The following scene has taken place, pretty much as described, several times over the past fourteen years — obviously the details vary from time to time, but the canvas is always the same: I am helping a freshman physics student in my office. The person came to ask for help or clarifications, typically on a homework problem.
Me: OK, so, we are then left with the following ratio, where you have at the numerator g, and at the denominator the square root of g. The ensuing simplification leaves us with just the square root of g…
Student: Excuse me… how did you get that ?
Me: You mean, how did I arrive at that ratio ? OK, let me redo the algebra for you…
Student: No, I have followed up to this point… but, how do you go from the ratio to having just the square root of g ?
Me: Well… um… you have g at the numerator… its square root… at the denominator… (I can tell that the person is not following… stares at the paper as if it contained hieroglyphs)
Student: I am sorry, I do not understand… how does that work ?
I am going to tell you now, the reader, what I honestly feel that I should tell the student, in a situation as described above . It is also what I used to tell the student, in my early years in this profession; over the years I have learned to tone it down, to be more ambiguous, vague — for my benefit, I have to confess, not that of the student.
So, I am going to tell you that if you cannot follow a simple algebraic manipulation (such as the above fraction simplification), it means that your algebra background is seriously deficient. The problem is, if you cannot do algebra you cannot possibly do physics, simple as that. Anyone who tells you the contrary is either crazy or a con man — in any case someone who has no genuine interest in your future, your education and your success.
So, the thing for you to do at this time, instead of wasting your precious time, hopelessly struggling with material for which you do not have an adequate foundation, is de-register from the course, and spend a term to take remedial algebra. While that might have the undesired, short-term effect of delaying your graduation, the long-term benefits, in terms of better grades and easier learning, will greatly outweigh the inconvenience.
Naturally, this advice implies no judgment whatsoever on my part on your scholarly ability, your intellect, your motivation to learn. I am simply suggesting that you spend a minimal amount of time (a term is enough — nothing, in the big scheme of things) shoring up a part of your high school background which is not as strong as it should be (obviously to no fault of your own), and without which you are bound to encounter needless difficulties, and do worse than you could and should — not just in physics, but in essentially all future courses with a strong scientific/technical component.
For me to recommend that you stay enrolled, that none of that really matters, that in the end you will do well anyway, is akin to a ski instructor telling someone who has put on skis for the first time in her life, standing on the edge of a black slope “Sure, go ahead — you’ll be fine, it’s no biggie, really”.
Is the skier surely going to kill herself ? Well, maybe not, but one thing seems clear: that is no way to teach someone how to ski. Because of curving and rampant grade inflation, a student may even be able to scrap a passing grade, but the weakness of one’s background in algebra will remain a problem, whether transcripts reflect it in full or not. I think my duty as an educator is to warn against that, as opposed to keeping quiet, pretending that it is not an issue, smiling hypocritically.
Well, like I said, the above is what I used to say in my early years in this profession. Based on my experience, however, it is advice that goes nowhere. It is typically taken by the student as a personal offence, and therefore often resented and practically always ignored. It can also set the stage for a difficult interaction with that student through the rest of the semester.
It is simply not what students want to hear. An instructor speaking candidly and honestly, for the sole purpose of helping students do the best thing, will be called “mean-spirited”, “arrogant”, “discouraging”, “elitist”, accused of “denigrating”, “giving up on” students. That instructor will likely face criticism by administrators as well, and possibly even by disingenuous colleagues, self-righteously sentencing that “a good instructor will be able to teach anything to anyone” — a fairy tale which may make for nice movie story lines, but which has little to do with how real life works.
The thing is, the goal of the University these days is not seen as educating, but delivering a product to paying customers. University wants to sell as many degrees as possible, and customers are always right. Therefore instructors must do whatever it takes to keep customers satisfied — if they are not, instructors are not doing their job.
Anyone working in retail will tell you that customers want to feel good about themselves, and any good salesperson will know how to flatter them, and keep the transaction as seamless as possible. In our case, they want to know that they will pass the course (the code word is “encouraged”), and that any annoyance, anything that looks difficult, will be removed by a “good” instructor. Thus, the job of the instructor is that of finding a way to make students pass, regardless of their actual performance, as painlessly as possible. And all of this should be done while retaining an appearance, a pretence of rigour — a delicate balancing act indeed.
In fact, in many respect, one is expected to act like a bad salesperson. A professional, responsible one (e.g., selling motorbikes, or firearms) will be expected to warn customers that may seem unable to make the proper use of the product that they are wanting to purchase. Good salespersons will not regard making the sale as the only priority — they will be rightfully concerned about a customer walking away with something that in the best scenario will not do any good, in the worst case may actually cause trouble. An instructor, on the other hand, has apparently no business thinking of what is best for the customer.
So, what do most of us tell the students in the above situations ? Well, essentially sweet little lies. We try to tell students, one way or another, that they really should try, if at all possible, to refresh their algebra. Deep inside, we know the truth. It is inescapable — “You, my dear student, may pass the course and even get that degree. However, there is no such thing as learning physics without algebra. It is simply not going to happen”. That is what we all think, whether we admit it, to others or ourselves, or not. But if they ask us “What do you recommend that I do ?”, we stay away from the dispassionate truth, because it will almost always come back to bite us.
As someone said once “fool me once… shame on you… fool me twice… um… er… can’t fool me again…“.
 Think I am making it up ? That things cannot possibly be that bad ? Well, if you do, I have got some Enron stocks for you…