Comments by "Solo Renegade" (@SoloRenegade) on "The Math Sorcerer"
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@thewryneckarchivist no, that's not it. They lack empathy to begin with. Empathy tends to grow with knowledge, not diminish.
Those who become mathematicians, tend to be those who never struggled with math growing up. They never struggled as their students do/will. They can't understand why students don't understand things, because they never struggled with it. To them concepts came easily, and too often they only know one right way to solve problems, their way. The Way that came so easy to them, even if that way is a more complicated way to solve things.
Teachers who also learned math through struggle make better teachers. They can see how a student is stumbling, recognize the struggle with a given concept, as they once experienced it as well. They can explain the problem in different ways, to help the student understand.
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Math teachers at the Bachelors or lower level should be people who are applied math degrees (engineers?), people who are good at math, but had to struggle to learn it like the average person. Math teachers need EMPATHY above all else. They need to be able to understand and relate to their student's struggles.
Math teachers who were naturally gifted at math and never struggled with it are TERRIBLE teachers. These math people should NEVER be allowed to teach math to lower level students.
Math teachers need to be able to teach things, explain things, more than one way. They need to understand that people don't "just get it". They need to be able to see why a person is struggling and immediately adapt and adjust their approach accordingly. They need to understand how and why students struggle, and adapt their teaching accordingly.
Math needs to be taught with real world applications.
Math teachers need to allow alternate solutions, so long as they are valid. Their way is Not the ONLY way.
Math teachers need to give partial credit on problems if the student shows their work and only screwed up barely. Take points off for the errors, and point out why they got the wrong answer, not just that they got the wrong answer. I've watched so many students struggle thinking they sucked, when in reality they were doing EVERYTHING right, just making a minor mistake here and there, but they lost all credit for the problem. Once I showed them the mistakes they were making, and how to avoid making those simple errors ever again, they started getting A's.
Lets say you have 5 calculus problems on an assignment worth 25 points. A person does the first problem right overall, but forgot to distribute a negative in one step, otherwise everything else was done 100% right. I'd take off 1 point for that and point it out, but give 4 points for doing the rest of the problem correctly. For each error they make I take off a point. And you can do this at any scale. If you had 25 problem assignment for 25 points, then I'd take off say .25 or .5 points for making a simple error in one of the problems. If we're doing Chain Rule, and the only mistake you made was totally messing up the application of the Chain Rule itself, then I might take off more points from that problem that a mere simple mistake (mark down 2 or 3 points out of 5, instead of just 1). But if all you do is tell students, "you're wrong", without telling them WHY, they will continue to struggle. Also, this approach teaches them to show their work, as they can get a higher grade by showing their work. if they don't show enough work for me to figure out where thy went wrong, and they got the wrong answer, then I take off full credit for that problem being wrong, rather than partial credit. They learn very quick to show their work after that.
Let's say there are 5 different way to teach something, and your personally preferred method of teaching/learning is #4. But #1 is understood by 66% of students, #2 is understood by 45% of students, #3 is understood by 12% of students, #4 is understood by 57% of students, and #5 is understood by 82% of students, the first time you teach the subject to them in class. Then you need to be using the #5 method, regardless of you personal feelings on the matter, and save #4 for when 18% of your students show up at office hours looking for help. You want to teach a topic using the method that consistently reaches the greatest number of students, thus minimizing the number of students who need additional help after class, and maximizing the number of students who can help the few students who still don't get it. And then you have far more time to spend with fewer students 1-on-1 in office hours, maximizing the chances of them succeeding. And during your office hours you can try any of the 4 alternate methods that it takes to make them get it. Maybe what works best for that individual student is actually #3 or #2.
In my years of experience teaching math to people of all ages, the number one reason people struggle with math is they never got a good grasp on the basics, or on basic algebra. Even when teaching/tutoring calculus students, the first thing I do with them if I've never worked with them before is test them on their basics (fractions, GEMA, groups, exponents, logarithms, subtraction and negatives, SOH CAH TOA, FOIL, graphing basics, etc.). If I find them lacking in anything critical, I first focus on remedial instruction before actually working on issues they have with their assignment. Then we get back to the issues at hand. And suddenly once they've been given fixes to things they struggle with, or finally got something explained to them properly for the first time in their lives, they start doing well in their assignments.
My catch phrase when teaching math is always, "Why didn't they just say that to begin with?". Students always end up asking why teachers didn't just teach it to them the way I did years ago. They tell me how intuitive my methods are for them, and they go on to have success, and I gained a reputation as the guy to go to for help. Empathy is key.
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@SmallSpoonBrigade I agree. It has been my experience than that vast majority of people have equal capacity to be good at something as another person. It comes down to personal motivation and desire to learn it. I am good at certain things in life because I Want to be good at them, and I put the time and effort in to learn them and practice them and get good at it. Other things I have no desire to learn, and so I don't, and I'lll never be good at those. Not that I couldn't , just that I don't Want to.
it's the exception to the rule that a person might have a true learning disability, genetic defect, or also be a naturally gifted person at a particular thing. Most people are perfectly normal overall, and perfectly capable.
Objectively, based on testing standards, repeated real-world performance both in multiple careers as well as in academia, etc. I can make the claim, and back it up, that I am in the top 1% of performers, intellectually, nationwide in the US. That being said, I have never encountered a skill or piece of knowledge that I have not been able to teach a middle schooler or high school aged student to do/understand. I love doing it too, seeing their eyes light up when they realize they can master "complex" ideas and skills is so rewarding. Turns out teaching is one of my talents, but the point is, every kid I have met or worked with has the potential to know and understand anything I do, or that others do. Some simply don't Want to learn, or don't Want to put in the effort to learn particular things. It comes down to personal motivation. Not everyone needs to be a musician, or a mathematician, or an engineer, etc either.
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@SmallSpoonBrigade Excellent advice! I second everything you've said.
I completed my Mechanical Engineering degree while working full time as an ME, spread out over 6yrs. I didn't have lots of time, so I didn't procrastinate on starting assignments, just like you suggest. I also happen to be an instructor as well in my previous careers.
I tell students to tutor each other. Work together outside of class. You learn more from trying to teach it to someone else, than someone trying to explain it to you.
At work even, I get stuck trying to come up with a solution to a problem, so I'll walk into another engineer's office and ask them to look at the problem. Often times I'll come up with the solution as I'm explaining to them what the problem is before they even have a chance to comment back. I do this knowing this may happen, which is why I do it. Sometimes verbalizing a problem aloud to another person makes all the difference in solving it. Also, two heads are better than one when it comes to problem solving. Sometimes the way I'm approaching the problem is different from how they do it, and they'll immediately see a different way to approach it I hadn't thought of. Or, I'll get fixated on a particular approach to solving the problem, and they'll point that out to me and suddenly the solution becomes obvious. Multiple heads looking at the same problem often results in better solutions that are reached faster.
But you comments on efficient time management are very true too. Working a full-time job and taking classes for 6yrs straight, even through summer, I still managed to finish as the top engineering student in the college, despite having less time than all of my classmates to work on the same problems, and less time to study. I made better use of my time than they did.
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7:55 I was one of these people. I learned to "procrastinate early". Let's say I was given an assignment on Tuesday, that was due next Monday, I knew I'd typically procrastinate until Sunday night at 10pm before finally starting it and freaking out, staying up late working furiously to get it done on time. So, I started lying to myself, and changing the due dates. So instead of waiting until Sunday night and ruining my whole weekend, I'd tell myself it was due Wednesday instead, and I'd get it done Tuesday night. Massively reduced stress, and then I could help classmates, which in turn made me even Better at the material, and I could go into Friday with no homework on my plate and have the whole weekend to do as I liked stress free.
I attended 6 colleges in 2 states over 17yrs and earned 4 degrees, all STEM, and graduated top of my class in every degree, and my lowest graduating GPA was 3.7, and my highest was 4.0.
I have turned learning into a science over the course of my life, and use a myriad of tricks to excel in any topic I wish to learn.
Being a Tutor, Mentor, and Instructor also helps you learn FAR better than just being a student. Over the course of those 17 years, I spent most of them tutoring and mentoring, and even was an Adjunct Instructor at one of the colleges while still taking classes as a student. Having to explain a concept to others so they will understand it, makes you understand it far better.
Do study groups, be a tutor, procrastinate early, take notes BY HAND and type them up later as you organize them (this is a scientifically proven brain trick and critical to learning things better/faster), show your work when doing math (I used to not do this too, but I learned that I could use my homework as examples later, or see where I messed up later, and was critical when I was tutoring others in math to see their mistakes as well, and as an instructor I will give partial credit for errors if work is shown to be otherwise correct). Practice, practice, practice. Get a proper amount of sleep EVERY night. Do Everything you possibly can to get a good night's sleep Every night (time, darkness, routine, lights, noise, temperature, diet, etc.). I have TONS of other studying/learning tricks, many times more. I am considering putting them all into a book. I've been known to give lectures and presentations to various groups on this exact topic.
School was my priority for sure, but not at the expense of my health nor life. And I even worked full-time as a Mechanical Engineer for 6yrs while earning my 4th degree and still managed to get my second highest graduating GPA (3.96).
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Cheating should be avoided, as school is ultimately about finding out who can and cannot do certain things, who is the best, etc. If you cannot do the task, then you should not be given the cert that says you can.
But also, many teachers are Not good at their job. They are making learning unnecessarily difficult for their students, either intentionally or unintentionally for a variety of reasons (I know because I spent 17yrs in the college system, multiple colleges, multiple degrees, am an instructor myself, and tutored hundreds of students, in many STEM courses and topics and dealt with constant recurring issues). In those cases I can appreciate a person having to game the system when the system is stacked against them, when the system is setting them up for failure. I have seen far too many professors try to ruin smart and capable students (usually not malicious or intentional, but results are what I care about and a professor that consistently causes issues is a problem), and their students have EVERY right to game it right back. School is supposed to be about learning, not about screwing over students. I use methods to help students learn faster, that others would call cheating. But I'm using psychology and science to improve learning, trying to get students over a certain hump without them even realizing it. Most professors don't know what I am doing either and dislike it, but I have gotten great results with people in very short time. There are a number of scientifically supported tricks a person can use to help themselves and others learn faster and more effectively. I have a system of grading, homework, testing, etc. that utilizes a number of science supported ideas to help students learn without them ever realizing how I am helping them, without ever realizing teh tricks I am using to help them learn more effectively. Many of my tricks do come up in ways on this channel all the time, but never in a larger cohesive and integrated way like I do. I focus on the theory of learning, theory of teaching, and study what does and doesn't work, Before focusing on the topic needing to be taught. My priority is teaching first, then the subject material and skills needing to be taught. If my delivery is wrong, the material wont matter as no one will understand it anyways.
In some cases, cheating is ok, depending upon the skill being tested. In aviation, utilizing resources available to you in the cockpit (notes) is not cheating. In fact, pilots need to learn TO utilize ALL available resources to ensure a safe flight. Some things you just have to know, but many things can be found in some way in the cockpit and it's ok to do so. Some fields require creativity, and depending upon what it is, that creativity is often times mistaken for cheating (context matters). If I told my students they could use a single notecard of notes, and one time a student comes in with both sides filled with notes, I'd be happy. I didn't say they couldn't use both sides. But next time I might hand out notecards with one side blacked out. Until a smart individual used a silver sharpie to add notes, I wouldn't care. the first student to figure out how to keep with in the rules even if others think it's cheating, I reward. I reward creative thinking, and encourage it. If they can find some way to game the rules, why shouldn't they? Most rules in life are a bunch of nonsense anyways. Some exist for good reason. If a student figures out a "cheat" because i wasn't specific enough, then I allow it.
In other places, cheating is not only encouraged, but REQUIRED. Particularly in warfare. To win and stay alive, there is no such thing as cheating, only winning or losing. You do whatever you can and must to stack the deck in your favor, win the battle, and stay alive. There is no such thing as cheating in warfare.
There is no cheating in nature either. Nature wont let you violate the laws of the universe, all else is fair game. Society creates and imposes rules on us, not nature. Society does this to promote cooperation, because we're all better off working together than screwing each other over, so we collectively come up with rules, rewards, and punishments to incentivize and discourage certain behaviors that are that are helpful or harmful to society. But such rules are artificial, man made, and we need to remember that. Also, there are certain things for which there is no justification for needing to memorize certain things, no justification for why notes shouldn't be allowed to be used. Not everything is useful to be stored in our memory.
Also, it has been my experience both as a student and as an instructor, that students tend to use or rely upon notes less when they are told ahead of time the test is open note, than if they were not allowed to use notes. It comes down to psychology. Now, keep in mind there Are right and wrong ways to conduct an open note test as well. An open note test needs to be structured in certain ways that the students will not have enough time to look up every idea or concept or answer. And if you help teach students how to prioritize problems in a test as well, they'll do better with or without notes. So many secondary ideas I use that would take me hours to explain and give specific examples of each. But done right, an open note test can result in far better results, little to no cheating, and students actually end up looking up far fewer answers as well. I see students walk away with far more confidence in themselves as well. It just has to be structured and handled correctly.
I could go on for hours on this topic, on my many ideas, tricks, etc. Discussing theory as well as real world application and results, examples, etc. I love this topic, because it matters so much and so few people understand it adequately. If society was better at teaching and learning, society would be far better off as a whole.
Context matters.
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I have a natural talent for learning things, and comprehending it deeply. But I still had to work hard at math my whole life just like everyone else, and struggled at times with things like fractions (becasue it was taught horribly in hindsight). But math was highly logical and it was my best and favorite subject in school. But I am not one of those with natural talent at math.
But In school and college I was a 4.0 student, always top of the class, always the curve buster, always one of the first to turn in my tests. But I worked hard to be that. I am highly competitive, and I focused not just on speed but precision and accuracy. I would turn in tests quickly, ace them, and get praised for my handwriting, showing my work, drawing diagrams and pictures to go with my work, etc. I didn't just turn in work as fast as I could, I was simply just that well prepared going into the test. By the time the test came around I could do it in my sleep. I had to work hard to get to the point in many classes, but it's not impossible.
I've had to work extremely hard my entire life to get where I am, to accomplish what I have, and to learn things. People always ask me, "how do you know so much?", as they see me as too young to know such things, not realizing many of the topics I know well I've been working on in earnest for 20-30yrs already, maybe more. they don't realize how hard I worked in short time periods, and the tricks i've learned along the way to speed up my ability to absorb and comprehend new information.
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