At first, i think slashdot is one of the worst places in the whole internet to ask for this. Too many wankers looking for social gratification. And obvious mythomaniacs. I have read a dozen comments then i stopped. You should ask in a maths forum. I am sure there you will find experienced and COMPETENT people.

I am an engineering physicist who did his Ph.D. in photonics and did some research in aerodynamics and plasma physics in a private NATO institution. Well enough to be published. Then i quitted because the salaries in research are too low. I sometimes regret the fun. I work in a bank now.

Firstly, in my county of birth, schools are divided up. You take an option as early as 3rd grade (13/14 years). The maths/science option is recommended to only the most promising students while the others are discouraged. Likewise, the worst students are sent to technical/professional (plumbing...) or social studies options. Also, there are entrance exams to enroll in engineering/military school (all options)/flight school etc... The prep courses for these exams are exclusively in maths/science options in elitist high schools. We are elitist. Elitism is not considered a problem here contrary to United States. Also there is no the typically U.S. stigma on nerds. Here nerds are considered winners.

So some of my experience may not be transposed to the U.S. Your mileage may vary but from what i heard from my American colleagues and my European ones teaching or doing a postdoc in the U.S. the situation appears similar or even worse.

When i was a Ph.D. student, i had to teach part time. Since tenured professors want to teach only in science/engineering they tend to foist the courses in non science faculties to young non tenured teachers or doctoral students. So i had to teach students in sociology, psychology and communication. There is no such things as a minor/major in my country. Before that i teached high school students as private professor. Some of my high school students or their parents say i have saved their life. I am immensely proud of that.

So i had experience in teaching non necessarily brilliant students. And recover bad situations.

Well, it went worse than with my high school students. They sucked. They all sucked. Some harder than others. Globally the problem is they have zero math and science education. They don't have a clue about how genuine science work. Worse, they believe they know it pretty well. So while they are ignorant they are also pretty closed-minded.

One of their main difficulties was their methodology. They didn't know how to solve problems. They rather clinged on learning per heart formulas. They were even more lost when asked questions in plain French. Even about basic problems. They didn't get the maths concepts. Many had problems with fractions. A primary school notion. Many had problems with asserting an equation and solve it. Funnily enough, asserting equations was harder for them than solving them. So before struggling in stats they were in fact struggling with basic maths and logic. Of course, they were all totally unable to integrate or differentiate, let alone understanding what an integration or differentation was. The sociology students were less worse because they had a "general maths" course in freshman which was nothing more than a revision of high school maths. But even them didn't do more than applying formulas. For them an integral was the area of a surface below a curve. I showed them examples of (simple) integrals calculating volumes, lengths and other things and fortunately they were happy about it. Not possible with the psycho and communication students though. Good luck making them understand what an infinitesimal is. They have a problem with abstract concepts in general. In stats, they did understand what a mean was but even the median was already harder. They were lost with the concept of dispertion parameter. None of them did understand well what was a probability density function or a cumulative distribution function. Again, some of them were able the recite per heart the definitions. But not use the concepts.

I spent more time teaching them basic high school maths than actual statistics but even there i had to be very slow and cautious. I never had had so slow students. When teaching concepts, i had to dig deep into their difficulties, step by step. For example solving a simple quadratic equation (something i learned at 12):

-4x+3x-5=0 ?

-(blank stare)

-Ok, then 3x-5=0 ?

-er...

-Hmm hmm, lets try 3x=5 ?

-uh, fifteen ?

-No, x=3 ?

-Ah, yes ! Three !

-Ok, then x+1= , with the same x ?

- Four !

And so on... But with a lot of patience i finally achieved to teach them a little high school maths.

I tried to rummage in Ph.D's to find examples they would like but i renounced after having read four of them. All crud. Rantings about "pedagogy" (i loved how one tried to explain how to teach chemistry while having no clue how chemistry worked: he was creating wrong equations) and marketing disguised as academic research (social psychology lol).

I was responsible for a group of around 25 students, a bit less in the begining, more than 30 near the end of the academic year. I was supposed to give them them exercises and give them a reminder of the theory. The actual course was given by a Ph.D. in maths from the science faculty. There was very little coordination between him and us, his assistants. He wanted to do an academic career in the university so he was afraid of pissing the other teachers. He asked us to be "cool" when grading the students. I was determined to quit after my Ph.D so i totally ignored his directives. I was supposed to grade one question for all the 200-300 students. Each assistant his own question. No one student got the half mark for the questions i graded. From all the non science/engineering students i had none of them deserved the half mark.

When i was student, i was told that psychology students were atrociously dumb. I dismissed that as typical banter between faculties. I was wrong. They are dumb. As are their little buddies from sociology and communication. Their teachers are unaware of this and outright arrogant. I tried to discuss a bit with some of their teachers but i was met with a lot of naivety. Not outright hostility. Just that their teachers don't realize what a true scientist is.

If i may hazard a few advices:

-Go to a maths forum, not slashdot.

-Be very patient

-Teach the basics, assure yourself they have understood a before doing b.

-Give them a lot of basic exercises, doing exercises teach more than exposing theory

-Exercises must exerct their problem solving abilities, not the formulas

-Don't assume they know much

-Deconstruct their reasoning and struggles to the very basic principle they don't understand

-Go slowly

-Be very rigorous, fill all the blanks, demonstrate all you expose and give tons of SIMPLE examples

-Don't let them believe they are mathematicians because they have solved an exercise. They tend to get arrogant.

-Try to negociate a lot of hours of exercises with a lot of personnel, each of your assistants will need a lot of time per student

-Don't put the emphasis on formulas, they are fascinated by them and tend to rote them without understanding them.

-Use as few figures as possible, they tend to be fascinated by stupid graphs too.

-Never use a maths software or a scientific calculator. That defeats the purpoise of understanding the concept in favour of button pushing

-Don't be afraid of abstraction. They'll struggle at first.

-Do not ask them to solve the hardest exercises in class leaving the easy ones for home. They would be blocked.

-Make them work a lot, interrogate them often and early in the year.

EDIT: Aaah, i had to post as plain ol text. Sorry for the precedent wall of text ladies and gentlemen !