Advice for a Mathphobe?

1) As a former mathphobe autodidact, I have to say that self-teaching math is a special challenge. Math requires working problerms, relentlessly. Understanding the concepts is (relatively) easy to do with self-teaching, but it won't (in and of itself) prepare you to use math.

As an aside, I suspect it is awfully easy for brillant people who are great at concepts to get the impression that they are bad at math... For every other subject, you can focus on the big ideas, which provide a framework for later filling in detailed facts. Then along comes math. If you stop concentrating on learning once you understand main mathematical ideas, but don't go through enough routine practice to have the calculations become second nature before moving on, math can be a pain.
2) I was a mathphobe until I got to physics, where I discovered I really liked it. Because I understood concepts well, I could look at a physics problem, know the relationships that things should have (e.g. if force is increasing, mass or acceleration must be too) and then I could finally intuitively see how my equations should work. I didn't worry about making computational errors because I could always check my units, and run things through a common-sense check, ect.
3) Statistics is almost a special case- it requires a different kind of thinking than calculus. I suspect a lot of mathphobes out there would actually like statistical reasoning, but they never get there.
4) I can't really say anything about geology, but there are some people out there who will tell you that you can't become a biologist without being good at math, and they are wrong. There's a ton of math in biology, but that doesn't imply the advance stuff is essential, and it certainly doesn't imply that someone who starts off poor at bench side calculations (solution preperation, ect.) can't function well in the long run.

I think you gave her a pretty good answer - particularly regarding the heads up that she'll likely be teaching chemistry, physics, or math(!) in addition to geology.

I'm so darn tired of students who have been scared into being scared of math by teachers who were scared into being scared of math... There's got to be some way to break this vicious cycle.

Amanda could have been me. I, too, am a fallen-away English major (Modern African lit and Jane Austen. Don't ask.) who grew up in Wyoming where life is severely dictated by geology, and I loved those rocks and all they meant. My dad was an oilman, and wanted me to be a geologist, but I was afraid of the math behind ANY science. While I was working in at Harvard's Museum of Comparative Zoology Library, I had lots of great conversations with some formidable geologists and decided that, if I could pass the required math classes, I'd go back to school in geology. I took evening classes at Harvard's Extension School with truly gifted, dedicated teaching grad students. I too found joy in math and stats, and while I didn't become a math maniac, I did thoroughly enjoy my geophysics and statistics classes, and used those skills often. I hope Amanda finds the kind of instructors I had. If she does, she'll never look back.

Wonderful post, thanks. I have been thinking about similar problems as Amanda lately, it was nice to get some perspective.

I managed to get through a geology undergrad program with severe math phobia. I didn't do as well in calculus or physics as I really should have. I did get into grad school, and at last started to master the phobia. My big problem was my father's attempts to "help" me do word problems in junior high and high school. He really shouldn't have done me the favor; he was far too impatient to be teaching anybody anything. I would suggest maybe taking trig at a community college before applying to a four-year institution. That way you'll be able to concentrate solely on that subject.

It might be unrealistic to expect someone to go to a community college for some math classes. Maybe it's different in the US, but in Canada our community colleges primarily provide trade related programs and computer courses. You have GED prep of course, but for the most part you can't just pick and choose what you want.

Personally, I'm not longer a mathphobe, though I am skeptical of my ability to pick up advanced math. Several years ago I attempted to relearn my high school math using some textbooks. I surprised myself by doing fairly well, but I haven't retained it. I should have continued on, but I got bored with the textbooks and was sidetracked by other things.

I'm sure there are some excellent books out there for people that want to teach themselves math, but I haven't had a chance to investigate further. As a general rule, I think it's wise to avoid most textbooks that are used in high schools.

From my own university path so far I always considered chemistry and physics far more important than mathematics and dispite having passed the math exam with more luck than anything else it has never given me any problems. Lacking a solid knowledge of basic chemistry and physics will make understanding even the simplest weathering processes a big challenge though.

Thank you so much for this post (and the helpful comments). I have a BA in sociology but have really fallen in love with rocks after college. I decided recently to get a BS in geology, but I found that eight years out of barely passing a calculus class my skills are lacking. I took a placement test at a local community college and only just got into a beginning algebra course. I'm studying now to re-take the placement test because I know that even if I don't get into calc, at least I can focus on college algebra and really try to drill the problems into my brain. I am willing to take the time because I enjoy math - maybe not the process, but that moment when something finally clicks in your head is very satisfying. However, all this stress is reminding me why i decided on sociology the first time around.

I've actually been wrangling with a similar problem recently; I am not what I would call a 'mathphobe' any more (I'm somewhat recovered), however, I am very definitely an average mathematician based on the algebra and pre-calc classes I took in high school and the algebra class I took in college (I am at a community college so we're required to take 'College Algebra' and Pre-Calc as basic math courses *sigh*) which puts me in a bit of a bind. I don't mind math, but I do not think I will ever become skilled enough in it to make it in a career that involves consistent, heavy use of upper-level math. Nor do I think I'll find myself, say, taking and passing a course in Linear Algebra. At the university I will be attending an undergraduate geology degree requires math up to Calculus 2. I think I can handle this; the main problems I have with math are a lack of rote memorization skills that are necessary to memorize formulas and methods of working out certain types of problems (the stuff from the beginning tends to slip from my mind by the end of a semester), however, some math-expert friends of mine have informed me that this should not be a problem once I start taking calculus classes since in calculus you are taught to mathematically derive this stuff rather than being expected to memorize formulas or put them on a cheat sheet. I'm hoping this is true but would like some thoughts on the subject from people here to give me a better idea of what I'm getting myself into.

I'd also like to know how much math a geologist is going to need to know to be a researcher (roughly)or how much a paleontologist will need to know. The reason I ask this is because I contemplated making an attempt at a physics degree in the past to find out that what will be required of a working physicist extends beyond calculus and differential equations and a course in linear algebra (what's required for an under-graduate degree in several institutions I've looked at, though I'm sure I left out a thing or two). My current plan for a course of action is to take a geology B.S. and then move into paleontology for my graduate studies. However, it is possible that I'll fall in love with geology while working on my B.S. and will decide to work on a graduate degree in that subject, instead. I like to plan ahead. Theoretically, I could also take a biology degree as an under-grad and use that to get into a paleontology program, however, I would still have chem and physics classes to deal with (math-based, of course) and I am hesitant to take a biology degree when the local university (sadly, I'm tied to this city by a house) doesn't even allow one to have a concentration in a particular area of biology (my interest is in ecology and evolution and I have no desire to be loaded down with microbiology classes that I have no interest in just to make sure I get a good 'generalized' degree). Not to mention, I've taken an intro biology class and it was dreadfully boring. For some reason the 'little things' in geology are quite interesting to me while this is not the case in biology. I'm also worried about the possibility of only taking calculus 1 (the requirement) if I take a biology B.S. and then getting hit with math requirements I'm not ready for in grad school as a paleontology student.

Damn, I can already sense that this post is getting far too long, so I'll try to summarize: How much math is a geologist or paleontologist (rough estimate) going to need to do research?

You might point your geology interested mathphobes to: http://serc.carleton.edu/mathyouneed/trig.html

Great thread here.
Jon - American community colleges are the same as the first 2 years of 4 year college, and will typically offer up to Calculus at least.
Thomas M. - you can do purely descriptive/documentary research but this will limit what you can do. The paleontologists seem to use a lot of statistics but not much in the vein of calculus/differential equations - similar to a ecologist or zoologist.

I am just starting to use significant math in my research, started by collaboration with a modeler and now I'm trying to learn more on my own. Wasn't motivated to do so until I started working on some really interesting questions that require it. Now I find myself really interested in it.

christie,

Is this what I could do assuming I wished to avoid math in geology? I'm curious what I could do with the required two years of calculus under my belt (if anything). I think I could also make it through some courses on differential equations if necessary, I have some books around for self-training. I just want to know how much math a geologist needs to take since its not uncommon for the amount of math one is going to need to use to be different than the amount of mathematical knowledge getting the degree requires.

Christie,

Ecology is one of the most mathematical areas of biology! Sure, there are plenty of people who don't go beyond statistics, but that means most ecological theory is inaccessible to them.

I am a former math-phobe. I survived three quarters of calculus as an undergrad (after retaking pre-calc) and thought I'd never see this stuff again. Wrong! I was lucky enough to take ecology with a theoretically-oriented professor who was an excellent teacher. For the first time, not only was I understanding the math, I was explaining it to other people!

The next year, for reasons still unknown to me, I decided to take Mathematical Ecology with the same prof. I worked really hard and enjoyed learning the material, but failed the midterm -- badly. After that, I decided to drop the course. (UCLA lets you drop until the very end of the quarter.) However, the professor stepped in and told me, in no uncertain terms, that quitting would be a mistake. He said I had excellent intuition, that I understood how the models we were studying worked. I was just making lots of computational errors.

A friend tutored me until the end of the course, and I found out that I just needed to relearn several things from algebra and one or two from calculus and go slower. Afterwards, I worked through some excellent books, which built up both my skills and my confidence. Outcome? I'm now a Ph.D. student in systems ecology (lots of food web and ecosystem modeling). I got A's in differential equations, linear algebra and a course on sets, proofs and logic, and a B in graph theory.

Here are the books I found so useful:
Mathematics for the Nonmathematician,
Forgotten Algebra,
Forgotten Calculus (best if you've taken or are about to take calculus)
A Tour of the Calculus (Best before you take calc - explains the concepts beautifully. If you don't like poetic writing, find something else.)

Oh, and Google "John Mighton" while you're at it.

Best of luck!
Jane

I have learned a few things as a high school and college math and science tutor. Most of the students who strugle with higher math and science do so because they can't do algebra. A solid background in algebra can serve as the foundation for understanding calculus and physics. Unfortunately, many math courses are taught in such a way as to get the student through the coruse while understanding NOTHING. And I think this more prevalent in comunity colleges. (That's what happens when institutions are more interested in profit than learning and teaching becomes a job rather than a career.) If Amanda finds herself in a class in which rote memorization is promoted over understanding the material, she should either switch sections or find herself a good tutor.

It will probably be necessary to pass first-year (two, possibly three, semesters) of calculus to obtain a BS.

My advice:

Practice, practice, practice. The university students that I have tutored did well when the practiced whether they liked it or not.

Take several community college courses, one at a time, to brush up on math. Start slow, perhaps an algebra review? The college should be able to help with placement. Then when you've shown you can succeed at calculus, you'd be ready for the BS.

Get a tutor. One of the hardest things to achieve is the "click" -- the point at which some concept suddenly makes sense. Different people learn in different ways. The way an individual professor or TA presents the subject sometimes just doesn't "click" with a student. A tutor should be able to approach the concepts from a different direction. Find a tutor that understands you and makes it "click". (Your college will have help sessions and other resources which *no one* ever uses. Find and use them.)

Practice, practice, practice.

Good luck!

Becca said "2) I was a mathphobe until I got to physics, where I discovered I really liked it. Because I understood concepts well, I could look at a physics problem, know the relationships that things should have (e.g. if force is increasing, mass or acceleration must be too) and then I could finally intuitively see how my equations should work. I didn't worry about making computational errors because I could always check my units, and run things through a common-sense check, ect."

That makes sense, since much of math was developed for describing physical stuff... like calculus. It is easier to learn the subject if you can see the application. (I actually learned calculus concepts in physics before getting them in my calculus class!)

Christie said "Jon - American community colleges are the same as the first 2 years of 4 year college, and will typically offer up to Calculus at least."

The community college my son goes to has math up to differential equations, advanced calculus and linear algebra. It also has chemistry, physics and biology courses that are equivalent to the same levels required for science majors up to their sophomore year at the local university. The major difference is that the classes have no more than 30 students (not 200), and cost substantially less. The state requires that the university take a certain number of transfer students from the community college system each year.

The community colleges have excellent resources to provide extra help to those who need it. They also offer classes at night, and other times.

Thomas M.: There are two main things you need to learn in Calculus... when you differentiate you are finding the slope of the line, and when you integrate you are finding the area under the line. Don't let it scare you. The biggest thing is to practice, practice, and practice. The best of luck in your studies.

Maria said "Moreover, I went to a school where history and literature majors were required to do differential equations."

I'm surprised that Caltech has history and literature majors!

Where's my comment? The brief comment about math in ecology got posted, but what happened to the longer one with the Amazon.com links?

Being able to "do" maths is like being able to read and write. Really useful. But for (most) adults it can be awfully hard to learn without motivation (imagine learning to read and write - as an adult - if it wasn't such an indispensable skill). You'll need large chunks of maths at various points in a career as a geologist (stay away from geophysics!). It will become as indispensable as being able to read and write is for a historian, and then, well, you'll just have to learn the bits you need. So starting now would be wise, but don't let it stop you. It's easier to learn if you *need* to learn.

I had bad math instructors, who couldn't grasp people who didn't understand math with ease. We got told we didn't belong in her class, or that we should know it already ( it was high school level upgrading thru the university. Gee. if we knew it, we wouldn't BE in that class.)

I apparently tested high for mathematical reasoning, but with a teacher who didn't click with anyone in her class, it was a struggle.

Practice, tutors, patience and a good instructor can go a long way.

I often ran into fellow classmates in the hall taking a deep breath and getting their head together when the instructor was being particularily infuriating.

Wow, lots of comments were in the moderation bin waiting to be approved. Yet several had the same thing to say about math (which is often compared to music):

Practice, practice, practice!

:-)

I graduated with a BS in geology having taken only one semester of calculus, my first semester in college. I never got the point of it.

In Introductory physics, the professor had to go over basic calculus...it started to become clearer.

After I began grad school, I began to appreciate what I was missing, so I took more calculus one summer (between weekends of putting gas tanks on Pintos); I took more calculus in grad school, after I had begun to be concerned about potential fields, gradients, and flow. The best learning experiences were those in which the teacher related the mathematics to concepts involving such things.

Two reasons people get fear of math. 1) arithmetic does not have answers that are "close enough". 1 + 1 = 2, not 3. Off by one is just wrong. 2) Math word problems are not often taught so one can learn them.

If you are comfy with a calculator doing your arithmetic, then maybe you don't need to solve that problem. Get a unit with good buttons and leaves a trace so you can find which button you missed. Otherwise, you can learn the soroban (abacus). I could do 20 digit divides in my head with this technique. Fast and reliable.

There are word problem techniques. Unfortunately, i don't know them. Word problems were always so "obvious" to me that i can't remember the thought process. I liked partial differential calculus much more than linear algebra because i could envision physical processes that were modeled better (for example, a rocket launch). If linear algebra came with more real world applications, the world would be a better place. But the problem starts much earlier.

I've never been a fluent math user or had much need for it, but I've come to appreciate the math in journal papers. Equations, I've realized, are like little numerical robots. When they're properly designed and carefully fit to the data, they can do astonishing amounts of work. So now I have fun sussing out the little guys, even though I'd be helpless at actually deploying them myself.