Math 227 Section A Syllabus Winter 2003

A graphing calculator is required. The TI-81,82 or 83 is recommended. Laptops or large-format calculators such as the TI-9X series may not be used during tests. Some tests/quizzes might be done without calculator.

I will presume that you are actually able to do on demand most of the things that are taught in the prerequisite classes. For this class that means Math 124 and Math 125 - the first two quarters of calculus. It would certainly be useful to have Math 126 too. Unfortunately, as with many things in this life, if you don't use it you lose it. Having taken these classes years ago is most certainly not enough. You must actually be able to perform the tasks learned in those classes. When prepared it takes most students 10 hours or more each week of homework to earn an A or B grade in a college credit math class. Attempting to refresh prerequisites while taking 227 puts the weekly time commitment beyond the reach of most students and almost always yields a poor result.

Important Dates :

Grades will be based on 5 Quizzes (10 points each), 3 Tests ( 50 points each ) and the cumulative final (50 points). The final score, in addition to its fixed 50 point value, can be used (if that is to your advantage) to replace one low or missing Test or the Quiz total. This can be a benefit if you get sick, are called out of town or just want to take a "personal holiday" on one test day. Homework problems will be recommended as we go along but not collected. We will, however, spend much of the class time going over the assigned problems. You are responsible for showing up on test days. Please DON'T ask to reschedule, and I don't give make-ups.

Grade lines will be given when I hand back the tests. Please record the grade lines I give as the course goes along so you know how you are doing. (Add up your scores, add up my grade lines and compare.) At the end of the course I will add up my grade lines to give the overall grade lines. There is no opportunity for "extra credit." Grade lines will be no higher than 65%-C, 80%-B and 90%-A.

Cheating is a poor way to try to pass a course and the faculty here at BC has agreed to be tough about instances of cheating and to announce this in our syllabi. If caught, at the least cheaters will receive an irrevocable 0 on the test in question and other administrative action is possible that may, for example, affect continued student status. Don't do it.

My tests are timed and there is a bit of "time pressure" if the student is uncertain of the material. This is intentional on my part.

One reason is that both you and I need a "reality check" periodically throughout the quarter. It is very hard for the student (and for me in conversations with students) to tell the difference between "familiarity" with the material in the sense of "recognizing" it if someone else does it, and actual mastery of the material. Even if you can get an answer, but only after false starts and checking the book and your notes and so on, you are STILL not quite there.

I don't want students to be "discovering" how to do unfamiliar problems on the tests. I want them to recognize the type of problem immediately and go right to the solution technique: to demonstrate mastery of the material. Acquisition of the ability to demonstrate mastery is the point of all your homework. My tests are designed to reveal who can do this and who cannot and at what level.

Few people like tests and, in particular, few of my students really like my tests. But there is an important point to doing it this way: I want students who earn a good grade in my class to feel confident that they have the tools they will need to succeed. This math class does not stand alone. It is part of a sequence leading to higher math classes and other classes where the material is applied. If the student is not "fluent" in the techniques of this course, he or she cannot hope to flourish in these subsequent courses. My usage of the word "fluency" is the same as if this were a foreign language class, and the reason the student must be fluent is the same.

Imagine the following scenario:

A student tells me that he or she can read French and I present that student with a copy of "Le Monde" and ask the student to translate the front page. The student replies that this is terribly unfair. The student says that he or she is "left brained" or "right brained" or something and cannot be expected to just sit down and read the paper, even though he or she says "I really do know how to read French. I just can't do it when you ask me like that."

The student claims that to demonstrate reading ability it is sufficient to be able to translate specific articles with much more time. The student claims that it would be more fair to allow the use of a dictionary and a grammar outline, and that this "test" would still demonstrate reading mastery.

After passing this test the student believes that a French literature and a French poetry class should be within reach.

Sound silly? Well this same argument, with "math" substituted for "French," is used without blinking an eye in almost every math class where tests occur. My response, when it is used in my class, is always the same.

To reiterate:

I know my math tests are fairly hard. That is because I need to find out if you have learned well the many techniques we study in the course. I need to find out if you recognize problems right away, or if it takes a long time before you can dredge something up. This correlates with how much time you have spent on homework outside of class, and with how well you will be able to use the techniques when they are small parts of much longer problems in later courses. Typically you will need to spend two to three quality hours of study outside of class for every hour inside to succeed. It may take some people more, and some less. However much time it takes you, your grade will be based on your ability to perform on the exams, and not on whether I like you or feel you deserve to pass or because you really need or want a certain grade or because you like math or don't like math. Except in the case of a documented disability, that performance must take place in the class on the day of the test within the time limits I set.

I do not give the "HW" grade to conceal, from those who will try to evaluate your transcript, the result of an unsuccessful attempt to take this class. If you need to withdraw you must do so by the withdrawal deadline.

If my attitude toward these matters does not work for you I strongly encourage you to shop around for an instructor amenable to alternative theories of education.

We can save quite a bit of class time by dealing with the repetitive "Will this be on the test?" question right here in the syllabus.

I will respond to the question "Will this be on the test?" by referring the student to the following statement:

My feeling on this matter is that if you concentrate on understanding the material and the ideas in the class the tests will take care of themselves. I try to telegraph clearly the type of material that will be on tests but I avoid saying that any particular problem will be on the test. This is because I want students to master everything and not focus on a few trees (at the expense of the forest) too early.

With that as the ideal, I do understand that students have to make decisions about where to target their study hours and how to prepare for and take these tests. I have some suggestions of several different kinds that apply not only to this class but to many classes and testing environments:

• The more basic a topic is the more important it is. Don't spend all your homework time on the really hard problems thinking you will "get back" to the easier ones later. Do all the easier ones first.
• NEVER get behind. This is vital. When you are behind any lecture time is largely wasted time and difficulties compound rapidly. Often when students get behind they never completely catch up.
• Even better, you might read in advance the section or topics in the text that you anticipate will be discussed each day in class. Look at the pictures. List special words in the text whose meaning seems to be new. Try a few of the easier problems. The goal here is to maximize the utility of a scarce quantity: class time. Remember that in college, unlike grade school or high school, two thirds or more of the learning must take place outside of class. The way you organize those hours should be tailored to fit your particular learning style or styles. You can use class time for the "early" part of learning a new topic, or the "later" part. But using class for the "early" part is practically no different from having the instructor read the book to you. It might have some benefit, but the instructor has little to offer at this stage beyond what is written in the text. It is only when your learning has progressed to a "later" stage that the experience and insights and connections that can be provided by a skilled practitioner will make sense to a learner. You will be better off if you do the preparation that will put you at a "later" stage by class time each day so you can take advantage of this.
• Come to class every day. Even if you are unprepared for the topics of the day, it is better to show up than to skip class. Many things happen in class each day, not just the introduction of new material. Questions about class organization pop up, old material is reviewed and hints for potential test questions are given. Pay particular attention whenever I say a topic is vital. That means that the topic will certainly be included in some form at least in the first draft of a test or quiz and likely the final too. You won't know about these things if you are not in class.
• Pay very close attention on the days that I return the exams. I will usually go over every problem on that day and talk about each problem and how it fits into the bigger picture. It is a good bet that anything that is discussed will find its way into later tests or the final.
• Don't be afraid to "leave your comfort zone." Everybody has talents and particular skills that come easily. Chances are you are already operating pretty efficiently in those areas, and even use those skills to compensate in other areas where they might not be the most effective tool. You will maximize the effect of study time if you consciously move away from your strengths. Let me give a simple example to illustrate the point. Suppose there is a test of two skills, one of which is your strong area and the other your weak area. Suppose you are at 90% of mastery in your strong skill and 50% of mastery in your weak area. If half the questions on a test correspond to each skill you might score (.9)50 + (.5)50 = 70 points on this test without further study. By concentrating study time only on your strength you could do no better than 75%. But by throwing all your study time at your weak area you could possibly do as well as 95%. In practice, a law of "diminishing returns" makes this effect even more pronounced, since the last 10% of "mastery" is probably harder to achieve than the first 90%. The bottom line : "Comfort Zone" = "Stasis." If you are in a state of confusion, as unpleasant as that might seem, at least it means that you are actually facing your weak areas. Progress lies down that road.
• Obviously, people who have efficient test taking technique do better on tests and in classes than people who don't. Remember the goal while taking a test. Perfection is not for us on this mortal coil. While 100% is nice, it is not necessary for an "A" and should not be your explicit goal when taking a test. The goal is to maximize your score given what you know in the time allowed.
• When you are taking a test with a time constraint, go over it several times. On the first pass read the problems carefully and pick off the easy (for you) points.
• On the second pass, concentrate on those problems that you know how to do but which involve longer calculations, more steps and so forth.
• On the third pass you want to work on the really hard problems or the ones that you don't know how to start. If you are going to run out of time on a test, you want that to happen with one of these left to do rather than an "easy" or "medium" problem.
• Also, even if you are not sure of a problem, write down as much as you can about approaches you think might help in solving it. If the logic takes you far enough toward a solution I might give some partial credit points.
• Finally, on every type of problem you should have a way of estimating or checking (at least roughly) to see if your answer is reasonable. If you come up with a solution and realize it can't be right but you cannot find your error tell me that. The fact that you realize there is something wrong will count in your favor and I will be hunting for reasons to give you partial credit. Think of these "estimation" techniques as insurance. A ten second check can provide backup support for ten minutes of work. If you don't have means of checking then every time your pencil touches the paper you MUST be right. You work without a net. Checking as you go gives you the freedom to be wrong - and then catch the problem for repair.
• Make up practice tests using the assigned problems and the things we do in class. There is a huge benefit to writing and debugging test-type problems. Also, taking these tests under test conditions makes the testing environment more familiar and less intimidating for some people.

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