White Bar

"The exertion of the mind...is the most strenuous and exacting work of all."

 

Hugh Nibley

How to survive a math or statistics class

Lightly revised on 2012-04-20

 

(Note: This is a work in progress. I haven’t finished hacking—I mean—writing this document yet. If you have found something that helps you succeed in your coursework that’s not listed here, or if you face a challenge for which the following does not help you, please email me at brownd@byui.edu so that we can discuss it.)

 

Much of the following is expressed in terms of math classes, but it all applies directly to statistics classes, as well as classes in other disciplines. I used to teach a study-skills-for-math course. Much of what follows is inspired by material from that course. The rest is inspired by my own considerable experience as a student of mathematics and statistics, and by things I've learned from working with students.

 

Not everyone will benefit from every tip listed here, but most people will benefit from most of them. They take time to implement. For a three-credit math class, most students find they have to spend an hour or two (or more!) outside of class each day on math, five to six days a week. (Yes, this is more than the usual "two-hours-out-of-class-for-every-hour-in-class.") If it turns out you need that kind of time but can’t make that kind of commitment, look at adjusting your plans or letting go of something that you’re doing.

 

 

Basics

The importance of basic things like good nutrition, adequate sleep and attention to spiritual matters cannot be overemphasized. Praying regularly, studying the scriptures, attending church meetings, magnifying your calling, keeping the commandments, and so on, clear your mind, make you a fit dwelling place for the Holy Ghost, and help you balance the use of your time. These things form much of the basis for success in all aspects of your life. They also increase your sense of well-being, your self-confidence, and your hope---something we all need when facing those tough math problems! I’ll assume you’re already doing all these things effectively. If not, then you need to make appropriate changes in your way of life, starting right now. Get appropriate help from knowledgable and authoritative sources, when necessary or desirable.

 

You will also find that it takes a great deal of discipline to inculcate good study habits in general, and good mathematical habits in particular. STAY WITH IT! I’ve known students to drop or fail the same course three and four semesters in a row. Usually, the main reason for not progressing is failure to persevere.

 

 

Emotional issues

Many students carry negative emotional baggage where mathematics is concerned. This baggage interferes with learning math. Sometimes, merely talking over bad memories with a trusted confidant is enough to relieve this burden. Some students benefit from writing about their bad experiences. Others actually need professional help, such as is available in the Counseling Center. Professional help may be especially needed if the student’s emotional difficulties with mathematics are connected with deeper issues, such as chronic illness, poor self-image, depression, learning disabilities, abuse, or many other things we could name. In any case, fasting and prayer are always appropriate tools for working through emotional difficulties.

 

 

Schedule time for Math each day

[The whys and how-tos will appear here some day, but refer to the section of this document entitled "Basics."]

 

 

How to read a Math book

Read the text before going to class. Connect what you read in each paragraph with what you read in other paragraphs. Sometimes in math or stats books, a concept is named or otherwise introduced before it is explained. So, sometimes you need to keep reading to understand a given sentence. Make an outline of the material you read. (Outlining helps more than highlighting because it engages more of your brain.) As you read, work the examples in the text; don’t just read them. Make a list of questions to ask your instructor or your tutor (but wait to ask until the material has been covered in class.) Make a glossary of vocabulary words and their definitions, with examples for each. Read the material again, as soon after going to class as possible, and compare what's in the text with what's in your notes from class (see "Attending Class," below), double-checking your glossary to make what you've put there is correct.

 

Try making vocabulary flash cards for memorizing vocabulary, and practice reading and writing sentences that use the vocabulary correctly. (If you find yourself using pronouns a lot while talking about mathematical or statistical concepts, try substituting the correct technical terms. If you can't, it probably means you don't understand the vocabulary yet.) Create your own examples of things defined in the material you're reading, (writing down the reasons why your example fits the definition) and ask a fellow-student, tutor, or your instructor to check your work. If you find the text just too hard to read, even after honestly trying, day after day, for a few weeks, look for another text that covers the same material. Try the library, your roommates, friends and family members. Also, there are some very good materials on the Internet. (There are also some very bad materials, and different authors may take different approaches. If you study math or stats on the Internet, try to find reputable websites. And check what you're learning there with fellow-students, your tutor, or your instructor, especially if it seems different than what you're learning in class.)

 

 

NOTE: Whether you get use certain suggestions in the next few sections may depend on your instructor's policies. Make sure you "follow the rules," so to speak.

 

Attending class

Attend class faithfully and punctually. If you're late for class, you're late---it's not the worst thing that could happen. Attend anyway, unless your instructor tells you otherwise. Take notes, however minimal, making sure you write the day's date and some words indicating what the notes are about. At the very least, you should write down any announcements your instructor makes. Do not hesitate to ask for clarification of unclear announcements. As course material is presented, you need to write at least enough so that you will be able to tell what was covered that day. You may not need to write everything your instructor writes on the board (or projects on a screen), but you may need to write things that your instructor does not write on the board! Always listen for the still, small voice during class. Often, this voice will tell you things that should be in your notes that no mortal in the room will ever think of telling you. These items can be the most important ones you write down that hour. And if notetaking isn't realistic, say, because you can't simultaneously concentrate on what you're writing AND what the instructor is saying, ask the instructor if you can copy their notes or have access to their PowerPoint slides, or whatever. You might also be able to work something out with a fellow-student.

 

At appropriate times during class, ask questions, including questions from the list you’ve made while reading the text. Try not to ask a question about material that has not been covered, unless it appears that the instructor has skipped the thing your question is about. Also recognize that questions about administrative matters (when is this due, what will the exam be like, when will we get our homework back, etc.) are usually most appropriate at the beginning or at the end of the class period. Depending on your instructor, it may be more appropriate to ask such questions by phone or by email. And some questions are best asked outside of class, especially if they concern you and no other student. And some questions---especially rude or sarcastic ones---are best left unasked!

 

Remember that the classroom constitutes a social context. Try making the best of that context for yourself, but also be sure to provide the best social context you can provide to the others in the room. All the ettiquette anyone's tried to teach you applies. St. Paul's description of charity in 1st Corinthians chapter 13 is very good advice for students in the classroom (and everywhere else!) Talking out of turn is ALWAYS a no-no, even if it's just to ask a fellow-student to repeat what the instructor said. Never make any disparaging comments about anything. In any case, everything that you say or ask in the classroom needs to be on topic and socially appropriate.

 

One of the biggest favors you can do for your fellow-students is to ask questions. I read somewhere that when one student has a question, typically about a thrid of the rest of the class has the same question. So go ahead and ask, unless the instructor has asked the class to hold their questions until further notice.

 

If you miss a class period, get notes from someone that takes notes (hopefully good ones!), but do not photocopy them. Copy them by hand, working through them just as you would your math text. This makes the material pass through your brain, whereas photocopying does not. As you copy the notes, try to understand what you’re copying. If, after you've made an honest effort, you still don’t understand, ask the person whose notes you have borrowed. There's a pretty good chance they'll be able to recall the context of the unclear item and to tell you what they were thinking when they wrote what they wrote. Often, that's all you'll need to be able to figure it out. But if that doesn’t help, ask your instructor, a tutor, another fellow-student, or some other knowledgeable person.

 

 

After class

As soon after class as you can manage, read the notes you took in class and compare them with the relevant material in the text, noting similarities and differences between the material as presented in class and the material as presented in the text. Sometimes, your instructor will intentionally skip material in the text, present material not in the text, or tell you to do something differently than the way it’s done in the text. Make sure you make note of these things, so as to save yourself trouble later.

 

At this point, you’ve been exposed to the course material three times already, have gotten answers to many of your questions, and have seen examples worked by others and tried some yourself—all before you even try the homework! Students who follow this plan find that their homework is easier for them (and they finish it more quickly), they get more out of class and homework, and studying for exams is easier. All these are signs that they're having more success mastering math!

 

 

Homework

Procrastination kills more grades than anything else, so get right to work as soon after you get an assignment as you can. (But make sure you've covered the material first, either by yourself or with the class, or preferably both.) You may need to work lots of exercises. If your instructor does not assign very many problems, you may need to work extra ones, just to solidify your understanding and help you gain confidence with the concepts and methods being used.

 

Spend more of your time and effort on problems that are hard for you than on the ones that are easy. After all, harder problems are usually harder because you have not yet figured out everything you need to. You'll have a better chance of figuring it all out by working on problems that address those things than by working on other problems.

 

Many students find that they don't understand exercises, problems, or questions they read. Often, this is because they need to (1) pay attention to the grammar, (2) make sure they have internalized every word and every symbol, and (3) make sure they actually understand the vocabulary. There is no shame in picking up a dictionary or referring to the text or the glossary you're keeping. There is no shame in asking questions about the meanings of the things you read. And there's no shame in asking about the grammar. (In fact, pretty much anybody would benefit from reviewing grammar from time to time.)

 

If you find yourself skipping over words, symbols, or technical terms while reading, there's a good chance you haven't yet figured out what those words or symbols or phrases mean. This suggests a course of action: Go figure them out, ask questions, get help, etc.

 

As you work problems, ask yourself not only how to solve them but why they are solved in the way you are solving them. How do the principles apply that you’ve been learning in class? How does the author of the problem use vocabulary terms? Are you using the terms correctly yourself? If you see more than one way to solve a problem, compare the two methods, looking for advantages and disadvantages to each, comparing their complexity and difficulty and how the different methods use the same or different concepts. Stop yourself from time to time and look back over the problems you’ve done already. Look for patterns in the problems themselves, in the tools you've used to solve them, in the presence or absence of vocabulary terms, in the principles and concepts used and in anything else that may seem even remotely relevant. If you can’t find any similarities or differences, talk to a fellow student, your instructor, your tutor or any knowledgeable person. They may be able to shed some light on things for you. And even if they can’t, sometimes just discussing math with someone else can enable your brain to make connections it couldn’t make otherwise.

 

Also look back and make sure you've done the right problems for the assignment, and that you've completed them all. Make sure you've followed all instructions. If you can’t finish the assignment on time, discuss it with your instructor. Even if they don't allow you to turn your assignment in late, they may have ideas about how you can find more success.

 

 

If at first you don’t succeed. . .

Bear in mind that you can learn a great deal by trying to solve a problem and not succeeding. Sometimes, trying to solve a problem in a certain way, then finding that it doesn’t work, can help you understand the bounds and limitations on a mathematical principle, tool, or method. It can also shed light on some concept that was less clear to you before. It can also suggest to you some other approach that may be more appropriate for the problem you're working on.

 

 

Beyond assigned homework

Keep studying your notes and the text, and keep working problems until you feel comfortable with the what, the how and the why of the topic at hand. If you get to the point that you can explain it more or less clearly and fluently to someone else, chances are pretty good that you understand it yourself. Then try again a week or two later and see whether you can still explain it. If not, well, you know what to study!

 

 

Studying for a math or statistics test

Contrary to popular belief, you can start studying for an exam long before you find out what's going to be on it. Most exams will mostly cover whatever your instructor has been covering in class since the last exam. This means that reading the text, going to class, taking notes and studying them, and doing the homework are all part of preparing for an exam. It also helps to write your own review of the material, rather than depending on the canned reviews you find at the end of the chapters in your math book, or even that your instructor may give you. Also, most people benefit from working extra problems. In fact, you'll benefit more from working additional problems than from going over problems you've already done.

 

One very important part of studying for a math or stats test that most students overlook is to truly learn the vocabulary. Like any other discipline, math and statsitics have their own jargon, which must be learned. If nothing else, knowing the vocabulary will help you understand the problems you've been asked to solve. It will also help you "get into the mindset" of mathematical or statistical thinking, which will help you solve problems. Often, translating directly from English (or whatever language) into math will, by itself, show you how to solve the problem you're working on. Then, when it's time to write out your solution, using the vocabulary correctly increases the chances of communicating clearly and correctly with your instructor. This is very helpful at any time, but especially so on exams! Confidence with the vocabulary supports confidence in pretty much all other aspects of your mathematical or statistical efforts. This translates directly to less stress before and during exams.

 

To learn the vocabulary, start by creating your personal glossary of math terms as you read the text. Be sure you write down the correct technical definition of each term, and at least one example. You can add an informal description of the term's meaning if it helps you, as long as the informal description agrees closely with the formal definition. (If you have trouble with this, feel free to ask a tutor, a classmate, or your instructor for help.) Practice reading (and understanding) sentences in which the vocabulary terms are used correctly. Get together with some fellow-students and quiz each other on vocabulary. Make flash cards with the term on one side of the card and the meaning of the term on the other. You can schedule time for studying your flash cards, but you can also use them for studying during odd moments when you have a little time, like when you're waiting for your ride or whatever.

 

[I'll add more to this when I have a chance, but if you only do what I've written above, you'll have gone a long way toward being ready for your exam.]

 

 

Preparing for the final exam

[Watch this space! Meanwhile, please note that all the stuff on preparing for exams is relevant here.]

 

 

Taking a Test

[Coming someday to a website near you!]

 

 

Study groups

I tell my students that they should feel free to study together, but everything they turn in must be in their own words. Other teachers may have other opinions on this point, so check with your instructor before working with your classmates. In any case, study the material yourself before getting together with others or your tutor to study. This will make group study time much more effective and efficient. Some students tell me that their individual study is so ineffective that they go straight to their study group. These students may do well enough in a group setting, but often cannot fend for themselves.One of the reasons for this is clear: They haven't had adequate practice studying effectively by themselves. If this is you, please implement those tips you find on this webpage that seem likely to be helpful.Most colleges and universities hire people for the express purpose of helping individual students improve their study skills. Please use the available resources appropriately.

 

 

Tutors

If you think you’ll need a tutor, get one early on, before a crisis develops. Tutoring can get you out of a bind temporarily, but tutoring is incapable of overcoming crises. (I learned this by tutoring for years as a graduate student.) If your personal study habits are good, then you’ll get more out of tutoring than you would otherwise. Also have a list of issues or questions ready when you go to meet with your tutor. It’ll make the appointment more productive. If, after a few sessions together, you feel that working with your tutor isn’t working for you, don’t hesitate to get a different tutor. You may have to advertise vigorously to find one, but it can be worth the effort.

 

 

Your instructor

Your instructor is an expert in the subject they're teaching you. They (presumably) have a great deal of knowledge, certainly more than your fellow-students or your tutor. They are an important resource for students. One of your instructor's jobs is to answer questions you may have. In my experience, most instructors are willing (if not happy) to do so. However, it is possible to abuse your instructor's willingness and obligations. You need to strike a balance between relying on yourself, your fellow-students and your tutor on the one hand, and your instructor on the other. Questions about administrative matters should always be directed to a person in authority, which is almost always your instructor, and not to other students or tutors. Questions about content, software, and the like need different handling.

 

When a student comes to me with a question about a topic, principle, vocabulary term, statistical or mathematical method, software, or what have you, I always appreciate them having first made an honest effort to develop their own understanding. Sometimes, an honest effort includes setting the thing aside and trying again later. Sometimes, it includes going back to the text and the notes over and over again, making sure you understand the vocabulary terms. Sometimes it includes taking one's questions to one's fellow-students or one's tutor first. Sometimes, there isn't time for any of that. As a rule, unless you instructor tells you otherwise, it's better to ask than to not ask. So ask your questions.

 

Now, if you go to your instructor with questions day after day after day, and if there's no indication that your ability to study by yourself is improving, you are probably wearing out your welcome. Also, you probably need a different kind of help than the help your instructor can give you. Ease off your instructor somewhat—at least for a while—and seek that help. Most colleges and universities have resources for helping students study more effectively and more efficiently. If honestly trying to do the things they suggest (and the things on this web page!) does not make a significant improvement in your success, please consider being tested for health or other conditions that might be impairing your ability to learn. (Frankly, for most students that find themselves in this situation, the real problem is a lack of confidence. This is not a strictly academic problem, and therefore doesn't fall strictly within your instructor's purview. Any college or university of any size will have someone who can help you with confidence and a host of other issues. Their title is often something like "counselor." Don't let that bother you. There's no shame in getting this kind of help.)

 

I've had students come to me with questions two and three and four times a week. If they've honestly done what they could to get their questions answered first, if their questions are substantial, and if I see evidence that they're actually learning (e.g., they don't ask the same question many times) then I'm happy to help. Of course, everyone has time constraints. The problem with being the instructor is that if a student doesn't get seomthing done then the student has a problem, whereas if the instructor doesn't get something done, then many students have a problem. So respect your instructor's time. Be prepared. Have a list of questions or other concerns. If any physical materials such as papers of textbooks are involved, have them right ready, so you don't use your instructor's time hunting for things you're pretty sure you put in your backpack. (Actually, this is good advice for any meeting with anyone!)

 

Hmm... The foregoing might sound discouraging to some. It's true that some instructors are more willing to help than others. But if you have legitimate questions and you've tried to get them answered, your instructor is obligated and usually willing to answer them, or at least to try to answer them. It's what we're here for, after all, we instructors: to help students. So don't be shy about it. Go ask your instructor your questions.

 

 

Technology

Technology presents its own set of challenges in a math or stats class. Tools used in such classes can range from paper and pencil, or compass and protractor, through calculators and desktop software, to distributed computing. Make sure you understand your instructor’s expectations for your use of technology. Don't just do the minimum required by your teacher, being grateful you haven't had to do more. Practice using the technological tools your class uses until you feel confident in using the tools, in troubleshooting your own minor technological problems, and in interpreting the results that the tools give you. Practice figuring out how to do things on your own. Read any instructions that come with your technology, including online manuals. Learn how to care properly for your mathematical tools. As with all things, do not hesitate to ask questions about how the tools work, and how to use them.

 

 

Getting behind

No one likes to think about it, but most of us get behind at some point. When a student finds they have too much to do, their math or stats class is usually the first thing to be sacrificed. The problem is that such classes are ususally the hardest ones in which to get caught up. If you find yourself falling behind, don't promise yourself for weeks that you'll get caught up. Go to your instructor at the first sign of falling behind. Make sure you understand how they handle things like late work or missed quizzes or exams, or whatever's relevant. Many instructors will sympathize to some degree but not allow anything to be turned in after it's due. If you wait to talk to them until you finally overcome your embarrassment and get around to it, you may find that you have missed too many deadlines to have any hope of passing the class. If you talk to them when you first start feeling things slipping, you'll be in a better position to prevent or avoid such undesirable consequences of falling behind. Of course, you'll need to prioritize and plan accordingly, but even if you have to make some sacrifices to get everything back in balance, you probably won't have a disaster on your hands.

 

If you're behind, you need to be honest with yourself about why you're behind, for two reasons: first, to have the best chance of fixing the problem so you can catch up; second, to help prevent or avoid getting behind in the future. Different reasons for getting behind often require dfferent treatment. Whatever your reason(s), catching up almost always requires that at some point, you will have a greater need for being organized than you usually do. Before saying anything about that, I'd like to take a look at some of the reasons for getting behind. The list won't be exhaustive, but it should serve to help you start thinking usefully about your own situation.

 

  1. Problems with physical heath: [To be continued...]
  2. Impairment of hearing or vision: [To be continued...]
  3. Problems with mental, emotional, or social health: [To be continued...]
  4. Lack of motivation: [To be continued...]
  5. Problems with spiritual health: [To be continued...]
  6. Having too much to do: [To be continued...]
  7. Being disorganized: [To be continued...]

 

[I'll put more here when I get the chance.]

 

 

Getting caught up

The sooner you start working on getting caught up, the better off you'll be. Here's a list of steps to take. It's a rough draft and needs substantial editing, but at least it can get you started.

 

  1. Examine the work you haven't done or finished and make a careful, thorough list of it all. At this point, you're just trying to identify all that needs doing; try not to worry about how you're going to get it all done.
  2. Make sure you understand correctly your instructor's policies on missing or overdue work. A conversation about your individual situation needs to wait, however, until you've used the following steps to prepare for it.
  3. Consider honestly the amount and kinds of help you need. Do you get slowed down by questions that go unanswered? Are you having organizational problems? Are you just discouraged? Think of every relevant thing you can. At this point, you're just identifying the help you need; don't worry about how to get it.
  4. Try to identify sources of social and emotional support, if you feel you're going to need them. Symptoms that you will need such support include fear, hopelessness, feeling overwhelmed, etc. (Your instructor doesn't need to hear anything about this.)
  5. Students that have been having more than the usual success are telling me it's all about simple things, like eating right, getting rest and physical activity, and giving a little more attention to their spirituality. So you might look into this, if you feel it's relevant. (Your instructor doesn't need to hear anything about this, either.)
  6. Estimate how much time it will take you to do what needs doing, as realistically as possible. You'll refine this estimate later, when you have had some experience actually working your plan.
  7. If it looks like catching up will take more time than you'll have, take a good, hard look at your priorities and consider cutting back somewhere (whether on quantity or quality). If you find you are unable to do so, it may mean that you need some of that social or emotional support. You be the judge. But if it really is impossible to get it all done, you have to let go of something.
  8. Prayerfully set some initial goals for getting it all done, realizing that your goals may need adjusting at some point. Normally, I recommend keeping current on the current material and filling in what's overdue as you're able. However, there may be other factors, such as your instructor's policies, the timing of exams, and so on, that may make a different approach more realistic.
  9. When you've done what you can about the above, go talk to your instructor, just as soon as you possibly can. Keep the conversation short. Tell your instructor exactly what needs to be made up, how you plan to get the help you need, and what your goals are for getting it all done. The fact that you've thought it all through will help your case. Of course, your instructor may see things differently than you, and can probably help you refine your estimates of the time required and other things. Be humble. Accept whatever counsel your instructor gives you (in righteousness, of course) and show a willingness to do what you can, when you can, and to "give and take," as the saying goes. Your instructor has had more experience in this sort of thing than you, after all. At the end of the conversation, make sure you and your instructor agree on what you'll be turning in, and when, and for how much credit, and on whether and how you will report your progress. This will help prevent future misunderstandings and their accompanying disappointments.
  10. As you work on your goals, be sure to turn in materials when your instructor expects you to. If you find you can't finish things in time, you might try discussing with your instructor a more realistic set of goals. But do not abuse their good graces. It's better to turn in something incomplete than nothing at all (unless your instructor tells you otherwise). Report on your progress according to the plan you have made with your instructor. This sort of reporting is very important, and can make all the difference between success and failure. Don't worry about things like being embarrassed or looking like you're falling short in some way. Just report, regularly and often. Accountability is important, and reporting gives your instructor a chance to support you, as well.
  11. Persevere. Keep up the good work, meet your goals as best you can and enjoy your new-found success.

 

 

Last words

If, after honestly trying you best to succeed in the course, you decide that you’re in over your head, talk with your instructor, your adviser and your Heavenly Father about it. They are here to help you.

 

If none of my ideas work for you, ask someone else for advice. There are plenty of good ideas out there. Your college or university probably has some kind of study skills center or classes on how to study. These can be well worth the investment of time or other resources. And don't overlook the possibility that there may be something different about you, something the mainstream of education isn't designed to handle. The things I see most often are Attention Deficit Disorder and math anxiety. There is help for such things. You owe it to yourself to be humble enough to look into them, if there's reason to believe some such thing is relevant.

 

Above all, hang in there. Persistence prevails. And who knows—maybe you’ll find out math isn’t so bad, after all!

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