Fundamental Concepts of Math for Educators, Math 301B, Sections 3 and 4
Syllabus, Winter 2007

Office hours for individual help are part of my job, so take advantage of them. If you can't come to any of the regular office hours, ask for an appointment. If you live far away or have a complicated work schedule, you can call for a phone office hour.

If math is difficult for you, you should probably plan on coming for help outside of class once a week, starting NOW.

If you need an accommodation for a disability in order to participate in this class, please let me know as soon as possible and also contact Services to Students with Disabilities at UH-183, (909)537-5238.

Important:

This is the second of a 3-quarter sequence: Math 301A, B, and C. My two sections (MW 6-8 pm and TTh 8-10 am) will be using a textbook I am writing, and the topics are not covered in the same way and order as in other sections. Please try to stay in one of these two sections for 301C; my sections of 301C will meet at the same times in the spring.

If you were in another section of Math 301A, you have covered topics in a different order. My sections of 301A covered measurement and geometry in depth, followed by a study of fractions (including decimals) and concepts of addition. This course will cover concepts of subtraction, multiplication, and division, arithmetic with integers, and algorithms for arithmetic. Other sections will have already covered this material, though in a different flavor. Then we will move on to proportional thinking, as described below.

If you were in a different section, you will need to read the sections of the book on geometry and measurement; review will be built into this course as we go. I will assign you to a group for help in quickly assimilating these concepts. In return, you are responsible for helping your group members on the arithmetic topics that you have already studied. The book sections are avialable on Moodle under Math 301ABC; I will give you a paper copy if you want.

Prerequisite and Course content

The prerequisite for this course is Math 301A with a C or better. (I will check.)

This class will provide an advanced (teacher's) perspective on some of the fundamental themes of elementary and middle-grades mathematics: numbers and operations, and multiplicative/proportional thinking, along with more topics in measurement and geometry. The state of California will shortly begin exit exams for high school graduation, including algebra. Algebra now or soon will start in 8th grade for most students, so a good preparation in elementary school is essential. While you may think you will only be teaching the lower grades, there is much you can do to provide a good foundation for these more advanced ideas.

Topics

Numbers and operations:

Concepts of and algorithms for addition, subtraction, division, and multiplication, with positive an negative whole numbers, fractions, and decimals.

Multiplicative thinking:

Rates and ratios; functions and graphs; problem solving with tables and graphs; converting between units of measurement

Geometry:

The Pythagorean Theorem (if time permits; otherwise this will be in 301C)

Technology:

Understanding and using calculators wisely; concepts using interactive demonstrations; introduction to spreadsheet software; introduction to dynamic geometry/graphing software

Structure of classes

A typical class will begin with some lecture, then switch to work in groups of 2, 3 or 4. Periodically I will interrupt the group work for class discussion and sharing of results. When groups have finished, selected students will present their results. I would like everyone to do at least two informal presentations during the course.
I will periodically rearrange the groups to give you a chance to see how other people think.
During group work, discussions about math are encouraged. Discussions about your personal life, or other classes, are not. Please stay on task, and help your group members keep focused.
Be respectful when others (instructor or classmates) are speaking to the whole class.

Materials

Required materials

No textbook will be used in my sections of this course. You will receive handouts in class, and they will also be posted on the web, at the course pages at http://csusb-odl.com/moodle/

Access to the Mathematics Content Standards and Framework for California Public Schools, Kindergarten Through Grade Twelve. I will be assigning readings from the K-7 parts. You can find the Math Standards on the web at http://www.cde.ca.gov/be/st/ss/mthmain.asp and the Math Framework at http://www.cde.ca.gov/ci/ma/cf/index.asp.

Standard and nonstandard math tools and general purpose tools:

• Scissors (there will be a lot of cutting and pasting in this class!)

• Tape

• Colored pens or pencils

• Lined paper

• Unlined paper

• Graph paper: In addition to small-square graph paper (most that you can buy is 4 to an inch) I often use centimeter graph paper (squares 1 cm on a side), inch graph paper (squares 1 cm on a side), isometric graph paper (equilateral triangles), and both square and isometric dot paper. The amazingly useful website http://www.incompetech.com has custom graph paper to download. Please make yourself some copies of the centimeter and inch graph paper to start with, and others later as requested.

• Two or more large envelopes for handing in homework that includes objects you have made. You can reuse the envelopes when your work is returned.

• Card stock in various colors---buy a package and share with others? This is for printing things to cut out. Last quarter I provided some, but many people found it convenient to print their own. You can buy small packets in various color assortments at craft stores like Michael's.

• Ruler (with both inches and centimeters), compass

• Please get a $1 Chinese-made calculator from somewhere like Wal-Mart. These calculators have certain interesting capabilities (some good, some bad).

• You should also have a better calculator with memory, root, and exponent keys. The calculator on your cell phone is probably not good enough. You might consider getting one with "extras", such as fraction arithmetic and integer division. The Texas Instruments TI34-II has these functions, as well as the functions found on scientific calculators. A fancy graphing calculator is fine if you already have one, but you don't need to buy one if you don't.

Manipulatives. Some are available for use in class, but you will probably need your own for homework. You can use the ones in the office hour room (JB 381) any time it is open. If you are feeling very poor or cheap, you can print out paper versions on card stock and cut them out, but they are not as nice to work with as the plastic ones.

• A set of Cuisenaire rods (available in the bookstore)

• A small set of base 10 blocks. You can get lightweight foam ones in the bookstore, or see me for hard plastic ones that go with the centimeter cubes.

• Abacus kit (tentative)

• Small counters in two colors; dried beans are fine.

• Algebra tiles (available in the bookstore)

Recommended materials

Little Kids, Powerful Problem Solvers, by Angela Andrews and Paul Trafton, published by Heinemann. (http://www.heinemann.com)

(for future middle grades teachers, 5-8) Teaching Fractions And Ratios For Understanding and More: In-Depth Discussion Of The Reasoning Activities In Teaching Fractions And Ratios For Understanding by Susan Lamon; pubished by Lawrence Erlbaum Associates, 2005. (http://www.erlbaum.com)

Other technology

In addition to calculators, this course will use computers.

We have just received a grant from the AT&T Foundation for a mobile laptop lab---a class set of laptops on a cart that can roll to any classroom. The object of this grant is to see what kinds of experience in technology will be useful to you as teachers, and whether having the computers come to the classroom will encourage professors to use technology in their classes more often. You will be among the first classes to use these computers.

We will also be using the Course Management System Moodle. Moodle is a course management system similar to Blackboard, but which is free and open source. It runs from the web page http://odl-csusb.com/moodle. If you were in my sections of Math 301A, you are already enrolled on Moodle; you just have to sign up for 301B (step 3 below.) If not, please enroll yourself in Moodle as soon as possible. Follow the instructions there on “How yo (sic) create a user account.” Here is a short version of the steps:

1. Click on Create new account and fill in the form. You don't actually have to use your student ID number. Note that “Surname” means your last, or family name. This information is available only to the instructor of the course; access to Moodle is not open to the entire Internet.

2. You should receive an e-mail from the Moodle server. You must click on the link in the e-mail to complete your enrollment; this is to prevent spam robots from getting in. If your e-mail has somehow filtered this out, thinking it's spam, ask me to have the administrator confirm you manually.

3. Once you are enrolled, click on the course (Math 301B, sections 3 and 4). You will be asked for the enrollment key, which will be given in class.

4. Also sign up for the “metacourse” where I store all the handouts and links for all 3 courses 301ABC.

All handouts will be posted on Moodle, as well as web links and some interactive demonstrations. Most of your homework will be handed in by uploading it to Moodle, and your grades will be kept on Moodle (visible only to you and the instructors.)

Required course work and grades

Participation

Class attendance and participation are mandatory.
Attendance: The discussions and activities during the class session cannot be replaced by reading someone's notes. If missing a class is unavoidable, it is your responsibility to find out what you missed from another student, from me, or from the class Web page and arrange to do the activities on your own. I will take attendance every class.

Policies: Up to 2 unexcused absences will not affect your grade (except that you will miss the class activities!) More than 2 unexcused absences will affect your grade, including an F in the course for flagrant absences. Persistent lateness will count as unexcused absences. I will excuse only serious, unavoidable family or medical problems.

"Participation" means behavior that helps everyone in the class learn. This includes contributing ideas, suggestions, answers, and even questions to the class discussion. A good question can clarify the issues that other people have been confused about, or too shy to ask. Remember, as a teacher, you will be leading the discussion for a group of 30 or so people, so this is a good time to practice. If you are a quiet person, contributing to your group's discussion is a good way to start. It may occasionally become necessary to give negative points for negative class participation: being off-task, and/or causing others to be off task by talking about non-mathematical topics, and so on.

If I am late to class, please start working on something productive; continue work on a problem or project, talk over difficult ideas with your group. Call my cell phone if you're wondering where I am, or need suggestions on what to do.

Homework and projects

Homework consists of the problems and exercises at the end of each section of the book; these are for learning the material and practice. Homework will not be collected or graded, but if you have some work you would like reviewed by me, please ask. Homework problems are fair game for testing on quizzes and exams after the sections have been covered in class, so make sure you understand them. The beginning of each class is a good time to ask questions.

Projects are more than simple problems or questions; they are either single big questions, or sets of related questions and activities. Sometimes there is something to make: an art work, a 3-dimensional geometric object, etc. Projects are to be handed in and will be graded. The concepts from the projects will also be tested. Projects will be due in class on Wednesdays or Thursdays, depending on when your class meets. There may be some projects involving computers which are submitted on Moodle.

Working together on homework is encouraged. However, work that is handed in must be in your own words. Keep in mind that homework is to help you learn the material, so if you use someone else's thinking, you probably won't learn enough to pass the exams. Copying another person's work is considered plagiarism. Substantially identical work will receive no credit. Persistent cheating may result in an F in the course. See the university catalog for the university policy (http://catalog.csusb.edu/, then look at the section on cheating.)

Late projects may or may not be graded, but you may receive some credit for doing it and turning it in.

Exams and Quizzes

There will be one midterm exam and a 2-hour final exam. There will be quizzes, approximately one a week. Quizzes will tend to cover only material since last quiz, but I reserve the right to include questions from previous topics (especially if lots of people hadn't mastered the topic on previous quizzes. The final exam will cover the entire course. Problems will resemble the homework problems, including the results of projects.

There will be two levels of quiz and exam problems:

Basic problems. These are problems at the 7th grade level and below. See the California Standards for what that means. Every credentialed Multiple-Subject teacher should be able to do all of these problems. There will be at least one basic problem on each quiz, and several on the midterm and final. Typically these are 1-step problems. Usually no partial credit will be given.

Regular problems. These are problems based on the course material, and require more sophisticated understanding than the basic problems. These are typically multi-step problems, which may require you to do something in more than one way and explain how the ways are related. For these problems, I usually give partial credit for any correct work you have done.

Evaluation

The 301ABC sequence is graded ABC/NC. This means that the lowest passing grade is a C (not a C-).
Your grade will be based on your course work, as follows.

Basic Problems: On the final exam, you must pass 85% of the basic questions to pass the course. If you have done that, then your basic score will become part of your exam score