Hey there everyone. I'm TAing a course for firstyear undergrads on calculus, I have my first ever session on Thursday so I want to make a good start. The problem is that the students will only have had one lecture prior to seeing me, and I am not supposed to teach the lecture content before the professors get round to it. So I am trying to fill 50 mins of TA time but I have very little material. The first lecture will be on antiderivatives, but I don't want to just set the kids off integrating for 50 mins so I was wondering if anyone had any good ideas or questions which I could ask on highschool level math? Basically I think I can put in anything to do with trig, logarithms and differentiation as well as anything really cool.
Thoughts?
Edit: Oh yeah, I'm from the UK and I'm TAing in the US so I don't actually know what a highschool math program actually contains.
Problems for Freshpeople
Moderators: gmalivuk, Moderators General, Prelates
Re: Problems for Freshpeople
I'm in the same boat you are... try asking the professor who's doing the lectures?
What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.

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 Joined: Wed Jan 13, 2010 1:29 pm UTC
Re: Problems for Freshpeople
He is in France
Re: Problems for Freshpeople
The most annoying thing I remember as a student of first year calculus was the various trig identies, and I suspect that's a common one. In particular, double angle formulas that seem to end up being required way too often when trying to integrate things involving trig functions.
The various high schools don't all necessarily contain the same material, and not everyone necessarily took all the same math in high school though, so even just casually talking with folks to figure out where people are and if they have any general questions might be useful, versus necessarily having a whole lot prepared. Rendering yourself relatively friendly/approachable now is apt to help make them more comfortable asking questions later on too.
The various high schools don't all necessarily contain the same material, and not everyone necessarily took all the same math in high school though, so even just casually talking with folks to figure out where people are and if they have any general questions might be useful, versus necessarily having a whole lot prepared. Rendering yourself relatively friendly/approachable now is apt to help make them more comfortable asking questions later on too.
Re: Problems for Freshpeople
There's really only two things you need to know about the HS curriculum in the US: (1) Most people know nothing about statistics; and when I say nothing, I mean that they couldn't tell you standard deviations, couldn't correctly identify the skew of a distribution, and probably couldn't give you an interquartile range of a data set. And (2) I think that's probably the only real difference. They've done a detailed study of quadratics including complex numbers, a semideep overview of other conics (but they won't remember it), they've learned logarithms and trigonometry, and probably have a relatively good background in probability. I think you guys emphasize vectors and matrices more than we do here, but they know about them (although you probably couldn't reliably get them to work with projections).
I agree that people have done different things, and you should of course try to learn ASAP where people are at. The things I talked about above seem to be relatively consistent in my experience, but the bigger factor is of course if they remember any of it. That said, if you're looking for something to prepare, I guess I can give a few suggestions
Given that the logarithm has a pretty interesting relationship to integration in the modern theory, it might be cool to do logy things. Related to that chain rule thing: might be worth talking about function compositions and inverse functions, and maybe some simple parametric equations in preparation for u'f(u)?
Edit: Oh and the trig identities! Right. That actually is probably the best thing to do. Yeah, I'm not really sure that those other things come close, now.
I agree that people have done different things, and you should of course try to learn ASAP where people are at. The things I talked about above seem to be relatively consistent in my experience, but the bigger factor is of course if they remember any of it. That said, if you're looking for something to prepare, I guess I can give a few suggestions
Given that the logarithm has a pretty interesting relationship to integration in the modern theory, it might be cool to do logy things. Related to that chain rule thing: might be worth talking about function compositions and inverse functions, and maybe some simple parametric equations in preparation for u'f(u)?
Edit: Oh and the trig identities! Right. That actually is probably the best thing to do. Yeah, I'm not really sure that those other things come close, now.
Approximately 100% of my forum contribution is in Nomic threads! In fact, if you're reading this signature, you probably knew that because you're reading a Nomic thread! But did you know that I've participated in both Nomic 16.0 AND Nomic 15.0? Woah!
Re: Problems for Freshpeople
I've been a freshman this past course. I live in Spain, so I'm not going to tell you about specific things that I considered difficult because the first year program is probably quite different there.
However, as I stated a couple weeks ago in a different thread, I was left was a feeling of confusion during and after the first year  I couldn't quite see the big picture of what they where teaching me and why. Maybe that's not a good explanation of my feelings, I explained it better in the thread (here: viewtopic.php?f=17&t=88223 )
With that in mind, I can tell you that I would really have liked some kind of introductory class, instead of a inmediate handson: Some quick overview about the theory that was about to come, what was calculus developed for, some historical notes.. I think that would be a good way to start the course.
Even better, if you throw in a couple of anecdotes about the mathematicians who developed the main theorems, or something like that, you will probably help them to overcome the intimidation which comes during the transition from highschool to university, and they'll have a good first impression of you as a teacher
However, as I stated a couple weeks ago in a different thread, I was left was a feeling of confusion during and after the first year  I couldn't quite see the big picture of what they where teaching me and why. Maybe that's not a good explanation of my feelings, I explained it better in the thread (here: viewtopic.php?f=17&t=88223 )
With that in mind, I can tell you that I would really have liked some kind of introductory class, instead of a inmediate handson: Some quick overview about the theory that was about to come, what was calculus developed for, some historical notes.. I think that would be a good way to start the course.
Even better, if you throw in a couple of anecdotes about the mathematicians who developed the main theorems, or something like that, you will probably help them to overcome the intimidation which comes during the transition from highschool to university, and they'll have a good first impression of you as a teacher
Re: Problems for Freshpeople
Just wanted to chime in again and say I couldn't agree more with rolo. In calculus, more than any subject we teach before it, there are a lot of residual marks from the people who created it: Leibniz's d and S, Cauchy's epsilon and delta, Reimann's formulation of integral, Euler's e, the conflation of the integral and the antiderivative signs, the big sigma, interval notation, even words like "continuity" and "derivative", and all those crazy little decisions (like "h" in the derivative definition) that somebody made one day on a whim that ended up being sucked into the mathematical canon.
Oh, and if you do talk about Cauchy/Weierstrass, please put in a good word for Bolzano. Seriously, this guy did so much work and he gets no credit :/
Oh, and if you do talk about Cauchy/Weierstrass, please put in a good word for Bolzano. Seriously, this guy did so much work and he gets no credit :/
Approximately 100% of my forum contribution is in Nomic threads! In fact, if you're reading this signature, you probably knew that because you're reading a Nomic thread! But did you know that I've participated in both Nomic 16.0 AND Nomic 15.0? Woah!
Re: Problems for Freshpeople
I'm not sure what a TA is, but if it's like a teacher then what you'd want to do is to go over stuff that the students 'should' know since you don't have any materials to go through yet. You should go through stuff that university classes assume that students remember from highschool but probably don't. This would obviously differ depending on the focus of the calculus course but I'm thinking of stuff like : you do remember how to manipulate logs and e^x? Do you remember what a derivative is? Do you remember what happens when you derivate the trig functions? Do you remember what the domain and range of functions are? What do graphs look like when the derivative of a function is 0?
I'm typing this assuming that highschool students know this stuff before going to university. If they don't, I would be very disappointed in the US education system and the pride they place in their universities.
I'm typing this assuming that highschool students know this stuff before going to university. If they don't, I would be very disappointed in the US education system and the pride they place in their universities.
Re: Problems for Freshpeople
liveboy21 wrote:I'm not sure what a TA is
TA  Teaching Assistant. The particulars of the position will vary from place to place; at the university I was at, the TA would be expected to mark certain assignments (ones that didn't count much towards the final mark), occasionally go through homework problems with the class, and be available to ask questions; thus freeing up the lecturer's time for such things as preparing and marking exams, doing research, and planning the syllabus.

If I may make a suggestion; first, enquire from the class if they've run into anything that they'd like to ask about. Handle any questions that they may raise (this may very well include stuff like "where will I use this stuff later?", so be prepared to answer that). Once that's done, or if there are no questions, then pose them problems. Not equations; describe a situation, tell them what you want to know, and ask them for the answer.
Example: A train travels east at 60km/h along a straight track. At the same time, another train travels west at 40km/h along the same track. At the time that these trains are 100km apart, a fly takes off from the 60km/h train. This fly flies from the one train to the other, and back, zigzagging from train to train at a constant speed of 300km/h; until finally, when the trains hit each other, and the fly is crushed between them. How far did the fly fly?
A good book of mathematical puzzles would be helpful. The point being, this way it's not just the mechanical action of plugging numers into equations and grinding them until an answer comes out; one has to first construct the equation, from a given situation. Learning how to apply mathematics to the world around one is at least as important as learning how to grind an answer out of an equation.

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 Joined: Sat May 12, 2012 4:42 pm UTC
Re: Problems for Freshpeople
50 minutes is perfect to handle just one subject!
Teacher Assistent seems to me to be just a function where you help students with their "homeworkassignments", or maybe come up with slight variances on them to help them better understand.
Better to do one thing good, then just to touch 10 interesting things. Students sometimes need to learn that solving one sum doesnt mean they fully understand the subject. Solving 10 sums in the same time it took as making the first means they understand, and are prepared for the next lesson.
(Yep, I like going slow)
Teacher Assistent seems to me to be just a function where you help students with their "homeworkassignments", or maybe come up with slight variances on them to help them better understand.
Better to do one thing good, then just to touch 10 interesting things. Students sometimes need to learn that solving one sum doesnt mean they fully understand the subject. Solving 10 sums in the same time it took as making the first means they understand, and are prepared for the next lesson.
(Yep, I like going slow)
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