Hello there, thank you for clearing this up for me. We don't really work on re arranging equations much at college to be fair so I'm pretty poor at it if I'm honest.

That's a shame -- and it is doing you a real disservice. My recommendation would be to take this on yourself and develop very strong algebra skills -- it will pay off handsomely as you start competing with the growing number of increasingly math-illiterate engineers that we are turning out.

It's not entirely the colleges' fault as they are having to deal with larger and larger numbers of students coming in that don't even have grade school (or what used to be grade school) basic arithmetic skills. However, the schools ARE at fault because they refuse to put their foot down and say, "Hey, this is the expected level of math competency you need to enter/exit this course and if you don't meet it, then you fail." Instead, they are in the practice of "accommodating" students that have poorer and poorer math skills. This is for a variety of reasons, some financial and some political. There is also a very pragmatic reason -- no teacher (I'm sure there are exceptions) enjoys failing students and will naturally (i.e., without realizing they are doing it) slow the class down and dumb down the material to the level the students are at. It's a marginal, incremental process and so you just don't realize you are even doing it until it has progressed another big step. And woe be to the instructor that tries to hold the standards firm.

 

Hi,

Well now in this day and age who would expect a college to teach such silly stuff like algebra and calculus <insert big sarcastic chuckle here>.

I dont know of any engineering that does not require at least some algebra.

 

Oh, they "require" it -- just look at the course prerequisites. But that doesn't mean that the students are actually coming into class having "learned" it (regardless of what their transcript says).

 

I taught a course that had prerequisites a long time ago. I started giving a test on day one about those requisites. After complaining about the poor performance on that test and identifying why that requisite course wasn't teaching it properly ... I ended up teaching that other course as well.

Holding one to standards is a rude awakening for those who are not able to meet them. In all cases it leaves you with two options ... train them or punish them.

On the philosophy on training them ... let them take an active investment in their future ... I would point them to the following:

http://www.constructionknowledge.net/public_domain_documents/Div_1_General/Math/Basic Math and Algebra NAVEDTRA 14139.pdf

http://www.constructionknowledge.net/public_domain_documents/Div_1_General/Math/Pre-Calculus and Introduction to Probability NAVEDTRA 14141.pdf

http://www.constructionknowledge.net/public_domain_documents/Div_1_General/Math/Introduction to Statistics, Number Systems and Boolean Algebra NAVE.pdf

There are plenty of test questions relative to each chapter for them to check themselves.

 

But these days if you tell students that they really need to improve their algebra skills, they file a complaint with the Dean of the college that you are "creating a toxic environment".

 

For a bit of uplift here. I struggled through my first 3 semesters at Michigan with a steadily declining GPA. In semester #4 I encountered a young assistant professor teaching a course I thought I would hate; it was "Strength of Materials". His manner was engaging and his enthusiasm was infectious. I worked so hard for the A in that class that I ended up doing better in all of my classes. My GPA reflected the ownership I had taken of my destiny and I haven't looked back since. So if you are in the teaching business, it only takes one student who sees the light for it to all be worthwhile.

 

So if you are in the teaching business, it only takes one student who sees the light for it to all be worthwhile.

In general, I agree. But from a practical standpoint a ratio of 1 in 1000 isn't likely to save the day. But I can't tell you the good feeling that comes when a student you had years before comes back to thank you for forcing them to do things they thought were a total waste (tracking units) but about which they have since become true believers.

 

Maybe it will cheer you up to know that as an undergraduate, we always tracked units and they had to be part of the answer. You got a big fat zero for a number with no units. We even had to know the units for constants.

 

I don't know the true extent of the emphasis on units, either now or back when I was an undergrad, nationwide (or worldwide). The only places I saw it consistently emphasized was in chemistry and, big time, in physics courses (which is where I became a convert). It's not too hard to find physics and chemistry texts that give more than lip service to units, but it is very hard to find an EE or ME text that does. Most will just tack the units onto the final answer and little more.

I used to have to pound it into students for about three weeks before they would get on board (often without even realizing it) and start tracking their units throughout their work. But the last several times I've had the opportunity (most CS courses don't really give you the chance) it was a semester-long ordeal with at least half of the class still not getting the hint or grasping how to do it consistently and properly, particular where exponents were concerned, even by the end of the course.

 

WBahn,

I will assume you track your units when you teach. Your example may convert someone. Do you sometimes throw in an incorrect equation that results in someone throwing the BS flag on you? That might create the signification emotional event about tracking units as they just copied down a lot of USELESS material.

Of course, your trickery will become well known for subsequent semesters.

That certainly will put your "acting" ability to the test, as you would know the "scenario" is BS.

I once gave a three page test with one question at the top of the page:

1. What is considered the greatest maritime disaster in the 20th Century?

2. Approximately how many lives were lost?

3. Name them.

Very few read the whole test ... but all realized it was BS when they hit question 3. Everyone had a sense of humor afterwards.

 

WBahn,

I will assume you track your units when you teach. Your example may convert someone. Do you sometimes throw in an incorrect equation that results in someone throwing the BS flag on you? That might create the signification emotional event about tracking units as they just copied down a lot of USELESS material.

In my first couple semesters teaching I tried to play these games, but I quickly discovered that there would be plenty of opportunities for me to demonstrate catching normally occurring mistakes that are bound to happen. Part of that is due to the split attention associated with working a problem on the board at the same time I am trying to keep the flow of the lecture in mind. Part of it is due to, as a rule, working problems on the fly (I seldom work problems that I have already worked out ahead of time). I praise students whenever they find a mistake before I do. I've toyed with the idea of giving extra credit, but the logistics of it just prove impractical.

 

5 time constants ==> I=Imax*(1-exp(-(5*tau)/tau)) ==> I=imax*(1-exp(-5))=0.99326*imax, it is delta= -0.67%.
T> 5 time constants=5*tau=5*L/R, T>5*L/R ==>R>5*L/T ==> Rmin=5*0.47/0.16=14.6875Ohm