Syllabus Foundations of Algebraic Thinking Fall 2003


MATH 522 / Sec 01 Foundations of Algebraic Thinking


5:00-8:00 PM / Monday / NSM A115


Students must have graduate standing and must have completed one year of full time secondary mathematics teaching.

Course Description

This course is designed for current secondary mathematics teachers. Mathematical topics include patterns and functions and their multiple representations, independent and dependent variables, discrete and continuous variables, linear and nonlinear relationships in context, connections to arithmetic operations, algebraic expressions and equations. The course also includes exposure to current research on the understanding of these topics by secondary students and their teachers.

Required Materials

Students need a course reader (available from our bookstore), a graphing calculator, and various low-budget items (i.e., graph paper, ruler, colored pencils) to be specified throughout the semester.


Jackie Barab Office: NSM A121

Office Hours: 3:00 – 5:00 PM Monday

9:00 – 10:00 AM Wednesday, Friday

also, by appointment

Office Phone: (310) 243-3580

Office email:

Office FAX: (310) 516-3627 (Write: Attention J. Barab.)


After completing MAT 522 the student should be able to

* represent linear and some nonlinear functions numerically, graphically, and algebraically.

* use a graphing calculator effectively in exploring properties of these functions.

* identify variables as independent or dependent and as discrete or continuous.

* use representations of functions and their properties to solve related problems.

* describe and apply the basic relationships among functions, equations, and inequalities.

* identify functions, relationships and their properties in given contexts.

* identify and create contexts for given functional relationships.

* identify function concepts within the secondary curriculum.

* demonstrate knowledge of current research on teaching and learning of algebra and



Syllabus Foundations of Algebraic Thinking Fall 2003


Course Requirements

Students are expected to attend all classes, to do all assigned homework, and to take the scheduled exams. In addition, it is important for students to participate fully in class, which may include small group work, whole group discussions, presentations, and individual written work. In order to participate fully, students need to bring all materials requested by the instructor.

Grading Policy

Grades will be based on a midterm exam, a comprehensive final exam, and daily work consisting of homework, attendance, class participation, and classwork. Attendance of all classes is expected.

Task Points

Daily Work Composite (including attendance) 100

Midterm Exam [Monday, October 13] 100

Cumulative Final Exam [Monday, December 8]__________ 150

Total Possible Points 350

Grades are based on a total of 350 points. They will be no lower than:

93% + A 87% + B+ 77% + C+ 67% + D+

90% + A- 83% + B 73% + C 63% + D

80% + B- 70% + C- < 60% F

Policy on Late Homework, Missed Classwork and Exams

Late homework and missed classwork will be accepted within a week of the due date for half-credit provided this work has not yet been discussed in class. If a student notifies the instructor on the day of an exam via phone or email and provides evidence of an appropriate excuse within the week, then make-up exam arrangements will be determined on an individual basis.

Academic Integrity

Maintaining academic integrity is of the utmost importance. The mathematics department does not tolerate academic dishonesty. For more details see the university catalogue under “Academic Integrity.”

Schedule Foundations of Algebraic Thinking Fall 2003

Week Topic

1 Birthday Cake Exploration; Painted Cube Exploration

2 Cup-stacking Exploration

3 Multiple Representations of Functions and Relations (a family of contexts)

4 From Number Charts to Graphs; from Patterns to Equations

5 Time-Rate-Distance Relationships

6 Slope – from Concrete to Abstract Representations

7 Grocery Store Exploration

8 Midterm Exam

9 Mathematizing “Melinda Mae,” a poem by Shel Silverstein

10 Identifying Function Concepts within the Secondary Curriculum, Part I

11 Let’s Make a Cell Phone Deal

12 Equations, Inequalities, and Functions

13 Identifying Function Concepts within the Secondary Curriculum, Part I

14 Bottle-filling Exploration

15 Common Misconceptions about Algebra and Functions

Dec. 8 Final Exam