Study Hacks Blog Decoding Patterns of Success Posts on Tips: Reading Assignments & Problemsets

On Becoming a Math Whiz: My Advice to a New MIT Student

April 28th, 2011 · 43 comments

Here’s how to become a math whiz:

Keep working on your problem set after you get stuck.

Don’t just sit and stare at it: think hard; until you’re exhausted; then come back the next day and try again. This will be uncomfortable, but that discomfort is the feeling of your brain stretching to accommodate new abilities.

This advice came to mind recently when I received an e-mail from a high school senior. “Yesterday, I was accepted to MIT,” he began. “I’m ecstatic, but on the other hand, I’m a little nervous…I was hoping you could give me some tips.”

I explained that I had been studying theoretical computer science and mathematics at a high-level for the past decade, much of it spent right here at MIT. Over these years, one conclusion has become increasingly clear: the more hard focus you dedicate to a technical subject — be it computer science, chemistry, or physics — the better you get.

Junior graduate students think senior graduate students are smarter, but they’re not: they simply have more practice.

Senior graduate students think junior professors are smarter, but they’re not: they simply have more practice.

And so on.

When I arrived at Dartmouth, to name another example, I didn’t consider myself good at math. I had taken AB calculus during high school (not BC), and had scored a 4 on the AP exam (not a 5). By my sophomore year of college, however, I had made a name for myself by snagging the highest grade out of 70 students in an advanced discrete mathematics class. What happened in between? A lot of hard focus.

Eventually, this all becomes clear, but for an incoming freshman, it’s not intuitive. When you struggle with a calculus problem set while a classmate knocks it out in an hour, it’s easy to start to thinking that you’re just not a “math person.”

But this isn’t about natural aptitude, it’s about practice. That other student has more practice. You can catch-up, but you have to put in the hours, which brings me back to my original advice: keep working even after you get stuck.

That’s where you make up ground.

Heidegger with Hefeweizen: Rethinking the Power of Context

December 2nd, 2009 · 33 comments

Boring on HorsebackA Quiet Pint

A few weeks back, on the recommendation of Ben Casnocha, I started working my way through David McCullough’s biography of a young Theodore Roosevelt: Mornings on Horseback. I was interested in the subject, but the early chapters of the book, which detail the late-19th century New York social scene, were not grabbing my attention.

Not willing to give up the endeavor, I made some changes. First, I prepared a plate of a pleasantly sharp Australian Cheddar that I had discovered on an absurd sale at our local Whole Foods. I then poured a glass of an Italian Abruzzo (a purchase inspired by my early-September visit to a vineyard in the hills outside of Bologna), and settled onto my couch — the splash of incandescent light from my reading lamp the only illumination in the room.

In this setting, my mind eased free of its previous resistance and began to absorb McCullough’s slice of life details. I found myself engaging the material in a way that just a few minutes earlier had been impossible. Something about the tang of the cheese, and the dry sweetness of the wine, supported by a creeping, yet controlled buzz, opened my mind.

This experience provoked an interesting thought: the context in which you do academic work is extremely important, yet most of us give it little consideration…

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4 Weeks to a 4.0: Master Your Assignments

April 13th, 2009 · 20 comments

4 Weeks to a 4.0 is a four-part series to help you transform into an efficient student. Each Monday between 3/30 and 4/20 I’ll post a new weekly assignment to aid your transformation.

Welcome to Week 3Time to Change

This is the third post in our four-part series 4 Weeks to a 4.0. In week one, I asked you to take control of your schedule, and in week two we overhauled your classroom notetaking. This week we advance to a crucial topic: your assignments. Nothing requires more time for an undergraduate than suffering through long readings or tackling impossible problem sets. Let’s learn how to dispatch them with maximum effectiveness.

Week 3 Assignment: Efficient Assignments

There are two major types of assignments: readings and problem sets. Below I’ve described a streamlined strategy for dealing with each. Your task this week is to adopt these approaches for dispatching your regular work.

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How to Ace Calculus: The Art of Doing Well in Technical Courses

November 14th, 2008 · 101 comments

Tangent Troubles

Calculus is easy. Or at least, it can be. The key is how you digest the material. Here’s an example: when you’re first taught derivatives in calculus class, do you remember it like this…

Derivative

Or do you intuit this image…

Tangent

As I will argue in this post, for any technical course — be it calculus, physics, or microeconomics — the key between an ‘A’ and a struggle comes down to this distinction. Below I’ll explain exactly what I mean and reveal how top technical students use this realization to consistently ace their classes.

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Monday Master Class: Conquer Complicated Material with the Mini-Textbook Method

June 23rd, 2008 · 9 comments

TextbooksComplicated Concepts

A reader recently asked me for some study advice. He was facing an exam in a course with unusually complicated material. The concepts were numerous, and tricky to understand, and connected to each other in non-obvious ways. It was clear that there was too much information to be efficiently handled by standard quiz-and-recall, so I referred him to my favorite under-appreciated study technique: the focused cluster method.

This was still, however, not enough. As the reader was quick to observe, there was so much material connected in so many different ways that even creating a quick rapid-fire question for each key point would soon spiral out of control. There would be way too many review questions.

Fortunately, I had another technique to suggest — an approach I call the Mini-Textbook Method. It’s slower than quiz-and-recall and focused question clusters, but, for complicated classes like the one haunting this reader, it’s arguably one of the best ways to conquer the material.

It works as follows…

The Mini-Textbook Method

When faced with a course with large volumes of complicated material, reduce your notes to a collection of textbook-style chapters. Write these like a real textbook. That is, use complete sentences and logical explanations. (You don’t, however, have to waste time on making the writing “good” or, even, grammatically sound. It’s only for you.)

Your goal should be to reduce and synthesize. A good rule of thumb is to have at most one succinct chapter per each week of notes.

Things you might include in the sample chapter:

  • A high-level description of the concepts covered in the chapter.
  • A list of definitions.
  • Good, succinct descriptions of the big ideas, theories, or frameworks.
  • A discussion of how the different elements from the previous item connect or compare and contrast.

The chapter writing process itself provides a powerful review, as it helps you construct a structure that transforms copious notes into coherent and compact form that is easier to review.

The next step of the process is to construct a chapter prompt sheet for each of these chapters. On the prompt sheet, record a basic outline for the chapter.

Finally, to review, do the following. For each chapter consider the corresponding outline. Load up your favorite word processor, and, using only the outline as a guide, attempt to type, from scratch, a new draft of the textbook chapter. Don’t peek at the original chapter.

Note, your goal is not to reproduce the exact wording of your original chapter. Indeed, every time you attempt a blind writing it might read much different. The key is to make sure you coherently explain all the ideas, definitions, connections, and discussions listed on your outline.

After your done, check your result against the original chapter; just like in the quiz-and-recall method, go back and try again later if there are areas where you had trouble.

Why This Works

For classes with a large volume of complicated, interconnected material, the advantages of this method are two-fold. First, condensing the material into textbook chapters reduces the amount of information to review. A synthesized chapter will be more succinct than a long multi-page list of the type of rapid-fire questions used in a technique like the focused-cluster method.

Second, typing the sample textbook chapter can prove quicker than trying to explain things out loud.The reason: it’s easier to express complicated ideas by typing rather than speaking. With typing, you can edit sentences, and go back and rearrange your structure as needed. When speaking, on the other hand, if the concepts are tricky and connected in intricate ways, you’re prone to getting tripped up.

Use With Discretion

This technique might be overkill in many situations. For upper-level classes, however, writing your own textbook from scratch, though somewhat slow, might still be the fastest way to actually master the material.

Monday Master Class: The Art of Pseudo-Skimming

February 25th, 2008 · 8 comments

The Tale of Two Reading StylesWords

Most college students are quick to learn the difference between skimming and reading. The former has you move your eye quickly across the page, picking up the occasional observation or idea. The latter has you actually read and process every sentence, and then try to record in your notes the salient arguments. We skim when the assignment is not too important. We read when we know we’ll later be tested on the material.

In this post, I want to teach you a third technique. One that occupies the middle ground between skimming and reading. It retains the comprehension benefits of reading while attempting, as much as possible, to achieve the speed of skimming. It’s a technique known to most upper-level humanities students; the key to taming massive reading lists without going insane. Different people call it different things. I use the term: pseudo-skimming.

It works as follows…

Pseudo-Skimming Basics

The core of the pseudo-skimming technique is to tackle the assignment paragraph by paragraph. Specifically, there are two types of paragraphs: important and filler. You only need to read the former; these hold the information that will come up in class discussion or make it onto an essay exam.

A general rule: the longer the reading, the higher percentage of filler paragraphs. This is good news. If you can identify which paragraph is which, and focus on reading only those that are important, you can significantly cut down your reading time without losing the important info missed by skimming.

The key is figuring out how to do this identification on the fly.

The Staggered Pace

The rhythm of pseudo-skimming is one of jogs and sprints. As you enter a new paragraph, you slow and read the first sentence. You ask: “what is this paragraph about?” If you get the sense that there is probably not much new meat here: abort! Jump to the start of the next paragraph, and ask the question again. Otherwise, stay the course, and actually read the damn thing.

There is a real art to this technique. You must intuit an answer to the importance question with a minimum of time. The more you read in the class, the better you’ll become at this. To help buff your skills, here are a few types of common filler:

  1. A long background story. Once you recognize the importance of the story (e.g., yet another example of the artists fighting!), you can keep aborting paragraphs until the story is over.
  2. Asides. If the author conducted a lot of historical research for the article, she can’t help but throw a few bits of extra information and explanations here and there. You’re not a historian. Skip!
  3. Exceptions. Professional scholars worry about being definitive, so they liberally sprinkle in exceptions and caveats to their arguments. If these run long, start aborting the paragraphs.
  4. Extra details. For a given idea, it is often sufficient to capture a few good pieces of evidence that supports it. If the author continues, in future paragraphs, with more details than you need, start skipping.

The Feel of Pseudo-Skimming

Once you catch the hang of pseudo-skimming, reading careful assignments takes on a different feel. There are relatively long stretches of you engaging the text, paragraph after paragraph, at a slow pace, internalizing the information. Then, suddenly, you are bounding from topic sentence to topic sentence, skipping paragraphs at a rapid rate. Wait! An important point! The pace slows again. And so on…

It may take a while to master this technique. But once you recognize the motivating idea — even for important readings not every paragraph needs to be read — you’ll find that the most beastly assignments suddenly seem a lot more manageable.

Monday Master Class: Rapid Note-Taking with the Morse Code Method

February 18th, 2008 · 34 comments

The Fast and the CuriousMorse Code

I’m currently taking a graduate seminar that assigns demanding articles of demanding length. Being somewhat busy, as I’ve mentioned before, I’ve recently been working to squeeze every last ounce of speed out of my note-taking habits. This has led me to a new note-taking approach I call the Morse Code Method. It’s engineered to be fast. Blazingly fast; yet still be able to support the type of detailed comprehension needed to survive a three-hour, 10-person discussion-based seminar.

It works as follows…

Brain Drag

Forget time for a moment. Your worst enemy when tackling a reading assignment is that weighty, sleep-inducing brain-drag that starts to grow over time, making concentration increasingly difficult. What brings this on? A big factor is halting your reading momentum. If you cease forward movement with your eyes so you can, for example, underline a few lines, or draw a bracket next to paragraph, or, dare I say it, highlight a sentence, it will require a large energy burst to get started once again. Too many such stops and starts and your brain will be fried.

The Morse Code Method is based on the following idea: you should never stop reading until you’re done with the entire article.

One continuous pass is the fastest, most energy-efficient possible way to get through a reading. It’s also the least painful.

The Dot-Dash Notation

This begs an obvious question: if you don’t stop your reading momentum, how do you make note of the important points? The answer is to deploy the following notation:

  1. If you come across a sentence that seems to be laying out a big, interesting idea: draw a quick dot next to it in the margin.
  2. If you come across an example or explanation that supports the previous big idea: draw a quick dash next to it in the margin.

From experimentation, I’ve learned that these dots and dashes are small enough that you can record them without breaking your reading momentum. In the end, your article will be a sequence of dots and dashes (like a Morse Code message!), effectively breaking down the reading into a useful sequence: big idea!, support, support, big idea!, support, support, support…

Processing

Once you’ve finished reading the entire article, it’s time to take notes. Review the sentences that you dotted and dashed. For the dots that still strike you as important, paraphrase the main idea in your notes, in your own words. (The paraphrase is key: it forces you to processes the idea in your brain, not just reproduce it like a photocopier). For each of the following dashes that still strikes you as important, paraphrase the example or explanation in a bullet point.

Go quick. Don’t worry about typos. Ignore fancy formatting. Just get the ideas down. As fast as possible.

Condensing

Now for the final step. This will only take you an extra couple minutes, but it’s the crucial boost that will transform you from “reasonably familiar with the readings” to “class star”:

  • Reviewing what you just recorded in your notes, think for a moment about the following: What is the main question being asked in the article and what’s the conclusion the authors point toward? Record the question and conclusion in your notes.

Now you’re done. Don’t skip this last step! It is here that you pull out the big picture ideas that will form the core of class discussions, papers, and exam essay questions.

How This Compares to Classic Q/E/C Note-Taking

Fans of Straight-A might wonder how the Morse Code Method compares to the classical Question/Evidence/Conclusion approach. The answer: it’s a variation. By having you read the article before identifying a question and conclusion, the Morse Code Method better handles complicated articles with subtle arguments. Also, by having you actually read — not just skim — every sentence, you’re better prepared for more detailed discussions. When deciding what tactic to deploy, choose based on the needs of the class.