Math 221
The Real Number System and Methods for Elementary School Teachers
Fall 2007

Course Home Page

Instructor

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

In general, it is better to send an email than to leave a voice mail, since I check email more frequently.

Time & Location

Monday, Tuesday, Thursday, Friday at 11:30 (section A) and 12:30 (section B) in North Hall 251

Office hours

My fall schedule is still being determined, but it looks like I will usually be available Monday, Tuesday, Thursday, and Friday 10:30-11:15.

Other times can be arranged 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.

Internet Resources

Email

I will maintain an email list of all students registered in this class and will use it to distribute information and reminders of various things pertaining to this course. If you prefer to read your email from an account other than your Calvin student account, send me email with the email address you prefer.

Web Pages

In addition to this home page, I will also maintain a list of web resources pertaining to this course. Items I have prepared and maintain online include

• a customizable calendar of daily readings, lecture topics, exams, homework etc. You are responsible for any information appearing on the course calendar.
• a list of homework assignments.
• information about tests and exams.
• links to other sites with interesting information for this course, or for teaching mathematics.
• You can also get pdf files of handouts I produce in case you lose one.

KnightVision

I am also making partial use of KnightVision. You can go to KnightVision to check your grades, send email to individuals or groups in the class, and to read all the other information (like this page) that I have on line.

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? 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

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 tests) so that we can work to fix the problem.

Required Textbooks

• Elementary and Middle School Mathematics: Teaching Developmentally (4e) by J.A. Van de Walle
• Mathematics for Elementary Teachers: A Contemporary Approach (5e) by Musser, Burger, & Peterson

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:

        20%    Homework, Projects, Lab reports, Quizzes, etc.
         0%    Worst Test
        45%    Other 3 Tests (15% each)
        35%    Final Exam (comprehensive)

If you final exam is your worst test, I will count the other four tests as 15% each and the final exam as 20%.

Final exam time: You may take the final exam at one of two times:

• Thursday, Dec 13, at 1:30 pm; or
• Friday, Dec 14, at 9:00 am.

Tests must be taken when they are scheduled. No make-up, alternate or late tests will be given. If you miss one test (for any reason) or if your final exam score is better than your worst test, then your final exam score will be substituted for that test.

Quizzes may be announced or unannounced and may cover any of the recent readings, exercises or class activities. Most quizzes will be group quizzes.

Homework. You will not be able to master the material in this course without practice. The primary purpose of the homework is to provide you with the practice and with a way to detect "weak spots" that need additional work. I will make assignments nearly every day. Some portions of these assignments will be collected and others will not. Please follow the guidelines below:

1. Typically graded assignments will be graded on a 5-point scale based on the overall quality of the work and the amount completed. It may not be that every problem is checked for complete accuracy.
2. Problems to be handed in should be worked neatly, showing all of your work and explaining your reasoning. The work should be organized in paragraph manner (work left to right and top to bottom; use English sentences to explain what you are doing, etc.).
3. Any work that is illegible or disorganized will not be graded.
4. Label each page with your name and the problem set number. Each problem should be clearly labeled as well. Leave a little space between problems.
5. Each problem set should be on a separate sheet of paper. If you use more than one sheet of paper, these sheets must be stapled in the upper left corner. If you use spiral bound paper, please remove the fringe along the edge of the paper.
6. Any assignments to be turned in are due at at class time on the day they are due. You may turn them in at class or put them in the box outside my office before class begins. Late assignments will not be accepted, but your worst two or three problem sets will be dropped.

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 designated as group work) should be written up independently. If you are working near someone else in the course when you write your solutions, be sure that you do not copy or lean to heavily on their work (neither of which is allowed) as you do so.

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. And of course, if you are not in class you cannot take a quiz or turn in assignments. Quizzes will not be made up for those who miss class, but I typically drop the lowest quiz or two (the exact number of quizzes dropped will depend on how many there are over the semester).

Preparing for class

You should bring with you each day:

• the homework due that day,
• your textbook,
• any additional readings due that day (or the previous day if we have not finished discussion from the class period before),
• 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 or homework.

Special Circumstances

Occassionally there are special circumstances that require that the rules and guidelines above be adjusted for a particular student. In such cases, it is the responsibility of the student to inform me of the situation as soon as possible, so that the appropriate arrangements can be made. This includes, but is not limited to, students with documented disabilities.

This page maintained by:
Randall Pruim
Department of Mathematics and Statistics
Calvin College
rpruim@calvin.edu