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Updated 26 Dec 2012

Math Students’ FAQ

From “The Hidden Script”
by Sandra Z. Keith and Janis M. Cimperman
in PRIMUS for Dec. 1992.
Used by permission of the authors, and
formatted for the Web by Stan Brown


A lot of math students tend to ask the same questions or express the same frustrations, and instructors may not always have good answers on the tip of their tongue. And sometimes the question the student asks is just the tip of the iceberg and there is a “hidden script”, a deeper question that is what’s really bothering the student.

Profs. Keith and Cimperman identified 15 of these questions and gave some very good answers; they have graciously given permission to make their Q&A available on this Web server. Other than formatting the material for the Web, I have made very few changes, which are indicated in [brackets].

See also: Why is Math so Hard?
How to Succeed in Math


1.  “I really know this material, but I just don’t do well on tests.”

This is a common complaint. But there is a distinction between knowing something and having seen it before. Sometimes you may recognize the correct answer; but with real knowledge, you can construct solutions and even reconstruct the theory with your pencil. While most teachers will say that students eventually mature into effective ways of learning, we have very little to guide students in this direction, particularly as reading texts, listening to lectures, and reading notes may tend to reinforce that learning is recognition.

To get to the bottom of the problem you may have to reconsider how you study, and find more ways to make studying active rather than passive. Just as sports or music or theater performances require lots of practice before you can “pull it off under the gun”, mathematics takes a lot of practice and drill — and adrenaline is not beneficial on mathematics tests. On a practical level, one can, with experience, learn how to anticipate tests. Rewrite your notes, make up review sheets, join a study group, and really study for tests (even if you didn’t have to in high school). Your teacher teaches what is important and tests on it; but you must come to tests over-prepared. If you have a serious anxiety problem, discuss it with your teacher; there may be anxiety workshops and specially trained counselors who can help, or your teacher may suggest another solution.

See also: How to Take a Math Test or Quiz
How to Study Math

2.  “The test is too long; if I’d had more time I could have done really well.”

Speed in mathematics is actually an important measure of how well we understand the subject. In the working world, doctors, police officers, and airplane pilots all have to make fast, accurate decisions. The writing you did on the test probably did not take more than [a fraction of the time], so we have to ask how the rest of the time was spent. Perhaps you are still feeling your way over subject matter that requires a quick reaction. Do you write a lot in hopes of partial credit?

A practical suggestion is to browse through the test, allot your time, and simplify answers last. Read the directions carefully, limit answers precisely to what is asked, and always check your work line by line, to avoid going off in disastrously wrong directions.

See also: How to Take a Math Test or Quiz

3.  “The tests aren’t like the homework.”

We do feel a definite security in seeing problems identical to what we did before, but to emphasize these problems would be to validate rote learning alone. In mathematics, we do homework for the purpose of learning the material, not the other way around. Use the class period as a guide to what your teacher thinks is important, and be sure to read the text. As you work homework problems, try to see the bigger picture: why am I being given this problem, and how does it reinforce and relate to the theory?

Also, the test problems may be closer to the homework than you recognize, but you may be falling into a rote mode as you do the homework. If your teacher does not use the precise wording of the book, or blends several problems, you may then feel lost. Scramble the order of problems you work as you study for tests. And browse through other books in your library, and study with friends so you can verbalize the material as much as possible, in many different ways.

4.  “Careless mistakes keep killing me. I made a lot of stupid mistakes.”

If this is a chronic problem, your mistakes may not be careless. There is a type of mistake that will disappear and a type that is related to more fundamental problems of understanding. But careless mistakes are nevertheless a problem; for example, careless mistakes are not permitted of bank tellers, construction workers, airplane pilots, or neurosurgeons. [Not even cashiers at McDonald’s!]

Check all answers for accuracy and reasonability, backtracking line by line; and reserve time on tests for a final check. If you practice being careful as you work homework problems, you can overcome the problem of “careless” or “stupid” mistakes. But it is interesting that many students would prefer to blame their intelligence or their carelessness before their effort becomes the variable.

See also: How to Work a Math Problem

5.  “Why didn’t I get more partial credit?”

Sometimes students see knowledge as something that generates grades, and feel that their partial knowledge should be rewarded accordingly. However, a lot of partial knowledge on many topics does not add up to real knowledge, and to learn for partial knowledge can eventually lead to a “mathematical shut-down” in understanding. A teacher naturally does not want to encourage learning for partial knowledge. What may seem to you a halfway answer would probably not be accepted in most careers in the real world where small errors could send an astronaut on the wrong orbit or produce other disasters.

On a practical level, neater, more organized work will help you stay under control while working a problem. A teacher is more likely to assign partial credit if you appear to be in control of the problem, rather than flailing; and the way you present the mathematics on your test (do you work down the page or scribble all over?) may affect this perception more than you realize.

6.  “I didn’t know what you wanted”, or “What do you want here?”

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This question can cause a teacher to feel put into the role of a demagogue whose “wants” are mysterious to you. They may answer, “I want the correct answer!” If the question is incomplete or ambiguous, your teacher will not mind clarifying the question, and you should make it your responsibility to come forward (but don’t ask this question if you only want to know if your solution is correct). You may have a better understanding of the question than you say, but you may just not be able to solve the problem. Sometimes you can explain on your test how you are interpreting the question, and respond accordingly.

7.  “I knew more than the other students, and helped them, but they got a higher grade on the test!”

This has happened to all of us! But sometimes it may not be the case that you know more than the students you help; some students can focus their questions directly on what they don’t know. Or perhaps, they were simply lucky on the test, in which case their understanding probably will not carry them very far. Actually on tests, teachers are testing on a basic level, so be sure you are secure about certain classic, basic types of problems. A review sheet will help.

8.  “Why can’t the top score be 100%? Aren’t you going to scale the grades?”

Many things affect how teachers grade which are beyond their control. Their grading is certification of your mastery of the subject, and they are comparing your performance with that of students in other classes. You would probably agree that certain talents (sports, acting, music) are individual gifts, but you may feel that in mathematics, learning should be democratic and no one should fail. Actually, teams can fail (as when they lose a game).

While knowledge is accessible to everyone, and in that sense democratic, your individual effort is a definite variable in your learning, and it must be your own responsibility to do well. If no one does well on a test and the teacher maintains that the test is fair, a good solution is to review the test with a study group or tutor — it is likely this material will resurface on another test for a second chance.

[Also, remember that a curve could actually lower your grade, on a quiz or assignment where most of the class did well.]

9.  “I just don’t use the book; I can’t understand it at all.”

The text definitely is necessary for this subject, just as a racquet is to a game of tennis or a violin to a violinist; the text is the main tool for the course! But we can’t expect simply to read, track, and understand a mathematics text. Skim the book, look at the problems, and see what is needed for a good understanding. This decoding process does not happen in one pass; you may need to reread some sections many times.

You can learn to make a text work for you, especially if you read it before coming to class and then again, after class. Try rewriting sections of the text, synopsizing it in you own words. And there are many other texts in the library that you can refer to. Frequently rereading a particular passage simply is no help to us, [and] all we need is another author’s language.

See also: How to Read a Math Book

10.  “Why do I have to memorize this? Memorization isn’t learning. Besides I know I’m going to forget it anyway.”

We memorize in order to facilitate learning, so we can function with the demands of the field. Memorization is not an end in itself, and it does not constitute learning. But when you use this information, you won’t forget it. Every field requires memorization, and most fields — biology, history, physics, political science, languages — require far more. We are only able to solve problems if we are familiar with the necessary terms and laws.

To improve your memory, don’t trust your recognition memory when it comes to a test. Practice writing out the definitions and theorems, and make outlines of the major points of the theory. Check back to your text for accuracy. It is easy to think that we know something until we attempt to put it in writing. By practicing studying continuously in this way, rather than cramming at the last minute, you will find memorization will feel more naturally like part of the learning process.

11.  “Why should we do these long problems?  They won’t be on the test anyway.”

These problems are useful because they synthesize the material and get us beyond rote skills. In track, for example, runners may lift weights in practice, although they won’t be doing this in the tournament. These problems push your ability to manipulate and control the mathematics by engaging you in multi-step reasoning, and they train you to recognize where be skills you are learning can be useful.

12.  “I’ve always been good at mathematics until this course.”

Mathematics courses are built on previous courses, but unfortunately, our performance in one course does not guarantee success in another. Mathematics is an extremely complex field, and every mathematics course has new challenges and introduces new ways of thinking. There are things that are important that we aren’t learning in this course, but what we are learning is important. Also, different teachers of mathematics may stress different things. Perhaps you should discuss with your teacher what it is that is not meeting the teacher’s standards.

13.  “I can never understand my class notes; I don’t read them. I didn’t follow you that day.”

Sometimes students write down material they don’t understand, feeling that in writing it down, understanding will come. But in class, teachers may present the theory, work examples, go over troublesome homework problems, give insights into the material, respond to questions or ask probing questions. With all this on a teacher’s agenda, your notes indeed may not seem too clear!

Ask for clarifications in class at the time. If you read the text before class, you may recognize material from the book, and where you do not need to take notes; but jot down what topics the teacher discussed. Reading the text beforehand will also help you focus your questions in class in ways that your teacher will probably appreciate. Bring your text to class. And rewrite your notes, incorporating material from the book and problems. You will have created an excellent study guide for yourself.

14.  “I couldn’t make it to class yesterday; did I miss anything important?”

You may be asking if you missed something with a grade attached. But in any case, the particular information is indeed important (or we might have been tempted to miss [class] ourselves!), but the most important thing you missed is the practice of seeing and doing things with new material.

15.  “Where are we ever going to use this stuff?”

People who don’t learn or understand this material probably won’t use it, but people who do may be surprised to find where it is useful. This applies not just to the content of the course, but to its association with careful creative thinking.

It will probably be up to you to find places where you can use this mathematics. But depending on your career, you may find that things that are now obvious to you are not known to others; or on the other hand, you may find it taken for granted that you know this material and much more. But most likely, you may actually use the subject of this course and the skills you’ve gained, without even realizing it.

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