” aren’t things that we have to make kids do, but that all kids want to do. Where there are no deadlines or barriers to learning anything, and any person of any age can begin to learn any subject at any time, as easily as getting addicted to the latest mobile game. How will this affect social mobility and intellectual freedom? How will it affect governments and corporations? How will it affect communities, families, and individuals? One thing I’m sure of is that I’m excited to see!

Posted in Online Tutoring, Tips for Parents

What If I’ve Never Tried Online Tutoring Before?

I often still hear from people who have never tried online tutoring before and aren’t sure if it will work for them or their children. When they go to look for tutoring, they have the image in mind of sitting down at a table with the tutor. Given this expectation, the idea of sitting by yourself in front of your computer to receive tutoring may seem off-putting. However, I haven’t found that meeting with students in person allows me to provide any better service than meeting online does. In fact, just the opposite is the case; in my experience, online tutoring, by providing access to the learning tools of the PC and Internet, works better than in-person tutoring, convenience factor aside. And, one of the great things about online tutoring is that it’s easy to try out just a bit to see if it works for you, so you don’t have to take anybody’s word for it but your own.

Chances are your kids already use Skype to video chat with friends and relatives, and if they do they’ll probably take naturally to online tutoring. For those “noobs” still curious about how online tutoring works, here’s a link to a video demonstration.