Ask the right questions: how to know what you don't know you don't know

academics study skills

Have an assignment due tomorrow, and have no idea where to even start? In office hours or class and so lost that you don't even know what your question is? No matter the context of your confusion, you're not alone! 

First, let’s understand what exactly these situations have in common: They stem from the classic problem of “not knowing what you don’t know.” It’s important as a student to understand how to get out of this state so that you can start asking questions that one-shot your confusions instead of “How do I get started?” or “How do I solve this problem?” that yield generic answers. Here are two main ways to get you out of the fog!

Follow the breadcrumbs

If you don’t understand the topic at hand, it’s likely because you didn’t understand something before this. Especially in fields like math and physics (my personal areas of focus), advanced courses may be filled with jargon, but they still rest on logic and fundamental concepts. To ask a directed question, you need to identify what actually confuses you

Let’s take a look at introductory mechanics, for example: 

A cannon-launcher with an adjustable angle fires a cannonball at 20 m/s straight out of the barrel. What’s the farthest from the launcher that the cannonball can land?  

This deceptively simple question has many concepts at play. Let’s start from the question itself, and at every step, we’ll ask ourselves: “How do you do that?” 

You want to find the farthest distance that the cannonball goes. In other words, your goal is to maximize the distance that the ball goes. Before you can answer this, you’ll need to know how to calculate the distance that the cannonball goes. This calculation now depends on the angle of the launch. To find this distance, you must use trigonometry to break the problem into x and y components, then use the kinematic equations of classical mechanics in 2D…

You can see how fully tracing the “how to” in a problem leads to many fundamental concepts and tools, as illustrated in the reverse flowchart. If you find yourself not knowing how to answer “How do you do that?” at any given step, that means you’ve found the question you need to ask! 

In this example, say I can trace back how to do everything until I need to optimize the distance traveled by the cannonball with respect to the angle. Then, the question I should raise to my friends, teacher, or tutor is “How do I maximize a function, again?” 

Learning shortcuts

Sometimes, you can trace back the “how to” diagram in theory, but actually getting to the answer feels insurmountable. In this case, you effectively have a data analysis problem — you need to efficiently put together your given information to get an answer. Let’s take the following example, adapted from Challenging Problems in Algebra by A. Posamentier and C. Salkind.: 

To conserve the contents of a 16 oz. bottle of tonic, a castaway adopts the following procedure. On the first day, he drinks 1 oz of tonic, then refills the bottle with water; on the second day, he drinks 2 oz. of the mixture, then refills the bottle with water; on the third day, he drinks 3 oz. of the mixture, then refills the bottle with water. The procedure is continued for succeeding days until the bottle is empty. How many ounces of water does he drink in total? 

In this example, the question appears at the end: “How many ounces of water does [the castaway] drink in total?” We’re given the pattern that the castaway uses to drink water, so we actually know exactly how much water he drinks on a given day. With that information, we can solve the problem! 

At this point, it’s possible to take a few different paths towards getting the final answer. The most straightforward way is to calculate the ratio of water to tonic every day, then figure out how much water was consumed that day. This method is tedious though, so you can imagine that a small adjustment to the problem — take a 100 oz. bottle and the same drinking procedure — becomes quickly intractable. 

In this case, your question should not be about the “how to” steps that you’ve thought of, but rather about a way to circumvent the steps you’ve come up with. A well-constructed question would start off with how you could solve the problem but end with “Is there an alternative approach?” By asking this type of question, you can easily match a shortcut with a calculation type, and eventually, you’ll be able to come up with the clever method all on your own!

Comments

topicTopics
academics study skills MCAT medical school admissions SAT expository writing college admissions English MD/PhD admissions GMAT LSAT GRE writing strategy chemistry physics math biology ACT graduate admissions language learning law school admissions test anxiety interview prep MBA admissions academic advice premed homework help personal statements AP exams career advice creative writing MD study schedules summer activities Common Application history test prep philosophy computer science secondary applications organic chemistry economics supplements PSAT admissions coaching grammar law statistics & probability psychology ESL research 1L CARS SSAT covid-19 legal studies logic games reading comprehension dental admissions mathematics USMLE Spanish calculus engineering parents Latin verbal reasoning DAT case coaching excel mentorship political science French Linguistics Tutoring Approaches academic integrity chinese AMCAS DO MBA coursework PhD admissions Social Advocacy admissions advice biochemistry classics diversity statement genetics geometry kinematics medical school mental health quantitative reasoning skills time management Anki English literature IB exams ISEE MD/PhD programs algebra algorithms art history artificial intelligence astrophysics athletics business business skills careers cold emails data science internships letters of recommendation poetry presentations resume science social sciences software engineering study abroad tech industry trigonometry work and activities 2L 3L Academic Interest DMD EMT FlexMed Fourier Series Greek Health Professional Shortage Area Italian Lagrange multipliers London MD vs PhD MMI Montessori National Health Service Corps Pythagorean Theorem Python STEM Sentence Correction Step 2 TMDSAS Zoom acids and bases amino acids analysis essay architecture argumentative writing brain teaser campus visits cantonese capacitors capital markets cell biology central limit theorem chemical engineering chess chromatography class participation climate change clinical experience community service constitutional law consulting cover letters curriculum demonstrated interest dental school distance learning electricity and magnetism enrichment european history executive function finance first generation student freewriting fun facts functions gap year genomics harmonics health policy history of medicine history of science hybrid vehicles hydrophobic effect ideal gas law induction information sessions institutional actions integrated reasoning intern international students investing investment banking lab reports logic mandarin chinese mba mechanical engineering medical physics meiosis microeconomics mitosis music music theory neurology neuroscience office hours operating systems organization pedagogy phrase structure rules plagiarism pre-dental proofs pseudocode psych/soc quantum mechanics resistors resonance revising scholarships school selection simple linear regression slide decks sociology software stem cells stereochemistry study spots synthesis teaching technical interviews transfer typology units virtual interviews writer's block writing circles