Tag: learning

Want Good Grades? Then Forget About Getting Good Grades!

Ok, I admit it. I have a habit of creating titles that create a disconnect. And are a little click-baity. But to be honest it only happens because I often like to write about misconceptions, and so by definition the title will appear counter-intuitive. Today I am going to write about something that over the course of my teaching career has met with perhaps the most resistance from students and parents, but which has also met with the most success when embraced.

If you want good grades, stop trying to get good grades.

Scandalous, I know. And trust me, I have heard all the rejoinders. So as you can imagine, I will explain.

See, in the current system of education, grades stopped being a measure of progress some time ago. What they have become instead is currency. A commodity that is pursued, traded and leveraged with as much vigor and ferocity as the dollar, euro, or yen. And I am not using hyperbole here. Schools these days have come to be viewed by many students, parents and even teachers as a marketplace. Teachers have the grades, students want them. And in this marketplace the end goal is to get as high a grade as possible. To very many – but to be completely fair, not to all – how that happens is not nearly as important as that it happens. To this category of student, the goal of school is not to learn, but to get grades. And this paradigm shift causes a fundamental change in how the entire process is viewed. I will list just a few examples:

  • Bargaining
    It has become standard operating procedure now that when teachers return graded work, the immediate next phase is the negotiation. Students dissatisfied with the magnitude of their grade will question, cajole and even harass the teacher about the grade, with the common theme that since the student believes the grade should be higher, the teacher has assigned a wrong grade. There are even times when the guise of reason is dropped completely, and the student will actually say things like “I need a 97% to get into <insert elite university program here> so can you raise my mark?”
  • Academic Dishonesty
    Academic dishonesty (aka cheating) is not a new phenomenon. What is new, however, is the pervasiveness of it, and the total lack of ethical struggle involved in making the decision to use it as a tool for getting high grades. After all, if the only purpose of school is to get a high grade, and if cheating accomplishes that, then where is the ethical problem? And so we see rampant use of things like plagiarism, paying others to do work that students then submit as their own, or gaming the system so that assessments like tests are skipped, then done at a later date after getting information from other students who were present at the time about what was asked.
  • Grade Mills
    Countless “schools” have popped up over the last decade or so who’s sole purpose is to guarantee official credits and high grades. The thinly disguised mission of these schools is to create a means by which, for a price, students can get a credit on their high school transcripts and also get an absurdly high grade. What separates a grade mill from a more legitimate private school is how accurately the student’s grade reflects their knowledge on completion of a course. I have taught many students who received a grade mill credit in a prerequisite course for the one I am teaching, with a grade of 100%, who do not possess the most basic skills meant to be learned in that prerequisite course.
  • Cramming
    This is definitely not a new concept in academics, but it has spread to more and more students, who in fact no longer recognize that it is not actually a means of learning. In courses where there are scheduled tests/exams, students do little to no work during times where there is no assessment looming. They attend class, possibly take notes, and otherwise devote minimal attention to the lessons, because “this won’t matter until the test.” They do not see this as an ineffective strategy at all. The belief that drives this is that the only time the subject knowledge will matter is when they are tested on it (and thus in a position to get grades), and so the plan is to study as much as possible the day – or even the night – before a test. Cramming all the information into their short-term memories just long enough to unleash it onto their test papers, to be promptly forgotten as they leave the room after writing the test.

These are not the only examples of what I am talking about, but they are the most common. And it is clear that none of these appear to give actual learning more than the slightest courtesy of a head nod. They are completely and totally about getting grades.

Sometimes, they even work. But that’s a trap. Because even when they work, they are only short-term solutions to a lifelong endeavour, and they all create stress and anxiety in the process.

  • Bargaining for grades, when it works, teaches that it is not about what you earn, but about what you can badger people into giving you. It shifts the perspective about where the effort should be placed. Rather than placing effort on producing good work, the effort is placed on convincing the teacher to assign a high grade. This creates an internal tension that results in generalized anxiety, because the student ends up in a position of having to convince the teacher of something that is not actually true, and for which there is no evidence.
  • Cheating works for its intended purpose (when you don’t get caught), but like grade mills, perpetuates the “appearance over substance” philosophy, and also imbues dangerous long-term values that erode at the ethical fabric of society. The stress this creates is clear – fear of getting caught, and the consequences. Additionally there is the gradual accumulation of anxiety brought on by creating an academic avatar that is more and more fraudulent and removed from the person who wears it.
  • Grade mills teach that appearance matters much more than substance – if you can appear to be someone who earned a perfect grade in calculus, it does not matter if you actually are someone with a deep understanding of calculus. It is hard to even wrap ones head around how many ways this is wrong. First, the injustice of potentially securing a spot in a college or university over someone who earned a lower grade, but actually knows much more calculus. Then, the fact that with the label of “100% in calculus” anyone who checks that label will assume that you are a calculus genius and expect that you are, creating significant stress on the person masquerading as the calculus prodigy. Finally, the pressure that the very existence of grade mills places on legitimate schools, who have little choice but to begin awarding higher grades so that their students can remain competitive when it comes to post-secondary offers of education, which is a non-trivial contributor to grade-inflation. The stress created here is very similar to that created by cheating, and has the added anxiety-producing bonus that at some point there won’t be a grade mill offering credits and grades for money, and that the student will actually have to perform as the person their grades have indicated that they are.
  • Cramming is arguable the lowest offense on this list, because in its purest form the student is not misrepresenting themselves at all. However it is fraught with disadvantages, from the fact that many students struggle to absorb and then reproduce the knowledge in a meaningful way, to the fact that when needed later – in the same course or in a subsequent one, the knowledge is no longer accessible. It also creates a great deal of stress and is a common cause of test-anxiety, which is a very real issue for many students who find they “totally knew this last night” but can not recall it when test time comes.

Perhaps most tragically, this issue causes stress and anxiety not just for the students engaged in them but for the many students who are not, because it creates an unlevel playing field that places incredible burden on the ones who are doing things the right way. Grade inflation is a real and dangerous phenomenon, where just like monetary inflation, a loaf of bread is still a loaf of bread whether the price tag says $0.75 or $2.99. The difference is that because we use percentages as grades, there is a ceiling, and so we are starting to distinguish by decimals. And that means that for any student mistakes cost much more than they ever did in the past.

Ok. So I’ve devoted the article to this point (approximately 5 minutes of reading time, if the algorithm that tells me how much I have written so far is to be trusted) outlining the issue. And maybe I’ve made it seem like hope is lost, because we do in fact live in a system where grades matter for universities, colleges, academic awards, and sometimes for that first job, and all of these vehicles by which students are getting the grades are either unethical or riddled with stress and anxiety. But hope exists! Because there is very good news.

To get good grades, all you have to do is actually learn the material!

Revolutionary, I know. It almost seems like I am joking. I assure you I am not. This simple fact is lost on more students and parents than I wish was the case. Clearly it would work though, right? Of course it would. Students, you can take all the effort you are devoting to “getting grades” and shift it to “learning material”. Immerse yourself in class. Ask questions of the teacher. Engage in discussion. Pay attention. Do work in increments (that is, homework), instead of cramming the night before a test or exam. Decide that you will be a master of the topic and use your teacher as the resource they are. Develop a love of learning – trust me, this is not as hard as you think – and as you grow into this person who legitimately strives to learn, the grades will automatically follow, as an afterthought!

Now I know from experience that this message lands differently on everyone. Some people roll their eyes, either inwardly or outwardly, and decide that the game as it is being played works just fine for them. Others hear me and know it makes sense, but feel that it’s too hard, and getting grades some other way will be the way to go. But, there is a significant portion of students I have talked to who have taken the idea to heart. And without fail they are the most academically successful, as reflected both in their grades, and in their facility with the material they have learned. These students inevitably report back to me that once they stopped their pursuit of high grades, and shifted their energy to the learning, they began earning higher grades than they ever had before. And their confidence grew as their anxiety atrophied. Because so much of the mentality of getting grades involves somehow gaming the system into awarding false credit, that when they shift into the person who actually has earned the credit they are receiving, they feel bulletproof.

And what a great feeling that is!

Thanks for reading,
Rich

Why Study Mathematics?

In my job, this question is one I get asked very often. To be honest, it usually comes in a slightly different form …

“When am I ever going to use this? What is it good for?”

As a high school math teacher for 15 years, this is one of the most common questions I received. When I began lecturing at university, I was surprised to find that I still sometimes get asked variations of this question. I suppose it’s a good question, if the idea is that at some point someone will say to you

“Determine

and have your answer on my desk by 5pm today. And don’t get any funny ideas about using WolframAlpha!”

Because the truth is, that rarely happens.

I often give a joking answer, and say flat out, “You won’t,” and then go on a rant about how math doesn’t need to be good for anything, because it is just good. Nobody ever stood in the Sistine Chapel, staring at the ceiling, asking what it was good for! They just appreciate the inherent beauty, because it speaks to their soul. Math is the same.

I think that’s a perfectly good answer, to be honest. But in a more serious light, I find the answer to the question is actually another question: “When are you not going to use this?”

Of course, there are direct applications of many branches of math. But those tend to be very specific, and these days depend heavily on software to do the heavy lifting, so I tend not to think of those. Instead, consider that football players perform bench press as part of their training, to the point that the ability to bench press 225 pounds for as many reps as possible is tested at the NFL combines. Yet not once have I ever seen a football player perform the bench press during a game. Why do they do it then? Couldn’t they just practice the skills they will actually use in a game? I can promise you that at no point during a football game does a player think “oh, this situation is just like bench pressing 225 pounds – I will apply that same skill now.” And I imagine there are very few football players who complain while lifting weights that they will “never use this in real life”. Of course, we know that the reason they train the bench press is that it increases strength and power, so that when the time comes that they need it, it will be there without consciously calling upon it.

Studying mathematics is the same. Math teaches so much if we are awake to the lessons. Here are some things I have learned, continue to learn, and apply regularly from my math studies, along with some examples of how they have impacted me personally.

Scale simple solutions to solve large problems

It is almost always the case that large problems can be effectively solved by breaking them into smaller problems, or by developing scalable solutions to simpler problems. For example, about 3.5 years ago I decided I wanted to learn to draw, so I took a piece of white printer paper and a mechanical pencil and drew a superhero-esque muscle man. It sucked. Like a lot. But I was not discouraged in the least by that. I was fueled by it. Why does this suck so much? I know how I want it to look, why can’t I make it look that way? I was excited by the fact that I could recognize how much it sucked, and by the prospect of working to slowly strip away the suckness. I spent hundreds of hours, solving small problems that were contributing to the suckyessence, and slowly scaling them up. Want to draw a heavily muscled arm? Learn to draw a cylinder. Then learn to draw little cylinders that lie on the main one. Then learn to draw “twisted” cylinders and tubing that changes diameter as it twists. Learn anatomy. Now put it all together. I intuitively understood platonic solids and how they interact with and reflect light. I applied these understandings to understand the types of skills I needed to hone with the way I held and manipulated pencils. I started looking closely at things I never paid attention to before. I still do this, and at no point during this process do I ever consciously say “Oh, that’s just like <fill in math course here>”, but at every point I feel exactly the way I feel when I am working on difficult math problems.

Being right also means proving you are

Math is really never about just “getting the right answer”. It’s about proving that an answer – or a result – is correct. The emphasis on proof is critical. In the real world, being right is rarely enough if you can’t convince others that you are. Careful, methodical, and audience-appropriate explanations are invaluable in this regard. Developing and writing proofs in mathematics is as much an art form as it is a science (perhaps even more so), and my studies in mathematics immeasurably improved my approach to constructing an audience-appropriate argument or explanation. This has had a profound impact on my communication skills, as well as my approach to confrontation. I have used this skill in more ways than I can list, but some examples are: when I have been in contract negotiations, when I deal with sales people when buying big-ticket items (and even when I bargain at markets), when I find myself moderating arguments between friends, family, colleagues or students, and when I used to work as a personal trainer and had to motivate and justify the kinds of exercise and diet choices I wanted my clients to make. In every single one of these situations, and more, I am really constructing proof. In fact, I would say that proof dominates almost all my communication.

Emotional attachment to a belief is irrelevant

Not wanting to be wrong about a belief, especially if it has been long-held, is normal. It is, however, illogical and possibly even dangerous in the face of proof to the contrary. Mathematics trains us to seek, understand and ultimately accept proof on its own merit, and not on any emotional yearning. It also trains us to be grateful when proven wrong, since it makes little sense to want to be wrong for even one moment longer than necessary. My training in math has led to a much more open-minded approach to new thoughts and ideas, and after careful consideration – which involves listening to argument dispassionately, asking relevant questions and weighing evidence – I find myself either happily embracing a new thought, or else more confident in the one I already had, having had the opportunity to test it rationally against a differing viewpoint.

Creativity and math are NOT mutually exclusive.

Not even close. Deep study of mathematics reveals and refines a strong creativity that aligns with and is mutually supportive of logic. This fusion is relatively rare, and people who have it are prone to what seem to be exceptional accomplishments. In truth, the exceptionality of it is not the accomplishment itself but the relative scarcity of people who can do it. One of my favourite examples is Leonardo da Vinci, who most people think of as a great artist, but who was also an accomplished mathematician and scientist, and who did not consider these as separate pursuits or modes of thinking. I find the same is true in my own life, although there are many people who wonder how a mathematician could be artistic.

Clarity lives just on the other side of contemplation

The journey math students regularly take from being completely mystified and often intimidated, to understanding and comfort is a lesson in overcoming that serves us well in all the challenges the future can bring. It instills a confidence that says, “I may not understand this right now, or even feel like I ever could, but I know I can do it.” General wisdom suggests that “easy” might seem gratifying in the moment, but true satisfaction comes from overcoming a challenge. Many people shy away from challenge for fear of failure, but studying mathematics teaches us that we can tackle large problems, even if they seem overwhelmingly daunting at the outset. An example that makes me laugh is the time I purchased a large and intricate piece of exercise equipment for my home gym (a functional trainer/smith machine combo). I bought it used, so it did not come with any assembly instructions, and perhaps embarrassingly, it didn’t occur to me to use Google. When I picked it up the seller had already “helpfully” disassembled it into n pieces, where n is large. I was completely baffled at how to reassemble it when I got it home. But I was not daunted. I laid all the pieces out on the floor, shuffled them around into sensible groups, and slowly assembled sections that made sense. I made mistakes and discovered them when they led to chaos. I backed up, took a different approach, and eventually put it together. The process was not “clean” – I hurt my hand trying to brace a nut while tightening a bolt, and cursed myself for not taking the time to get a wrench to hold it in place. But the result looks like it was assembled by a pro. I’ve had it for many years now, and it still works perfectly. I am fully aware that my engineer friends would consider this a trivial exercise, but for me it was a hard-fought and well-earned victory. This type of approach has stood me well time after time.

You don’t always have to see the whole path to the goal

How often have you been working on a difficult proof or problem, not really knowing if you were getting anywhere good, nevertheless continuing to take small, logical steps – always forward, occasionally pausing to reorient yourself to see if the direction made sense – when suddenly you found yourself having completed the entire thing? Some mathematicians call this the “follow-your-nose” principle of proof. A leads to B which leads to C etc. This might be the most important lesson of all. If you have a long-term goal that seems incredibly distant and perhaps overly ambitious, consider that if you just point yourself in the right direction and take small steps, occasionally reorienting yourself, you do eventually get where you want to go. Plus, the journey is so rewarding. In my life I have used this principle I learned from proof over and over and is in fact how I ended up lecturing at university, something that has been a dream of mine since the 12th grade.

And that concludes my very long answer to the common question! I hope you found something of value.

Thanks for reading!

Rich