Note: This course is open only to students majoring in early grades and middle grades education and does not meet general studies requirements in mathematics.

Prerequisite: High School Algebra I and II and Geometry (B or better in each); Math 95, 97, and 99 (C or better in each) or the equivalent.

Instructor: Dr. Linda Sheffield

Office: BEP 262

Phone: 572-5431

Office Hours: M 10:00 a.m. - Noon; Tues. and Thurs. 9:00 - 10:30 a.m. and by appointment.

Email: Sheffield@nku.edu

Webpage: http://www.nku.edu/~sheffield

Text: Long, C. T. and DeTemple, D. W. (2000). Mathematical Reasoning for Elementary Teachers, 2^nd Edition. New York: Addison Wesley.

Course Description: The main emphasis of this course will be on understanding the meaning behind the basics of mathematics. Knowledge of this is essential for the intelligent teaching of mathematics at any level. Topics for the first semester of Mathematics for Elementary Teachers include problem solving, patterns, functions, logic, number sense, numeration systems, number theory, computation, integers and rational numbers. (This corresponds to Ch. 1-7 of the text.) You are expected to attain an understanding of the conceptual foundations of these topics and a practical concrete knowledge enabling you to pose and solve problems in these areas and to explain the topics to others. The course will be taught in a manner consistent with the National Council of Teachers of Mathematics Principles and Standards, and you will be expected to take an active part in constructing your own knowledge of mathematics. You are expected to work individually and in small groups during class as well as when doing homework, studying for exams and working on projects. Mathematics is sometimes thought of as the study of patterns and that will be emphasized in this course along with communication, problem solving and connections.

Written, oral, and visual modes of communication are essential to understanding and doing mathematics. You will need to be actively engaged in making observations, seeking patterns, and making and testing conjectures. These should be discussed and analyzed with others in small groups as you work on homework and projects.

During the course, you will work both individually and cooperatively on problem solving activities. When appropriate, calculators and physical models will be an essential part of these investigations. Problems should be approached with a desire to discover all that you can about any given problem. The solution to the initial problem should be looked upon as the beginning of this investigation. This solution should lead you to some interesting extensions where you ask such questions as: Why? What if I changed this…? Is that always true? Is that ever true? Is there another way to solve this? How can I convince someone that this is correct?

As you solve problems, you should always be on the lookout for connections. You should try to connect the solutions from one problem to those you have solved earlier as well as connect the mathematics you are learning to everyday problems and to other subject areas. You should use your mathematical reasoning and inquiry skills to connect the abstract concepts to real world examples, physical models, and pictures and diagrams.

Keep in mind that this is a mathematics class and not a methods class. We will often use manipulatives during class to give you a strong foundation for the mathematics that underlies the elementary and middle grades curriculum. The Chinese refer to this as developing a "profound understanding". It is important for you to master this profound understanding yourself so that you will later be able to share this with your own students.

Objectives: At the completion of the course, you should be able to:

1. Correctly explain and give examples of basic concepts related to each of the topics listed above.
2. Pose and solve problems in a variety of ways requiring the use of the basic concepts connected with each of the given topics.
3. Construct concrete models and make connections within mathematics and to other subject areas for each of the basic concepts.

Student Requirements

1. Do assigned readings and problems from the text and other sources both individually and in small groups. It is important not only that you have read the text before coming to class, but also that you have worked diligently on the problems. Even if you cannot solve all the problems in any given homework set, you need to work on them to be able to understand the discussions during class. I suggest that you get a notebook for this class and separate it into three sections. In one section, put terms, vocabulary, important concepts and questions that arise as you read the chapters in the book. In another section, put your notes from class. In the third section, put the answers to the homework problems including questions that arise as you work them. There are answers to several of the problems in the back of you book. In addition, at the reserve desk in the LRC, you will find a copy of the Instructor's Solution Manual where you can find all the problems worked out. If you are really stuck on a problem, you may want to check this out. University guidelines recommend that you spend two hours outside of class preparing for each hour in class. The average student should expect to spend at least 6 hours per week on this class; some of you will need to spend considerably more time. Homework will be assigned daily. Individual homework will not generally be collected, although you are responsible for knowing how to solve all the problems assigned. Many quizzes will take problems directly from the homework. Assigned homework is considered a minimal amount needed for a well-prepared student to be successful in this class. Many of you will need additional practice and should complete additional problems. It is strongly recommended that you work all assigned problems and read each section to be discussed before each class session. You may want to set up a study group with two or more students in the class to work and discuss the homework. Five-ten minutes will be spent during each class period going over any questions on the homework. Time will not permit solving all the problems in class. Participation in class and evidence of having completed assignments will be considered for grading purposes. If you have difficulty with any section, be sure to come to talk to me immediately. You may also get help in the Learning Assistance Center, BEP 230, where you may find a free tutor.
2. Participate fully in class. Attendance will be taken. This is the time to bring up those questions that you have in your notebooks from your readings and from doing the homework. In addition to taking an active part in discussing any of the material that I will present, you will also frequently be investigating problems cooperatively with your classmates. If you must miss a class for any reason, be sure to notify me as soon as possible and get notes on what you have missed from one of your classmates.During class each day, you will be expected to be an active learner, participating fully, asking questions whenever necessary, suggesting new interesting avenues to explore, and taking notes on new information learned. Following class each day, you should rework any problems that might have been troublesome during class, follow up on extension ideas, complete the homework for the following class period, work on portfolio problems, discuss assignments with your classmates, read the section for the next class, visit me or the Learning Assistance Center with any problems, and prepare for any tests or quizzes.
3. Successfully complete exams and quizzes. Quizzes will be given approximately once for each chapter. The top five quizzes will be counted towards the grade. Although homework may not be collected, homework problems often appear on tests and quizzes. All tests, including the final exam, will be comprehensive. You will be expected to have a calculator in class each day, and you may use it on homework, quizzes, and exams.
4. Complete mathematics portfolio problems either individually or in small groups. Portfolio problems will be longer problems that you will be expected to work individually or cooperatively with other students. You may choose a group of up to four people to work with and will be given approximately two weeks to work each of these problems. You may wish to use your solutions to these problems in your own Education portfolio.
5. Complete individual assignments. These will be shorter than the portfolio problems and must be done individually.

Grades Recorded

Portfolio Problems (3)	30 pts. each	90 pts.
Individual Assignments (3)	20 pts. each	60 pts.
Quizzes (best 5)	10 pts. each	50 pts.
Tests (2)	100 pts. each	200 pts.
Comprehensive Final	200 pts.	200 pts.
Total		600 pts.

Freshman Midterm Grades Due: March 14, 2001

Drop Deadline: March 23, 2001

Extra Credit: Occasional bonus problems or extra credit assignments may be given.

Grading Scale:

90% - 100%	A
80% - 89%	B
70% - 79%	C
60% - 69%	D
0 - 59%	F

1. The instructor reserves the right to make changes in the syllabus, and/or class calendar if circumstances so dictate.
2. Quizzes are generally unannounced and may not be made up. A missed quiz will be scored as a zero. Your five best quiz grades will be counted.
3. Cheating, plagiarism, and illegal copying of software will not be tolerated. See the Rules and Regulations concerning this in the NKU Student Handbook.
4. If an exam is missed due to an unavoidable situation, the instructor may allow a make-up. It may be different than the original exam. It may be written or oral. Any exam may be subject to oral questioning. You must contact the instructor before the next class period if an exam is missed.
5. To receive full credit, assignments must be completed and handed in on time. Assignments that are turned in late will result in a 10% reduction in the grade if they are turned in less than one week after they are due. Assignments that are 1 - 2 weeks late will receive a 50% reduction in the grade. Assignments more than two weeks late will receive a 0.
6. Please get in touch when you foresee a prolonged absence. Also, please do not just disappear from class or from school. Talk to someone and go through the proper procedures if you are withdrawing. Last day to drop with a grade of W is March 23.

Return to instructor by Thursday, January 11.

On the form below, please fill in your name, phone number, NKU email, and address. These will be kept confidential. I must check all prerequisites for this course, so please include that information. (I will be checking university records to verify this.) Also, please sign in the space provided to acknowledge that you have received and understand the course syllabus.

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Name _______________________________________ Date ___________

Address: _______________________________________________________________

Home phone number _________________ Best time to call _________

Other phone number where you can be reached (work, etc.) _________________

NKU Email _______________________________________

Previous Math Courses Taken: Grade in Course (if known)

High School

College

I have read and understand the information contained in the syllabus for Math 140, Math for Elementary/Middle School Teachers.

Student Signature ______________________________________

(Do not Print.)

Date	Topic	Assignments
Jan. 9	Problem Solving	Sec. 1.1 - 1.3
Jan. 11	Critical Thinking	Sec. 1.4 - 1.6
Jan. 16	Sets, Operations, and Counting	Sec. 2.1 - 2.2
Jan.18	Addition and Subtraction	Sec. 2.3
Jan. 23	Multiplication and Division	Sec. 2.4
Jan. 25	Functions, Chapter Review	Sec. 2.5
Jan. 30	Numeration Systems	Sec. 3.1
Feb. 1	Nondecimal Positional Systems	Sec. 3.2
Feb. 6	Algorithms for + and -	Sec. 3.3
Feb. 8	Algorithms for x and ÷	Sec. 3.4
Feb. 13	Mental Math and Calculators	Sec. 3.5 and App. C
Feb. 15	Review for first test	Ch. 1 - 3 review
Feb. 20	EXAM 1
Feb. 22	Divisibility of Natural Numbers	Sec. 4.1, 4.2
Feb. 27	GCD and LCM	Sec. 4.3
Mar. 1	Clock Arithmetic, Ch. Review	Sec. 4.4
Mar. 6	Representation of Integers	Sec. 5.1
Mar. 8	Addn. & Subtr. of Integers	Sec. 5.2
Mar. 20	Mult./Div. of Integers, Ch. Review	Sec. 5.3
Mar. 22	Fractions and Rational Numbers	Sec. 6.1
Mar. 27	Arithmetic of Rational Numbers	Sec. 6.2
Mar. 29	Rational Number System, Ch. Review	Sec. 6.3
Apr. 3	Review for second test	Ch. 1 - 6 review
Apr. 5	EXAM 2
Apr. 10	Decimals	Sec. 7.1
Apr. 12	Computation with Decimals	Sec. 7.2
Apr. 17	Ratio and Proportion	Sec. 7.3
Apr. 19	Percent, Ch. review	Sec. 7.4
Apr. 24	Spreadsheets	Appendix B
Apr. 26	Review for Final Exam	Ch. 1 - 7 review
May 3	Final Exam 10:10 - 12:10

Note: Portfolio projects and individual assignments to be handed in will be given once the semester is underway. This schedule is subject to change depending on how we progress throughout the semester. Changes will be announced in class.