Augusta State University

Department of Mathematics and Computer Science

MATH 2008 * Foundations of Numbers and Operations

Fall 2009 *Allgood Hall E362

Instructor

Linda Crawford, Ph.D.

Allgood Hall N322

(706) 667-4477

lcrawfor@aug.edu (observe: it is lcrawfor-----there is no “d”!!)

Office Hours

· Monday & Wednesday, 2:30-3:45

· Tuesday & Thursday, 11:30-12:30

· Other times by appointment

Course Description

This course is an Area F introductory mathematics course for early childhood education majors. This course will emphasize the understanding and use of the major concepts of number and operations. As a general theme, strategies of problem solving will be used and discussed in the context of various topics.

Prerequisite: MATH 1101, MATH 1111, or MATH 1113

COURSE OBJECTIVES: This course focuses on preparing early childhood education majors to:

· Understand and use the major concepts of number and operations in mathematics for grades P-5.

· Solve problems using multiple strategies, manipulatives, and technological tools; interpret solutions; and determine the reasonableness of answers and efficiency of methods.

· Communicate using precise mathematical terminology

· Construct and justify arguments as well as interpret solutions; and determine reasonableness of answers and efficiency of methods

LEARNING OUTCOMES: All students will learn to:

· Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

· Understand meanings of operations and how they relate to one another.

· Compute fluently and make reasonable estimates.

· Apply multiple problem solving strategies and understand how approaches to solutions relate to one another.

COURSE OUTLINE

A. Number Sense

1. Sets of Numbers: Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers

2. Even and Odd Integers

3. Order Relationships

4. Estimation

B. History of Numeration

1. Numeration Systems

2. Place Value

C. Number Theory

1. Divisibility Rules (and why they work)

2. Greatest Common Factor (Concept and Algorithm)

3. Least Common Multiple (Concept and Algorithm)

4. Prime and Composite Numbers

D. Concepts of Operations

1. Operations on Sets of Numbers

2. Identity Elements for Addition and Multiplication

3. Inverse Operations

4. Exploration of Other Bases

5. Proportional Reasoning

E. Problem Solving

As a general theme of the course, problem solving strategies will be discussed and used in the context of topics A-D above. Strategies may include

1. Inductive Reasoning

2. Deductive Reasoning

Supplies

· Textbook: Bassarear, T. (2008) Mathematics for Elementary Teachers, 4th Edition. Boston: Houghton Mifflin Company

· Colored pencils

3-ring binder
Scientific or graphing calculator (to be used only when permitted)

Some of the assignments will be in PDF form so you will need Adobe Reader software—this can be downloaded free from http://www.adobe.com/products/acrobat/readstep2.html

I often use Windows Journal to grade assignments you submit electronically. You may need the computer program Windows Journal Viewer to open the returned assignment. You can download it free by clicking on Windows Journal Viewer.

Some assignments will be submitted through GeorgiaVIEW Vista (WebCT Vista). You can also access Vista through the My Courses tab on Pipeline. If you need help with Vista, visit the online support center.

If you need help with technology, check with the Information Technology Student Help Desk--either in person or by phone. The number is 706-737-1676. Information about the Help Desk can be found at http://www.aug.edu/its/Welcome.html.

If you have a disability and wish to receive accommodations in class, please apply with the Office of Disability Services.

Assignments to be turned in are due at the beginning of the class period. Put the assignment on my desk when you arrive for class. Even if you are absent, your assignment is still due at the beginning of class. If you will not be in class on a day that an assignment is due, you may email it to me or place it in my mailbox before class starts or send it with another student. A late assignment will be accepted only in extreme and documented situations.

If You Have to Miss a Class…

MATH 2008 class sessions are interactive, providing many opportunities for you to express your own ideas and to listen to the ideas of your fellow classmates. Much of what you learn in the course takes place by participating, sharing, and interacting with others through small-group and whole-group discussions. This kind of learning cannot take place if you are absent so regular attendance and punctuality are required.

Frequently, ideas that we introduce in one session are expanded upon and developed more fully in later sessions. Thus, every class session is important. However, if you find that you are unable to attend a particular class session or might miss a part of a session (by coming late or leaving early), please contact me as soon as possible. Make arrangements to turn in assignments if you are going to be absent—even if you are absent you are expected to turn the work in when it is due. You should ask a classmate to obtain any handouts given out during the class you will miss—do not ask me for handouts that you miss. You are also responsible for any announcements made during the class.

Prior to returning after a missed class you are responsible for meeting with a classmate(s) to discuss the class session you missed. After this meeting you must write a 200-300 word “ Missed Class Paper” (typed) which includes the names of your classmates with whom you met, a description of the activities of the class you missed and how you engaged in these activities with your classmates, any research you might have done (use your book and the web as resources), an explanation of your understanding of the mathematical ideas investigated in class, any insights you gained, and any questions you have about these mathematical ideas. The paper is not to be merely a list of what was done in class but instead shows your effort at making sense of these ideas and what learning you have gained. This paper as well as any accompanying work from the missed class is to be handed in at the beginning of the next day’s class. Two points are deducted from your participation grade for each absence; one point will be returned if your “Missed Class Paper” meets the criteria outlined above.

Roll will be taken; any student who is absent more than 10% of the class time may be dropped with a WF. Excused absences count toward the 10%.

The percentages to determine your course grade:

· Tests (at least 3)

Tentative dates: Sept. 17, Oct. 13, Nov. 12

40%

· Other written or presented assignments—for ex, homework, quizzes, solutions of problems, reviews of websites or journal articles

20%

· Participation—click here for more information

10%

· Comprehensive final exam—Thurs., Dec. 10, 10:00-Noon

30%

Other Written or Presented Assignments

The written or presented assignments may include quizzes, homework, in-class presentations, out-of-of class projects, reflective writings, reactions to readings, analyses of student work, analyses of mathematics lessons, solutions of problems, etc.

Homework

You will be assigned reading, writing, questions, and problems to be completed for homework. All in-class activities will be based on the assumption that the required homework assignments and readings have been completed. This does not mean that all of your answers have to be perfectly correct. It does mean that you should have thought hard about each problem, made several attempts at solving it, and developed questions and conclusions about your solution strategies. Not every homework assignment will be collected and graded. Most homework assignments are listed on the assignment page; however, you are responsible for any assignment announced in class and not listed on this page.

Class Participation and In-Class Activities
Much of the success of this course depends on your level of interaction and participation throughout the semester. As you will soon discover, we will spend most of our class time sharing ideas, solution strategies, insights, and questions. During class sessions, I will assess both your preparation for class (e.g. whether you completed readings and assignments) and the quality of your participation in course activities by observing and interacting with you. I will be paying particular attention to your willingness to listen, to discuss, and to contribute to whole-class and group activities. Clearly, successful participation in this sort of class depends upon regular attendance.

Each class period will generally include a discussion of the homework and a review of the activities from the previous class. Although the discussion will take different forms on different occasions, it will always be the case that your ideas, strategies, and questions will guide the discussion. Sometimes, you will be asked to present a problem to the class. Other times, you may be asked to share your work in a small group. Other times, you and a small group of your classmates may work on a new problem related to your homework. While I promise to support you in finding answers to your questions, please be warned that my support will NOT consist of simply explaining solutions of problems to you. My job is to help you develop meaningful understandings for yourself, with the help of your classmates. Because this is a student-centered class, it is of utmost importance that you attempt all of the homework problems before class and do the assigned readings so that you can participate in the discussion. Satisfactory participation in this part of class means that you are willing to share your thought processes, questions, and solutions with the class (even when you don't think you have "the right answer") and that you also support your classmates as they participate.

During each class you will generally engage in some form of investigation of a mathematical topic. Typically, you will work cooperatively with 3 or 4 of your classmates, using various curriculum materials to guide your work. This in-class work will provide a conceptual basis for your understanding of the course material. Because your subsequent readings and homework assignments will build on these investigations, they require your careful attention. On occasion, without announcement, your in-class investigations may be collected. Also, you should be prepared to provide a written reflection on the in-class work. Some class time will be spent discussing questions and ideas that arise from the group investigations. It is imperative that you spend time outside of class reflecting on the group activities so that you fully understand the concepts. Merely hearing another’s explanation is no guarantee that you understand.

Your participation grade is determined using the Rubric for Participation. Two points will be subtracted for any absence (you may receive a refund of 1 point—see the section “If you Have to Miss a Class”).

Course Notebook

You should organize all materials (handouts, class notes, homework, readings, writings, tests) in a 3-ring binder. This notebook will be a record of your work in the course and will also serve as a tool for reflection. It will also be a valuable resource to you when you begin teaching.

Professional Organizations

You are encouraged to join the following professional organizations:

Georgia Council of Teachers of Mathematics (GCTM) at http://www.gctm.org (GCTM student membership is free if you’ve never taught before; otherwise, it is $20.)
National Council of Teachers of Mathematics (NCTM) at http://www.nctm.org/membership/ ($39 student e-membership includes your choice of journal--Teaching Children Mathematics is recommended for K-5 teachers)--Go to sampler.nctm.org to register for 120 days of free access to the Prospective Teacher Sampler of resources ANDfor full access to the online version of Principles and Standards for School Mathematics.

Classroom Policies

· It is a policy of Allgood Hall that food and drink are not allowed in the classrooms so cups, bottles, etc. should be capped and stored in your bag. Furthermore, food and drink interfere with group activities and the use of manipulatives.

· It is distracting to me and disruptive to the class activities if you leave the classroom during the class period. Thus, I ask you to refrain from "taking a break" except for an emergency.

· Visitors, including children, are not permitted without my prior permission.

· You are expected to check your campus email regularly.

Academic honesty

Cheating will not be tolerated. This pertains not only to in-class work but to outside assignments as well-any assignment that you submit as your own should be a report of YOUR thinking. Any student who is caught cheating will face serious consequences. You should read ASU's statement on academic honesty in the catalog.

Dates to Remember

Mon-Tues, Sept 7-8 Wed-Fri, Nov 25-27	Holidays
Mon, Oct 12	Midterm date (if you plan to withdraw, do so no later than this date)
Thurs, Dec 3	Fall semester classes end
Thurs., Dec. 10, 10:00-Noon	Final exam
October 14-16 (Wed-Fri)	GCTM Conference at Rock Eagle—a limited number of rooms are available for preservice teachers at $5.00 per night (GCTM membership required for this rate)
November 18-20 (Wed-Fri)	NCTM Regional Conference in Nashville
March 5-7 (Fri-Sun)	Teachers Teaching with Technology (T³) International Conference in Atlanta –Registration ($145) is complimentary for preservice teachers—register by January 22.