MATHS 310: Topics in Algebra for the Elementary and Middle School Teacher (3)
Syllabus
1. Prerequisite: MATHS 202 with C– or better grade
2. Course Description: Development of algebraic concepts including variables, functions, and matrices, and applications of these topics in the elementary and middle school curriculum.
3. Course Objectives: The course is designed to strengthen prospective elementary and middle school teachers’ conceptual understanding of variables, functions and algebraic structures. Students are expected to learn about algebra as a system for representation and to develop algebraic reasoning skills. The emphasis is on problem solving, algebraic reasoning, communication of mathematics, connections among concepts, and representation of algebraic relationships.
4. Course Rationale: The course is designed to provide prospective elementary and middle school teachers with experience in the development of algebraic language and symbolism as tools to communicate mathematical ideas. Standards and recommendations for the mathematical content knowledge essential for preservice teachers made by the National Council of Teachers of Mathematics, the Mathematical Association of America, and the Indiana Professional Standards Board guide the selection of topics presented in this course. Because elementary and middle school mathematics curricula lay a foundation for the formal study of algebra, prospective elementary and middle school teachers need to have a conceptual understanding of variables, functions, and algebraic structures. Furthermore, they must be prepared to guide their students in informal explorations in the use of algebraic symbols to model problem situations.
5. Course Content: The course serves as an initiation into algebraic culture through the use of generalization. It includes the historical development of algebra as a symbolic language used to communicate mathematical ideas and provides experiences with representing and solving problems requiring the use of variables. Various representations of functions (tabular, graphical, symbolic, and verbal) are explored. Algebraic reasoning is developed using concrete models and technology. Specific applications for elementary and middle school mathematics are explored.
A. Recognize, extend, analyze, and describe a wide variety of patterns.
B. Represent and solve problems requiring the use of variables.
C. Investigate multiple representations of functions (tabular, graphical, symbolic, verbal).
D. Discover and analyze various types of functional relationships (linear, exponential, polynomial, and rational) which arise from diverse problem situations. Investigate both continuous and discrete functions.
E. Analyze change in various contexts.
F. Examine operations on expressions and ways to find solutions to equations, systems of equations and inequalities using concrete, informal, and formal methods.
G. Use matrices to record information. Perform matrix operations by hand and with the graphing calculator. Examine properties of matrices. Solve systems of equations with matrices.
H. Explore ideas for teaching algebra to elementary and middle school students.
I. Discuss the development of algebraic language and symbolism and how these have influenced the way we communicate mathematical ideas.
6. Course Format: Students work individually and in small groups to solve problems and participate in activities in class and to complete assignments outside of class. Faculty engage students in interactive lectures and whole-class discussions. Faculty and students use graphing calculators to solve problems and explore various representations of algebraic concepts. A TI-73 graphing calculator is required.
7. Special Methods for Evaluating Student Performance: Methods used for evaluating student performance may include but are not limited to the following: exams, quizzes, homework assignments, essays, journals, and projects.
8. Evaluation of the Course: The departmental Teacher Education Advisory Committee and Undergraduate Programs Committee periodically evaluate these courses. The instruction of the course is evaluated by departmental student evaluations and peer evaluations.
[S. Stump, 1/01]
[V. Mascioni, 4/04]