Caltech CalculusQuiet Study

This is the first post in the finals diaries series, which follows a group of students through their quest to improve their study habits in time for spring exams. We start with Travis, a freshman physics major from Caltech. In May, he faces a brutal multivariate calculus exam. This leaves him a little less than a month to toss out his existing habits, which he candidly describes as “less than stellar,” and embrace a more efficient academic lifestyle.

Plan A

As with all of my volunteers, I asked Travis to describe his current plan for preparing for this test. He replied:

It will boil down to taking a couple of weeks before finals and figuring out what I don’t know, trying to brush up on what I may have forgotten, and doing some example problems.

This, of course, is exactly the type of vagueness that drives students to last minute scrambles and incomplete preparation. Luckily, Travis still has time to change his ways.


The Date/Action List

Let’s be blunt: the “plan” Travis sent me is not a plan. It’s a collection of vague behaviors. So I choose to ignore it. Instead, I asked Travis to construct a date/action list. You’ll learn more about this technique in next Monday’s 4 Weeks to a 4.0 post, but the basic idea is as follows:

  1. Create a list of specific actions that can each be completed in
    one sitting    . The key word is “specific.” Terms like “review,” “go
    over,” and “study,” are not allowed. It needs to be more on the level
    of: “construct a review guide for lectures 1 – 4 consisting of…”
  2. Date each action with the specific day between now and the exam in
    which you will complete it.

This list of date and action pairs is a real study plan. Anything less specific is a recipe for stress.

Plan B

Travis liked my suggestion and was quick to construct his first attempt at a date/action list. It read as follows:

  • April 25: Draw up review sheets for previous lectures, including key concepts,definitions, etc; cross-reference with textbook, as well as relevant example problems
  • April 30: Choose 5-10 example problems (see review sheet) to work through. Ask TA’s for help if needed.
  • May 8: New review sheets for lecture April 25 – May 8. Focus on tying together new material with old stuff.
  • May 9: Work 5 example problems from material from Apr 25 to May 9.
  • May 11 – May 15: EXAMS!

This is much better than his first plan (“figure out what I don’t know…do some example problems”). But there’s still work to be done.

Fixing Travis’s Date/Action List

The date/action list Travis provided suffers from a few common planning flaws. (Making smart study plans is hard! A lot of students underestimate the experience and effort that goes into preparing in an efficient manner.) For example:

  • He discusses constructing “review sheets” but doesn’t specify what these actually contain.
  • He adds “concepts” and “key definitions” to his review sheets but schedules no time to review these items.
  • He proposes to study 10 – 15 example problems from each set of review sheets, but it’s unclear that these will cover all the material that needs to be learned. (It’s just an arbitrary number.)
  • And of course, the biggest planning sin of all, he deploys ambiguous verbs. “Work through” example problems doesn’t tell me how, exactly, he is going to make sure he has mastered the insights.

Here were my suggestions:

  1. Be more specific about “review sheet.” Consider building a mega-problem set for each week of lectures (a popular concept from the red book). That is, a collection containing a representative problem from the book, class, or problem set for every concept that could be covered on the exam.
  2. Replace the ambiguous action “work through” with a specific active recall strategy. For example, to review a given mega-problem set means that you can answer every question, while narrating your steps outloud, without peeking at your notes. If you can do this, you’re done with the mega-problem set. If you can’t, review the right answers and come back later to try again. Nothing less will work for math.
  3. You will need more than 1 day to complete this review. I would suggest at least 3 to 5 sessions. A smart trick is to schedule a TA visit in the middle of these sessions to brush up on the problems that confused you during the review. This leaves time for you to practice your new understanding.

Moving Forward

I’m currently waiting for Travis to construct a revised date/action list inspired by my suggestions. Here’s the thing: the eventual study plan we develop will include a lot of steps. But we’re talking about multivariate calculus at Caltech: you shouldn’t expect it to be easy, regardless of how smart you are.

The type of plan I’m pushing on Travis is the type of plan that leads to top scores. It’s also low stress, as it rarely requires more than a couple hours of work on any given day. We’re a long way from “figure out what I don’t know and do some example problems,” but we’re honing in on what actually works.

Stay tuned for more updates on Travis and our other finals diary volunteers.

(Photo by Hermes)