I just got this question in a comment to another post, and I thought I would throw it out there for readers to help with:
Anyone out there have to take a year of calculus even though it wasn't their strongest subject? How did you survive?
I would love to know answers to this question as well. Not because I'm struggling through calculus myself, but because many of my students are, and I'd like a larger toolkit of suggestions for them. At the end of this summer, I went to a discussion with the math department about ways to help students succeed in the precalculus-calculus sequence, and if anyone has great ideas, our math department has a big education grant and might be able to implement some.
(In the meantime, lacking any better ways to help my students succeed in calculus, I let my structure lab go early - during the stereonet lab, no less - because half the class had a group calculus exam scheduled to start right when the lab was supposed to end, and I didn't want them to go into their exam feeling overwhelmed and confused by stereonet rotations. Oh, and to former students, I was planning to give them a short lab next week anyway, so I'm just going to do rotations and drill-hole problems then.)
My approach has been to point out the connection to calculus concepts whenever I see them. (Strain rate? Derivative! Oh, and how is a graph of stress vs strain rate related to a graph of stress vs strain?) That, and to make the students use algebra as much as possible in a geology context, because it seems like succeeding in precalculus and calculus is often a matter of doing algebra well. It would be nice to have more suggestions beyond the math cheerleading, though.
20 comments:
Cal was the bane of my existence as an undergrad. I barely made it through Pre-Cal, and I took Cal twice as an undergrad, and was never able to pass. I was tested and found out I had a math learning disability my Sr. year. When the last semester of my Sr. year rolled around and I had already been accepted to grad school at another program I realized I was not going to be able to conquer cal as an undergrad. This really sucked for me, since Cal 1 & 2 are the only classes I lack to have my Geology B.S. I had to settle for the Earth Science B.S. at the last moment so I could graduate and move on, which was the advice I got from advisers.
During grad school I did not have to take Cal, so it was not an issue (and I was still able to get my Masters in Geology!). After graduation I got a job at a 4 year college as a research assistant and was able to take classes for free. During this time I finally took Cal and passed! I just had to take it during a period in my life when I could devote all of my attention to it.
I know all of this might not help your students now. My suggestion might be to possibly take the classes in the summer (uggg) so you have more time to devote to a very difficult subject.
Agh. Calculus is a distant and painful memory, but I remember getting through it in college (one semester) because I took AP calc in high school, and I had an awesome teacher. He incorporated so much into a year of high school math that I was actually ahead of the game when I started college, and I was able to keep the momentum up just long enough to earn a respectable grade at the end of the semester.
My best advice is to find a good teacher early on - don't just go to class and sit there being confused, because it will all snowball on you until you can't understand any of it. If that teacher happens to be a professor, a TA, a tutor or even a genius classmate that you bribe with cookies, so be it - do whatever it takes to find someone who can explain things in a way you can grasp.
I kind of regret not having gone further in calc, since I'm coming up against partial derivatives in fluid dynamics equations, but I still have my old book and notes, and I should be able to teach myself some of it. (Unfortunately, my tuition waiver doesn't give me enough leeway to take too many out-of-department classes, so another calc class may have to wait.)
It was always something I hated. We had our math together with the biologists, chemicists, (geo)-physicists and all other kinds of natural and earth scienticsts that you can imagine. I did differential equations and odd formulas I will only need if I start doing rocket science. I hated it. To make matters worse the teacher was from the department of theoretical mathematics. He showed us wonders of math but was unable himself to solve the actual examples he gave us for practise. The practise teacher simple told us to consult the books if we didn't understand something. (well and the recommended books were not given completely solved examples) You can imagine this combination lead to failure rates in math exams of 80 to 90% on an average basis. Maybe I was just unlucky but my math teacher at University were just trying to complete their programm. If anyone got it was not of their concern - or so at least it made us feel. I eventually switched university and came to Berlin after a 4 year odyssee of math problems with above described teachers. I went to math class again, teacher and practise teacher actually answered even the most stupid questions without making us feel stupid. That was very important. There was no script to download on the internet. We had to write down manually what they put on the blackboard. That was good practise. It was still hard. I have an extremely hard time understanding what I do in math and why. I got lucky. I had to have my classes from my old uni recognised in Berlin. The dean respondsible told me I don't need further math because I already have two classes of math-similiar topics. (statistics/stochastic and descriptive geometry). From hindsight what is important: Understanding and friendly teachers, good practise examples (like geology problems) in class and practise tasks to do at home, clear books and not too big classes. Oh and...i don't know how but math needs to be more motivating and rewarding than most other classes because most people dislike it.
Relevant and practical problems are definitely helpful, that way students can see why someone would bother to learn such difficult nonesense. Unfortunately for me and for beginning students - at least for learning calculus beyond simple derivitaves and simple integrals - the thing that really got me to see what integration was all about was an upper-level or grad course, Thermodynamics. Ground-water Hydrology helped some, also, because of real-world applications.
In calculus classes, if they would just sometimes explain what it is that's really being done, instead of following some cookbook-like approach - do this, do that, here's the answer - it might help at least as far as the big picture go. (It might not make doing the problems that much easier, but might make them seem more worthwhile or comprehensible.)
great topic - I see many students who struggle with not only calculus, but also the required year of courses in physics & chemistry.
I wish I had some great answers for this, but alas I don't. You are right that showing them the connections to the material they are studying in geoscience is great.
I have both an A.B. and an M.S. in Geology, and I never took calculus.
That probably shouldn't happen.
N.R.:
Even though Physics requires math and even though I didn't take Chemistry in high-school these were pretty easy classes for me (my friends had a hard time though). Both subjects were taught very understanding orientated. I know WHY and WHATFOR I do something, and what it means. I think I was one of the rare cases who passed physics with a very good grade at ease but failed math more than once.
Math should be really presented as being a nice and useful tool. Instead it is too often presented as doing math for the sake of doing math alone. If people would want that, they'd study mathematics and not geology. no? :)
Maths for geologists has to be taught by a geologist, not a mathematician and using geological examples in my view.
Only then will students see the relevance of what they are doing and get a grasp of what is going on.
I try to embed any maths within the geology curriculum rather than try to teach it separately.
I took calc 1 and 2 after being out of school 8 years in the military. I knew that I was way behind the fresh-out-of-school undergrads so I had to apply myself that much more. The strategy I found to be extremely successful was to work practice problems every day, 7 days a week, for at least 1 hour, above and beyond any other school work assigned. I bought every study guide I could find and had practice problem books which were extra supplements for the text. I worked out of 4 or 5 books in addition to the assigned text. This method worked so well for me that I applied it with equal success to chems, physics, genetics etc. This was while working full time supporting a family of four. It took a great deal of time but it was worth the effort. I tell my students, if you are not getting the grades you want, you are not working hard enough.
Studying with other students is the trick. Turn it into a social event. That helps turn it from drudgery into something fun.
I was lucky enough to take calculus with a wonderful group of people of varying ages and backgrounds. We really got close and helped eachother learn. Teachers could probably encourage this by pairing people up with lab partners, or small teams, and having them work problems together.
Ultimately, the only way to learn math is by concentrating hard and working problems. But if you get stuck, its great to have somebody there to share the pain.
Like Rebecca Foster, I had to take Calc and Physics with Calc during the summer to be able to make it with a passing grade. I wouldn't be surprised if I had a math learning disability or very low-grade ADD. Pushing myself to do math homework was about the hardest thing I could ever do, and it was easy for me to get distracted (possibly due to high frustration levels). I know others like me - one friend finally finished her degree (while working a high pressure job) by taking ritalin to do her Calculus course while holding down a full-time job.
My husband recently asked me what calculus was all about. Not having taken math since sophomore year in high school, he remembered that geometry was about circles and polygons and trigonometry was about triangles. He wanted to know what shape calculus was about.
I don't use calculus every day, in fact i'm pretty rusty on some of the details. I THINK IN CALCULUS every day though. Partial derivatives are a pretty useful construct for watching institutional changes (or lack thereof) at a university.
Partial derivatives are a pretty useful construct for watching institutional changes (or lack thereof) at a university.
Brilliant.
Yes, I think calculus is most useful as a way of thinking (or an additional way of thinking) about the world. (I got an A+ in microeconomics, not because I had any brilliant insights about money, or because I could crunch numbers, but because I could translate the econ jargon into "slope of the line," and that made it easier to keep all the graphs straight in my head.)
I actually just got into a discussion with another faculty member about how to help our students "survive" their physics & chemistry requirements, not to mention math. The best recommendation I got was from the TA I have for physical this semester who told the students that mineralogy would make chemistry make sense.
I think the best ways to survive is to a) make the classes work on problems that they can relate to (my high school teacher had a mythical duck that did all sorts of crazy stuff to teach us about momentum, gravity, etc.) and b) repetition. Just like stereonets are not the most obvious concept (sorry Kim), after you work through a sequence of problems, usually they suddenly make sense. We need the same "ah-hah" moment for our students in the correlates.
And personally, I survived calc in college, but when I took linear & diff eq in grad school they were quite a bit easier because I could understand why I needed them. It did also help that another geo grad student and I were taking the classes together and could work through the problem sets.
Maybe what we need is geology cadres to go through calculus, chemistry & physics together--they can help each other and we can give them ideas about why the material is worth learning.
Elli - this year, one of my students told me that stereonets were cool because they let him solve problems that were really, really hard otherwise.
The bad news is that this is the first time someone has said that in, ummm, 16 years of teaching.
(He had done problems in ore deposits that used trig to solve for dips of beds and so forth. Stereonets really are easier than trig. So despite my practical examples - I mean, I motivate the stereonet lab by asking students which two of three bedding measurements are closest to one another - the best motivation is to have needed a tool and not had it in the past. The question is, would the students feel annoyed and manipulated if I set them up for frustration early on?)
I usually look interest if some class or problem starts with a very frustrating experience. My mind just says: "I hate this" and from that point on class can be interesting or not, I don't care. Personally I would rather recommend getting people exciting about what they do, realise what it is needed for and motivate them for later.
i meant to say "lose interest" and not "look".
You people have no idea how comforting reading all of this has been. I thought I was the only geology major with some anxiety about taking calculus (though I can certainly see the worth in doing so) and/or worries about the year of chem and physics I'm going to have to get through and this was probably a result of me being one of the few people that is, eh...let's say 'brave' enough to major in a science when math is not my strongest subject.
I agree with the tip about telling them that chem will make sense once they take mineralogy. I have a really good physical geology prof this semester that took some time to go into detail (no doubt in a simplified nature) about minerals, their chemical structure, etc. It actually made chemistry interesting!*
*With all due respect to the chemists out there - this is an amazing feat. Chemistry is the one natural science I have not contemplated majoring in at one time or another.
I enjoyed calculus theory, however I was very weak in algebra and trig when I took calculus turning it into a nightmare for me. I was also taking a course load of 27 hours in a desperate attempt to graduate before my money ran out. Still, calculus was pretty cool even though I flunked it. At the time I had 260+ hours and the school waived the calculus requirement for me and let me graduate anyhow (probably figured it was the only way they'd get rid of me). BTW I didn't completely flunk it (i.e., handing back blank test sheets), it was more like I was consistently a week behind the class. If there was a cut-off between a D and F I'd usually get the F. In a fair and just world I'd be able to teach a geology course to that SOB math professor.
Calculus wasn't too bad for me. My trig is weak, so I did struggle a little bit with calc because of that.
My problem is application: the abstract pure math stuff is fine, but go apply it to a situation, and I start to really stumble. That's why I'm having a huge challenge with the required physics classes. The math is so easy it's almost embarrassing, but I can't get the problems set up. It's driving me crazy.
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