Getting over math anxiety
January 18, 2010 11:47 AM Subscribe
I have deep and life-long math anxiety. I want to overcome it. Help?
I am, and always have been, a very anxious person, and I have many early childhood memories of my parents telling me that math is very boring and very hard but very important, and if you don't do well in it, you are doomed to a life of penury. Unsurprisingly, this did not really prime me for a successful math career. I always (seriously - I remember doing this as early as 1st grade) self-sabotaged by not paying attention to the teacher during math, so that I wouldn't have to face what I felt would be my (inevitable) failure if I put in a good-faith effort. Then I did poorly in math and concluded I was stupid. The problem was exacerbated by a few truly horrible math teachers, who treated me with condescension or outright hostility, despite my being an otherwise exceptional and very precocious student. This pattern continued all throughout high school and whenever I attempted anything mathematical in university. I unfortunately pursued some mathematical material in undergrad in an effort to burnish my (obviously pretty low) intellectual self-esteem, but couldn't turn off the self-sabotaging behavior, and so the cycle began again. (Besides, math is cumulative, and missing out on all that background material did not help.)
Except for this summer, when I had to take a pretty difficult logic/proof/propositional calculus class, made the terrifying decision to really work at it, and got a 90. And then I took it's successor class in fall term, and got an 85. When I got that first 90, there was a period of a week or two when I would think back on it and feel a deep well-spring of pride: It was the first time I had set out to challenge my (perceptions of) my limitations. And I succeeded. It was a big victory for me.
I want to do that again. I think it would be really, really good for me to spend my spare time working my way through basic high school and university math, at my own pace, and with an orientation of compassion toward myself, so that I can learn that I am a fundamentally strong and competent person, someone capable of approaching what scares me and overcoming it. I want to give myself a chance with math.
I know the basics of arithmetic - addition, subtraction, the multiplication tables, long-division, the number line, decimals, fractions, etc. I know some really simple geometry (special triangles, the Pythagorean theorem), and some really basic algebra (e.g. solving reasonably simple one-variable inequalities and equations.) Anything too far above that, and I start to get increasingly fuzzy and insecure. (I know this is not very specific, sorry.) I'd like to start reviewing from what I know and work up to, at least, first-year university calculus and linear algebra. (I know that this will take a while, I'm prepared for that.) So what I'm looking for is:
1) Books that I might find helpful (though I can't afford really expensive textbooks)
2) Free online resources
3) Tips for dealing with the onslaught of negative feelings that I will bring up by doing this
4) Any strategic/"game-plan" type advice for building up a knowledge of math from pretty shaky foundations
I should mention, also, that I don't really want to hire a tutor - because this makes me emotional, and I hate being emotional in front of strangers, because tutors are expensive, and because I'm embarrassed of all this.
I am, and always have been, a very anxious person, and I have many early childhood memories of my parents telling me that math is very boring and very hard but very important, and if you don't do well in it, you are doomed to a life of penury. Unsurprisingly, this did not really prime me for a successful math career. I always (seriously - I remember doing this as early as 1st grade) self-sabotaged by not paying attention to the teacher during math, so that I wouldn't have to face what I felt would be my (inevitable) failure if I put in a good-faith effort. Then I did poorly in math and concluded I was stupid. The problem was exacerbated by a few truly horrible math teachers, who treated me with condescension or outright hostility, despite my being an otherwise exceptional and very precocious student. This pattern continued all throughout high school and whenever I attempted anything mathematical in university. I unfortunately pursued some mathematical material in undergrad in an effort to burnish my (obviously pretty low) intellectual self-esteem, but couldn't turn off the self-sabotaging behavior, and so the cycle began again. (Besides, math is cumulative, and missing out on all that background material did not help.)
Except for this summer, when I had to take a pretty difficult logic/proof/propositional calculus class, made the terrifying decision to really work at it, and got a 90. And then I took it's successor class in fall term, and got an 85. When I got that first 90, there was a period of a week or two when I would think back on it and feel a deep well-spring of pride: It was the first time I had set out to challenge my (perceptions of) my limitations. And I succeeded. It was a big victory for me.
I want to do that again. I think it would be really, really good for me to spend my spare time working my way through basic high school and university math, at my own pace, and with an orientation of compassion toward myself, so that I can learn that I am a fundamentally strong and competent person, someone capable of approaching what scares me and overcoming it. I want to give myself a chance with math.
I know the basics of arithmetic - addition, subtraction, the multiplication tables, long-division, the number line, decimals, fractions, etc. I know some really simple geometry (special triangles, the Pythagorean theorem), and some really basic algebra (e.g. solving reasonably simple one-variable inequalities and equations.) Anything too far above that, and I start to get increasingly fuzzy and insecure. (I know this is not very specific, sorry.) I'd like to start reviewing from what I know and work up to, at least, first-year university calculus and linear algebra. (I know that this will take a while, I'm prepared for that.) So what I'm looking for is:
1) Books that I might find helpful (though I can't afford really expensive textbooks)
2) Free online resources
3) Tips for dealing with the onslaught of negative feelings that I will bring up by doing this
4) Any strategic/"game-plan" type advice for building up a knowledge of math from pretty shaky foundations
I should mention, also, that I don't really want to hire a tutor - because this makes me emotional, and I hate being emotional in front of strangers, because tutors are expensive, and because I'm embarrassed of all this.
it sounds like you have a fighting chance with basic calculus. i would recommend picking up a copy of Stewart's calculus, not because it is particularly great, but because over the years they have really smoothed out the edges so that you don't need to be very skilled or know very much to get through it. (you can pick up a used copy or download a copy from some magic place)
the strategy is simple: start at the beginning, read the chapter and then start doing exercises. Stewart will have introductory material which will cover all of the prerequisites. the problem is that there will be things in the chapter you may not understand, and you will get stuck on problems. there isn't any easy way around this. you will have to be persistent and not get depressed when you get stuck. easy right ;)? drinking lots of coffee will often help you feel more confident.
you can do the same with introductory linear algebra. in some ways it will have less prerequisites than calculus. If you were happy with logic, you might find more abstract mathematics (like linear algebra) more rewarding than slogging through calculus.
but in the end, math really isn't all that important to being successful in life. don't listen to your parents: if it starts to feel too bad, you won't be a failure if you quit. honestly, most people who pass intro calculus are not much better off mathematically than you are. don't be too hard on yourself.
posted by ennui.bz at 12:06 PM on January 18, 2010 [1 favorite]
the strategy is simple: start at the beginning, read the chapter and then start doing exercises. Stewart will have introductory material which will cover all of the prerequisites. the problem is that there will be things in the chapter you may not understand, and you will get stuck on problems. there isn't any easy way around this. you will have to be persistent and not get depressed when you get stuck. easy right ;)? drinking lots of coffee will often help you feel more confident.
you can do the same with introductory linear algebra. in some ways it will have less prerequisites than calculus. If you were happy with logic, you might find more abstract mathematics (like linear algebra) more rewarding than slogging through calculus.
but in the end, math really isn't all that important to being successful in life. don't listen to your parents: if it starts to feel too bad, you won't be a failure if you quit. honestly, most people who pass intro calculus are not much better off mathematically than you are. don't be too hard on yourself.
posted by ennui.bz at 12:06 PM on January 18, 2010 [1 favorite]
They've been around a long time, but Ken Stroud's books are wildly popular, at least in the UK. When I was at university (twenty years ago), everybody on a course with a mathematical requirement would have a copy of 'Engineering Mathematics'. There's a shorter version, 'Foundation Mathematics', which covers the basic parts of the larger book - that's the one I'd recommend for your requirements.
posted by le morte de bea arthur at 12:07 PM on January 18, 2010
posted by le morte de bea arthur at 12:07 PM on January 18, 2010
why not start with recreational mathematics?
because recreational math puzzles are often harder than basic calculus problems. at least with a textbook you have some sense of what you need to know to solve any problem (just look at the chapter it's in...)
posted by ennui.bz at 12:08 PM on January 18, 2010 [2 favorites]
because recreational math puzzles are often harder than basic calculus problems. at least with a textbook you have some sense of what you need to know to solve any problem (just look at the chapter it's in...)
posted by ennui.bz at 12:08 PM on January 18, 2010 [2 favorites]
I never tried to solve most of them. But it was fascinating to read about them, and read the answers later.
More important, Gardner's column served as a general survey of Mathematics for me, delving into things like probability theory and topology and giving me a good broad idea of what math is about and how it can be used. And Gardner is an amazing writer. (He's 95 now, and still writing.)
posted by Chocolate Pickle at 12:12 PM on January 18, 2010
More important, Gardner's column served as a general survey of Mathematics for me, delving into things like probability theory and topology and giving me a good broad idea of what math is about and how it can be used. And Gardner is an amazing writer. (He's 95 now, and still writing.)
posted by Chocolate Pickle at 12:12 PM on January 18, 2010
The Heart of Mathematics is one of my favorite mathy textbooks. It's not particularly numerical, but it shows how maths and analytical thinking can infiltrate pretty much everything. You can buy it, or get a google preview. (the Amazon prices for it are pretty inflated atm, I bought mine last summer for under $30.)
posted by Wulfhere at 12:32 PM on January 18, 2010 [1 favorite]
posted by Wulfhere at 12:32 PM on January 18, 2010 [1 favorite]
Well, if you got an A in a proof class, then you're well prepared. Pretty much every algebra problem is a proof; given the formula x^2-1=0, use algebraic rules of equality to prove x = -1 or 1. Many colleges offer a remedial math section to bring students up to speed.
One idea that occurs to me is to walk into a local community college (CC) bookstore and buy their college algebra textbook (used). The thing about math textbooks is they're roughly equally terrible; just make sure it has problem sets and answers in the back, as you have no grader! Then must up the discipline to not look in the back until you've worked through problems. If you're comfortable with it, have a friend "grade" for you.
Maybe even grab a free course catalog so you can be sure there aren't any important prereqs you're missing; and see if they have any online course offerings. CC tuition is pretty cheap, after all, and distance learning makes it easy to follow a pace of learning without tremendous scheduling problems. If you're worried about your GPA but willing to take a class then CCs can be handy; it won't wreck your institutional GPA, it's cheaper and comes with lesson plans.
As for resources, Wikipedia is fairly useful as a reference, but sometimes it's easy to stumble upon a section written by mathematicians for mathematicians, even though the subject is also taught to high schoolers. Still, once you hit calculus and linear algebra that should matter less.
posted by pwnguin at 12:38 PM on January 18, 2010
One idea that occurs to me is to walk into a local community college (CC) bookstore and buy their college algebra textbook (used). The thing about math textbooks is they're roughly equally terrible; just make sure it has problem sets and answers in the back, as you have no grader! Then must up the discipline to not look in the back until you've worked through problems. If you're comfortable with it, have a friend "grade" for you.
Maybe even grab a free course catalog so you can be sure there aren't any important prereqs you're missing; and see if they have any online course offerings. CC tuition is pretty cheap, after all, and distance learning makes it easy to follow a pace of learning without tremendous scheduling problems. If you're worried about your GPA but willing to take a class then CCs can be handy; it won't wreck your institutional GPA, it's cheaper and comes with lesson plans.
As for resources, Wikipedia is fairly useful as a reference, but sometimes it's easy to stumble upon a section written by mathematicians for mathematicians, even though the subject is also taught to high schoolers. Still, once you hit calculus and linear algebra that should matter less.
posted by pwnguin at 12:38 PM on January 18, 2010
Free online resources
I just posted a link to Salman Khan's massive (and award-winning) collection of educational videos in another askme thread. Covers pretty much everything you mentioned, and then some.
(There's also an online application (under development) that provides extra exercises for parts of the math stuff).
posted by effbot at 12:41 PM on January 18, 2010 [1 favorite]
I just posted a link to Salman Khan's massive (and award-winning) collection of educational videos in another askme thread. Covers pretty much everything you mentioned, and then some.
(There's also an online application (under development) that provides extra exercises for parts of the math stuff).
posted by effbot at 12:41 PM on January 18, 2010 [1 favorite]
So, you have a history of bad experiences with math, but you had a really good experience in this lambda calc class...have you considered NOT working on all the normal calc/geometry stuff until you get some more wins on the board?
The thing is, math is *not* cumulative, generally. In fact, its provably not cumulative. Not even close.
Lambda calc is something you never did in school before, and it probably didn't really build on anything you did do in school. Also, its cool as hell. Calculus is boring. Calculus is like "wow, integration! Differentiation! So neat that that hack actually works! Ok...why is this book 700 pages long? Oh, I see, its because you have to do increasingly complex versions of the same problems." There are no more 'Aha' points. Its all very practical: lots of real-world work involves hard-ass calculus problems, but its not very fun.
So, I suggest working on some discrete math. The intro-y stuff that will follow from where you are now is super-broad but a lot of it is more cool than doing a bunch of calc: probability, graph theory, combinatorics, set theory, number theory...
American school math (I'm guessing you're America-educated cause of the stuff you outlined) is...I don't really get what they were thinking, actually. You get this half-baked build-up to 20th Century French Guys math, then you abruptly switch gears in high school and prepare for/endure years of calculus. You basically ignore all this cool crap, and you ignore stuff that's a lot more useful to a well-informed people, in my opinion, like probability and statistics. You liked that prop calc material, you might also enjoy computability theory, algorithms, and stuff like that, the mathematical formalizations of computer science.
Anyway, in short: screw calc, consider leaving the world of continuous numbers behind for the more-awesome one of countable stuff: discrete math.
posted by jeb at 12:46 PM on January 18, 2010 [2 favorites]
The thing is, math is *not* cumulative, generally. In fact, its provably not cumulative. Not even close.
Lambda calc is something you never did in school before, and it probably didn't really build on anything you did do in school. Also, its cool as hell. Calculus is boring. Calculus is like "wow, integration! Differentiation! So neat that that hack actually works! Ok...why is this book 700 pages long? Oh, I see, its because you have to do increasingly complex versions of the same problems." There are no more 'Aha' points. Its all very practical: lots of real-world work involves hard-ass calculus problems, but its not very fun.
So, I suggest working on some discrete math. The intro-y stuff that will follow from where you are now is super-broad but a lot of it is more cool than doing a bunch of calc: probability, graph theory, combinatorics, set theory, number theory...
American school math (I'm guessing you're America-educated cause of the stuff you outlined) is...I don't really get what they were thinking, actually. You get this half-baked build-up to 20th Century French Guys math, then you abruptly switch gears in high school and prepare for/endure years of calculus. You basically ignore all this cool crap, and you ignore stuff that's a lot more useful to a well-informed people, in my opinion, like probability and statistics. You liked that prop calc material, you might also enjoy computability theory, algorithms, and stuff like that, the mathematical formalizations of computer science.
Anyway, in short: screw calc, consider leaving the world of continuous numbers behind for the more-awesome one of countable stuff: discrete math.
posted by jeb at 12:46 PM on January 18, 2010 [2 favorites]
Good for you!
Books:
For particular math subjects or skills, check out your local library. It will likely have study guides available and you can borrow several to see what style works best for you.
For problem solving, check out Polya's How to Solve It. It's an excellent resource on how to approach problems.
Online resources:
Purple Math -- This has some excellent lessons in algebra and basic trig. It sounds like the material is appropriate for your level of knowledge. I'd start working through the lessons in order. Don't forget to check out the preliminary topics; these are very important! You might want to check out homework guidelines briefly, even though you will not be turning your work in.
Jefferson Math Project -- This site is aimed at NYS math teachers, but it has many worksheets and videos available.
When you've made a bit more headway, you may want to take a look at Common Errors in College Math Understanding these errors and why someone might make them will help your math understanding.
Tips:
Keep some sort of notebook/organize your work. Being able to look back at what you've done can give a great sense of accomplishment and can serve as a wonderful resource in the future.
Practice, practice, practice! Reading about math is helpful, but you need to DO math to really learn it. Find exercises online or in a book and try them to the best of your ability before looking at the answers.
Read the math aloud. It can sound silly, but understanding each part of a problem or exercise is necessary and reading math aloud can help you understand the language of math better.
Also, I know you've asked this anonymously, but feel free to MeFiMail me if you want to talk math ideas. I'm currently studying to become a math teacher and would be happy to discuss math with you. Good luck!
posted by wiskunde at 12:48 PM on January 18, 2010 [1 favorite]
Books:
For particular math subjects or skills, check out your local library. It will likely have study guides available and you can borrow several to see what style works best for you.
For problem solving, check out Polya's How to Solve It. It's an excellent resource on how to approach problems.
Online resources:
Purple Math -- This has some excellent lessons in algebra and basic trig. It sounds like the material is appropriate for your level of knowledge. I'd start working through the lessons in order. Don't forget to check out the preliminary topics; these are very important! You might want to check out homework guidelines briefly, even though you will not be turning your work in.
Jefferson Math Project -- This site is aimed at NYS math teachers, but it has many worksheets and videos available.
When you've made a bit more headway, you may want to take a look at Common Errors in College Math Understanding these errors and why someone might make them will help your math understanding.
Tips:
Keep some sort of notebook/organize your work. Being able to look back at what you've done can give a great sense of accomplishment and can serve as a wonderful resource in the future.
Practice, practice, practice! Reading about math is helpful, but you need to DO math to really learn it. Find exercises online or in a book and try them to the best of your ability before looking at the answers.
Read the math aloud. It can sound silly, but understanding each part of a problem or exercise is necessary and reading math aloud can help you understand the language of math better.
Also, I know you've asked this anonymously, but feel free to MeFiMail me if you want to talk math ideas. I'm currently studying to become a math teacher and would be happy to discuss math with you. Good luck!
posted by wiskunde at 12:48 PM on January 18, 2010 [1 favorite]
Are you at a university right now? If so, check your university library for books. (For example, mine has "Algebra 1 Grs. 6-12 Teachers' Ed."). I would not approach high school/college algebra without a text book, if only for the problem sets, and most other branches of mathematics will throw in occasional algebra steps assuming that you can follow it. That being said, I would agree that discrete math (set theory, combinatorics) is just fun and doesn't require too much foundation. There's a pretty large gap between that type of stuff and more computational (or even, yuck, applied) math like intro calculus and the first semester of linear/matrix algebra.
Also there may be free tutoring on campus. I understand that you're embarrassed to talk to someone, but even with books you may need further explanation at some point. A lot of people just need me to explain which steps the solution manual is skipping/glossing over. We see everything. If you feel like you have to explain things, you can always pass it off by saying it's been a while since your last math class.
posted by anaelith at 2:42 PM on January 18, 2010
Also there may be free tutoring on campus. I understand that you're embarrassed to talk to someone, but even with books you may need further explanation at some point. A lot of people just need me to explain which steps the solution manual is skipping/glossing over. We see everything. If you feel like you have to explain things, you can always pass it off by saying it's been a while since your last math class.
posted by anaelith at 2:42 PM on January 18, 2010
For the traditional algebra/trig/calc grind, Paul's online math notes are exceptionally helpful. He has everything from cheat sheets to tutorials with example problems and solutions for all the major topics of those disciplines. Go through them, and try to work out the example problems as you're reading along -- it's saved my rear whenever I missed class.
Also, while he's talking more about CompSci types, Steve Yegge wrote a long blog entry on learning math yourself. Skip to the section "The Right Way to Learn Math" and you'll get his argument for the "liberal arts education in math", that is, how to gently introduce yourself to a lot of subjects and go in for more depth when you're interested or have a need. And we both echo jeb's sentiment -- don't feel pressured to jump into calculus right away, it can get a little tedious and it's not exceptionally helpful outside of physics. That said, there are a lot of concepts in calculus that are fairly interesting as long as you don't get bogged down in all the different ways to integrate. I hear Epp's text is good for discrete math, but you'll need to look for the previous version to get a reasonable price on it.
posted by ayerarcturus at 7:54 PM on January 18, 2010 [1 favorite]
Also, while he's talking more about CompSci types, Steve Yegge wrote a long blog entry on learning math yourself. Skip to the section "The Right Way to Learn Math" and you'll get his argument for the "liberal arts education in math", that is, how to gently introduce yourself to a lot of subjects and go in for more depth when you're interested or have a need. And we both echo jeb's sentiment -- don't feel pressured to jump into calculus right away, it can get a little tedious and it's not exceptionally helpful outside of physics. That said, there are a lot of concepts in calculus that are fairly interesting as long as you don't get bogged down in all the different ways to integrate. I hear Epp's text is good for discrete math, but you'll need to look for the previous version to get a reasonable price on it.
posted by ayerarcturus at 7:54 PM on January 18, 2010 [1 favorite]
Dropped out of high school, having taken no math class higher than PRE-ALGEBRA. Went back to school years later for a degree in CS. Turns out my school required all BS-CS students to minor in math. Oh hell.
So what did I do?
I started in the lowest math class my school offered. Basic math, it was. Let's just say it was Algebra. Lots of it was easy and "duh," but lots of it was actually new to me. And I didn't feel embarrassed at all, because everyone was in the same boat with me. Even wound up making some good friends.
I then took the next one down, pre-calc. Then calc. Then calc 2. Then discrete math. Then calc 3. Then advanced stat. Then linear algebra.
See a pattern?
So I'd say start out by taking the most basic math class you can find, get good and comfortable with it, and then just work your way up from there.
posted by Afroblanco at 12:44 AM on January 19, 2010 [1 favorite]
So what did I do?
I started in the lowest math class my school offered. Basic math, it was. Let's just say it was Algebra. Lots of it was easy and "duh," but lots of it was actually new to me. And I didn't feel embarrassed at all, because everyone was in the same boat with me. Even wound up making some good friends.
I then took the next one down, pre-calc. Then calc. Then calc 2. Then discrete math. Then calc 3. Then advanced stat. Then linear algebra.
See a pattern?
So I'd say start out by taking the most basic math class you can find, get good and comfortable with it, and then just work your way up from there.
posted by Afroblanco at 12:44 AM on January 19, 2010 [1 favorite]
I'm very similar to you (i.e., parent's attitudes toward math, very high anxiety, intellectually insecure). I got F's in math (Algebra, Trig, Pre-Calc) throughout grade school and high school, and I thought I was an idiot. I didn't have the balls to approach Math again until five years later when I enrolled in a PreCalc course.
Many things that I completely didn't understand in High School suddenly "clicked" when I started taking math again in college. I'm not sure why this is, but I'm guessing it has to do with being older; maybe my brain is simply more developed now.
My advice to you is to keep going. Dive right in, and take the next, successive math course. Don't worry about catching up on earlier stuff, because you will have many opportunities to learn it as you along. And also--and this is very important--whenever you come across something you don't understand, bother the hell out of your instructor until you understand it. That's what they're there for. Never be afraid to ask them a "stupid" question.
posted by capitalist.pig at 4:36 AM on January 19, 2010
Many things that I completely didn't understand in High School suddenly "clicked" when I started taking math again in college. I'm not sure why this is, but I'm guessing it has to do with being older; maybe my brain is simply more developed now.
My advice to you is to keep going. Dive right in, and take the next, successive math course. Don't worry about catching up on earlier stuff, because you will have many opportunities to learn it as you along. And also--and this is very important--whenever you come across something you don't understand, bother the hell out of your instructor until you understand it. That's what they're there for. Never be afraid to ask them a "stupid" question.
posted by capitalist.pig at 4:36 AM on January 19, 2010
I'm currently working my way through 'The humongous book of statistics problems' and liking it a lot. You might want to look into 'The humongous book of calculous problems' from the same series.
posted by rjs at 10:11 AM on January 19, 2010
posted by rjs at 10:11 AM on January 19, 2010
If you like logic/proof/propositional calculus, you're on the express lane to the future of computer science, economics, and many other fields.
Suggestions:
Lockhart's A Mathematician's Lament
Keith Devlin writes some great essays and books.
posted by at at 1:13 PM on January 19, 2010
Suggestions:
Lockhart's A Mathematician's Lament
Keith Devlin writes some great essays and books.
posted by at at 1:13 PM on January 19, 2010
This thread is closed to new comments.
I learned about how much fun mathematics is by reading Martin Gardner's "Mathematical Games" column in Scientific American. Those columns are available in collections, and reading a couple of those should help you begin to get past your anxiety.
posted by Chocolate Pickle at 11:58 AM on January 18, 2010 [1 favorite]