Goodbye, Princeton. I loved you while it lasted.

I will no longer be recommending Princeton Review’s Math 2 prep books, because their latest edition features a test that is a problem-by-problem parody of an official College Board test.

I don’t have a problem with close copies of official tests — on the contrary, that can be a very sensible strategy for creators of practice materials. However, my methods rely on a rich collection of problems that are different enough from one another that the student can come to generate underlying principles that apply broadly to many different kinds of problems.

Those methods of mine are undermined by problems that closely mimic other problems in the training corpus.

Therefore, I have to reject PR tests, because they follow a strategy that undermines mine.

(Alas, poor Yorick.)

How to Be a Bright(er) Student: Dealing with Repeated Challenges

January is AMC crunch time.  Later will come SAT Subject Tests and AP’s. Examine your test prep strategy.  How will your hard work pay off, not only at test time, but also later in life? How will you utilize the skills you’ve refined over the course of your preparation to create a better you?

The mechanic who would perfect his work must first sharpen his tools. – Confucius

Now, let’s shift our focus from the creation of future you to the tools we will give him or her. I’d like to focus specifically on the theme of repeated challenge, since that’s what the future version of you is going to be grappling with. From our point of view, we might even say that that is the point of future you: he or she is going to handle challenges like your current challenges, only better. So let’s see how “better handling” of repeated challenges actually works.

How most of us think about repeated challenge

Most of us believe, incorrectly but stubbornly, that after we’ve overcome a challenge once, we will automatically overcome all future similar-looking challenges, as illustrated by this story:

Henry has done most of his homework for a class, but the last question is of a type he doesn’t think he has seen before. He tries a few methods suggested by the current chapter, but nothing seems to work. He feels a little anxious, but he decides to give it a break for dinner.   After dinner, he goes back to your desk, and the solution hits him! He finishes the question and finishes his homework, and closes his notebook triumphantly.  


Next week, he gets stuck again while working on his homework. Again it’s a type of problem he doesn’t think he has seen before, just like last week. And he figures that he’ll probably solve it quickly and easily, just because he solved it quickly and easily last time.

Note the mistake in the story Henry tells himself: it wasn’t quick and easy the first time, and it won’t be quick and easy the second time either. But if we are very careful to keep track of the details of how we solved the problem the first time, our chance of success the second time is much higher. Over time, this repeated process will become quicker, and it will seem easier and easier. But only over time, and over many repetitions, and probably with some mistakes and failures mixed in.

How most of us deal with repeated challenge

After overcoming a challenge, we move on immediately, and expect that we will be able to recall any important parts of the solution later. For example:

Grace has done most of her homework for a class, but the last question is of a type she doesn’t think she has seen before. She tries a few methods suggested by the current chapter, but nothing seems to work. She feels a little anxious, but she decides to give it a break for dinner. Just as she’s leaving her room, the solution hits her, based on an obscure method from a previous chapter. She goes back to your desk, finishes the question and finishes her homework, and closes her notebook triumphantly.


Next week, she gets stuck again while working on her homework. She thinks about the problem for a few moments, and no ideas come to mind. But then, she thinks back to the last time she had a mystery problem. She remembers that the solution came to her when she decided to break for dinner. So she decides to do the same thing this time. 


But it doesn’t seem to work this time. She finishes dinner, returns to her desk, and still there is no solution. There must be something she did last time that worked, but she just can’t remember all the details. She’s stuck.   That’s funny, she thinks. It seemed so obvious at the end last time.

How to better handle repeated challenge

If you want to handle repeated challenge in the best way, you have to start by realizing that the goal isn’t to change your challenges. The goal is to improve your ability to handle them. This takes an extra step or two that we’re not used to: reflecting on current successes just after they happen, and leaving notes for your future self to benefit from. Here’s how that looks in practice:

Rusty has done most of his homework for a class, but the last question is of a type he doesn’t think he’s seen before. He tries a few methods suggested by the current chapter, but nothing seems to work. He feels a little anxious, but he decides to give it a break for dinner. Just as he’s leaving his room, the solution hits him, based on an obscure method from a previous chapter. He goes back to his desk, finishes the question and finishes his homework, and closes his notebook triumphantly.


Then, thinking forward to “future Rusty” and the challenges he will have to overcome, he opens his notebook again and spends a few minutes writing down what he just discovered. It comes back in slow motion, and he gets it all down: the feeling of being stuck (so future Rusty can recognize it for what it is more easily later), the ideas he considered and rejected (so future Rusty can get better at analyzing options), the decision to break for dinner (so future Rusty can learn from his lucky experiment of solving a problem by giving it some space), and the flash of insight itself (which, Rusty now realizes, actually came from a mental survey of cryptic hints the teacher had given when assigning the homework). Now he has it all down.


Next week, Rusty gets stuck again while working on his homework. He thinks about the problem for a few moments, and no ideas come to mind. But then, he remembers that he had this feeling last week. He turns back in his notebook, and reads the notes he left himself a week ago. Suddenly it’s much clearer. He goes through the current problem step by step; he reviews what the teacher has said this week; he re-solves last week’s problem. He still can’t find the answer, but he doesn’t worry about that. Instead, he breaks for dinner. He’s pretty sure he’ll figure it out, even though he doesn’t yet know what the solution will be.   Sure enough, while Rusty is eating, he thinks of something that might work. When he gets back to his desk, he works out the entire idea. It works! He breathes a small sigh of relief.

Okay, so what are the steps again?

Whenever you solve a problem that you think you might face again, think forward to what will happen when you are confronted with a similar problem in the future. That will give yourself the idea of what to do this time, so that you will be able to take advantage in the future of what you learned just now. So:

  1. Think about what you just did
  2. Think about what was helpful about it
  3. Write a note to your future self

Don’t skip that third step! Writing that note to your future self means you don’t have to rely on your (let’s face it, imperfect) memory. This habit is a bit like being a time traveler, in a way: once you ask yourself what your future self would want you to do right now, you’ll find yourself taking actions that set you up for huge successes. With practice, you’ll get these successes again and again. In this way you can think of yourself as a team of you’s: past you’s, current you, and future you’s, all working together to shape the path to best fit the team (i.e. to best fit you).


If you want to get good at something over time, you have to analyze your performance. “Reps” alone won’t do it.

Expert level

You will face different kinds of repeated challenges in the future. Not just tests and courses, but interviews and jobs, and difficult conversations, and planning for a career and family, and beyond. The same tools apply.

Would you like to read more?

This post is an excerpt from my new book, “How to Be a Bright(er) Student: The Craft of Developing Your Brilliance”, a step-by-step guide to unlocking your inner potential and become the math whiz you were always meant to be. Available on Amazon.

How to Be a Bright(er) Student: Work like an Expert

February is the final date of the AMCbut it is also time to start your prep for SAT Subject Tests and AP’s. Examine your test prep strategy.  How will your hard work pay off, not only at test time, but also later in life? How will you utilize the skills you’ve refined over the course of your preparation to create a better you?

If we do only what is required of us, we are slaves; the moment we do more, we are free.


Let’s pay attention to how learning the advanced stuff is different.

Some people never figure out this difference. They have some success learning the first lessons of a subject, and then they form a habit of “protecting” their knowledge of the basics against new information that could threaten what they “know.” (See Chapter 5, “Harnessing your mindset,” to remind yourself how this can happen.)

By contrast, you will instead maintain a growth mindset (also known as “beginner’s mind”), which means thinking of your knowledge as a way to get to expertise, rather than thinking of it as an accomplishment.

Concepts, tools, skills

When you’re doing it right, it goes like this: first you get the concepts, then you get the expert tools, then you develop skill with the tools.

For example, when you learn physics, one of the things you discover early on is the idea of “projectile motion,” i.e. the way things move when they are flying through the air. Once you understand this concept, you learn the equations that govern this behavior. These equations are the tools that let you predict exactly where a flying thing will be, and when.

But the really interesting learning is the part that is supposed to happen next. This is where you transition from knowing all the stuff, to understanding how to use it effectively.

Once you’ve gained those expert skills, word problems become not just doable, but obvious. You’ll watch baseball and see what it means for an outfielder to “be where the ball is going to land.” These are practical physics skills that you can learn after you know the basics, but they don’t happen automatically. You still have to work in order to get there.

A few examples

Let’s see how people do this in practice—both correctly and incorrectly—through a few general examples.

Consider people trying to learn math, especially math like, say, precalculus. They often spend their time memorizing formulas. But you now understand that although formulas are necessary for understanding math, they aren’t enough. Formulas are only tools. Once you’ve learned the formulas and read the explanations, you need to transition to learning the expert skills. In the case of math, this skill comes from solving problems. By trying (and, usually, failing a lot), people learn a lot more useful math a lot more

What about people trying to learn a language? They usually start with memorizing vocabulary. Of course, you have to know what the words mean before you can start putting them together in any useful way. (This is the basic concept of learning a foreign language: as Steve Martin said, “They have a different word for everything!”). The most common mistake here is to try to memorize all the vocabulary at the beginning. What’s smarter is to get a small collection of vocabulary words down cold, then start reading, speaking, and writing in the target language using that implied vocabulary. By doing this you work the necessary skills (reading, speaking, writing) that are built on the fundamental tools (meanings of words), as soon as possible.

Sports also have their drills that lead to mastery of the basic patterns of movement and attention required for success (as well as general conditioning). Once you have these tools, you can (and should) immediately start building the skills needed to win at the sport.

How we usually go wrong…and how to do better

Each subject has its fundamental knowledge that must be completely committed to memory before mastery becomes possible. But each subject will also allow you to keep working on the fundamentals instead of graduating to the skills of mastery, if you’re not careful.

That’s why it’s important not to confuse the fundamentals with the skills that are meant to be built on top of the fundamentals.

Why would we keep working on fundamentals? The answer’s simple. It’s because it’s always comfortable to work at something you’re already good at. It’s harder to work at something new. So, if you want to master a subject, there comes a point at which you need to decide that you’ve mastered the necessary core knowledge, then tear yourself away from working at the fundamentals, and start working at a new, higher level.

And this is why many successful language-acquisition programs insist that students begin speaking as soon as they have a minimum vocabulary. It’s also why math is best learned by solving problems rather than by reading explanations. (And it’s why no one’s ever gotten good at a sport by watching it from the bleachers.)

As soon as you can, you have to transition from learning more fundamentals to practicing. And that means learning from your mistakes.

Deliberate practice

Anders Ericsson (mentioned earlier, in Chapter 3, “10,000 hours?”) describes the idea of deliberate practice – an effort to systematically practice just beyond one’s skill level – as the key to accelerated improvement in any discipline. This sort of deliberate practice is difficult and demoralizing, as it involves constant failure. And it can be exhausting, because it challenges your mind at multiple levels at once. Not only are you grappling with uncomfortable new processes and techniques, but you are also monitoring your own process, and devising new challenges for yourself on the fly. So, it’s hard. But it works like nothing else.

In a test-preparation context, this means that you must begin taking practice tests as soon as you can reasonably expect to be able to answer some of the questions asked. As you struggle with the material, you will not only learn which bits of fundamental knowledge you are missing; you’ll also learn whether your pace is correct, whether your nerves are hurting or helping you, at what time of day you do your best work, how much sleep you need, and on and on and on.

With each mistake, you have an opportunity to be completely honest about the reasons for your error, which in turn leads to ideas about how to correct future errors by changing not only your knowledge, but also your habits and even your outlook.

Obviously, this is not the same as just doing an activity. For example, playing a sport for fun for eight hours a day is not the same as deliberate practice; deliberate practice would involve setting up drills to specifically focus on deficiencies in one’s skill and practicing those drills until the deficiency is corrected.

Ericsson draws the conclusion that natural talent means nothing without deliberate practice. In fact, in situations where we think of somebody having natural talent, an investigation shows that they just got started on their deliberate practice earlier than most.

When you want to get good at something, aim to do it the way masters do it. Then, when you fail, be gentle and honest with yourself. Look for exactly what you did wrong, observing yourself without judgment. Then address the mistakes, whatever they may turn out to be.


Mastery of the basics is just the beginning.

Would you like to read more?

This post is an excerpt from my new book, “How to Be a Bright(er) Student: The Craft of Developing Your Brilliance”, a step-by-step guide to unlocking your inner potential and become the math whiz you were always meant to be. Available on Amazon.

10,000 hours?

You don’t have to make yourself miserable to be successful. Success isn’t about working hard, it’s about working smart.

Andrew Wilkinson

When it comes to homework, more is not better.

You’ve probably heard  of Outliers (“The Story of Success”), Malcolm Gladwell’s 2008 opus, based in part on research by Anders Ericsson. Even if you haven’t read it yourself, it’s probably been quoted to you. It’s the main source of the idea in popular culture that true mastery requires ten thousand hours of practice, which in turn has been used to justify all manner of craziness, including too much homework.

Let’s set the record straight: Gladwell’s book is not the source of the craziness per se. The craziness happened because somewhere between Ericsson’s original research and the reports on Gladwell’s book in the popular press, the proper context and conclusions got lost.

Gladwell (or at least those who reported on his book) popularized the idea that across a wide variety of fields, and especially in cognitively demanding ones, true mastery generally requires a minimum of ten thousand hours of a particular kind of practice.

A common misreading of this observation was the notion that since it’s the magical 10,000 number that determines successful mastery, one should get in as many hours as one can, as soon as one can. Hence, for example, never-ending homework assignments.

This sounds good, but unfortunately it isn’t what the research actually showed.

The right kind of practice is smart.

The research showed that the right kind of practice leads to improvement, and the wrong kind of practice does not.

This is true no matter how much practice you put in. However you define “mastery,” the right kind of practice will
get you there fastest. Furthermore, continued correct practice will continue to improve your skills. (The 10,000 hours number comes from the observation that when you are competing with other people, being the best depends on putting in an enormous quantity of the right kind of practice, because everyone you are competing with will be doing the same.)

Let’s get practical. How do we do this, and what else can we learn here?

The main thing is to stop practicing mindlessly. Believe it or not, practice doesn’t actually make perfect, no matter what people say. Instead, practice simply makes permanent; only perfect practice makes perfect.

So what is perfect practice? It’s a situation that challenges your current ability. So strive at every session to work ever so slightly beyond the highest level you can reach. It’s demanding, frustrating, and often annoying work. Generally, it can’t be done for more than about three hours a day. It is not generally pleasant. But it works.

Make your work better.

So remember: quality, not quantity of practice is the most important factor. Even a hundred hours of quality practice will move the needle. On the other hand, though, you could spend your whole life practicing something by rote and never get any better. (Do you hear me, teachers who assign piles of mindless work?)

Your goal shouldn’t be to do a ton of work, and your teacher’s goal shouldn’t be to pile it on. Instead, the goal should be to make your work better. The better your work, the less of it you will need, and the faster you will progress. Avoid the kind of inefficient work that doesn’t get you closer to mastery.

You don’t need more smarts

Another important lesson here is that although talent matters, it doesn’t matter much. Most of life isn’t actually a “more talent is better” situation. Rather, it’s more like “you must be at least this tall to ride this ride.” Some talent is necessary, but beyond that, more is not appreciably better. “A basketball player only has to be tall enough—and the same is true of intelligence. Intelligence has a threshold,” says Gladwell.

So, do smarts matter? Yes, but not as much as you think. You are already smart enough to be doing what you’re attempting. Believe it or not, being smarter wouldn’t help you all that much.

In pretty much any area of human endeavor, people have a tremendous capacity to improve their performance, as long as they train in the right way. If you practice something in the right way for a few hundred hours, you will almost certainly see great improvement. And from there, you can keep going and going and going, getting better and better and better. How much you improve is up to you.


All that matters from now on is how well you learn.

How to Be a Bright(er) Student: Be Your Own Pilot

Spring is the busiest time of the year for most high school students. But seniors, you face a special challenge: your support system has already done its work, and you’re on your way to college. But are you empowered to start making even more of your own decisions?  Being an effective self-advocate and self-manager is absolutely essential for success in the next phase of your life and career. Let me help you help yourself along the right path by giving you a preview of what’s to come, and some ideas about how you can grapple with it successfully.

Should you fail to pilot your own ship, don’t be surprised at what inappropriate port you find yourself docked.

Tom Robbins


The more decisions that you are forced to make alone, the more you are aware of your freedom to choose.

Thornton Wilder


A good plan violently executed now is better than a perfect plan executed next week.

George S. Patton

Getting help

As you may have noticed, making important life decisions is mostly regarded by our culture as something best left to the experts: first your parents make decisions for you, then college counselors, then graduate advisors, then professional mentors and managers, and on and on and on.

This isn’t necessarily such a bad thing: experience often leads to better results. (Also, there are certain kinds of mental tasks related to decision-making that become biologically easier in ones early 20’s, so advisors for students may be especially helpful.)

Sometimes these experts will be amazing professionals with fantastic, groundbreaking advice for you, and sometimes they’ll just be a “safety net” of decent advice, so your very worst decisions won’t be too bad.

You need to be able to tell the difference. Ultimately, you’d prefer to make your own decisions, perhaps informed by the wisdom of others, but not defined by it or by them.

Going it alone

Next, consider that most decisions are informed by your “autopilot.” You make decisions at least partly (if not entirely) by seeing that the current situation matches some past situation (possibly in relevant ways, and possibly not), and then doing in the present whatever you think was the right thing to do in the past. (See Gladwell’s Blink and Kahneman’s Thinking, Fast and Slow for more in-depth knowledge on this.) This is not a bad thing, but it’s useful to understand how to balance this important but unconscious force with your conscious, executive mind.

And even your conscious mind can have arguments with itself. Aligning your identity, your emotions, and your cognition behind a single decision can be hard work. For example, there might be disagreement between what you want, what you think you want, and what you want to want. It’s so complicated that it can be hard to get started.

But a good system can help you overcome these difficulties. Through practice, you’ll come to better understand how to align these drives within yourself. The process of making decisions will become easier. I recommend you find one you like. To get you started, I’ll provide one of my own.

Mine is a method for making decisions that helps balance your mind, heart, and gut. So it avoids a lot of the problems with “unbalanced” decision making. However, it takes a long time to get really good at it, so think of this as a long-term project. If you give this a try for now, and keep up with it, then sooner or later this method will become part of what makes you especially capable.

It works on problems big (“What should I do with my life?”) and small (“How can I solve this difficult homework problem?”). I call it the Pilot Program.

Before we get too far into it, let me acknowledge that there are many, many excellent processes out there for setting and achieving goals. There are two ways in which the Pilot Program is different from most:

  1. It uses a “ready, fire, aim” strategy. This means that you start quickly, even before you have all the details worked out, and you fine-tune everything later. This strategy helps you avoid overwhelm and perfectionism, and it helps you build momentum fast. Yet it’s also accurate over the long run, because of the fine-tuning that is built into the system.
  2. The focus of the Pilot is on constant improvement, which allows it to transcend mere goals and aim for more powerful targets: vision and values. As a result, the Pilot Program is not limited to short-term projects, but rather can be applied on a large scale—as large as you can imagine.

The five parts of the pilot program

The five parts of the Pilot Program are: a Desire, an Action List, a Journaling Plan, Course Correction, and a Finish Line.

Desire: What I want to have achieved, what I want to have, what I want to have done, or what I want to be.
Action List: Specific actions I should take in order to get closer to that vision
Journaling Plan: The location of my notes on my progress, and my schedule for reviewing the notes
Course Correction: The actions I should take in order to fine-tune all five of these parts, as I gain experience by doing them.
Finish Line: How I’ll be able to tell that I’ve succeeded.

A quick example

Here’s a quick example of how this might work:

To be a straight A student.

Action List
1. Discover what straight-A students do that is different from what I am used to doing
2. Identify the parts I can’t easily do
3. Learn how to do those things
4. Turn that learning into habits

Journaling Plan
Every week, I write down in an online journal what I’ve done during the week that is likely to raise my grades.

Course Correction
Every week after journaling, I read through the whole journal from the beginning, and then I do two things: (1) make any changes to the Desire, Journaling Plan, action list, Course Correction, or finish line, according to my best judgment at the time, and (2) write notes telling myself what I should try to do the following week in order to stay in alignment with those parts.

Finish Line
I have a report card containing nothing but A’s for the current grading period.

A life-size question

Now let’s say you’re trying to figure out what to do with your life. That’s an awfully big question! But the size of the question isn’t a problem. Here’s how it might work:

To know what I want to do with my life.

Action List
1. Ask some older people what they do, and whether they like it
2. Think about what they say and how it applies to me

Journaling Plan
I record all the interviews, and after each one I listen to it again and take notes, focusing on how I think the ideas in that interview apply to me (or not).

Course Correction
I think about which interviews seem most and least helpful, and I use that information to determine what sort of person to try to interview next.

Finish Line
I have written down a specific “life Goal” that I believe is worth pursuing.

A research project

Here’s a different way in which someone might use the Program to come up with their Desire:

To know what I want to do with my life.

Action List
1. Ask myself what I want to do
2. Pay attention to what I find myself saying

Journaling Plan
Every time I ask myself the question, I come up with a one-sentence answer and write it down on a piece of paper taped to my wall.

Course Correction
Once a month, I spend ten minutes reading the paper and remembering what made me give each of those answers.

Finish Line
I have noticed myself giving the same answer three or more times.

As you can see, two different people could use this method to solve the same problem, and wind up with very different paths and very different results.

Let me be clear: the method isn’t easy. You have to really think about each of the parts, and that takes time. Sometimes, it also requires courage. But the personal attention you put into it is also a major strength of the Program. Since the parts all come from you, they aren’t nearly as vulnerable to anyone else’s bias. You are making all the decisions. You are also deciding the very rules of the game. This means that your decisions using this method are more likely to have high integrity. In other words, true to yourself.

So you get to decide how much “outside bias” you’re going to let in to your process. Let me suggest some guidelines for deciding how much bias to let in, and how to avoid that bias when you want to.

How much bias

A good guideline is replicability: if many people before you have gotten what you want, and it’s clear how they did it, it’s probably best to let others’ guidance help you. This can mean researching how to do it, or trusting an expert to help you find the best path. Note: this doesn’t mean to relinquish all control (or worse, responsibility for the outcome); it just means that you’ll probably do better with advice than without.

By contrast, if the result has not been replicated many times, or if it isn’t clear how it’s been done in the past, then you may be the best guide for your own process, because (1) you care more than anyone else, and (2) you probably know yourself better than anyone else. (One key exception: one or both of your parents might be even better guides than you yourself are.)

Another good guideline is boundedness: problems and questions that are well-defined, short-term, multiple-choice, and/or straightforward are usually best answered with outside help or bias. However, more nebulous, long-term, open-ended and difficult-to-even-define problems and questions usually benefit from removing as much bias as possible from the decision process.

One last thing: it’s okay to use one method now and another later. For example, many people enlist the help of a college counselor (high bias, high expertise) to figure out where to go to college, and only later use their own process (low bias, high integrity) to determine what sort of career to build on the foundation of the college career.

How to avoid bias

Read through each line of your analysis. Ask yourself: why is this here? Whenever you have a hard time answering that question, find and remove the bias.

How bias can help

The form of the question often gives you some idea about what kinds of answers would be good or bad answers, and this can help you, especially when you’re just getting started.

For most problems, there are solutions that are considered “out of bounds.” That is: there’s a strong sense of what you are “allowed” and “not allowed” to do. For example, take the SAT. There, it is not considered valid to write in your own answer choice on the multiple-choice sections. This means that most problems carry with them implicit hints about how the problems should be solved. As you learn to recognize bias, you will learn to recognize solution “hints.”

One other way in which bias can help is that it can show you what everyone else has tried, so that you can try doing the opposite. Some very successful companies, for example, got their starts by trying to do what was considered at the time to be “obviously” impossible.

How eliminating bias can help

At its most extreme, the Pilot Program helps you to examine all the possibilities. Even the “crazy” and “impossible” ones. So make sure you take advantage of that leeway by including all the “outside the box” possibilities in your analysis.


Making your own decisions is actually a lot harder than it sounds. A reliable method helps. Here’s one such method. Getting good at it really pays off.

Expert level

Once you get comfortable doing this, remove the explicit Desire and Finish Line from a project, and continue only with the Action List, Journaling Plan, and Course Correction.

You’ll often find that an area of self-improvement is made much more powerful by removing the “fixed destinations” from your thinking and framework, and instead, putting your focus on open-ended, continuous improvement. This is related to the Mindsets described in Chapter Five.

Creating the habit of continual improvement, where it’s about always taking the next step (Action List, Journaling Plan, Course Correction) is one of the most powerful meta-habits you can build.