Office Hours: Tuesdays and Thursdays, Triad, Wing C (McSiip Office)from 11 – 12:30.  I will also usually be at the Math Department, Robinson (3^rd floor) about 1:30p.m.  Please note that these times may vary; checking with me is the best way to make sure we connect.

Phone: 256-4500, ext. 3871 (Math Dept.), ext. 3924 (Triad) or 610-565-1391 (home).

E-mail: caldwell@rowan.edu-- I generally check my e-mail on Tuesdays and Thursdays throughout the day.

Text: Mathematics for Elementary Teachers via Problem Solving (Activity Book and Resource Manual) by Frank K. Lester & Joanne O. Masingila

Calculator: The Texas Instruments Math Explorer Plus is the recommended calculator for this course.  Students having graphing calculators, however, need not purchase an additional calculator.

Course Description: This course concerns the development of number systems and algebraic structures, including the natural numbers, the integers, rational numbers, real and complex numbers.  Concrete examples of selected algebraic structures such as modular arithmetic and matrices may also be included.  You will be required to reason mathematically, solve problems, and communicate mathematics effectively at different levels of formality, using a variety of representations of mathematical concepts and procedures.

This course is probably going to be different from your previous mathematics courses - big mathematical ideas serve as course organizers, cooperative small group work on activities is expected, reflective writing is required of all students, and alternative assessment procedures are used. We will also be working throughout the course on improving your estimation and mental mathematics skills.

OBJECTIVES:This course is intended to provide an opportunity to develop your knowledge of the content and discourse of mathematics, including:

- mathematical concepts and procedures and the connections among them;

- multiple representations of mathematical concepts and procedures;

- ways to reason mathematically, solve problems, & communicate mathematics effectively at different levels of formality;

- the nature of mathematics, the contributions of different cultures toward the development of mathematics, and the role of mathematics in culture and society;

- the changes in the nature of mathematics & the way we teach, learn, & do mathematics resulting from the availability of technology;

- the place of "school mathematics" (what you have learned in elementary school & high school) within the discipline of mathematics;

- the relationship of mathematics to other subjects and its applications in society.

We will use physical materials and models to explore fundamental properties of number systems, to describe real-world relationships, and to explore selected algebraic structures.We will also develop conjectures and intuitive proofs of number theoretic properties.This course is especially appropriate for those students preparing to be elementary or special education teachers.
 

 

1.2Creating and using pictures, charts, graphs, variables, equations, inequalities, and other 

algebraic notation to recognize and describe mathematical relationships

1.3Functional relationships which arise from diverse problem situations

1.4Number sequences, patterns, and functional relationships

1.5Concrete examples of finite and infinite sequences and series, approximation of nonterminating decimals and approximation of functions

2.Nature and Use of Number

2.1Role of numbers as a logical, predictable system for expressing and relating quantities

2.2Features & basic computational techniques in selected numeration systems today & in the past

2.3Operations, properties, and uses of whole numbers, fractions, and decimals

2.4Estimation and mental arithmetic, calculators, computers, paper-and-pencil algorithms, and manipulative materials as tools for use in solving problems

3. Number Concepts and Relationships

3.1 Fundamental properties of number systems

3.2 Elementary number theory

3.3 Infinity and its role in the study and historical development of mathematics

4. Algebraic Structures

4.1 Examples of functions arising from a variety of problem situations 

4.2 Properties of functions

4.3Properties of the integers, rational numbers, real and complex numbers (including order, denseness, and completeness)

4.4 Concrete examples of selected algebraic structures 

Evaluation:The grading scale used is 90%=A-, 80%= B-, 70% = C-, 60%=D-.

There will be two exams plus a comprehensive final.  Each exam will be 25% of your grade, as will the final.  The remaining 25% of your grade will reflect your performance in the following areas:

Math Autobiography & other written assignments 2.5%

Problems of the Week- ten problems to be solved individually10%

Projects – four projects to be completed in groups10%

Class participation2.5%

Math Autobiography: Tell me the story of your own experiences with mathematics.  Include the following:

� what you think mathematics is all about and how your ideas about math have changed over time

� your own attitudes to math and how they have changed 

� your accomplishments and frustrations (recent and in the past) andareas in math that interest you
 

 

Reflective Writing: You will frequently be asked to write in this course in response to a particular question; these reflective writing assignments are to be sent to Dr. Caldwell via e-mail (caldwell@rowan.edu) before the next class.While you will not always get a response to your reflections, you will frequently receive some type of comment back.

Projects: These generally will be completed in cooperative groups and will be more challenging than typical homework problems.Projects which are turned in after the due date will be penalized one point per day.

Attendance/Class Participation: You are expected to attend each class; it is impossible to participate in the problem solving activities unless you are present.Since the activities are designed to help you build upon your own understanding of mathematics, Agetting the notes@ from someone else will simply not work!Attendance will be taken at the beginning of each class session.

Makeup Exams: Makeup exams will be given only if you have called and left a message prior to the start of the exam indicating the reason for your missing the scheduled exam.Valid reasons should be beyond your control (e.g.,illness, accidents, hospitalization); oversleeping is not a valid reason to miss an exam.Makeup exams will generally be scheduled as soon as possible.

ASSIGNMENTS: The following calendar provides a tentative outline of the pacing of the course, as well as due dates for assignments.Further details concerning assignments will be given via e-mail.
 

Date	Topic	Activities	Assignments Due
1-20	Introduction	1.1-1.3
1-25	Problem Solving	1.4-1.6	Math Autobiography
1-27	More on Problem Solving	1.7-1.8
2-1	Numeration Systems	2.1-2.4	POW 1
2-3	Place Value	2.5-2.7
2-8	Number Bases	2.8-2.10	POW 2
2-15	Sets; Meanings of Operations	3.1-3.3	Project #1
2-17	Operations with Integers and Whole Numbers	3.4-3.5
2-22	Alternative Algorithms for Operations with Whole Numbers	3.6-3.12	POW 3
2-24	EXAM #1
2-29	Factors	4.1-4.4	POW 4
3-2	Divisibility, GCF, & LCM	4.5-4.9	Project #2
3-7	Modular Arithmetic	4.10-4.13	POW 5
3-9	Fraction Models	6.1-6.5
3-21	Exploring Fraction Ideas	6.6-6.10	POW 6
3-23	Problem Solving & Operations with Fractions	6.11-6.13

 

3-28	More on Operations with Fractions	6.14	Project #3
3-30	EXAM #2
4-4	Ratio & Proportion; Decimals	7.1-7.4	POW 7
4-6	Decimal Operations; Equivalence	7.5-7.7
4-18	Percent	7.8-7.11	POW 8
4-20	Irrationals; Properties of Operations	7.12-7.14	Project #4
4-25	Variables, tables & graphs	8.1-8.4	POW 9
4-27	Functions	8.5-8.8
5-2	Iteration; Exponential Growth	8.9-8.11	POW 10
5-4	Expressions & Equations	8.12-8.14
5?	Final Exam (comprehensive)

Rowan 101: The purpose of this seminar is to introduce you to skills and expectations that you will need in order to function successfully at Rowan.Specifically, the seminar has the following goals:

1.Further strengthen writing and critical thinking skills through their application to mathematics.

2.Nurture library research skills within a course context.

3.Reinforce the value of cooperative learning.

4.Strengthen time and classroom management skills.

These four goals are addressed Ahands-on@ by applying them in this course.For example, you will learn library research skills by completing a library research task as part of one of your projects.

The smaller size of this class will enable me to give you more attention than you will most likely receive in your other classes at Rowan.In order to get to know you better, each of you is required to schedule time to meet with me twice this semester during my office hours.At these meetings, you may ask me anything you would like about life at Rowan!If I do not know the answer, then we will work together to find out.You will also have some assignments to complete that will help you to become more familiar with Rowan – such as who to see when for what – as you complete your freshman year.

In this class, we will be doing many activities in small groups.I hope that each of you extends the life of these groups outside the classroom, using your classmates as resources to help you better understand the content of this course.