Why you understand the math but CAN'T solve problems

you've just learned about the new math concept everything makes sense to you you feel energetic and motivated to tackle the questions until you get a wrong answer the motivation slowly Fades away you feel the frustration building bringing your math practice to an end you can't help but wonder why you understand the math but just can't get the questions right hi welcome to my channel my name is Han I just graduated from Columbia this may I studied math and operations research in college as someone who has been battling with math for over 17 years now I have not always been a math person when I was in high school I really struggled with math I often received C's and D's in my math classes and no matter how much time and effort I put in it I just cannot get the questions right and receive the scores that I wanted on exams I thought I might not be smart enough and couldn't pursue a career in stem especially there were students in my class put in way less time than I did but Reed really good grades so after thousands of hours practicing math and learning from some of the best teacher in the world I finally realized that I was just doing it wrong so in this video I'm going to explain to you why you understand the math but you just couldn't do the questions right I will also show you that how you can fix it with some actionable tips that completely transformed my experience with studying math and helped me succeed in some of the hardest classes Columbia University let's just get into it for a context let me explain to you how I was studying before I realized something was wrong I would really pay attention in class and carefully take notes I spent hours looking at how to solve different math problems going over each problem carefully to see how it's done you may stop me and be like hold on that doesn't sound bad it sounds like you were a really hard worker but if you pay close attention the problem here is it's solely passive learning and no Active Learning at all passive learning is a method of learning where students receive information from outside sources and try to internalize it which include listening to lectures reading and watching demonstrations and active learning means you're actively involved in the learning process basically means you're doing something besides just receiving the information and which includes discussions practicing questions and teaching others in our education system there are lots of passive learning and very little Active Learning many research Studies have shown that passive learning is not as effective as active learning in math and science education so if you feel like you're spending lots of time in studying math but still not get good results it's probably because you are doing too much passive learning and not enough active learning math is a skill to help you solve problems you have to know how to use it by doing it you wouldn't say that you can drive a car just by watching someone else drive and memorizing all the traffic rules you have to get into the car and practice this way you can know how it feels which part you have problems or any complications you may run into so I hate to break this to you but if you only read and listen how the math is done sometimes you may think oh I understand the math but actually you don't so how can we actually do more active learning in our math studying if there's one thing I wish you can take away from this video is if you get a question wrong always redo it independently until you get it right lots of time people get really upset when they get a question wrong and start thinking oh what is wrong with me I just cannot understand why I cannot do math you know what the question in front of you is literally telling you what's wrong what I often did was if I get a question wrong I just read through the answers and try to understand it and just move on but again the problem here is if I only read the solutions and try to understand how it's done it's still a form of passive learning you wouldn't go to the doctor spend two days doing all the lab work for a physical exam and receiving a result that says you have a heart issue and you just go oh crap they say I have a heart issue and just move on with life you would actually follow up with the doctor take pills every day or pursue whatever the necessary treatment it is until the disease is cured or under control every time you practice a question it's a diagnostic process to see whether you understand the math concept and your ability to solve the questions and you need to realize that the diagnosis is not the most important part and what truly matters is the treatment you've already invested all your time and efforts in reading the question trying to understand the question thinking about the question write the question if you don't follow up with what's wrong it's really just a waste of time so follow up with the question that's wrong figure out precisely which Step you made a mistake really trying to understand why you made that mistake and how you can prevent it from happening again and doing the question again is the followup doctor appointment that they will tell you whether the disease is truly cured or not cuz the doctor May tell you yeah you know what you're good to go or they may tell you it's still there you still haven't fix it or they may even say that ah your heart disease is cured but now you have a liver disease so make sure you test yourself by doing the questions again until you get it right so how do you actually follow up with your math disease and then found the treatment for it AKA how to fix the problem so ENT entally you compare your wrong answer to the correct answer and figure out which exact step that you had the problem in my experience there are four type of problems let's just dive into each one of those firstly an understanding problem might arise when you feel to grasp a math concept or the equation you recently learned or perhaps you don't understand the question itself to help you understand math better consider use the fan technique it is a learning method that used by the no prize winning physicist Richard fman basically the way you understand a concept is by explaining it as if you're explaining it to a child while doing this notice which part did you struggle to explain what details did you miss what part is really hard for you to put into simple words answering those questions will show you which part are you missing the act of explaining to yourself or teaching others is a form of active learning sometimes when we thinking about things in our own mind we think we understand it well but we may miss some important stuff so the best way to uncovering those details is to explaining it out loud verbalize it and teaching someone else who doesn't know about the topic and the more you can put it into simple terms the better understanding you have about the topic secondly you might face issues with memorization when you can't remember an equation function or the specific step GS required to solve a particular type of problem in my opinion in math memorization is really often unnecessary because everything can be proven if you're really motivated not to memorize anything you don't even need to memorize 1 + 1 = to 2 because there are 162 pages of proofs in abstract algebra to prove y 1 + 1 equal to 2 therefore I highly recommend you try to understand everything before you just straight jump into memorization but in our daily math studying memorization does have an important role because it really can save us time in situations where memorization is necessary the best of techniques is active recall and space repetition s some questions may need a specific trick or tactic that you're not just familiar with and my recommendation will be just practice more questions but whenever you encounter a new trick pay attention how it applied in what type of question and then collect that trick in your math problem solving toolbox next time you see a similar question you can just pull up your toolbox and use the tricks that you've collected like a Pokemon situation the fourth you do actually know how to answer questions and you could have done it correctly if you hadn't just made a single silly mistake believe me I understand the frustration I experience it all the time especially with more challenging problems the answer just become really lengthy and requires so many steps making it really hard not to make mistakes so pay close attention to the common mistakes that you make and keep these in mind the next time you work on the question is a calculation error or did you misread the problem for example I used to make silly mistakes like in the last line it was 45 but the next line I just randomly magically write 6 5 so I noticed that and trying to figure out why turns out the way I wrote four was really close to Six so I just changed the way I write for and then just pay more close attention so that's today's video thank you so much for [Music] watching

Channel: Han Zhango

Views: 51,006

Keywords: how to learn math, study tips, how to study for exams, ivy league, study tips 2023, study tips and lectures, math, how to study smart, study mathematics, math tips and tricks, math tips for sat, math tips for act

Id: -t6P3CjJhO4

Length: 9min 53sec (593 seconds)

Published: Sun Oct 08 2023