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Saturday, June 17, 2017

Test Prep Champions

The Ultimate Guide To Multiple Choice Test Success: Mind-Blowing Secrets For A Higher Score

How To Beat Multiple Choice Tests (Even If You're Not A Great Test Taker)

Multiple choice questions test prep guide introduction photo

I have a love/hate relationship with multiple choice tests. I love them when I do well, and hate them when I don't. Most students say they feel the same. 

The truth about multiple choice tests is that most of the time they don't just test your knowledge of the material; they test you on your test taking skills. 

If you're a good test taker, this isn't a problem for you. However, if you have some room for growth with your test taking skills, multiple choice tests can be a real drag. 

This is such a shame, and I put together this guide because I'm sick and tired of seeing diligent, hardworking students get lower grades than they deserve!

The good news is that your skills for answering multiple choice questions can be improved, and my goal here is to show you exactly how you can start enhancing your abilities immediately!

Some Interesting Facts

In Rock Breaks Scissors: A Practical Guide to Outguessing and Outwitting Almost Everybody, author William Poundstone details an analysis he conducted on standardized test answer patterns.

For true/false questions, he found that true answers are more common than false answers, and that two dissimilar responses in a row (true, false, or false, true) are more likely than two similar responses (true, true, or false, false).

Poundstone found that for questions with all of the above or none of the above as answer choices, the all, or none, options had a 52% chance of being correct.

Multiple choice questions and answers data shows 52% of all/none of the above answer choices are correct

Multiple choice questions and answers data shows that the probabilities of answer choices being correct varies based on the number of answer choices
He also found that the probability of an answer choice being correct varies with the number of answer choices such that:

  • There is an equally likely chance each answer is correct when the question has 3 answer choices (for example, A, B, and C).

  • There is a slightly higher chance that answer choice B is correct when the question has 4 answer choices (for example, A, B, C, and D).

  • Answer choice E is most likely to be correct when the question has 5 answer choices (for example, A, B, C, D, and E), 

  • Answer choice C is least likely to be correct when the question has 5 answer choices (for example, A, B, C, D, and E)

What can we learn from this? 

Should you take it to the bank that true answers are more common than false answers on your next test? 

Well, maybe. 

But there's an even bigger takeaway here, namely that a lot of research has been done into how to ace multiple choice tests. 

What you're about to learn in this guide are proven strategies to help you gain a huge advantage on your next test, regardless of the different types of multiple choice questions you get! 

A 3 Phase Approach

I recommend a 3 phase approach, in which you cycle through the test questions in 3 waves. Let me give you a brief overview of how it works. 

During the first phase, you're going to read each question and do all of them that you can answer in about a minute, while marking all of the questions you can't answer to come back to. 

In the second phase, you're going to go back through and use a combination of the strategies you'll learn below to answer the questions you marked in phase 1. 

The third phase is all about taking a guess on the questions you still haven't figured out, and checking the answers you already put down.

This approach works for a variety of reasons. One is that when you skip the hard questions at first, your brain "works" on them in the background while you do the easier ones. 

Another reason is that many students suffer from the jitters when they first get into the test. Anxiety and stress levels can spike quickly, and working on the test questions in cycles like this helps you get the nerves out of your system. As you get settled in, you'll have a better chance at getting the harder questions right than if you try to do them right away.

Final Thoughts Before We Jump In

Before we move ahead, I just want to say that everything you're about to learn is based on the assumption that you're preparing well before going into your tests.

Having a complete understanding of the material should always be your first line of defense, and without this foundation in place, this whole guide probably won't be much help.

There are no magic bullets here that will work without first putting the work into learning the material! This being said, tons of students go into tests prepared, and still don't do as well as they were hoping. That's who this advice will be most beneficial for. 

As I said at the start, just knowing the material well doesn't guarantee a good grade, and that's where these tips come in!

Also, you may find some advice here that contradicts things you've learned before. If your way's not working, I strongly encourage you to try some of this advice, even if it's totally different from what you've done in the past.

There is no one strategy that will work for everyone in every situation! Everyone has their own personal learning style, so feel free to use all of this advice, some of this advice, or none of this advice!  

Let us now look at each phase in more detail!

Phase 1:

Read each question, and then think about the answer before you go to the choices

For the first phase, you'll just go through each question. See if you can think of about what the answer should be in your head after reading each question, but before looking at the answers.

It's important to clarify what the question is asking before you try to answer it. This may sound like common sense, but you'd be surprised by how many times students lose points because they pick an answer that's factually correct, but doesn't actually answer the question!

We're now going to look at an example that I've intentionally tried to make as simple as possible for teaching purposes. Although you can probably figure it out just from your common knowledge, I encourage you to focus on understanding the strategy behind the question, and not on the question's content! 


Which of the following drinks is most likely to keep you up at night?

A. Water, because it hydrates you

B. Pepsi, because it comes in multiple flavors

C. Milk, because it builds strong bones

D. Pepsi, because it has caffeine

In this question, all of the answer choices contain true information. However, factually true answer choices don't always answer the question! D is the best choice here.

Read carefully for absolutes

Absolutes are words such as never, all, none, always, and must. 

Be skeptical of answer choices that contain these absolutes, especially when all of the answer choices except for one have them! There's usually a good chance that the lone answer without an absolute in it is the correct answer choice.

In most school subjects, it's rare for there to be no exceptions, which words like all, never, etc.. rule out! Be aware that sometimes an answer choice with an absolute will be the correct answer choice, but it's worth taking a second to pause and think critically when these words come up!

Watch out for negatives

For example, you may get a question that asks "which one of the following is not correct?"

I recommend circling the word not and similar words so that you don't get confused!

Along these same lines, watch out for questions that ask : "which one of the following is false," or "all of the above are true except _____." It may be helpful to circle the words false and except so that you're aware of how they change the meaning of the question.

Note that if a sentence has a negative followed by another negative, the meaning of the sentence is the same as it would be without the negatives!

Switchback words also switch the original meaning of the sentence

Switchback words include like, but, although, and while. Don't get tripped up by them!

Whenever you get a question with absolutes, negatives, or switchback words, stop and read the question twice! You should also mark the question before moving on to come back and check it quick at the end.

After you've read the question carefully and noted anything special in the wording, go ahead and try to brainstorm the answer in your head before you check the answers. 

Now, obviously if you get something like "which one of the following is false," this strategy won't apply, so you can skip this step in those cases! After you brainstorm your own answer, check and see if your answer matches any of the actual answers. If it does, then that answer is probably correct!

However, you'll still want to make sure you can eliminate each other answer choice before moving on! 

Use Process Of Elimination

I recommend crossing the entire answer out when you eliminate it rather than just crossing out the letter in front of it (if you're allowed to write on the test)! 

The key rule is that if you can make an argument for why an answer is wrong, cross it out! NEVER eliminate an answer just because it doesn't seem right! On tests, you never want to rely on your intuition unless all else has failed. 

Take the time and mentally explain to yourself why the answer is incorrect quickly before you eliminate it. Perhaps even jot down a few words about why each answer is wrong before moving on, just because it makes it easier to confirm for yourself that you're making the right choice.

Mark Reservoir Questions

A graphic showing multiple choice tips on reservoir questions

Reservoir questions are questions that contain information you can use to answer other test questions. Questions with answer choices like all of the above or which of the following is false can be great sources of information! 

The reason I call these questions reservoir questions is because they give you a short list of factual statements that you may be able to use to figure out other questions you aren't sure of!

If you're sure at least two of the answers are correct for all of the above questions, you can just pick all of the above

This is especially helpful when you're given a question with 5 answer choices, and you're sure 2 of them are correct, but are unsure of what the other answer choices mean. Since you know they're all true just because you correctly recognized two of the answers, you can use these answers to help you on questions you aren't sure of!

Now, you won't always be able to do this, but still, sometimes this information will trigger something in your memory that you can use to get other answers correct!

Phase 1 Summary:

  • Read each question carefully before you go to the answers. 
  • Next, try to think of about what the answer should be in your head if applicable. 
  • For questions with absolutes, negatives, or switchback words, read extra carefully and mark the questions to double check them at the end. 
  • If your answer is close to one of the actual answer choices, make sure you can eliminate the others, and then stick with that choice!
  • Be on the lookout for any questions that are about similar topics, and mark them. You may be able to use these questions as "reservoirs" to figure out other questions!
Whenever you get to a question that you can't answer within about a minute, mark the question, move on, and come back to it! 

Phase 2: Apply Multiple Choice Strategies

You will now cycle back through all of the questions you marked from phase 1. You should be fairly confident at this point that all of the answers you've put down are correct.

It's now time to employ a few strategies to ensure you don't leave any points on the table for the questions you have left! Remember, the answer to each question is on the page, you just have to identify it!

Strategy 1: Recycle information from "reservoir" questions

Ask yourself if there's any information in the other questions that can help you. If you followed the method in phase 1, you'll have already done this!

Sometimes professors leave info in questions that can be used to answer other questions on the test. This almost always happens by accident.

Everyone has their blind spots, so sometimes even proofreading a test multiple times doesn't make this obvious. 

Even if your professor hasn't left any blatant info on the pages, you can almost always find enough info to get a hint or two.

Remember, all of the above questions are valuable questions to look at for this!

Strategy 2: Look for two answers that are similar

If you ever get a question where two answer choices are very similar to each other, but not to any of the other answers, chances are one of the two is correct!

Often this will happen with answer choices that contain conflicting information. 

Also, watch for answer choices that contain synonymous (two words that mean the same thing). If the answers both mean basically the same thing, then they can't both be right!

Strategy 3: Pick the longest and most precise answer

Did you know that longer answers are correct more often than shorter answers? This is even more true on average when an answer is not only longer than the others, but also more precise.

This is true because test writers often need to add more words to make sure an answer is objectively correct and without room for ambiguity. For wrong answers, they're less likely to be as precise.

This knowledge is especially helpful when you've eliminated the answer choices down to 50/50. Look at the longest and most precise answer and consider very carefully if it's correct!

Strategy 4: Pick a benchmark answer to compare the others to

Sometimes more than one answer will have some truth to it. For questions in which multiple questions seem plausible, you'll want to go with the answer that is the most plausible! 

A good way to do this is to make one plausible answer a benchmark answer, and then compare this answer to the others until you find an answer that seems more plausible, which then becomes the new benchmark.

For example, let's say answer A seems plausible. You compare it to B, but B doesnt seem as plausible. Comparing A to C, it turns out that C is more plausible, so you can eliminate A, and C becomes the benchmark. You just have to compare the remaining answers to C, and if neither are as plausible, C is your answer!

The key here is to try to make a logical argument that each answer is more plausible than the benchmark, and if you can't, pick the benchmark as your answer! If you can, then eliminate and select a new benchmark!

Strategy 5: Counting

This strategy is only applicable in certain cases, but it's one of the most reliable methods for getting the answer correct! It's best illustrated with an example.


The earliest evidence of lemonade was found in which country during which year?

A. Egypt, 2000 AD

B. India, 2250 AD

C. Egypt, 1000 AD

D. USA, 1000 AD

The strategy here is to count up the number of times each country shows up in answer choices:

Egypt → 2 (A and C)

India → 1 (B)

USA → 1 (D)

We then do the same thing for the years:

2000 AD → 1 (A)

2250 AD → 1 (B)

1000 AD → 2 (C and D)

Because Egypt and 1000 AD show up the most in answer choices, we can conclude that the answer that contains both is correct. Here, this is answer C!

Let's look at one more example of this technique before we move on.


Which answer choice includes only drinks with caffeine?

A. Orange juice, coffee, milk, Pepsi

B. Coffee, cider, pepsi, tea,

C. Mountain Dew, pepsi, coffee, apple juice

D. Pepsi, Coffee, Mountain Dew, tea

The strategy here is to first take stock of how many times each drink appears:

Orange juice → 1

Apple juice → 1

Coffee → 4

Pepsi → 4

Mountain dew → 2

Cider → 1

Milk → 2

Tea → 2

Now, we add up these values based on the drinks in each answer choice:

A. Orange juice, coffee, milk, Pepsi → 1 + 4 + 2 + 4 = 11

B. Coffee, cider, Pepsi, tea → 4 + 1 + 4 + 2 = 11

C. Mountain Dew, Pepsi, coffee, apple juice → 2 + 4 + 4 + 1 = 11

D. Pepsi, Coffee, Mountain Dew, tea → 4 + 4 + 2 + 2 = 12

Since the total value we got for D is the largest, it's safe to conclude D is the correct answer.

Both examples are slightly different, but both illustrate how the same basic counting strategy can be applied! Don't be afraid to actually write out the numbers on your test if it helps you!

Again, you could probably answer this one based on common knowledge, but the important thing is to understand the strategy so you can apply it to harder questions!

Strategy 6: The Cornell Method For Qualifiers (source)

According to basic grammar rules, a qualifier is a word that qualifies or modifies the meaning of another word. Qualifies are typically adjectives or adverbs, but not always.

To use the method, it's best to be familiar with this list of qualifier families:
  • All, most, some, none (no)
  • Always, usually, sometimes, never
  • Great, much, little, no
  • More, equal, less
  • Good, bad
  • Is, is not
Whenever you see one of these words in an answer choice, replace it with each of the other qualifiers in the same family. If another qualifier from the same family as the original qualifier in the question is a better fit, then the answer is false and can be ruled out!


Is the following statement true or false?

Statement: Students are always unable to sleep after drinking caffeine late at night

The strategy here is to replace the word always with each of the other qualifiers in the same family to look for a better fit:

Students are always unable to sleep after drinking caffeine late at night

Students are usually unable to sleep after drinking caffeine late at night

Students are sometimes unable to sleep after drinking caffeine late at night

Students are never unable to sleep after drinking caffeine late at night

See how changing the qualifier dramatically changes the meaning of the statement?

The best answer seems to be the second choice, but the third choice is also plausible. The first and last choices with the words always and never aren't plausible answers; some students have no trouble falling asleep after drinking caffeine, while many others avoid caffeine purposely after a certain hour because it keeps them up.

This method may not be desirable for everyone; with tons of stuff to memorize already for most tests, it may not be worthwhile to memorize the qualifiers in each family. Hopefully though you can at least see the logic behind this method, and how it can be helpful!

Phase 3:

Okay, so you went through the questions once and answered everything you could. Then you went through them again and applied the strategies discussed above to answer as many as you could. What's left?

At this point, you probably won't have that much time left, but that's okay! It's now time to put your best guess down for any unanswered questions, so go with your gut!

The key rule is this: logic first, gut second. Since you've already tried to reason your way through these questions unsuccessfully, just go with your best guess! You don't have to get them all right to get an A. You just have to get most of them right!

In short, the third phase is when you'll answer the remaining questions, and will also review the other questions with the time remaining.

Should you always stick with your first choice?

A graphic showing sticking with your first choice for multiple choice questions isn't always a good idea

Most students have heard millions of times that you should always stick with your first choice. The main reason why this can be helpful is because it prevents you from second guessing yourself.

For example, let's say you're taking a 50 problem test, you have 5 minutes left, and need to check all of your answers. In the heat of the moment, it's easy to work yourself into a frenzy as you review your test under a strict time limit and to start changing a bunch of answers out of panic!

Again, logic first, everything else second! Making crucial decisions based on your emotions during crunch time is not a great strategy, so here's what I recommend instead:

Examine the answer choice you first picked, and examine the answer choice you think may be correct instead. Now, make an argument for why each answer is correct individually. 

Write out your thoughts on the paper, or do it in your head - whatever works! Go with the answer that you can make the strongest argument for!

There is actually a fairly large body of evidence that going with your first guess isn't best, and yet this myth is still pervasive.

In a collaborative research paper written by researchers at the University of Illinois and Stanford University titled Counterfactual Thinking and the First Instinct Fallacy, the investigators said this:

“Most people believe that they should avoid changing their answer when taking multiple-choice tests. 

Virtually all research on this topic, however, suggests that this strategy is ill-founded: most answer changes are from incorrect to correct, and people who change their answers usually improve their test scores."

Another study that examined the accuracy of students' second guesses vs first guesses said this:

"More often than not, the students’ revisions – changes from a first instinct to a new choice – resulted in a correct answer. 

And on questions that caused the most uncertainty, sticking with an initial response was a bad idea: they were wrong more than half the time (source)."

Why "go with your gut" is bad advice

Have you ever read the answer choices to a question and gotten a strong gut feeling that one of them was right, even though you weren't sure exactly why?

In Thinking Fast and Slow by Nobel Prize winner Daniel Kahneman, Kahneman proposes that the brain uses two different systems for processing information, which we can call system 1 and system 2. 

System 1 operates automatically by creating impressions, intuitions, and gut feelings for system 2. System 2 acts on the input from system 1, and handles your conscious reasoning and decision making.

We can think of system 1 as the fast system, and system 2 as the slow system. Essentially what's happening in these situations is that your brain unconsciously picks something up from the answer choice before you're consciously aware of it, and your fast thinking system 1 produces the intuition feeling.

The problem is that these intuitions aren't always correct! Sometimes professors will include questions with a twist, and relying on your intuition for them will lead you astray!

You must stop and use your slow thinking system! Make what's unconscious conscious by reasoning it out. Your gut instinct may in fact be right, but it's worth taking the extra time to check!

As I said above, the one exception is when you're completely stumped and have no idea what the correct answer is. In these cases, by all means, go with your gut!

Other General Advice And Suggestions:

  • I recommend putting your name on the test first so you don't forget at the end!
  • Read all directions carefully! Reading them once is good, reading them twice is better!
  • Ask if you can write on the test, and if so, take advantage of this!
  • Be sure to mark the correct answer on the answer sheet. You don't want to lose points for circling a different answer than the one you intended!
  • Make sure you copy any work you do on scratch paper over to the answer key correctly!
  • Don't assume simple answers are wrong just because they seem too obvious; most tests will have at least a few "gimmes"
  • As long as there is no penalty for guessing, NEVER leave any question blank!
  • If you're stuck on a question, sometimes rephrasing it in your own words helps
  • Make sure the wording in the question and the answer choice you've chosen agree grammatically
  • Some times teachers include silly answers as a joke; realize that these are almost always just there for fun and DON'T put them down as guesses!
Other References Not Cited Above:

Thanks For Reading!
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Friday, June 9, 2017

Test Prep Champions

7 Surprising Things Research Shows Can Bring Your Grades Up

This list may shock you, but the data shows these 7 things can bring your grades up! How many have you heard of?

Click Start Below If You'd Like To Begin With A Short Quiz To See Which Ones You Know Already!

A photo of an N64, because research shows some video games can bring your grades up

1. Playing more video games- specifically strategy and role playing games (RPGs)

In a study, researchers followed over a thousand teenagers who participated in "strategic video game play" during high school. The games were mostly RPGs and other strategy games.

After 4 years, the students reportedly had higher levels of self-belief in their problem solving abilities. The researchers concluded that the students' higher self-belief in their problem solving skills lead to higher grades.

The Takeaway: Try out strategic video game playing if you want to improve your confidence in your problem solving skills, and thus your grades! If you're planning to try this, I recommend The Legend of Zelda: Ocarina of Time for the N64 (my personal favorite game of all time).

If you can make it through the Water Temple, you should feel pretty good about your problem solving skills!

See: More Than Just Fun and Games: The Longitudinal Relationships Between Strategic Video Games, Self-Reported Problem Solving Skills, and Academic Grades

2. Typing your essays in Georgia font

A photo of a student typing, presumably in Georgia font, which research shows can bring your grades up
A college student named Phil Renaud recorded his essay grades for 52 essays he wrote in college. 

He wrote each essay in one of 3 fonts: Times New Roman, Trebuchet MS, and Georgia. 

The essays were for a variety of different classes including philosophy, economics, marketing, political science, and computer science, among others.

Renaud earned an A minus average on the 52 essays, and earned the most A's while typing in Georgia. He claims he did not change his writing style significantly, and also that he put less time into some of the essays he wrote in Georgia.

Here's part of Renaud's explanation:

"Georgia is enough like Times to retain its academic feel, and is different enough to be something of a relief for the grader. Trebuchet seems to set off a negative trigger, maybe just based on the fact that it's not as easy to read in print, maybe on the fact that it looks like something off a blog rather than an academic journal (source)."

Not still convinced of Georgia's superiority? Here's some more evidence in its favor.

Carnegie Mellon University researchers ran a series of typography tests, and found that study participants preferred Georgia font to Times because they found Georgia to be "sharper, more pleasing, and easier to read. They also found that Georgia was easier to read compared to Veranda (source).

The Takeaway: If your professors let you pick your own fonts for your essays, try writing them in Georgia! What do you have to lose?

3. Using your school's library more

A photo of a library, because research shows using your school's library can can bring your grades upUniversity of Michigan researchers teamed up to analyze data on undergraduate freshman library use during a fall semester. 

They found that students who took advantage of library services had higher grades and higher retention rates than students who didn't use library services.

Straight from the study:

"Analysis of the data suggests first-time, first-year undergraduate students who use the library have a higher GPA for their first semester and higher retention from fall to spring than non-library users."

The Takeaway: If you want to raise your grades, go camp out at the library as much as possible!!!

See: Library Use and Undergraduate Student Outcomes: New Evidence for Students’ Retention and Academic Success

4. Cutting down on cell phone use

A photo of a cell phone, because research shows cutting down on cell phone use can bring your grades up

In a 2015 study, investigators examined the relationship between cell phone use and GPA for 536 undergraduates at Kent State. 

The researchers concluded that cell phone use is associated with lower GPAs!

The Takeaway: If you're like most people (myself included), the mere thought of limiting your cell phone use brings on a feeling of dread. 

At the very least, I recommend trying not to use your phone during class, and also when you're studying!

See: The Relationship Between Cell Phone Use and Academic Performance in a Sample of U.S. College Students

5. Printing out your lecture slides before class (if your professor posts them)

Downloading and printing lecture slides before class improve students' test scores by 3.48%, according to a university study titled Does Downloading PowerPoint Slides Before the Lecture Lead to Better Student Achievement? 

A powerpoint slide photo, because research shows that printing out lecture slides before lectures can bring your grades up
This could amount to a few extra points depending on the test, and every point counts if you want to get straight A's!

In a separate study titled the Effect of Posting Lecture Slides Online on Attendance and Student Performance, researchers concluded that when professors post lecture slides before class, it increases student attendance, participation, and also exam scores!

The Takeaway: 
Hopefully this one's pretty self-explanatory! If your professors are generous enough to post the slides before class, don't forget to use them!

6. Avoiding homesick distress

Going away to school and leaving your family behind is a difficult adjustment for most people. It's normal to feel some homesickness sometimes as a college student, especially during freshman year. 

A picture of a distressed student, because research shows avoiding homesickness can can bring your grades up
However, one type of homesickness known as "homesick distress"can negatively impact students' academic performance!

The authors of the study said this:

"Homesick distress resulted in a significant, albeit small, explanation of the variance of first-semester GPA."

The Takeaway: If you feel like you're experiencing homesickness to a severe degree, consider reaching out to your school's counseling center! Your GPA might depend on it!

See: Homesickness at College: Its Impact on Academic Performance and Retention

7. Requesting a smarter roommate

A picture of roommates together, because research shows roommates have an impact on each each other's study habits

Bruce Sacerdote--a Darthmouth economist--published a study in 2000 in which he revealed his finding that randomly assigned roommate pairs shared more common study habits at the end of their freshman year than random pairs.

In the study, Sacerdote concluded that college roommates have an impact on each others grades. This can be positive or negative!

Interestingly, he also found that peers living near a student in the same residence hall had an impact on whether or not the student joined Greek life, but not on the student's GPA.

The Takeaway:
Obviously requesting a new roommate isn't going to be realistic for everyone. If your roommate isn't as studious as you, don't worry about it, just work up to your own standards! The data suggests they may eventually follow your lead!

See: The Definitive Guide to Acing Your Schedule, and Peer Effects with Random Assignment: Results for Dartmouth Roommates

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Tuesday, June 6, 2017

Test Prep Champions

How the Brain Learns Math and Science: Focused Mode vs Diffuse Mode Thinking

How your brain uses both focused and diffused thinking styles to learn challenging subjects!

Published on June 6, 2017

Wouldn't it be great if you never had to worry about getting a good grade in a math or science class again?

A photo of a brain represented as a puzzle with a puzzle piece missing, part of the lesson on How the Brain Learns Math and Science with the focused and diffuse modes

Does having more confidence in your abilities to the point where you've eliminated all math/science anxieties sound too good to be true?

It doesn't take an Isaac Newton, Albert Einstein, or Stephen Hawking to recognize that these things probably wont ever be completely possible to achieve.

However, here are a few things that are very possible to achieve:
  • Speed up your mastery of math and science subjects!
  • Reduce stress about your ability to conquer these subjects!
  • Improve your grades in tough classes!
If you think that any of this might be helpful for you, then please keep reading because in this post I'm going to share an important discovery about how the brain learns math and science. You can begin using this to advance your results as soon as you're ready!

We've all been there. 

You're working diligently to crack a math problem. You're pretty sure your strategy is right, but the numbers are still coming out wrong.

You check your calculations again, but get the same answer. Your muscles tense up. You bite your lip.

Your blood begins to boil. You crumple the scratch paper mess on your desk up into a ball, throw it aside, and rip the textbook open yet again.

Maybe if you just re-read the chapter for the thousandth time, you'll get the right answer, you think to yourself...

...but in reality, you probably won't!

The truth is that mastering math and science subjects is hard! While persistence is a necessity, there comes a certain point when it stops being helpful.

The human brain has two different modes of information processing at its disposal, and trying to brute force your way through a problem like this prevents you from utilizing both methods!

Focused Mode vs Diffuse Mode Processing

In A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra), Dr. Barbara Oakley talks about two different systems the brain uses for learning. 

When you're focused intently on something such as reading a blog post, solving a math problem, or thinking logically, you're using the focused mode.

On the other hand, when you're relaxed and not actively trying to solve a problem, you're using the diffuse mode.

Once when I was taking physics in undergrad, I left the library after working on a tough problem for a while without making much headway. 20 minutes later when I was on the bus, I got a sudden flash of insight out of nowhere, and realized exactly how to solve the problem!

Those who have studied math/science subjects for a while have probably experienced something similar. 

The reason is because the brain processes these subjects by alternating between the focused mode and the diffuse mode.

Below is a short list of some characteristics of both modes.

Focused Mode:
  • Where learning starts
  • Conscious processing
  • Activated by concentrating on a task
Diffuse Mode:
  • Activated by relaxing and not focusing on anything in particular
  • Produces "flashes of insight"
  • Helps you grasp the "big picture"
  • Works on problems in the background
Utilizing Both Modes Makes All The Difference

We need to use both the focused mode and the diffuse mode in problem solving. However, you can think of them as both canceling each other out. For example, when you try really hard to solve a math problem, you're using the focused mode, which prevents the diffuse mode from assisting with solving the problem!

When you then switch gears, the diffuse works to solve the problem, but blocks the focused mode from assisting!

This switching from focused mode to diffuse mode and vice versa is how hard math and science problems are solved, and how challenging abstract concepts are understood.

I strongly encourage you to take Oakley's advice to heart! 

This means trying your best to gradually learn the material starting with the focused mode. When you hit a stumbling block, take a break and let the diffuse mode take over, then come back to it at a later time. 

You'll probably find that the material seems somehow "different" during your next session.

In reality, the material is exactly the same as it was the last time you studied it; your understanding has just gotten better. 

Keep doing this, and eventually I guarantee it will stick for you! The key is to get to this point BEFORE your tests, rather than after your tests (or never), and your grades will skyrocket!


In conclusion, I want to revisit the benefits I mentioned at the start of the post to show you exactly how you can use this new knowledge.
  • Speed up your mastery of math and science subjects 
Understand that these subjects are complex, and thus require lots of repetitions to master. Spacing your study sessions out allows both the brain's focused and diffuse modes to coordinate together to generate true comprehension. 

I strongly recommend starting your studying as early as possible (even before class if you can). Your brain needs lots of time to process the material using both modes before it's going to click!
  • Reduce stress about your ability to conquer these subjects 
It's easy to come out of a lecture feeling somewhat demoralized after a lot of the material flies over your head. Remember though, just because you don't understand the material now doesn't mean you won't crack it eventually! 

I can recall another time in undergrad while taking organic chemistry when it took me about a full week of repeated attempts to finally get a certain topic down to perfection (for those wondering, it was stereochemistry).

Was this stressful? Sure.

Did I have doubts about my ability to master it? Yes, I'll admit I did from time to time.

But I stuck it out, and finally the day came when I sat down for some focused studying, and the material was crystal clear!

The key is to stick with it and don't get discouraged because you're not getting it as fast as you'd like to, or as fast as other people are. Although it can sometimes feel like everyone else understands the material but you, I can assure you this is rarely ever the case (more on this topic in another post...)!
  • Improve your grades in tough classes
Hopefully by now it's clear how understanding the brain's two modes of learning can help you achieve better grades. Of course this is a major oversimplification, as the science of learning is much more complicated than this. However, it's still very helpful to think about learning math and science subjects in this manner. It's now up to you to apply this knowledge, and watch your grades shoot up in the process!

Want to learn more? Check out Dr. Barbara Oakley's book A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra).

I can almost guarantee it will be one of the best decisions you've ever made if your goal is to improve your performance in math and science subjects quickly! Thanks for reading!

Disclosure: Both of my links to this book are affiliate links. Basically, this means I'll get a commission on sales from people I recommend who buy it. I only ever recommend books if I've read them myself and am willing to stand behind the quality for 100%! 
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