How to Solve Technical Problem Sets: Learn as Much as Possible from the Work you Do

I’ve talked before about how to build adaptive-sets of problems to practice, and why you should use this as your primary vehicle for studying.  This article is a detailed description of how you should be solving individual problems when practicing, or working through your adaptive-sets and problem-sets so that you optimize your studying, and learn as much as possible from every problem you solve.

How to Solve Technical Problems:

Start the problem:

Write out the problem statement on the top of your piece of paper.  Then begin working on the problem.  Write down how you think you should solve the problem (an equation, method,“just like problem 9 in ch 2”, …).  It is important to recognize what strategy you used, and to record it, so you can recognize patterns, both in what methods work for which problems, and which problem types you commonly misidentify.

Starting the problem

Setting up the problem

Attempt to solve the problem:

Try to solve the problem using the method you previously described.  First attempt the problem blind, without looking at any resources other than the problem itself.  If you found yourself stuck or uncertain during your blind attempt, take a look at your running crib sheet for relevant equations you may not have memorized.  Then, if that wasn’t enough, use easily available and relevant resources like: your fully-written out solutions to previous problems, similar problems your professor solved in class, or example problems in the textbook.  After exhausting all these resources try to find similar (but not identical) problems online.  Work your way though the problem, and when you think your solution is complete, check it mentally, box the final answer, and make it clear which pieces of work are part of your final solution, and which steps are wrong or irrelevant (which parts of your solution would you want to be graded if this problem were on an exam).  Don’t erase the extra information, just draw a simple, light, single line through it.

An example solution, notice my initial assumption was wrong, but after looking at an example problem I figured out the correct steps

An example solution, notice my initial assumption was wrong, but after looking at an example problem I figured out the correct steps

Immediately Check Your Work:

The most important part of dedicated practice is immediate and objective feedback.  To get feedback from your attempt you’ll need to compare it to the correct solution (found via a solutions manual, professor, online, etc…).  If your final answer isn’t the same as the final answer in the solution you are comparing it to, circle the problem on your adaptive set, you’ll need to redo this problem later.  If your answer is right, you still aren’t in the clear.  Go through your solution step by step and compare it to the correct solution.  Ensure that each individual step is correct.  It isn’t necessary that each step is identical, just that it communicates the same information as the correct solution.  Note, there are multiple ways to solve a problem, so don’t be overly concrete in the way you interpret this, just make sure you’re doing the right steps in the right order, and recognize that there are multiple ways to present the same correct solution.  If your solution is different than the solution you know to be correct, but you still think you’re right, you should probably cross of the problem on your adaptive set, write a question mark by it, and show your solution to your professor during office hours, asking them “would this get full credit if turned in on a problem set/test?  Am I correct?  I know this is different, but is it still right, and what are the advantages of their approach vs. my approach?”.

When you notice the spot where your solution diverges from the correct solution, mark it clearly with a line. Circle the problem on your adaptive set, you’ll have to come back to it.  Spend some time figuring out why you went wrong at that point (what incorrect assumptions were you making?).  Write an explanation of what you did incorrectly, why its wrong, and what would be the appropriate correction, near your line.  On the same piece of paper cross off the remaining wrong steps (with a single strikethrough so you can still read it later), and write the next correct step and an explanation of why its the correct step to take.  See if you can get to the correct solution with the new step.  While you’re working, guess what you think the next step will be, cover up the correct solution with a piece of paper, and reveal the next line after you’ve made an attempt at that step.  Repeat this process to go through the solution line by line, making sure that at the end you have the correct solution written out, with all the wrong steps crossed out.

Adaptively learn from your attempt:

At this point you should have a completed correct solution, even if that correct solution is full of crossed out misguided steps.  Now it’s time to use this solution to help you solve similar problems in the future.  At the bottom of your paper you will develop an algorithm for how to solve similar problems.  Start by identifying what type of problem you just solved.  Be general enough in your identification process that your solution algorithm will teach you how to solve any problem of this sort, but specific enough that your solution algorithm will completely guide you though every problem in this category.  Some examples of problem types I commonly identified in college were: finding eigenvalues, projectile motion, Gauss’s law, or double-slit interference.  Now make a list of the steps required to solve the problem based on looking through your (now) correct solution.  These steps should be idiot-proof, with no interpretation required, but they still shouldn’t do all the work for you.  Use the example I’ve included on how to find eigenvectors as a general guideline.  Examples of good steps for your algorithm are: recognize symmetry, fill out the Gauss’s law equation with the known variables, row-reduce the matrix to echelon form (assuming you are already comfortable with that, or have another algorithm for doing so), or set the derivative equal to zero then solve for x.  Examples of bad steps for your algorithm are: solve, find the appropriate equation (too general), or something that is so hyperspecific it only works for the particular problem you just solved.  The goal is to have an algorithm that you will be able to look at (and eventually intuitively understand and remember) that will take you directly from the problem to the solution as soon as you identify the problem type.  Finally, go through your solution and write down every equation that you used, but had to look up, on your running crib sheet.

My simple algorithm. Note that I already have another algorithm for how to find eigenvalues, calculate a determinant, etc...

My simple algorithm. Note that I already have another algorithm for how to find eigenvalues, calculate a determinant, etc…

Save your work:

Save your solution attempt in your solutions binder, whether it was right or wrong.  If it wasn’t your first attempt, replace your old (incorrect) solution with this more recent attempt.  You may want to revisit this solution when you are struggling with a future attempt of the problem or it may come in handy when you are asking a professor a question in office hours.

As you continue to solve more problems this way a few extremely beneficial things will happen.  First you’ll notice the types of problems you’ll see in the course, and that there aren’t as many as you may have originally thought.  My technical courses would typically assign 50-300 problems a semester, and after using my problem solving technique I would realize that there were often as few as 3-20 different problem types the whole year.  Learning how to solve 10 types problems is much more manageable than having to be able to solve one of 200 problems at a moments notice.  This practice will also help you identify what types of problems are on each test, allowing you to quickly complete the types you are comfortable with, and save the more difficult problem types until after you have racked up as many easy points as possible.  Next, you’ll become much faster at solving problems.  Every time you solve a particular problem type you’ll write out a new algorithm, which will lead to you developing better and more intuitive algorithms that you’ll begin to naturally memorize.  Reducing hundreds of hours of time spent listening to abstract lectures, reading confusing textbooks, and solving difficult problems to a relatively short list of extremely straightforward problem solving algorithms is the ultimate study hack for a college class.  With a single piece of paper (you may need to write small) you can explain to yourself how to solve any problem within the scope of the course, and if you’re allowed a crib sheet on your exams, you can use this paper to ensure success (although when you reach this point, you probably won’t need to use it because of the intuitive problem solving skills you’ve built developing your algorithms).  Finally, this will help you identify what you should study, so you don’t waste your time studying the wrong things.  If you recognize that you are consistently getting a certain problem type correct, take a break from solving that type of problem, and when you recognize the few types of problems that are the most difficult for you, make sure you’re next adaptive set is focused on practicing those problem types.

If you’re in a technical course you’re going to be solving problems anyway.  I can’t promise that my method will ensure that you learn as much as possible from each problem, become a faster test-taker, or consolidate a semester college course into a single piece of paper, but it worked for me!

If you give it a shot let me know.  I integrate this method into my tutoring practice and my personal problem solving practice, but I’m always looking for more feedback!

Weekly Block Schedules: How to Use Less Willpower and Time to Accomplish More

My learning method relies on using deliberate practice as the primary vehicle to improve course performance, gain insight, and learn the course material.  Since most of the learning happens through practice, you need to prioritize practice, and make sure that you are getting enough of it.  This is honestly the hardest part of college in my opinion, making sure you study enough (and don’t waste study time on low intensity studying).  For my first few years I felt as though I lived in a perpetual state of work, studying from when I woke up until I was too exhausted to continue.  When I started experimenting with my study methods (which led to the development of the method I am describing in this series of articles) and keeping track of my time I realized that I was wasting more than half of my “working-hours”.  Then I discovered and started using the time-management method I’m presenting below, which led me to accomplish much more without relying as heavily on willpower, feeling exhausted, or needing to work from sunrise to sunset.

I performed a time-audit on myself, which helped me notice that I spent more time deciding what and how to study instead of actually studying.  I have explained earlier how to spend your time studying, and your mega-sets will give you a good idea of exactly what you should be studying (which problems you are doing today), when you decide to study for each course, but even deciding where, when, and what course you will be studying for can be expend a lot of willpower; willpower that you should be using to actually learn something.  Willpower exhaustion is a real thing, and when you’re taking multiple classes with tests, homework assignments, lab reports, and projects due sporadically (and weighted differently) simply choosing when everything will get completed can leave you completely depleted of the willpower you’ll need to execute a difficult or unpleasant task that actually affects your grade.  It’s also a massive waste of time to switch from topic to topic whenever you “feel like it”, and every time you switch tasks it takes your brain a while to refocus.  Deliberate practice requires deep focus, and the 5-20 minute periods it takes you to remind yourself how to row reduce a matrix, or if your code should end in semicolons or newlines can eat away your day.  Studying when your brain is only working at a fraction of its full capacity is another time-suck.  You end up spending (at least) twice as much time to get the same amount of work done, and the quality is almost guaranteed to be worse.  When I see people studying late at night in the library I feel sorry for them, not only have they failed to recognize their optimized study times, but they are sacrificing sleep (which is essential for your memory and cognitive function) and they probably think learning takes much longer and is much more painful than it actually is.  The most devastating side effect of being an awful planner is that you miss out on the activities, events, clubs, friends, and experiences you want, and should be a part of, without gaining any academic benefit over students who have automated systems in place that ensure they learn more than you and have more fun than you.

I understand I’m making very bold claims in this article.  I’m suggesting that by planning your week you can accomplish more in less time, avoid staying up late and missing out on hanging out with friends, and that it will be easier to stick to than whatever you’re doing now.  I firmly stand behind these suggestions because it’s exactly the system I followed, and worked for me, year after year, and allowed me to have my nights and weekends free to learn how to skateboard, run a club gymnastics team, make new friends, and experience the unique events that make life and college so great.  I almost missed out on these by being a workaholic and thinking that time spent studying had a one-to-one relationship with course performance.  Once I set my ego aside and tried something new I was amazed at how much my performance improved; I prevented myself from burning out and losing everything I had worked for, and I got my life back.  So here’s the time management secret of number one students, weekly block schedules.

How to make a Weekly Block Schedule:

How to Start:

Use some sort of planning software, whether it’s google calendar, or just filling out columns in excel spreadsheets, it doesn’t matter.  What is important is trying to fit an entire week on a single page, in a bright, easy to understand, color coordinated manner.  Start by laying out a week, from Sunday to Saturday, making sure all of your waking hours are visible on the schedule.

Block Out the Mandatory Reoccurring Events:

Here’s where the things you “need to” be at, that happen in predictable times each week, like classes, labs, your hours at your job, reoccurring meetings (even if some of these things slightly change each week, still schedule them first), will be laid out.  It is important to do this first because these are the time commitments that are non-compromising, and you need to be sure not to double book any of these times, even though without a block schedule it is unlikely that you would miss any of these activities.  I like to pick a distinct color for each class so my study time for each subject is easier to track at a glance.  I tend to use a dull or faded version of the color for lectures or labs since they are low intensity learning.

Briefly mark off (but do not schedule) the office hours for each class on your schedule, this will come in handy later.

Step 1. Remember only colored segments are "scheduled".

Step 1. Remember only colored segments are “scheduled” at this point.

Block Out the Necessities of Life:

Waking up and going to bed at the same time every night is important, and without a clear visual understanding of your remaining free waking hours.  There are plenty of reasons to try to fall asleep and rise earlier, but pick whatever you are certain you will stick to with little resistance.  Block off where you will fall asleep every night and when you will wake up.  (If you have chosen to schedule less than 7.5 hours of sleep a night, stop reading now, close this page, and drop out of college.  Only a complete and total idiot would sleep less than “a full night”.  You’re in college to become smarter, and being sleep deprived is like being perpetually drunk: your body will fall apart, you will burn out, and you will become progressively stupider.  Disagree with me, I don’t care, if you didn’t value my opinions you would not have made it this far.)

Now include getting ready for the day, however long that takes you after you wake up. Include your normal grooming/showering time, and pick when you will be eating meals each day.  It’s alright to not schedule dinner, since you might not be studying that late on a regular basis.

Leave Saturday Open:

This doesn’t necessarily need to be Saturday, but pick a day where you have no reoccurring time commitments (and if you don’t have a day like this, try to make one), and block the entire day off as a free day where you do absolutely no studying, or work.

Step 2

Step 2, that’s actually what I wrote on my Saturdays in Fall 2013

Block Out your Deliberate Practice:

Now that you have laid out the essentials of everyday you can clearly see when you have time to study.  Different classes take different amounts of weekly study time, but I typically start with an even amount for each class, then cut back or add to certain classes based on my performance, and confidence with the course material.  Since studying means doing problem sets, whether they are mega-sets, practice tests, or homework assignments, I write “(name of course) p-set” in each of these blocks.  I have found two hour blocks to be most effective for me, but some things (like coding or using engineering software) have an associated start up times and are easier to accomplish when I have some momentum, so I block our longer sections for these subjects.  Trying to coordinate your study time with the office hours for a particular course is helpful too, since you will not have to take time away from another course to visit your professor, and if you get stuck on specific problems you can just walk over to the appropriate office and ask for help, without it disrupting your progress for the day.  Choose a deeper shade of the same color you chose for each class to represent that this is the intense part of studying, and where most of the learning will actually happen each week.

If you are a serious student, college is and should be your full-time job.  Following this analogy I found that 8 hours a day was very appropriate for myself, and most other students.  Those 8 hours include class (even though you aren’t learning a ton from class), so the studying should fill the remaining 3-7 hours a day.

Pick a time after which you will not be studying everyday:

The same time every day.  Following the full-time job analogy I usually chose 4 or 5 PM, and after this time, do not do any studying.  Having a concrete end time every day helps you get more done and waste less time, especially when you have assignments due the next day.  Parkinson’s law states that the time required to complete particular task will often fill the time that is allowed to complete it, so by limiting your study hours each day you will become rapidly more efficient, and be totally free to live like a normal human instead of a study slave.  The nights (or whenever you want your free time to be) are yours, don’t let poor planning take that away from you.

When completing this step you should have a schedule with 8 hours a day (6 days a week) of study time.  And a clear line after which no studying is scheduled (and you are banned from studying until the next day).

Step 3. Important things to note: I did my best studying in the morning, so I put the classes that were most important/difficult there, Proofs and E&M were by far my hardest classes, Computational Physics was a computer science class, so I used longer blocks, Advanced ODEs and Physics Math were pretty easy and I ended up doing most of my studying during the actual class time, I never really attended Physics 204 (Alex Sieber can confirm this), you can figure out which classes were which based on color coordination

Step 3. Important things to note: I did my best studying in the morning, so I put the classes that were most important/difficult there, Proofs and E&M were by far my hardest classes, Computational Physics was a computer science class, so I used longer blocks, Advanced ODEs and Physics Math were pretty easy and I ended up doing most of my studying during the actual class time.

Schedule in the Fun:

Just as we recognized that studying that isn’t scheduled is less likely to happen, the same idea applies to fun.  Include the clubs you want to go to, concerts and events you want to attend, and whatever else you are looking forward to, or want to do for fun.  When looking at your schedule, seeing the fun and the end of your daily working hours, motivates you to keep going.  Instead of the perpetual slog though 4 years of college, I find myself thinking “okay just two more hours then I’m off for the night and get to meet my friends at the skatepark”, which really helps me finish strong everyday.  Scheduling in fun also gives you a reflective pause to look at your week, and decide what you want to do instead of relying on impulse and circumstance to help you live an interesting life in a proactive and mindful manner.  There is no need to fill up the remaining hours in the schedule, unstructured free time is awesome, but if you are the type of person who jam packs their day with eight hours of work followed by eight hours of fun and eight hours of sleep, go for it!

Finished Product. I would then print the sheet out, fold it up, and carry it in my pocket with me at all times, crossing off a block once I completed it to get a small reward for completing my scheduled task. I would write in pen on my sheet the fun activities I planned for my free time as I planned them, as these parts of my life were (intentionally) left to be more spontaneous.

Finished Product. I would then print the sheet out, fold it up, and carry it in my pocket with me at all times, crossing off a block once I completed it to get a small reward for completing my scheduled task. I would write in pen on my sheet the fun activities I planned for my free time as I planned them, as these parts of my life were (intentionally) left to be more spontaneous.

If you’re feeling overwhelmed, undisciplined, or are studying late at night, take the rest of the day off and make a schedule for the rest of your week.  I’m very confident that after only a few days you’ll be feeling less anxious, having more fun, learning more, and “working” (or doing what feels like unpleasant work) less.  Rule your weeks before they rule you!

The final results of the semester

The final results of block scheduling my semester

If you want the excel file I used to format this (and the rest of my weekly schedules) send me an e-mail at CharlieGriffin@email.arizona.edu with excel schedule file in the subject line, and I’ll send it your way as soon as I can!

Adaptive Sets: Where the Actual Learning Happens for Technical Courses

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.

How (and Why) to Speed Read Textbooks Before the Semester Starts

Side Note: After getting e-mails and requests to talk more about the learning method I developed and used in college I’ve decided to write more about it, and turn it into a small project.  I want to make a guide that is as good as possible, so I’m doing a little giveaway to help you (the readers) help me.  The first person to read this article, apply the knowledge (speed read their textbooks) and e-mail me, sharing how it worked will get a PDF with 5 articles from the guide I’m working on.  Some of these articles will never be released for free on my website, so jump on this while you have the chance!

Some of my favorite textbooks to speed read

There’s no way I’m reading these the same way I read novels

How (and Why) I Speed Read Textbooks 

Getting ahead is one of the biggest favors you can do yourself in college.  Whenever I started to fall behind in my classes, it always seemed like an insurmountable task to catch back up.  When I’ve procrastinated an assignment (or studying for a test) until the last minute, catching up always becomes a stressful mix of all-nighters, sloppy work, and negative feelings about the class, my work, and often my image of myself as a student.  When I’m catching up I feel like I expend more effort convincing myself to work than I do actually working, and the sense of accomplishment I should feel from finishing my work is replaced by guilt and a feeling that “I shouldn’t have gotten this far behind in the first place”.

In just the same way that getting behind can start a downward spiral, getting ahead can positively reinforce me to stay ahead, and stay on top.  If you look at individual classes as races (to complete all the work and studying) there become two main strategies for winning (succeeding): getting a head start and keeping a reasonable pace ahead of everyone else (low stress, more strategy), or running sporadicly, at a pace you feel like, when you want to, then sprinting until either you reach complete exhaustion or the semester ends (whichever comes first) once you realize that you’re not winning the race (high stress, low strategy).  In this article I will explore the first steps of the low stress strategy, that is how to get ahead at the start, and an easy way to stay ahead.

The most effective way I’ve found to do this is to read ahead.  More specifically I am recommending completing the reading for the entire year before the first day of class.  This might sound very difficult and time consuming, but I will share my strategy for why it isn’t, how it will take less than five hours (per class), and probably save you 20-50 hours (per class).

In my experience, almost every professor lectured either directly out of the assigned textbook, directly out of another textbook, or from a set of lecture notes or powerpoint slides (or some combination of all of the above).  Whether or not you think lectures are an important part of the learning process, the lectures and reading materials lay out the professor’s expectations for what the students should learn throughout the course.  If you had access to all the materials ahead of time, and were familiar with them before the first day of class, there is no doubt you would have a head start on all your peers.  You could start working on the assignments and projects immediately (even final projects, and homework assignments due at the end of the year), and you would have a frame of reference on where the course was going instead of being blindly led by your professor along with the rest of the class.  The ability to start assignments early will allow you to front-load the course work, have more time to get your assignments revised before turning them in, and cue you in to what topics in future lectures will actually affect your grade (or are worth paying closer attention to).  Covering the material early allows you to start studying for exams and finals on the first day of class, gives you the opportunity to ask better questions at office hours and in lectures (since you’ll actually know what you’re talking about), and will show your professor that you are serious about learning the material (which often leads subjective grading decisions to be made in your favor).  The perspective you gain from this will help you identify the sections you need to spend more time understanding early, and (possibly more importantly) the topics you already know, or have previously mastered, so that you can weight these much less heavily (or even skip) while studying.

Aside from being useful for understanding lectures, it also allows you to jump right into the work that matters, that will actually improve your performance and understanding of the material, the practice.  As I explain in my test taking article, practicing taking tests and solving the types of problems that appear on tests is the most straightforward method for improving test performance, and other study strategies are low intensity distractions.  Spending too much time reading and re-reading the course materials will either take away from the time you should be learning something, or will add pointless study time to your life, which will take away from the activities and freedom that are essential to your success as a student living a balanced life.  My philosophy is to do the work that matters, and skip (or speed through) everything else.  Speed reading the text gives you a good idea of the scope of the course, as well as where you can look in the future when you need a specific question answered, but it will not trick you into thinking you actually learned how to solve problems or any important skills from reading without applying your knowledge, which people often fall victim to when they spend hours making sure they “understand” each concept before moving on to the next one (e.g. reading slow).  Below I have outlined the exact plan I used to speed read my textbooks for every course in college before the first day of class.  Following the same philosophy I outline for learning and reading, don’t think you’ve learned anything by simply reading this article; give it a shot, then form your judgements about speed reading later.  If it does fail miserably (which it never did for me) you will still be ahead of your classmates and your professor will already take a slight bias towards you.

Figuring Out What To Read:

This is easy, and will save you a lot of time.  Meet with or e-mail your professor before the semester starts asking, what text book the course and lecture follow.  Tell your professor you want to get a head start on the course over break, and be sure to ask if the lectures are based on any other books or notes that aren’t mentioned in the syllabus, as well as exactly what chapters the students are expected to master over the course of the semester.  I understand that this information is often in the syllabus, but a few of these conversations led me to books that professors use to find exam problems, that none of the other students knew about, which quickly became an extremely unfair advantage for me.

How to Speed Read:

Once you’ve identified the reading materials, collect them in one place, and give yourself exactly five hours to read all of it.  I prefer reading actual textbooks or pieces of paper to electronic documents, but work with whatever you have.  It’s important to have everything in one place while you read so you can estimate how you’re progressing through the material.  My speed reading method is to put my finger on two or three locations (depending on the page width) on each line, that roughly evenly divide it (see image).  This way you read faster, and your finger dictates your reading speed, not the cadence of your self talk.  While reading I hold my tongue on the top of my mouth to make sure I’m not saying the words in my head as I read.  Saying everything you read in your head will seriously slow you down, and whether or not you normally do this while you read, you shouldn’t do it while speed reading textbooks, since you’re not here to enjoy the story, you’re rapidly covering the material so you can dive deeper and shortcut your way to the actual learning.  The reading itself consists of looking at the text above your finger (not every word, you’ll catch a few words each time you change where you’re looking, and will get better at this the more you practice speed reading).  Don’t take notes, don’t highlight anything, at least not now.

An Example of Where I would Place my Finger for a Specific Line in a Textbook

An example of where I would place my finger for a specific line in a textbook

Choosing a reading speed is simple.  Titrate your speed by keeping track of your progress.  Since you are going to finish in exactly 5 hours, if you’re less than 20% done after the first hour speed up, and if not, slow down.  Changing your speed is easy, since all you have to do is change the rate at which your finger is moving through the book.

There are a few major differences between this method and reading a textbook like a novel.  First this is much more intense.  It’s easy to get overwhelmed with information, and that’s why I suggest doing the reading in 1 hour chunks, taking a 10 minute break to do some sort of light exercise (like walking, jumping rope, etc…) every 50 minutes.  The combination of the intensity, and the rapid progress motivates me to finish the 5 hour reading sessions in a single day, as I don’t want to exhaust my brain on days when I want to practice the material, and it feels like a great accomplishment to finish a textbook, especially when you’ve done so in one sitting.  Second, it feels very different.  If you are new to reading this fast you will feel like you’re missing a ton of material, and maybe even like you’re missing everything.  All you can hope to gain from reading is memorized knowledge, which quickly fades if not reinforced, so this feeling will actually give you a better perspective on what you’re accomplishing by reading, and while you may not be able to pull exact phrases from memory, you’ll be surprised in lecture, as the concepts are revisited, how much you actually picked up in your initial run though the text.  Don’t give up when you start feeling like this, just push through and finish without taking any extra time, use first hand experience and objective results to draw conclusions on how this method works for you instead of giving up the second it feels different than what you’re used to.

The same technique applied to more math heavy sections. The orange lines are my finger placements. Notice I read math like any other text.

The same technique applied to more math heavy sections. The orange lines are my finger placements. Notice I treat math like any other text.

Don’t Read the Textbook Again:

Look things up in the book when you want to answer a specific question, or revisit a specific example, but do not read the book or sections of the book cover to cover again.  If you ignore this last step, the whole exercise will not save you any time.  When you feel like reading in the future do some meaningful studying instead.

That’s it, one simple five hour investment will save you the 2-3 hours you would normally spend reading each week, and give you a small head start, that will get you in the right frame of mind to excel for the rest of the year, without feeling any time pressure or guilt about being behind.  Once you’ve finished do something to reward yourself for being so far ahead and to overcome the brain fog and intellectual overwhelm that this speed reading session has probably created.  Have some fun, and think about all the fun you’ll be having in the future while your peers are stuck at home reading a boring textbook, then remind yourself that right now (before the semester starts) you’re the top student in the class.

My Low Stress Method for Mastering Test Performance

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Test performance matters.  In most of my senior and junior classes, exam scores have typically accounted for ~85% of my final grade.  However, professors have rarely given the students in these classes any guidance on how to succeed on tests, and when they do, the information has been almost totally useless.  I always make it a point to ask, both in class and at office hours, what recommendations would you make for students hoping to do well on this exam, and the response is almost always, if you know all the material you should be fine.  Not only is this terrible advice, but it is so wrong that I suspect the professors are being intentionally misleading.  Yes, the goal of a class (from the perspective of the professor) is that the students internalize all the important (as decided by the professor) material, then demonstrate it.  Let’s suppose that I have learned all the course material to the point of perfect recall, but I have not prepared for the test itself: the format could confuse me, I could run out of time because knowing something, and being able to do something quickly are two very different things, I could provide solutions on my exam that misrepresent my knowledge (not giving the professor the work or format they are looking for), and I could misunderstand the intention of the questions.  In fact its not uncommon for smart, hard working students to do poorly on tests because they are self-diagnosed “bad test-takers”.  In my experience taking heavily test based courses I’ve learned that this actually means that they are “bad test-preparers”, and that they are usually completely unaware of what this distinction means.

What I have found is that there is no shortage of information about inefficient test preparation methods given out by academic advisors, resident advisors, teaching assistants, and college workshops, but techniques that actually work are very difficult, and sometimes even impossible to find.  While this inefficiency is startling, it is also exciting for students who are aware of the preparation techniques that lead to a near perfect test performance.  My ability to properly prepare for exams has helped me achieve greatness as a student, and has significantly decreased the stress, uncertainty, and disappointment associated with the process (and the results).  The most valuable asset that I have learned as a student is my ability to test out different strategies and to see what works for me.  If it weren’t for my excitement about self experimentation and my ability to try new novel approaches (while selectively ignoring conventional wisdom), I would never have learned the strategy that I am presenting below.  What follows is not a perfect prescription for high exam scores, it is however the strategy that I have developed from six years of constant experimentation, which has lead me to score either a perfect score or the top score in all of my classes >50% of the time.  The best advice that I can give any ambitious student is to unlearn the techniques they already know for studying (primarily because most advice is total garbage, e.g.; review your notes, draw a flow diagram, pay attention in lecture, form a study group, …), and instead become objective, try something new, and compare your results.

Disclaimer:  I am heavily involved in math and physical science courses.  This strategy is made specifically for technical courses (Chemistry, Physics, Engineering, etc…) where problem solving is the goal of exams.  I have found it to work for all courses with some simple modifications.  For example in an English course the “problems” are essay topics.

The Study Strategy that Maximizes Test Performance:

14 Days Out: 

Starting two weeks in advance may seem more time consuming and impractical, but it allows you to take advantage of techniques to learn the material better (spacing), become more comfortable and powerful during the actual exam (simulations), and eliminate stress, late nights, or ever having an overwhelming amount of work to do (front loading and focus).

Deciding What to Study:

First construct a quick list (don’t spend more than 20 minutes on this) on everything that has been covered so far.  Do this using the past homework assignments as a guide.

Meet with your professor.  A private meeting or office hours is ideal because you can get more information out of them, and doing so privately gives you a small edge over the rest of the class (who probably aren’t going to study until 2 days before the exam anyways).  Express to your professor that you have been working hard all year and that you want to put in the work to do well on the exam.  This lets them know you are concerned with learning, not finding loopholes to a desired grade, which helps them feel more comfortable giving you helpful information.  Write down everything they say as they say it, then go through your list of topics one by one.  Ask can I expect to see this on the exam, for each one.  If they say no, cross it off, one less thing to study, less time wasted.  Finally ask, what are the most important testable topics covered on the upcoming exam?  Add whatever they say to your list.  Now you know what to study.

Figuring Out the Logistics of the Exam:

Now ask the professor every logistical detail about the exam.  The most important questions are; what resources are we allowed to use (crib sheets, calculators), what is the format of the exam (solving problems, multiple choice, how many problems, what length, are the problems similar to the homework, …).  Now you know how to study.  If you get are allowed a resource during the exam, do all of your preparation using that resource.  You wouldn’t practice for a basketball game on a 20 or 5 foot rim, you should use a regulation court.  That’s it for the day, just keep all of this information on one sheet of paper and use it as your guide moving forward.

13 – 10 Days Out:

Spend an hour or two a day, whatever feels good, but won’t burn you out, practicing for your exam using the following procedure.

Select a Problem Similar to a Possible Exam Problem:

Use whatever conclusions you gained from your list to find these problems.  If it is similar to the textbook problems, choose a textbook problem on a topic covered on the exam that you haven’t already solved.  If there is a practice test do that first.  If you can’t find the right problems, create them.  Look at past exams, other textbooks, modify in class examples.  You will rarely ever have to try this hard, usually solving the unassigned problems in the textbook and completing a practice exam (if it is available) is all you need to do.

Solve it with the Allowed Resources:

Focus, shut off outside distractions that won’t be available on tests and complete individual problems in a single sitting (no starting a problem at one session and finishing it at another).

Check Your Solution Immediately After:

Notice where you went wrong if you made a mistake, circle the problem and try it again later (add it to your pool of good practice problems).  Then organize these correct solutions in a folder and repeat.

9-7 Days Out:

Again, don’t overwhelm yourself.  You should be covering all of the topics, and gaining speed and accuracy in your problem solving abilities as you practice.  Continue to work problems, but do so in discrete intervals the length of the test time (e.g. One class session, the length of the final exam period).  Getting used to sitting still and focusing for the duration of the test is a valuable asset that can be easily trained.

Ensure Your Solutions are Worth Full Credit:

Meet with whomever will be grading your test (professor, TA, etc…) and show them your folder of completed problems with correct solutions.  This will let them know you are working hard, and if you make a mistake on the test they will be more likely to give you the benefit of the doubt, since you are demonstrating you are a good student.  Also asking for help allows them to partially share your success.  Show them your work and ask would this be worth full credit on an exam, and if not what changes would you recommend I make?  This ensures that on the exam you show exactly the amount of work they want to see, and you don’t waste time overanalyzing your results, or lose points for a partial explanation.  Also identify your weaknesses, where you struggle.  Ask how to solve problems you have trouble with, and focus your future studying more on these tricky problems, since there is no reason to spend your time practicing concepts you have already mastered.

6-3 Days Out:

In addition to one hour (no more) of solving new problems a day, which is meant meant to ensure that no matter what problem is asked on the exam, you are familiar with it and have solved something similar before (in my experience, often lazy professors pull problems from the textbook and you might be able to reproduce the entire solution from memory), add the most important element of the preparation process.

Simulating the Test:

Reproduce an environment identical to what you expect to see on the test.  Develop a test using problems you have not solved correctly before (and don’t look at the solutions until after you complete your test simulation)(Note: problems you have failed to solve correctly in practice are also perfect for these tests) and the information you understand about the logistics of the test (number and type of problems).  Take a break after writing the test to forget the problems (so you actually have to read them), then return to it and take a timed practice test.  You want to produce an environment more stressful than the actual test so it seems easier and you get a sense of relief when you take it (an analogy for this is practicing uphill runs for a flat race).  Choose challenging problems.  Give yourself less time on each subsequent practice test.  For example for a 60 minute test I practice by allowing myself 50 minutes on day 6, 45 on day 5, 40 on day 4, 35 on day 3.  After you finish spend at least an hour away from the test so you forget why you made the mistakes you may have made.  Then grade your test in the harshest manner possible (never give yourself the benefit of the doubt).  If you get a perfect score, it means your test was too easy and your next one should be more difficult (use more difficult problems).  Do this once a day.  To master something you must practice, so practicing the test itself should be the most straightforward strategy to improving your test score.

Correct Your Test:

After each test you take, research and write out full correct solutions.  Recognize where and why you made errors.  Problems you missed on past practice exams are fair game for future practice exams.

2 Days Out:

This is the last real day of studying.  Sharpen your tools, finalize your resources.  Make sure your crib sheets are complete, your calculators are fully powered and you are confident you understand what will be on the exam.  You can stop casually doing problems now, and instead focus all of your time on your test simulations.

Impossible Tests:

Make two worst case scenario tests.  Put on the most difficult problems the professor could possibly ask.  Focus on the topics you struggled with, and give yourself half of the time you will be allowed on the actual exam, and grade yourself brutally.  This will be a struggle, but it won’t necessarily be time consuming.  After completing these, grading them, and writing out complete idealized solutions, make one final exam simulation.  You should seek to make it as realistic as possible, and give yourself 3/4 of actual allotted time.  After the intense practice testing the realistic test will feel easy (or at least easier than you anticipated), you will probably complete it early because of all your practice with less available time.  You will most likely do very well, which will boost your confidence, and destroy all your pre-test anxiety.

The Day Before:

Take the day off.  Laugh at all of your friends and classmates who are staying up all night studying, are incredibly stressed out, and are unknowingly shooting themselves in the foot by taking the test with a sleep deprived mind.  They can’t possibly cram what you’ve done over the past couple of weeks into a single evening.  Have relaxing fun, and go to bed early.  I like to watch a movie the day before a test to keep myself composed and cool.  You over prepared (in intensity) for the exam, you should do well.

If you try this technique I would like to know how it works for you.  E-mail me with the subject line Conquering College at CharlieGriffin@email.arizona.edu to share your experience, or if you would like advice on how to do better in other areas of your classes.  I have a few articles already written from my college experience and I’d be happy to share them with anybody who is dedicated to taking action towards improving their academic performance.