Shall we go for a run, anyone? If you sat and watched me lecture on running, and you understood everything I said 100%, but you weren't actually actively running, would you feel comfortable going out for a 10 mile run on Saturday? How about a 3 mile run? What if you showed up for my coaching sessions every week, diligently listening to what I said, and running on the track for a half hour a few times a week. Would you be comfortable going out for a 3 or a 10 mile run now? How about if you put off all your practice until the day before you were going to do the 10 mile run or the 3 mile run. Could you cram all your practice in the day before and have a good 10 mile run? Could you have a good 3 mile run?

Unless you are doing a lot of running on your own, you answered no to all of these questions. You know that in order to do something tough like run 10 miles, or even 3 miles, you have got to practice running or you won't be able to do it.

Math is a lot like running. You have to practice math to be able to do math. To perform at a 3 or 10 mile math event -- an exam or a final -- you have got to be doing some regular extended practice. This is why teachers assign homework. We are trying to get you that practice. I want you to succeed, and I know that in order for you to succeed, you are going to have to practice some mathematics. Just like with running, you are better off spreading out your practice. In math, working problems 30 minutes to 1 hour a day, every day, is better than trying to do everything in one day right before an exam. Besides, if you leave everything for the last minute, where can you go for help? The students with the highest grades in the class almost always have perfect or near-perfect homework scores. The worst grades in the class inevitably go to students with lackluster (at best) homework scores. Coincidence?

Yeah, but I'm no good at math.

Some people are better at math than others, just like some people run faster than others, and some people need glasses to see while others don't.

The truth is that most people are capable at being competent at math. Just like most people without serious health issues or disabilities can learn to run 3 or 10 miles.

By the way, I'm no good at running. I'm not talented at it. I'm not fast, and it's not easy. I've still done a half marathon.

The hardest part was to get started which required me to believe that I could do it and to find steps I could do to get me there.

If you will work on the first, believing you can do it, and bring in the motivation to try, I will help you identify the steps to take. Math is hard. I've had bad teachers. You've got a point there. Math is hard. You can't skip one part and still be able to do the rest. Later material depends on earlier material. There are also some bad teachers out there. I've heard some horror stories. I've lived through a few horror stories. You already know that there are a lot of worthwhile things that aren't easy. In martial arts and Zen philosophy, you'll often hear, "Just chop the wood and carry the water." That's all I want from you: just do work you know you have to do. Do that homework diligently and well. If you are conscientious with today's job, the big picture will come together. What is math good for anyhow? Sometimes it is hard to see what application a given piece of math has in the real world. This is often because we are learning one skill in order to progress to a harder skill.

Most of us learn to crawl before we learn to walk. We needed to have our bodies understand crawling before we were able to have our bodies understand walking. How often do we crawl once we have learned to walk?

Likewise, what is a pushup good for? It is good for building strong muscles.

What is math good for? It is good for building "brain muscles". Logical, clear thinking.

And what is that good for? It is good for increasing your income. More math = More money. Whether or not you see the point right now, chances are good that your wallet will see the point after you graduate.

You might want to check out:

• When will I use math?
• NPR on Math Skills Translate into Bigger Paychecks.

Steps to success

Do your homework. We covered that one already, and you've been hearing it for years. Math is a subject best studied with a pencil in hand. Do you have a hard time getting started? Does the thought of spending hours on math homework make you want to scream? Instead of putting everything off to the last minute and struggling with it for hours, try using the 15 Minute Rule. Even you can handle working on math for a measely 15 minutes.

• Ask questions. And when you get an answer, summarize that answer to the person who explained it to you.

  The smartest student I ever taught would always say to me, "Let me see if I understood you correctly." He would then tell me what I just told him. Usually he had it. Sometimes we realized we needed to talk further. He didn't have the highest IQ or the best math abilities, but he used his intelligence better than anyone I have ever met before or since.** He also got a solid A in my class. No surprise there.
  

• Explain to someone else. This is probably an even better way to learn than doing homework. Every math instructor you will ever meet will tell you that we learned a lot the first time we taught a class.
  
  
• Find a friend or a group to study with. One caveat here: you have to find someone or a group that you actually study with. If you copy someone else's work, that won't help you, duh. Everyone tries each problem, and you help each other out when you are stuck.

  If you are more motivated by people than by problems (I am), this might really help!
  

• Take advantage of all the resources at your disposal. Class, your teacher, Week in Review, Help Sessions should all be no brainers.

  Another resource is Google. What? Isn't that cheating? If you look up a solution, understand it, and cite where you got it, that is not cheating. The fact that you had to work to get it will help it stick with you.

  You might also want to check out Wolfram Alpha.

  Now that you understand that problem, go explain it to someone else!
  

Math Anxiety.

If you have math anxiety, please go visit the Student Counseling Services.

If you have repeated, debilitating anxiety, please talk about it to your personal physician or visit Student Health Services (free to students during regular hours!) and emphasize to your physician that you are in real distress. Don't tough it out, get help. I've suffered from debilitating anxiety too; it makes it difficult to get through the day and really difficult to do math. Here are some links on math/test anxiety: Brain Study Points to Potential Treatments for Math Anxiety TAMU's Student Counseling Services Self Help Sheet. Math Academy's coping with math anxiety. Math.com's Math Anxiety Page. About.com's Overcoming Math Anxiety. Texas State University's page on What to do about Math Anxiety. The College Board's page on Battling Math Anxiety.

What other people have had to say to me about this essay on success at math.

Andrew: A good thing I find is to start homework early -- not just so you're not rushing it, but also because problems sometimes need to "percolate" -- you need to sleep on things when you get stumped.

Nancy Goroff: Your comments are terrific. One of my favorite chem textbooks states in the introduction (paraphrasing here) "Chemistry can only be learned with a pencil in your hand." I have had many students come to me trying to figure out why they were doing poorly, when they'd been working so hard. It turned out, inevitably, that what they'd been doing is reading, and rereading, the textbook, but they had never quite gotten around to doing the problems.

Timo: Liked it. I would like to stress what Andrew said: start as early as possible and look up stuff you don't understand. Then just let it "sink in". I often take a sheet of paper and start doodling if I have no clue on how to tackle a problem.

Are you a student or have you struggled with math? Do you have any suggestions for me to put here? I would love to hear from you! You can email me at jmlinhart@math.tamu.edu.

What other instructors and institutions suggest for success at math.

• Janice Epstein's tips for success at college math.
• Joe Kahlig's study skills for success. Taken from Department of Student Life.
• St. Louis University's Success in Mathematics page
• Adult Learning Success at Math
• The Purple Math Homework Guidelines is a really good guide with specific suggestions for how to do homework.
• Middle Tennessee State University's help for math anxiety and math study skills

(C) 2009 Jean Marie Linhart, all rights reserved.
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