Success And High Expectations In Mathematics For All Students: Fill & Download for Free

This year my wife did something I never thought possible. She teaches 5th grade. She had to cover for one of her other teachers who was coaching for a softball tournament. What’s remarkable? It was literally the first day of school after Summer Vacation.If you ask most public middle school boys in the United States what they want to be when they grow up, the majority (around 60%) want to be some professional athlete. When I was teaching, I conducted this experiment numerous times. Again, and again, and again, the results were about the same. It doesn’t matter that the vast majority show no particular gifts in athletics. It doesn’t matter that the realities have not yet sunk in of just what kind of genetic freaks it now takes to be a professional athlete. They are told that if they just try hard enough, they’ll be winners. More to the point, if they lose the game, the only possible reason was because they didn’t try hard enough… for their coach.What exactly does this have to do with math? Nothing, directly, but the answer makes it blatantly clear why we suck at math.It isn’t about math. It’s about heroes. The United States doesn’t know how to build heroes anymore.Let’s talk about how heroes are created anthropologically. It isn’t just that someone does a heroic act. Afterall, what defines a heroic act? The culture does.Collectively and subconsciously, the culture considers the values that are important to it, then distills that into an idea of what the best personification of that person is. Then they call that “a hero”. We then look around society for the people who best personifies that idea of “hero”, and we shower them with praise and honors, grant them wealth, and erect massive statues to honor them. And the hero of heroes, those which master the traits and values of heroism, as dictated by the masses? We might as well call them gods.You know who the “gods” are in America by looking at whose 20 foot face decorates our places of worship… i.e. the malls.Given how much power, credibility, wealth, and fame is given to people whose only skill is dribble a ball, sing songs, or recite lines in a specific order while holding a particular facial expression, it’s clear what traits America has determined to be a heroic.In the schools, it’s even worse.The situation is bad because kids, contrary to what the question seems to imply, aren’t stupid. They are horribly intuitive and that’s what’s causing so many problems. They see this pyramid of values and see where it points, to people who become prominent with absolutely no need for academic intelligence. Our children are already stretched thin with challenges unheard of, even to my generation. They are intelligent enough to know that their own mental health requires them to be liked far more than to be successful, at least in the short term. Then they go to college and play catch up, but in high school? Who has the time to be popular and smart?This isn’t even due entirely to the culture either, though culture definitely has a role.When you take it back down to the public schools themselves, look at who gets paid the most. If you thought it’s the teacher who gets the highest results in standardized tests, you’d be wrong. Way wrong.This is true for colleges, but the pattern continues at the local level too. By far and away, the wealthiest teachers are actually coaches. Granted I said wealthiest in the way that one refers to the tallest 3 year old. It might be really tall compared to the other kids, but nothing that special compared to the rest of society. But it says a lot to a teacher who makes very little as it is, that if they were to become a coach, they get an automatic stipend worth more than anything else they could possibly do. In some cases, this translates to 20% more to do about 60% of the classroom teaching which is the job most Americans think schools are meant to create.Next note the distinction I made between “teachers” and “coaches”. I say that the two are different because far too many aren’t the same. While they may technically be a History teacher, many coaches in the United States actually only teach in the classroom as a means to coach a sport they fantasize about as kids. When you ask them their career goals, they don’t talk about teaching History at bigger and more prestigious schools, or even in colleges. No, they talk about coaching the sport they coach at bigger and better schools… and even college… or even the pros.I want to qualify that statement. There are a few coaches who were the best teachers I have experienced. They kept the balance between athletics and academics in its proper place, but the rest seem to settled on the opposite end of the spectrum.Again, kids aren’t stupid. They can see the priorities that these coaches have clearly tells them that “sports are more important than my classroom,” and the subconscious message students receive is that sports are more important than academics. This doesn’t stop when coaches will push students on the field, but shrug off a failing student. It makes it clear where they view the future of their career when you think about the same man screaming at a kid who drops a ball, but not upset when a kid “gets what he deserves” for failing a test. It should bother people when educators have low expectations in the classroom, but impossible expectations on a sports field. It isn’t about the team. That coach only cares about his career and that should bother parents of students.In this weird way, policy that encourages teachers to become coaches, affected students into obsessing over sports, which caused more need for coaches as kids no longer cared about other things. It isn’t just math. Americans aren’t as good at so many of things we should be wiping the floor with the rest of you. Of course, it makes sense when, “to be cool” (to align with the shared cultural idea of hero amongst children) a kid must admit that they, “suck at math”, even when they don’t. That’s because math isn’t important… to an athlete. Most other countries, as we’re told through anecdotes, the smart kids are the cool ones. How curious.So kids face this unintentional indoctrination from a very early age to push away any subject that won’t help them gain appreciation from the most important people in their lives. Since society dictates that most of their waking hours is at school, and since public school prioritizes more honors and funding to coaches, that person is more often than not a coach. If the coach isn’t genuinely drilling into them a need for math, which almost none of them ever will, the kids will get the message that math doesn’t matter.And here we are.I don’t want to belittle certain key factors. Teachers are underfunded in the classroom. They certainly don’t get as many resources to teach math as the cost of a new stadium, sports equipment, or insurance, that is. The time constraints are also mitigating in that it is very hard to cram in whatever needs to be learned in only an hour. Because of new age thinking, homework is a naughty word, even though no one bats an eye at the amount of time spent away from home to practice or play sports. All this is true, but the reality is that kids don’t learn who don’t care. There are stories from around the world of kids holding class under bridges and who have to pay every day that they get the chance to. Those kids want it. The big problem isn’t the funding or even the coaches. It’s a society that doesn’t know how to make heroes with values that matter in the times we live.Liked this? You might also like my YouTube Channel. You can also connect with The War Elephant on Facebook. If you want to help me make more content like this, please visit my Patreon Page to find out more.

They don't have the freedom to be whoever they would like to be.This is Yunhao Fu.Too many eyes were on him when he was a teenager. He was an exceptional teenager.“Two time Olympian” is what media uses to sum up Fu’s life. As a middle schooler, Fu scored 42/42 twice in a row - 2002 and 2003 - in the International Math Olympiads (IMO), being the gold medalist twice. In the 30-year history of the Chinese national team, only three players have achieved this result.Those familiar with IMO would know that it is extremely difficult to get any medal for it. IMO’s level of difficulty fluctuates. The two IMOs Fu participated happened to be among the relatively difficult ones. Thus, he may be one of the greatest math medalist in history. For a long time, he was regarded as a symbol of the Chinese mathematical community.The IMO contestants generally continue to engage in mathematics research and establish an outstanding academic career. Many have speculated about his future — Get a PhD in Princeton? Become the youngest professor in Harvard? Establish a significant theorem that changes the entire history of science?To their disappointment, he didn't do any of these. He didn't follow the conventional path of a math prodigy. Instead, he evaporated from the academia.Today, a middle-aged Fu is working as a lecturer at a non-prestigious normal university, where students graduate to become elementary and secondary teachers.This time, the media addressed him as “The Failed Genius”.The media reports depicted him as a loser, a melancholic figure stuck in the past success, and as a wasted prodigy who never lived his life to the fullest.The people who have watched him peak in his teenage years are very disappointed at what has become of him. In their opinion, if he is a champion, his life must be pursuing the sea of higher mathematics; anything else is considered a failure, including engaging in hard work and producing qualified middle school math teachers. They believe that a career path revolving around academic research is the superiority and the choice a prodigy like him has to make; ordinary work is low and shameful and beneath his intelligence.If a once successful genius didn't follow the expected path but simply remains an ordinary invisible human being, it is a failure.No one really asked or cared how Fu made his career choice, or what Fu would really like to do with his life.If he displayed unusual aptitude, he must do something with the talent. Whether he liked to go deeper into this field doesn't matter.If he is highly accomplished as a kid, he must get the get into college, get this Ivy League PhD degree, work at some big-name corporations or become a tenure at a prestigious university. Otherwise he's a failed genius and wasted talent.However, what if he loves being a lecturer and passing on his knowledge to future K-12 teachers?Believe it or not, there are a handful of people who would willingly forsake a lucrative career, only to pursue something they enjoy.However, the media only assumed that he picked this job because he didn't have better options.For what is worth, Fu claimed that he enjoyed being a lecturer and never regretted his choice.This is all it matters.There is no principle to dictate what kind of life a math genius should live. Nor should there be one.

Actually there is!I’m an electrical engineer and the math you have to take to pass those classes are about as brutal as they come. Calculus 1,2,3, Differential Equations, Linear Algebra, Complex Analysis, probability and stochastic processes for scientists and engineers. Diff eqs and complex analysis are perhaps the hardest courses I’ve ever taken.I was never stellar at math through high school, in fact, when I first started college at a community college, I was placed in pre-calculus. For those of you who don’t know, in America unless you pass the entrance exams for Calculus, Physics and Chemistry, you will not go straight into Calculus 1 or Physics 1 or Chem 1A. Basically you have to take remedial classes like pre-calculus or pre-physics or pre-chemistry. Then you wonder why it takes 5–6 years to get through undergrad for basically most engineering majors! Everybody I knew in my EE classes took about 5.5 years because we had to do something like 135 units which was the most for any major at that university.I struggled in the beginning then ‘I thought’ I found out something about myself, which might be one reason some people aren’t good at math. At first I thought I had what is known as:DyscalculiaI used to joke with myself and say, “That means, you can’t do Calculus”. If you laughed at that joke, you are a true geek like me.. just admit it, it’s ok!Actually it means: Difficulty in learning or comprehending arithmetic, such as difficulty in understanding numbers, learning how to manipulate numbers, and learning facts in mathematics. It is generally seen as a specific developmental disorder according to the web.But soon I figured out it was pretty unlikely I had that, if I did it was probably not a significant contributor.After years of self diagnosis and adjustment, I found out a few things but before I tell them to you, I want to discuss why math is feared and why high school and college are actually contributing to what is know as math anxiety.Every math and engineering class I’ve ever taken had the following format.You can follow the textbook roughly and the easy worked out examplesYou can follow the easy examples the prof will do in classYou can manage the homework with some helpBUTThe exams are a completely different story. In exams, this is what happens.They are usually problems you’ve never seen; that is, most of the time you have no clue how to solve it. And if you spend 5 minutes thinking about one problem, you are basically wasting time and you can’t afford to do that.It is speed contest. This is the biggest thing because in most cases you are given way more problems than you can solve in an hour and the person who solves them the fastest and most accurate wins. Speed!The above is what builds what is called math anxiety! This is primarily due to the fact that you have little time to solve huge problems and if you don’t, you get penalized. Once this behavior is learned, students eventually just give up or just say to themselves, “Oh well, I’m not good at math”. So it’s not enough that you can do them, you better be quick at it!So the system is inherently built to scare you with mathematical finesse.I think 50–100 years from now, the system will be much different and the expectations won’t be as crazy. Realistically, once you get out of college, you hardly use any math even in electrical engineering because that’s what computers are for. They model, simulate and calculate circuits, communication systems and all other aspects of engineering better and faster than you can on paper. Honestly, unless you are going to do a PHD or become a professor, you really don’t use all that math once you start working.What worked for me ?First, I tried to understand how I learned. Figure that out first for yourself. Some of us are visual learners, some are auditory learners. Most people have a combination of both. In my case, I was extremely visual to the point where if I couldn’t visualize it, it made no sense to me. This is why I sucked at pure math.What I’m getting at is that, when there is no application, it was hard for me to just solve a problem because I needed to be told, “Why we are doing this and what purpose does it solve?” and obviously no one will answer that. instead you will be given something like the following to evaluate.The above made no sense to me from a pure math point of view. My questions were:What does this represent in the physical world?What does the input and the output mean?What real world problem does this model or solve?Why exactly do you want me to solve this? Other than to just do it.A lot of Calculus and differential equations although some of it is applied, is usually just “solve this or that” because that is what is required. So my biggest problems was, without context to the real world, I had trouble relating.Unfortunately, if you don’t go through the practice of just doing it for the sake of doing it, you will fall behind fast and that’s what happened to me.To me pure math like Calculus 1, 2 and 3 and then differential equations made zero sense because it was mixture of.Do it because we told you so.What math tricks do you recall or know?Showoff your mathematical finesseHow fast can you do it?In essence, it was sort of a discipline where if you know how to crack the system (as most of us have learned either consciously or unconsciously) you were good. That is, you could basically skate through all the way up to diff eq by just knowing a few tricks and not really understanding what was going on. Until of course you were asked to do a math proof where half the class would fail.To get through pure math, I would try to understand the following.Basic math concepts without any math. Even if you are great at math, you’d be surprised at how many things you never knew or missed because you were too busy just plugging in stuff into an equation and solving for speed.Understanding the symbols in math. This was one of my biggest challenges. The math symbols are basically another language and you need to know it to the point where you can decode it. Not understanding the symbols and the language of math is perhaps the biggest contributor to math anxiety.Become a master at arithmetic and algebra. Believe it or not higher math is dependent on and built upon basic skills. For example, one could argue, solving differential equations is simply the use of algebra and basic calculus. In the end, a tiny algebra mistake could cost you half the credit for the problem on a test! It did for me!Understand all the basic math functions. This is important and part of understanding the math language and symbology because you need to know what basic arithmetic, algebraic and transcendental functions do and how to use them and what operations can be used on them. I’m talking about the underlying concept and purpose.keep practicing with homework problems and other problems from the internet or guide books to build speed.After I got through pure math which was a nightmare, I finally started to understand math once we started applying it. I caught onto to math in Physics because it taught me that we can actually model most of the things that happen in nature with math and be pretty accurate. It was intriguing to me that most of the things like a falling body, or a trajectory or planetary motion could all be described using math. We lived in a mathematical world! I almost feel that should have been my first lesson before arithmetic instead of the common rote memorization of arithmetic skills that is encouraged.During my second semester of Physics which was all about Electricity and Magnetism, I totally bombed the first exam and got a D or something but I did okay on the next two exams. When I talked to the professor he said, “Oh I have to think about you. You did bad on the first exam but you got the highest score in the class on the final” and he gave me an A-.Then as I got into more electrical engineering classes, the math got more brutal but what sort of helped me was the following and also a book called, “how to solve it” by George Polya. A classic! In it he talks about things like.Always strip a problem down to its basicsTry to solve it in pieces if you canTry to see if you could solve a lesser problem and build from thereTry to see if you know a trick or something you did in a similar problemAlso, I remember a friend of mine when we took a class titled “Signals and Systems”. By far this is one of the hardest classes you take as a EE. By this point, you pretty much have to know every single math trick you can think of and be ready to use it in your sleep. We were doing Fourier transforms for signals and communications. This was one of those gateway classes that a lot of people did bad on. That is, it really tested you if you were EE material. I noticed my friend was getting all A’s and I asked him, “How are you doing this?”. And he told me, “Oh, I just sort of found a trick to this class!” That is, he saw a similar sort of pattern to solve all those problems. Sometimes it’s all about knowing that math trick or a property you can exploit or sort of anticipating the type of questions the professor might ask and just sort of mastering those skills.I hope the long explanation above helped. I personally think everybody is capable of learning math but you have to find out how you learn and exploit it to your best ability and put in the time to understand it. Don’t worry about how fast somebody else can solve a problem, you goal should be to understand for yourself no matter how long it takes. Good luck!EDIT - Some more information.A few of you asked me where to find a list of basic concepts. Well that’s the hard part. The problem is that you have to hunt around the internet for a pre-made list or find a book that might talk about the conceptual aspect of math instead of speaking to you directly in math symbology. Or you have to get a list of things you should know and do extensive google search on each topic and make your own notes. I did find a simple document from the University of Ithaca, NY. It may seem like this is something that your high school teacher would pass out but honestly this is the type of stuff you need to understand. For example, even at my level, there were one or two things I never knew and I’m not ashamed to admit it! That is, I found myself saying, “Oh I never thought about it that way!” Take a look at this link for 12 basic math concepts you probably picked up in high school. You should really know this before going into pre-calculus. The main problem with math is professors usually gloss over the conceptional explanation and just start using symbols, equations and proofs. Bottom line is that you need to speak the math language. Literally what that means is that just like you are reading the words on this post, you need to decode math symbology quickly. Hopefully the link stays up. Thanks!https://faculty.ithaca.edu/novak/docs/Twelve_Concepts.pdf