I entered the academic world after 21 years working at an industrial research lab. Even though I’d held a visiting lectureship and a visiting professorship during that time, I wasn’t really properly prepared for the world of students.
The university I worked for wasn’t in the UK and so I was aware there might be cultural differences. One of those cultural differences was in the attitude to ‘cheating’. One student, for example, sheepishly handed in his homework late.
The reason?
His sister hadn’t been able to do it for him on time.
I really am not kidding. He gave me the reason without any apparent sense of shame or appreciation that this was not acceptable. His expectation was that I’d be perfectly OK with this - the only problem he saw was in the lateness.
But many of the problems I faced when dealing with student issues were not, primarily, culture driven.
The lecturers were buffeted from both sides, often having to fend off attacks from the ‘management’ as well as the students. My first inkling of this was during my first semester when the Dean told me I needed to adjust the grade boundaries to achieve a more ‘acceptable’ GPA on an exam I’d set. One lecturer described his first few years working there as a gradual process of lowering standards and manipulating grades until the management no longer gave him any hassle.
But the students were just as bad. The student cohort was made up, roughly, of 80% local and 20% expat students. We had an exchange program with students from Eritrea. The Eritrean students were usually very good and got excellent grades. At one point a delegation of local students went to the Department Head and demanded (yes, demanded) that the tests and exams of local students be marked more leniently in order to achieve grade parity with the Eritreans. They’re better than us, one student said, and so you need to take that into account when grading1.
Diversity administrators everywhere must be squealing with delight and admiration at this student-led protest to achieve equity.
But there were more substantive (systemic?) issues that were a bigger problem.
Most of the students had no idea how to effectively study. I’d always open any lecture course with a mini-review of how to develop a good understanding and, therefore, get better grades.
There were 3 key elements to my advice
Practice
Practice
Practice
It was very difficult to get across to the students just how critical, for the technical disciplines, continual practice is2.
Most of them seemed to adopt the position that all they needed to do was to turn up to lectures and take notes and, provided they memorized the notes, they’d get good grades. One student even went so far (with another lecturer) to raise a formal complaint that there was a question on an examination that she hadn’t seen before in class, and so this question needed to be removed from consideration when it came to her grade. Thankfully, the management weren’t on the side of the students this time.
There were some curious side effects of this “head-stuffing” attitude to learning and understanding. One lecturer teaching the first Calculus course covered a problem where an observer is watching a rocket take off vertically. The problem was to work out the rate of change of the angle between the top of the rocket and the observer given the upward rate of change of the motion of the rocket. He covered this problem in class. He gave them homework problems based on it. He did everything he could to help them understand it.
Except one thing.
When it came to exam he thought he’d give them an easy question (easy for anyone who’d understood the technique) but he phrased it in terms of a balloon rising vertically this time. He was astonished to find a significant minority (about a third) of students couldn’t do this question, despite having successfully completed their homework questions, because it was now about balloons and so it was a different question!
The inability to abstract the essentials of what the question was about seemed to be a serious problem.
This is a known problem and is largely responsible for the difficulty in algebra. Students are often OK with manipulation of questions when all the quantities are given numerical values. But if the same question, requiring the same techniques, is cast in terms of letters, they get hopelessly lost. They can’t make that abstractive step.
There were many deep systemic issues I noted. Lack of facility with algebra was one. An almost complete inability to sketch graphs of simple functions was another. An almost non-existent ‘feel’ for numbers and sensible results was yet another. I reached out to colleagues across the world to ask whether they’d experienced similar problems. Sure enough, they had.
I began to suspect that one of the factors involved in these difficult to remedy systemic issues was in their overuse of calculators.
If I asked you to multiply the numbers 4,879 and 3,906 together you’d probably reach for your calculator. Fair enough. So would I.
But we already know a fair bit about this product without doing so. We know, for example, that the last digit is going to be a 4. We know that the answer will be less that 20,000,000 and more than 12,000,000 (we can firm up a bit on that with a bit more thought - we know, for example, it’s going to be closer to the 20,000,000 figure than the 12,000,000 figure).
We can do all of this stuff (and more) in our heads. If you get a bit more experienced you can re-write this product as
If you know how to expand the brackets here then you can get much closer to the actual value. With practice, you can do this kind of thing in your head and arrive at a much better estimate for the value.
But the vast majority of students won’t go through this kind of process either before or after punching the numbers into their calculator.
I once saw a student working out the following by typing out the approximate value for pi into their calculator
The answer is, of course, just 1/2. But why couldn’t the student “see” that?
My favourite example was in one of my classes. It was the 2nd Calculus course and so more advanced integration and differentiation techniques were covered, along with things like series. I noticed that the students (most of them) were really weak in (a) sketching graphs and (b) interpreting them. It was a serious problem that was really hampering their ability to understand what was going on. These were engineering students, after all - and the ability to visualize things has to be one of the most important things for any prospective engineer3.
I decided to break with the program and give a 2 lecture class on how to sketch and use graphs (I was a bit ahead on the syllabus anyway). I gave a quiz to see how well they’d understood things. Graph sketching should be a quick thing and so I set about 20 questions around graph sketching. With so many questions, I thought, they’re going to have to use the rough and ready approaches I’d covered, rather than trying to laboriously plot things by typing values into their calculators. I wasn’t looking for works of art - just a rough sketch of the behaviour of the given function with some appropriate annotations.
One question I set was testing their understanding the cosine function. I asked them to draw 3 different cosine functions on one set of axes.
In each of the functions the A and B were different. The cosine function wiggles - it’s a nice easy function.
The first cosine function I asked them to sketch had A = 1 and B = 1 (this is the pictured graph). They all got this right.
The second one I asked them to sketch had A = 2 and B = 1. This has the effect changing the size of the wiggles - so instead of oscillating between the values of +1 and -1, it oscillates between the values of +2 and -2. They pretty much all got this right too.
If we increase B we make the wiggle ‘faster’ - we increase the frequency. The question was meant to test whether they’d appreciated these properties; increase A, increase the size and increase B, increase the frequency.
So, for the third graph on the same axes, I asked them to sketch the cosine function with A = 1 and B = 4 (no increase in size, faster wiggle)
It was meant to be a really easy question.
I was astonished to find, upon marking, that nearly 2/3 of the class had drawn the straight line y = 1 as their answer for the third cosine function. They had wiggly graphs for the first two functions, but a straight line for the third function. WTF?
I had no clue as to what had gone wrong. I had to ask the students. It transpired that they’d plugged values into their calculators. They had managed to choose the values corresponding to the maxima of the function. Each value of x they picked returned the value 1 - and so they just joined the dots to get a straight line.
It was like literally nothing had passed through their minds other than “type in values, join dots”. Not one of them remarked upon how it was odd that the first 2 cosine functions they drew wiggled, but the third was just a flat straight line. The great calculator God hath spoken!
I came to the conclusion that the students had effectively delegated their thinking to their calculators.
Rigger’s Maxim :
We should control our tools; we should never let our tools control us
I wonder if this isn’t part of what’s going so badly wrong these days? We unleashed a great “social media” experiment on the population and it’s had a number of catastrophic side effects (well documented by Jonathan Haidt, for example). Social media can be a wonderful, brilliant, thing - provided we do not let it control us. It’s a great tool, but like all tools it needs to be used safely.
How much of our moral “calculations” have we ceded to the computation of social media? The mob mentality, and subsequent brutal response, that can be instigated by an ‘unwise’ or ‘unfiltered’ thought is one of the less appealing aspects of social media and can cause us to question our own judgement, our own sense of what is right and wrong, and even our own sanity.
It’s technologically-driven ugliness when it gets like this. The tool we are using begins to control us. Fear drives us to moderate our posts, to avoid speaking about certain issues in certain ways. And that’s just the malevolence of the mob. Once governments get involved in what you can and can’t post, then we’re in for coercion and enforcement on an even greater level (as bad as the mob are, it will get much worse when our overlords step in. For our own good, obviously).
As the genderwoo zealots know, social media is a very powerful tool. We know it’s used as a methodology of social contagion, but in their eyes there are zillions of pre-trans individuals just waiting out there desperately wanting to live the rainbow if only they could be directed to the right social media resources.
Might I be betraying my Catholic roots if I ventured the advice that we need to stop playing with our tools quite so much?
In case you’re wondering, their, erm, “request” was denied. But just the fact that the students thought it reasonable and acceptable to make such a request in the first place is somewhat telling.
I’m sure it’s important for non-technical disciplines too, but I don’t have any experience in that regard.
You can get by without it - and some really brilliant engineers, mathematicians and scientists don’t seem to rely on it very much - but I would argue that, for the majority, it’s a critical skill to acquire.
“Does that answer make sense?” is an underrated question, and “check your work” highly underrated advice.
From a spiritual perspective I know I am an immortal being having yet another physical lifetime in this lower spiritual region ( a physical matter universe). I call this planet an amnesia model planet, based on the human occupants lack of memory of past lives.
I remember many of mine. Bearing in mind for very long time there were only a small number of millions of available bodies to use, the beings here were of a certain experiential caliber. However my current theory on what happened was that a planet occupied by mostly retarded or degraded beings was somehow destroyed, leading to the need to find a planet capable of allowing all these souls to continue their soul’s journey… unfortunately for us older natives, we now have to live with them.
Not only have they taken on bodies here, but now they have finally taken over in all areas of society. On a more local level you can see what happened in Texas when the Borg ( leftist planetary interlopers) took their insanity to what was once a lovely city (Austin) and infected and destroyed it. Earth was once simply planet Amnesia, now it’s also planet Retardia.
There is no hope. You can’t fight these degraded beings in such numbers. The solution is to not choose Earth next time around.