Math 221 A
The Real Number System and Methods for Elementary Education
Fall 1998

Instructor

Randall Pruim
office: North Hall 284
phone: (616) 957-7113
E-mail: rpruim@calvin.edu

Office hours

Monday, 12:30-1:20 (before class)
Tuesday and Thursday, 2:30-3:30 (after class)
Wednesday, 1:30-2:20 (at class time)

Other times by appointment. You can also drop by my office any time. If I am in my office, I will usually be able to see you. I will keep a copy of my schedule online.

Web Resources

• a daily syllabus of readings and topics,
• information about projects,
• information about tests and exams,
• homework assignments with due dates.

In addition, I will keep a list of other sites at http://www.calvin.edu/~rpruim/courses/m221/elsewhere/. It will include any web pages I mention in class, plus other things I discover that are related to teaching mathematics in elementary and high school.

If you find something good, please email me the URL (http:// etc.) and a description of the content and I may add it to my list.

Course Description

• Content. The content component of this course will focus on a careful study of the real number system, which includes most of what you probably think of as "arithmetic". Of course, you all went to elementary school and learned much of this there. But a good teacher must have a knowledge of these topics that is both deeper and broader than that of a student. You are expected to have a certain amount of "know-how" about things like addition, subtraction, multiplication, division, fractions, percents, decimals, etc. Thus the primary emphasis will not be on how to do these things, but on why we do them that way, what they mean, and how to teach them. By reviewing these topics in a systematic way, you should also develop a sense of how these various topics fit into the larger K-8 curriculum. (A good fourth grade teacher needs to know what second and third graders have learned and what her students will go on to learn in the fifth grade and beyond.)
• Methods. How can/should we teach mathematics to young children? We will spend a great deal of our time answering this question. Recommended methods have changed dramatically recently and may be very different from what you remember from grade school. For the most part we will learn about methods for teaching mathematics by using them to teach (and learn) mathematics. Much of our class time will be spent in small groups doing just this. Some of these "laboratories" will use materials suitable for use with grade school children (and you will sometimes be required to "forget" some of what you know so that you can simulate grade school students at a certain level), other activities will be adapted to your level of mathematical ability and experience so that you can learn something from them while learning the methods.
• Issues. Should calculators and computers be used in grade school? If so, how? Do boys really do better at math than girls? If so, why? Are schools in other countries doing a better job of teaching mathematics than are American (or Canadian) schools? What topics (and methods) are most important for students at various levels? Some of our time will be spent discussing some of these and other issues that face elementary school teachers and systems. There is not always consensus on these issues, but you need to be prepared to articulate and support a position (and to evaluate the arguments of others).
• Core. In addition to being a part of your professional training as an elementary school teacher, Math 221 satisfies your core requirement in mathematics. Thus another goal of Math 221 is to give you a perspective on the discipline of mathematics and to equip you with computational and especially reasoning skills that will serve you well outside the classroom as well inside.

Important Information

Time & Location

Mon, Tue, Thu, Fri: 1:30 - 2:20 in NH 251

Calendar

Syllabus: A daily syllabus, including readings and topics discussed in class will be maintained online.

Exams will be given in class on the following dates: Monday, September 28; Thursday, October 22; Thursday, November 12; and Monday, December 7.

Final exam: Monday afternoon, December 14, 1:30 pm.

Exams must be taken when they are scheduled. No make-up, alternate or late exams will be given. Your final exam score will be substituted for any exam that was missed (for any reason) or for any exam on which you did worse than on the final (maximum of 2).

Required Textbooks

Elementary and Middle School Mathematics: Teaching Developmentally by J.A. Van de Walle

Mathematical Reasoning by C.T. Long and D.W. DeTemple

Additional readings will also be assigned. Note that the texts listed above will also be used for Math 222.

Grading

Grading will be based on the following approximate weighting:

0%

Exercises

10%

Quizzes and in-class work

10%

Homework Problems

10%

Projects & Papers (6)

45%

Mid-term exams (4)

25%

Final exam (comprehensive)

Exams will not be rescheduled for any reason. Your exam score will be used in place of (at most two) exams that were either missed or on which you did worse than on the final.

Projects. You will have 6 short projects during the course of the semester. The details are outlined on a separate page that was handed out in class.

Quizzes will be unannounced and may cover any of the recent readings, exercises or class activities. Some quizzes will be done individually, others will be done in small groups (one quiz for the group, all members receive the same score). The quiz component of your grade will also include anything produced as a result of or in response to group activities done in class. Sometimes, especially early in the semester, I will provide you with a list of questions regarding readings. Answers to these questions will not be collected, but you should be prepared to discuss them in class or to answer them (or similar questions) on a quiz or exam. You may find it very useful to write out brief answers or notes based on the questions. When you are not provided with questions, you may find it useful to take some kind of reading notes, or even to write your own questions.

Problems. One goal for this course is to make you better problem solvers and to expose you to a variety of interesting problems. Assigned problems require written solutions. By a solution I mean more than just answers. In particular, all reasoning must be clearly explained.

Exercises. In addition to problems, I will provide you with lists of exercises. Exercises, as the name suggests, are designed for training and practice. These will be more like what you may remember from school as "math homework". Exercises need not be turned in but are intended to let you know if you know things you are expected to know. Since your backgrounds vary, some of you may have more difficulty with the exercises than others. In addition, you may find some of the exercises very easy and others much harder. If you have difficulty with any exercises, read the appropriate portion of the text (usually LDT), ask your classmates for help, ask in class or come and see me. We may discuss exercises on their "due dates", even though you are not turning anything in. Do not think that because they are not collected or graded that the exercises are unimportant.

Attendance

I will not be recording attendance. Nevertheless, skipping class can have a detrimental effect on your grade in several ways. Most importantly, by missing class, you are missing an important part of the course. Since your participation in your small group is important for this class, you are also letting down your group. And of course, if you are not in class you cannot take a quiz or turn in assignments. (You do not get credit for a group quiz if you are not present when the group does the quiz.) Quizzes will not be made up for those who miss class, but I typically drop the lowest quiz or two (depending on how many there are over the semester).

Preparing for class

You should bring with you each day any readings due that day (or the previous day if we have not finished discussion from the class period before), a calculator, and any other materials I announce ahead of time. Of course, you should have read (and thought about) any assigned readings prior to coming to class. You may want to have your notes handy, especially if you have questions regarding the readings.

Any assignments to be turned in are due at 5 pm on the day assigned. You may turn them in at class or to the box outside my office after class until 5pm. Resist the temptation to work on assignments during class. If I feel that this temptation is not being resisted, then I will move the due time to the beginning of the hour.

Joint Work

You may find it pleasant and useful to work together on many portions of this course. I encourage you to do so. BUT you must abide by the following guidelines:

• Balance. If you work together, do not work in a group that is too unbalanced. Certainly there are times when one person in a group has the key insight that solves a problem, but if the same person is always having all the insights, or if you are not contributing to the group effort, then you should probably seek out a different group.

  Balance also extends to preparation. Do not get answers or hints from someone who has completed the work before you have even begun. Ideally, each member of the group should come with roughly the same amount of background work done.

• Independence. Work that is turned in for a grade (except work explicitly done by your group) should be written up independently. The best policy here is to write solutions to problems, project papers, etc. physically alone (i.e., not while you are sitting next to or near someone in the course). This will alleviate the temptation to "copy" or to lean too heavily on someone else (neither of which is not allowed), mistakenly thinking that you would have been able to do the work on your own.

See me

If you are having difficulty with any portion of the course, do not hesitate to see me (during the office hours listed above or at some other time). Do this as soon as possible, certainly well in advance of any deadlines (like exams) so that we can work to fix the problem.

Page Created: 31 August 98
Last Modified: 
Thu Jul 29 19:58:58 1999
Maintained by: Randall Pruim