The price and the value

Working with me and my team is more expensive than working with most tutors. That’s because what we do is actually different in a few ways. Here’s how to make sure you’re getting good value for your money.

Does one of these describe you?

  • You need the right answers to math problems
  • You need to know the techniques for solving certain math problems
  • You need to know how to read a math book more easily and effectively
  • You need better study skills
  • You need to feel less anxiety in your class or during tests

If so, then we can help you, but you can probably find good help for less money. (Even if you need many of the above things, it’s probably worth looking around.)

Or are you looking for something more like this?

  • You want your classes to go better, but don’t know what more you could be doing
  • You want to understand your own mind better, and understand why you’re actually having trouble
  • You want to get better at solving problems, especially when you feel underprepared
  • You want to learn cognitive skills that will benefit you for decades
  • You want to excel at math competitions through creative thought, rather than by memorizing obscure math
  • You want an expert co-strategist

If so, then I respectfully suggest that you’re in the right place. The price is high, because it’s difficult to do this work well.

But that’s exactly what we do, and we’re grateful to get to do work we love.

Thank you for allowing us to give these benefits to you and your family.

What straight-A students get wrong

Adam Grant just wrote a lovely piece in the New York Times that points out that, as he puts it, “academic excellence is not a strong predictor of career excellence.”

He’s right, and for the right reasons, but a quick skim of the piece might lead you astray.

The key insight isn’t that “slackers win over the long haul.” Instead, it’s this: we’re always choosing between “explore and exploit,” and exploration is more powerful early on.

So don’t blindly optimize for the rules you’re given.  The dominant strategy over the long haul is to run little experiments that help identify options that are not “on the menu” but which are nonetheless available.

What this means for students in high school and college is that it’s not necessarily best just to do whatever everyone tells you to do, as well as you can figure out how to do it. It’s better to reserve some of your time and energy for little trials and explorations.

Study a new subject.  Try a new study method.  Meet some new people.  Experience the discomfort of failure (preferably, in a context where the long-term consequences will be minimal). And so forth.

 

 

A few quick examples of how I use this with students

  • When my students make errors, I help them see whether it’s an “I didn’t know enough math” error or a different type entirely, e.g. “I didn’t approach this as creatively as I could have,” or “I was on auto-pilot, rather than giving this my full attention.”
  • In Chapter 20 of my book How to Be a Brighter Student, I get into this in some detail. I’ll include an excerpt in the comments below.
  • When students experiencing trouble shifting to this perspective, we often discover the need to discuss mindset and/or stress. (If you have the book, see Chapter 5, Harnessing Your Mindset, and Chapter 9, Stress: A Primer, for more detail.)

 

Some detail from Chapter 20 of  “How to Be a Brighter Student

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 after one’s early 20’s, so advisors for students may be especially helpful.)

Sometimes these experts will be amazing professionals with fantastic, groundbreaking advice for you. On the other hand, 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
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.

Math under pressure

This outstanding TED Talk by Barnard’s president is mainly about choking under pressure. But how interesting that the example Professor Beilock spends most time on is girls’ learning math.

One of the excellent points she makes so well is that there’s a difference between knowing how to do something, and being able to do it when the pressure’s on.  And as you have probably experienced yourself, the pressure is in some sense always on.

I’ve experienced this since my school days, and I’ve done my share of studying this issue and experimenting with various best practices. When it comes to preparation for math tests of any kind, I consider this issue to be of equal importance to actually learning math.

I know. It sounds like heresy. But I know it’s right. So we use a three-pronged approach to preparing for math tests and math competitions alike:

  • Learn the necessary math to fluency
  • Identify and resolve all your performance/execution issues (per the above)
  • Strengthen your ability to critically deconstruct and to creatively synthesize

We give equal weight to these keys to success, because we understand that it isn’t just about what you know. It’s also about what you can do, and how you feel when you do it.

 

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.)

Dealing with repeated challenges (part of “how to be a brighter student”)

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).

Summary

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.