I am sick of having to say "I'm not good at math."

March 24, 2010 9:54 AM

I have always had difficulty with mathematics. Now I'm in my mid-thirties and have gone back to school to study engineering. Things are not going appreciably better than they did the first time I went to university. What can I do to fill the gaps I have and become a skilled problem-solver? I want to go from being a C to being an A student.

I am in an engineering program at a European university.

The mathematics curriculum consists of:

Mathematics I
Numbers and number systems
Vectors
Matrices and determinants
Equalities and inequalities
Sequences and convergence
Functions
Trigonometric functions
Differentiation

Note: I have passed Mathematics I but I did not do very well. I had particular difficulty with inequalities, functions and trigonometric functions. Polynomials, upon which all that is based, have never been my strong point.

Mathematics II
Integration
Series and Taylor series
Differential equations
Multivariable differentiation
Multivariable integration
Complex numbers

Some background:

I skipped Grade 1 (for reasons other than my glowing math ability). I was dropped into Grade 2 without any additional help (I was considered a "gifted student", so I can only presume that nobody considered this necessary). This proved to have disastrous consequences.

When I was in Grade 1, we were doing exercise sheets. I struggled to learn my multiplication tables. It was all very abstract and all extraordinarily boring. Looking back, I think my problems started then, when my brain was in the early stages of construction.

Well, that's not how math is taught to young kids today. The emphasis is on building mathematical intuition, on tangibles, and on keeping it fun.

My problem:

I have problems with things that feel basic to me. I make errors in algebra and in working with polynomials. Problem-solving remains a slow and painful process. I have trouble keeping enough of the problem elements in my head to actually solve the problem. I'm slow. That is probably what kills me more than anything in exams. Given enough time (LOTS of time), I could solve the problems I'm given.

But I also make catastrophic errors, such as missing signs and symbols from one step to the next. The result is often that, even though I understand the process, I end up with a completely wrong answer. I don't get the satisfaction that comes with successfully solving a problem. That hurts my confidence, which makes me second-guess everything I do. I've tried just doing the problems and trusting myself. I end up with a LOT of wrong answers. I can usually find where I made the error (or errors!) that led to the incorrect answer, but that doesn't stop me from repeating them. I understand the importance of doing lots of problems, but I'm so slow that I don't get a chance to do very many. I know that volume is important here.

I find that I have trouble staying concentrated while working a problem. Sometimes, only half my mind will be working on the problem, and the other half will be thinking about something else. I know, I know, with thinking habits like that, it's no wonder that I'm having trouble.

I have trouble with mathematical abstraction. If I look at a variable in a physics problem, for example, I have difficulty seeing "through" the variable to what it actually represents.

I have trouble working through a problem on paper in an orderly, sequential fashion.

I know I am capable of this -- I have at least one A in mathematics in my university career. I just don't know how to get there from here.

To summarize my problems, then:

Errors in algebra and polynomials, quadratic, cubic and quartic equations
Problem-solving is slow and painful.
I have trouble keeping track of problem elements in my head.
I'm slow.
I make catastrophic procedural errors, like missing signs or symbols between steps.
I have trouble focusing when working on a problem.
I have difficulty with mathematical abstraction.
I have trouble working through a problem on paper in an orderly, sequential fashion.

Here is what I seek:

1. Book(s) (or other materials!)
Keeping in mind the curriculum I mentioned above, materials that will help me re-build my foundations, manageable enough that I can work with it on the side, say an hour a day, but that's also challenging enough that it will keep me focused. Emphasis on self-study, here. I also have the sense that the books I have worked with so far haven't been very good. Unfortunately, I haven't had a lot of things to compare with, because the books I have were mandated by the university I did my first degree at and were expensive enough to begin with. (Examples of what I have: Keith Nicholson's Elementary Linear Algebra 2nd Edition, James Stewart's Single Variable Calculus - Early Transcendentals 2nd Edition.)

2. Strategy
The problem is not my willingness to do the work. The problem is to work on the right things, so that I don't waste my time on things that aren't going to help me with the math I do today, and to keep things in balance, so that maintaining my abilities doesn't take over my life. I want to develop new habits that will make me competent in mathematics for life. What should they be?

3. Exercises to improve my focus and problem-solving ability
I often feel like I'm fighting against patterns that were established very early in my life. Given what we now know about brain plasticity, though, I don't think I'm ready to give up on myself yet :) What should I do on a regular basis to improve my focus, problem-solving ability, and thinking speed?

posted by rhombus to education (30 answers total)

If you don't have KA Strouds Engineering Mathematics then pick it up now. It's excellent. Lot's of examples and problems (with answers) to work through.
posted by oh pollo! at 9:59 AM on March 24, 2010 [3 favorites]

I'm an engineer who struggled with geometry in high school (I was trying to memorize proofs instead of using logic to solve them). I also attempted to teach my stepson Algebra (we decided that I couldn't cram algebra in his head if he didn't want to do the work). Some of the problems you're having sound like some of the problems my stepson had -- specifically the missing signs/symbols between steps, focus, and working through a problem in an orderly fashion.

I wonder if rather than trying to get through Math II or whatever course you're on at the moment, if it would make sense to step back and make sure you know the basics. For instance, knowing addition/subtraction/multiplication/division tables cold up to 12. Then, making sure that you develop good neatness habits with solving equations so that you always remember signs and symbols. When you're doing that, seems like you might want to work relatively simple problems so that you can build speed. By googling "math problem speed", I found the following website Math Practice which lets you auto-generate algebra practice worksheets. Finally, I would suggest you get a ton of (again relatively simple) word problems so that you build speed in quickly isolating the key variables. To keep it interesting, perhaps you can race yourself -- trying to build speed and accuracy.

I don't know what kind of engineering degree you're working on -- I'm an electrical engineer and have spent my career in high tech working with electrical, computer, and mechanical engineers. Strong math skills are key to being successful at any of those jobs.

The last suggestion I have is to look at why you want to be an engineer. Maybe there are some aspects of the job that appeal to you that could play better to your strengths. Engineering is a lot of problem solving -- if that's something that you find kind of boring or you find it difficult/unpleasant to work on a problem until it is solved -- I'm not sure you're going to enjoy being an engineer.
posted by elmay at 10:18 AM on March 24, 2010 [1 favorite]

Math is like music.

a) you need a teacher/coach/tutor. one who will help show you the correct techniques and what you're doing right and wrong.
b) you need to practice. A LOT.

Imagine you were told that you had to perform an oboe solo in 6 months. (I assume you don't play the oboe) For, say, the Queen or that hot chick in algebra class or your wife or whoever gets you nervous the most. Imagine how much practice you would put in for that. You must put in that much work to get good at math.

Yes, some people are naturally good at math. If you're not one of them then knowing that is a huge first step. Get a competent tutor and practice, practice, practice.
posted by GuyZero at 10:18 AM on March 24, 2010 [3 favorites]

I tutored math, amongst other subjects, for many many years. Often, I would run into high school juniors whose problems actually began eight years earlier. Find someone talented and local, who will learn how you learn best. A good math tutor can, by looking at your mistakes, at your facial expressions, at the points where you unconsciously hold your breath, where your problems are, then teach you how to think about math, all over again. He or she can then bring you up to speed.

Every student is different, in that the number of variables in math skills and hangups, as well as the weightings on each. You want someone who will understand that, who will understand you, then tailor exercises to break through barriers and build you up where you are weakest. At each level of math, you build upon previous levels whose execution ought to be automatic, even reflexive.

Distraction can be worked through. Not waved away, not cured, but worked through. I had a kid who struggled with Tourette Syndrome, ADHD, and OCD. The medication for one would often make the others worse. He could still factor out polynomials without a great deal of thought, once we had practiced enough and patched the things which prevented him from doing so. It was not easy for either of us, but it was doable. His speed was important, as it enabled him to simply do rather than be caught up in the process. And then we moved on to the next thing.

Other kids, other adults, other problems. For some, destroying abstraction is important. They must know why this is the way it is, that it isn't just all made up and relate everything back to concrete entities. Others must visualize. I never had two the same which meant that, although I wandered back and forth through mathland, I never had the same trip, despite leading people one by one to similar destinations.

Find your Virgil who will guide you safely through the Pit.
posted by adipocere at 10:21 AM on March 24, 2010 [3 favorites]

2nding Engineering Mathematics. It is a great book. I've started using it a bit for the kid I tutor.

Also, consider getting a tutor. He/she can help you work through the problems where you stumble and help you with general approaches and the thought process for working through problems in a sequential fashion. Don't go to Sylvan or similar---you'll overpay. Find another student who is awesome at the material, can explain it well and is looking for a little extra dough.

Also, remember, people who make math look like a piece of cake have had a lot of practice on that type of problem. Just like anything else, it takes a lot of practice of doing and seeing the same problems over and over and taking the wrong approach the first dozen times before you can just look at a problem and know exactly how to solve it.

Finally, since you are using math in engineering, one thing that helped me a lot was to focus on the engineering applications of the math. The theory would always tie me in knots, but as soon as I saw the engineering application it would all make sense.
posted by chiefthe at 10:24 AM on March 24, 2010

people who make math look like a piece of cake have had a lot of practice on that type of problem

This is true.
posted by dfriedman at 10:30 AM on March 24, 2010

Did someone say math? Khan Academy might be of help.
posted by Theloupgarou at 10:44 AM on March 24, 2010 [6 favorites]

Theloupgarou beat me to it by 10 minutes. Khan Academy is magic.
posted by the jam at 10:53 AM on March 24, 2010

If there is any tutoring or special help for the course you are taking, or any way to meet with the istructor, take advantage of that, and do it as often as you can. This kind of follows the music teacher analogy in a way. If you can learn how the instructor thinks and what to expect on exams, this familiarity may help you more quickly and efficiently break problems down into component parts.

Also, when you do homework, make sure you develop the habit of checking your answers, paying particular attention to the areas where you know your weaknesses lie. I would suggest doing the entire problem set, then going back and checking at a later time; I think you'll be more likely to catch mistakes with a clear mind.

It sounds like you know what you're doing but have always had bad habits with regard to signs and stuff. You need to break those habits.
posted by Doohickie at 10:55 AM on March 24, 2010

I run an engineering UG course at a UK university and Maths is always among the biggest concerns for us, as it tends to be the area where a cohort has the greatest range of abilities and prior training, which can lead to students getting left behind, which slows them down across the board. Different universities take different approaches to this, and this may be dependent on which country you are studying in also (e.g. some will have a sink or swim policy).

Potential sources of help:
Approach your maths tutor and ask whether he can offer advice or tips. If you can identify others in your cohort who also struggle then get together with them and enquire upwards whether there is any possibility of extra tutorials. Ask your programme leader if necessary. Whether this happens will depend where you are studying. Certainly in the UK, your programme leader would not want to risk failing students over maths.

Consider finding out when level 1 maths is being taught and see about going to the classes. this will let you catch up and fill in holes in your knowledge. Most institutions would allow this.

Don't worry about those who make it look like a piece of cake, some will be better than you at maths, some will have just come off doing maths to a high-ish level up to 18 years of age. Focus on getting your maths acceptable and aim to get the best marks across the board, playing to your strengths. You can still get a top class engineering degree.

Do get Stroud. At a previous institution of mine all engineering UGs had to work through X chapters per week, set yourself a target like this and force yourself to learn the stuff.
posted by biffa at 10:56 AM on March 24, 2010

I hope my suggestion won’t be too basic. Now although I have always had a really easy time with math and music, other things were really challenging to me (i.e., basic grammar or how to pronounce certain words, I kid you not). So as an adult I’ve had to sit down and teach myself complex skills, while simultaneously working through the basics, and that is the perspective that I am giving you here.

I usually google interactive [basic grammar for me or for you, polynomials] and I find that what your own university can’t teach you, well, other universities can. Check out a few of the websites – if they walk you through the basics and have problems that you can solve that are interactive work with those.

I just did this now and found Virtual Math Lab. I noticed that even have videos with sample problems. Anyway, I would start there – learn other ways to understand this material. Do sample problems until it is second nature; I think that may be your biggest struggle right now. The drifting off – that happens to all of us if we feel it is overwhelming, challenging, boring, etc. Don’t worry about that for now.

This may or may not help you, but because I often (now) have to write material and it needs to be correct, I make a little checklist with the things that I frequently mess up and should double check. For me, it is things like –a) Table numbers in order, b) Table numbers in text match actual table numbers, c) acronym defined the first time, etc. Maybe you can create a similar one for yourself a) are the signs listed in all the steps, etc., but include things that you frequently have problems with. Use that checklist all the time.
posted by Wolfster at 11:06 AM on March 24, 2010

I might get nailed to the wall for this, but here's a different answer:

Problem-solving is slow and painful.
I have trouble keeping track of problem elements in my head.
I'm slow.
I make catastrophic procedural errors, like missing signs or symbols between steps.
I have trouble focusing when working on a problem.
I have difficulty with mathematical abstraction.
I have trouble working through a problem on paper in an orderly, sequential fashion.

I would never try to take your hopes and dreams away, but have you considered a career related to engineering that uses a less math-reliant skillset? You're gifted, but what you're gifted at doesn't seem like it has much to do with mathematics, from your description.

What about a career that overlaps with engineering in a way that you can still really enjoy, but without all the crucial math skills?

I know some very capable engineers, and I know they'd be nervous hiring an engineer who didn't have latent math skills, or an obvious gift in that area.

I had a Computer Science professor who told me once, "if this stuff doesn't come naturally to you, or if you're having trouble learning it, you might want to reconsider this as a career or focus of your studies."

I cried that day, but then I switched to a different focus. I still use what I learned in CS, but in a way that makes me about 10 times happier. I didn't have the latent talent that would make a good computer scientist, but I had latent talent in another area that was more enjoyable to me.

Sorry if this gets you down...just an idea. I'm sure if you really set your mind to it, you can indeed overcome the math problem that you are confronted with right now.
posted by circular at 11:13 AM on March 24, 2010 [2 favorites]

I am a licensed Civil Engineer, and Math is absolutely vital to what an engineer does. The closest I came to flunking out (and it was pretty damn close) was in calculus, mostly due to inadequate preperation in algebra.

My university work included 4 semesters of calculus and differential equations. I have never had to integrate or differentiate anything from scratch in my professional life and doubt I will ever have to, that is what computer programs or books are for. However having a grasp of how many things relate to each other in a concrete way (which is what calculus is for-describing the rate of change)and differential equations (describing complex relationships) is absolutely something you must do to be a good engineer.

The best way is to get the basics down cold. This means being able to solve algebraic problems well and accurately. This involves lots and lots of practice. Which is what I had to do to get through calculus. I did it by getting some old algebra textbooks from a used bookstore and working through stuff as I discovered I didn't know how to do it in calculus. It made the homework take me twice as long as it should have. I would highly recommend a tutor or maybe a community college class in high level algebra or precalculus class, which will cover trigonometry. And realize that it can be done and it is a skill like any other. No one is born knowing how to do it and it has taken mankind at least 10000 years of civilization to develop our current math techniques. You are not going to just get it unless you possess extratrodanary talent.


So anyway, treat it like you would learning any other skill (cooking, driving, playing baseball, whatever) and don't think of it as a matter of talent or gifted thinking. Find a good instructor/tutor and just make it your number one goal.
posted by bartonlong at 11:14 AM on March 24, 2010 [1 favorite]

Write down everything you know (= everything given in the problem), in an organized way. Then write down what you want to show. Then write down something that's equivalent. See if you can now see how to get started.

Do not skip steps. (Especially with algebra!) Do not skip steps!

Do piles and piles and piles of problems. Start the homework as soon as it is assigned. If you get stuck, go ask for help.

Work with other students.

Stuck? Write something down. You can't do math without writing stuff down.

If you are inclined to make silly mistakes: do not skip steps.
posted by leahwrenn at 11:17 AM on March 24, 2010 [1 favorite]

Practice on the basics is key. I had to do dozens of problem sets as a youngster before I could grok long division. Keep gathering problems, write everything out longhand on paper, check your answer with a calculator. Keep going until your fingers can't do it anymore.

Oh, and, here's a quick test - after doing a few problem sets, drink 3-4 cups of strong coffee, and try another few problem sets a few minutes later. If the caffeine helps you focus, consider talking to a psychiatrist about evaluation and chemical treatment for Adult ADHD. I'm not saying you have it, but if you have trouble focusing and your mind jumps you over steps, that sends up a flag for me that it's worthwhile for you to get it checked out.

Good luck!
posted by Citrus at 11:38 AM on March 24, 2010

Building on adipocere's post, I recently read an interesting article in the NY times about improving teaching. Along about page 6, they talk about a researcher,Deborah Loewenberg Ball , who has looked at what it takes to effectively teach math. Her papers are focused on training teachers, but you might be able to read them to get insight into how you are learning math and what might work better for you.
posted by elmay at 11:48 AM on March 24, 2010 [2 favorites]

I suppose it shouldn't surprise me that my post made it sound like I might have ADD, but if you'd ever met me in person, you'd see how unlikely that is. I honestly think it's a matter of not learning it properly from the basics up, which has led to some bad thinking and work habits. I'm obviously not alone, either. What might be different is that I'm being honest about it :)

As for the choice of career... as I've mentioned already, I've managed decent marks in math before, and when I am applying it to a real-world problem, I find it quite exciting, even fun (shocking, no?). Design and invention are fun for me. I also have well-developed communications and management skills that will be useful in an engineering career. Not all engineers have to be number-crunchers.

I think too many capable people are scared away from math for all the wrong reasons. I think it's typically poorly taught. When I see good explanations, I want to scream, "Why wasn't this explained to me this way in the first place? It's so CLEAR."

I might do the "coffee test" just for kicks, although the last time I drank three cups of coffee I nearly threw up :)
posted by rhombus at 12:16 PM on March 24, 2010

Definitely most math is very, very poorly taught. They just throw it out there and enough people are naturals at it that even bad teachers get most students to pass the necessary tests. IMO university-level math has even worse pedagogy because of the selection bias that got everyone in there in the first place lets them get away with it.
posted by GuyZero at 12:20 PM on March 24, 2010 [1 favorite]

1. Buy a lot of paper.
2. Use it up.
posted by Rafaelloello at 12:43 PM on March 24, 2010

Get a tutor. They can watch you as you work through a problem and catch your mistakes as you make them. They also can explain it in a slightly different way than the prof or textbook. Math is a skill that takes practice...the more you do the better you get at it (and faster).
posted by CdnMathTeacher at 12:49 PM on March 24, 2010

When I see good explanations, I want to scream, "Why wasn't this explained to me this way in the first place? It's so CLEAR."

Again, get a tutor. After working with one for a while, he/she will know how to explain things clearly to you.

And find applications in your major for the math you are being taught. Seeing applied examples often brings clarity. The only way I understood differential equations was from seeing them applied in my dynamics class---before that, I just didn't get the point.

Again, practice, practice, practice.
posted by chiefthe at 12:49 PM on March 24, 2010

Consider Kumon as a tutoring service. I'm not sure if they tutor at the level you need, but their technique is foolproof for taking kids from behind in math to well ahead of their grade level.
posted by Dasein at 2:05 PM on March 24, 2010

I took a look at the excerpts of Stroud available on Amazon -- Impressive! It seems to make no assumptions about existing knowledge and goes from the fundamentals to the advanced stuff. And it has lots of exercises.

I was debating whether to invest in Spivak, but I think Stroud will be more complete. I'm not studying mathematics, after all.

I'm on the hunt for a tutor also.
posted by rhombus at 2:16 PM on March 24, 2010

I was debating whether to invest in Spivak

for the love of god (or if you don't want to feel frustrated and stupid) don't get Michael Spivak's Calculus book...


When I see good explanations, I want to scream, "Why wasn't this explained to me this way in the first place? It's so CLEAR."

this is the way learning goes, the first time everything is opaque, the second time two,... the n'th time the heaven's clear and the light of truth shines through and you wonder how it could have been anything different. also, explaining something you know to someone who doesn't know is not all that easy, especially if it is basic material you 'know' without thinking about or have tuaght a billion times. you aren't doing yourself any favors by getting hung up on whether things are adequately explained... you may be right, but it doesn't change anything.

you sound pretty typical, especially the degree to which you are down on your abilities versus other people. in the end, average is average. if you are struggling, i think if you are going to spend extra time on anything it would be to review the things you had trouble with in Math I using the Math I materials. reviewing is really hard to do, but will be much more useful than going outside your curriculumn.
posted by ennui.bz at 5:25 PM on March 24, 2010 [2 favorites]

Another vote for Stroud, plus a recommendation for a text book called Mathematics For Engineers by Croft and Davison. This is designed for self-study, and leads you through key topics in a workbook style where there are spaces to write in. There's also traditional examples and problem sets. The examples are quite often tied closely to real world engineering problems, which is helpful. I found it very useful indeed. It's pitched at first year level for UK degree courses but I still have my copy on my desk while I write up my PhD.
posted by Tapioca at 6:43 PM on March 24, 2010

Instead of a lot of paper, get a small (paper sized) white board. Grocery stores here carry them in the school supplies section, or at the very least an office supply store should carry them. Too many people have bad habits such as skipping steps to save space (BAD) or correcting mistakes by over writing to the point of illegibility (BAD).
posted by anaelith at 8:15 PM on March 24, 2010

Can you find any copies of the Saxon math books? I was able to take a look at some through interlibrary loan.

They really try to present things so that you do really well on the problem sets, which builds your confidence and really strengthens your skills. A lot of ambitious homeschoolers really like Saxon.
posted by kristi at 12:56 PM on March 27, 2010

I was debating whether to invest in Spivak

for the love of god (or if you don't want to feel frustrated and stupid) don't get Michael Spivak's Calculus book...

I'm surprised to hear this. Lots of people rave about Spivak. Care to comment?
posted by rhombus at 11:19 AM on April 7, 2010

These are all wonderful suggestions. Thanks to all who answered! I have a tutor now, and I've managed to find a couple of excellent books to help me. It's amazing how much good stuff is actually out there if you know what to look for.

Again - many thanks to all who answered! AskMeFi rocks.
posted by rhombus at 11:21 AM on April 7, 2010

Okay, I just had to add this.

I got Stroud. It is absolutely INCREDIBLE. Quite possibly the best mathematics text I have ever read!

Programmes, Frames, every new concept gets tested immediately, and there are loads of practice problems.

THANK YOU!
posted by rhombus at 8:22 AM on May 9, 2010