My entire study strategy for succeeding in college relies on one simple principal, that an individual learns and improves through practicing the actual skill they want to improve at.  For technical courses: math, chemistry, physics, astronomy, engineering, tests and homework consist of problems for students to solve, and projects are usually just more difficult problems.  You’re tested and graded on your ability to solve problems because the goal of the course is to show you’ve internalized the relevant basic scientific principles and can apply them to novel situations to independently draw conclusions.  In fact, this is the entire point of an education in a technical field, to be able to use the ideas of the field to solve new problems, whether that means inventing a new piece of technology, understanding how something works, diagnosing an issue, or using basic assumptions to discover new ideas (particles, sources of energy, algorithms, etc…).  The method in which you are graded in technical courses strongly supports this claim.  In my technical courses; problem sets, and tests (which are just timed problem sets) accounted for 90-100% of my grade.  The other 10% was occasionally assigned to a project, which again, is just another problem set.  Grades are meant to be a reflection of how much you learned in your time in college, and students who are the best at solving problems end up receiving the best grades (and have learned the most).

So now that I’ve established the importance of having a strong problem solving ability, how do you go about improving it?  Problem solving is a skill, and like all skills, the best, fastest, and most straightforward method of improving is to practice solving problems.  It sounds really simple, but I was surprised by how many of my classmates wasted hours rereading textbooks, looking at lecture slides, and asking the professor questions like “what is this?” and “how does this work?” instead of just practicing problem solving and letting the intuition fall in to place as they deepened their practice.  Children don’t learn to walk from powerpoint slides, birds aren’t lectured on how to fly, and I’m willing to bet that you couldn’t read a tutorial on how to backflip and immediately walk outside and execute a perfect one, no matter how correct or detailed the tutorial was.  Similarly, you shouldn’t expect to learn math from reading, listening, or even watching other people do problems.  Learning happens from experimentation, randomness, and practicing things you have yet to master.  I had to stop watching YouTube videos and start throwing my legs over my head (hundreds of times) before I landed my first backflip, and you need to stop procrastinating through passive (or non) learning methods, and start throwing yourself into the actual work.

The results I received in my Graduate Nuclear Physics Theory course using the Adaptive-Set method

The results I received in my Graduate Nuclear Physics Theory course using the Adaptive-Set method, one of many success stories.

To master problem solving you need to 1. Do a lot of problems and 2. Pick the right problems to do.  Below I will present the simple method I used to accomplish both of these objectives, without relying too much on willpower, or worrying how to study.  I spent over 95% of my time on each course solving problems, using this exact method, and on a typical week all of my study time was dedicated directly to following the procedure I outline below.  This method dominated my study time so heavily that the word “studying” to me means working through problems using Adaptive-Sets.  I believe that this is the most efficient thing you can do to both learn and succeed in technical courses, and it worked out well for me.  If this seems unconventional, just try it for one week before making any judgements.  Active studying feels more intense than passive studying, but that’s because you’re actually learning something when you’re actively studying.  Spend your time studying more intensely, and you’ll be able to spend more time learning and less time studying.

The Adaptive Method for Developing Problem Solving Intuition

At the Start of the Course/Before the First Day:

Since your homework mostly consists of problems, you should definitely focus on these problems and use them to find the types of problems you should be solving.  Ask your professor what problems will be assigned over the course of the year, all of them.  Also ask them what chapters they will be in, what sources (other books, online, etc.) they will use to find the problems for the homework assignments, and what resources they would recommend for students who want to find more interesting problems, especially if the professor is uncertain about what problems they will assign for the rest of the year.  Find the homework assignments and test problems from past semesters and years, and keep them all on a list, along with all the homework problems you collected from your professor.  This list will be your Adaptive-Set, and will be the focus of your studying for the entire semester.  List the problems by number and source only, and leave space between the numbers.  I have an example of one of my Adaptive-Sets below.

The Adaptive-Set I'm using to complete a Mathematics for Computer Science course on MIT OCW. That's right, this method is so effective I'm still using it, even though I'm out of college.

The Adaptive-Set I’m using to complete a Mathematics for Computer Science course on MIT OCW. That’s right, this method is so effective I’m still using it, even though I’m out of college.

During the week (Monday-Friday):

In the time you have allotted to study for a specific course, start by choosing a problem from your Adaptive-Set. I usually like to start with a problem in the earliest chapter or from the first homework assignment.  Then move to the earliest problem in the next chapter after attempting the first problem.  This allows me to spend my time equally over all the different types of problems and the topics included in the course.  It also effectively starts your studying for the final and future tests on your first day of studying (since you’re covering everything from the start).  I choose the problems that will be due on graded homework sets first (usually completing the next due homework assignment before jumping through the chapters) which helps me stay ahead and not stress about problem sets, and allows me to ask the professor for help multiple times on trickier problems.

How to do the Problems/Use the Adaptive-Set:

Choose a problem.  Attempt it.  Use whatever available resources you feel appropriate, but don’t look at the solution until you’ve finished your attempt.  Give it your best shot, if you get stuck look through the book and online, but don’t give up or look at the solution, just continue to move forward even if you think what you’re doing is wrong.  You are making your best attempt at solving the problem.  While attempting, write out every step for your solution, and even include why you made the choices you’ve made while solving it (e.g. Why you used a particular equation), so when you look at the solution in the future your thought process will be clear.  After you’ve made your attempt, compare your solution with a correct solution (or if it’s not available compare your answer) immediately after finishing.  If you get the problem correct, cross the problem off your Adaptive-Set, and find a similar problem that is more difficult.  If your solution is incomplete or incorrect, circle it on your Adaptive-Set, read through the correct solution, identify the exact point where you started to go wrong, and “cool-off”, which means ignoring the problem until your next study session (>24 hours between attempts of the same problem is ideal).

At the Start Of the Next Week (Sunday (note: I do not work or study on Saturdays)):

Spend some time looking at your Adaptive-Set.  First add the new homework problems, or interesting problems that were suggested by your professor over the past week.  Dedicate some time to finding new problems for your Adaptive-Set.  First look at the problems you have circled.  Try to find an easier or version of the same problem (for instance, if it’s a circuit problem, find a similar circuit problem, if it’s a thermal equilibrium problem, find a similar thermal equilibrium problem, …) and add it to the bottom of your Adaptive-Set.  You’ve already added new problems based on the problems that were too easy for you (the ones you already successfully solved).  Now you should use the problems you struggled with as a valuable piece of information about what you don’t understand and need more practice on.  You will still be redoing the circled problems, but it’s important to strengthen your weaknesses so you don’t have any blind spots coming into your next test.  Underline the problems that will be due in the upcoming week, so when you go through your Adaptive-Set next you’ll know to start with these problems.  Once you’ve finished updating your Adaptive-Set, continue to work your way through it.

Once you’re in the habit of doing this it makes studying much more straightforward.  You stop wasting energy deciding how you should be studying, searching for problems, and you have a clear way of measuring your progress (how many problems you’ve crossed off/circled, and how many times you’ve circled particular problems).  The Adaptive-Set is specifically developed to grow according to what you know well and what you’re struggling with, so you are never wasting time solving problems that are too easy for you. Following the simple steps for adding new problems makes the Adaptive-Set a highly personalized system to ensure that you are spending your time deliberately practicing, which is the most effective learning method I’ve found so far (Malcolm Gladwell and K. Anders Ericsson agree, don’t believe me, check out their research).  Repeating this exact procedure week after week is pretty much all I had to do to ace all of my classes in college and consistently learn more than my peers.  Stop wasting time on ineffective methods, and make your first Adaptive-Set today.

My textbooks became adaptive sets of their own. Square means do the problem, the rest of the rules are the same.

My textbooks became adaptive sets of their own. Square means do the problem, the rest of the rules are the same.