Course Home Page - Teaching Algebra and Trigonometry

MED534-970 | Teaching Algebra and Trigonometry
Professor: William Blubaugh
11/2/2001 9:23:47 AM Mountain Time

HOMEPAGES: University of Northern Colorado / William Blubaugh / MED534-970

ADMIN ONLY LINKS

Teaching Algebra and Trigonometry Notebook.

Program Requirements

This course, MED 534 - Teaching Algebra and Trigonometry, is an elective course of our Master of Arts in Mathematics: Teaching Emphasis degree program. The program consists of 30 semester hours of graduate courses. Fifteen of these hours are the required courses (below).

Required:
MATH 528 - Discrete Mathematics
MATH 534 - Continuous Mathematics
MATH 543 - Modern Geometry
MATH 550 - Applied Probability and Statistics
MED 600 - Introduction to Research in Mathematics Education

The fifteen elective hours consists of at least 5 semester hours from Group A (below) and at least 6 semester hours from Group B (below).

Group A:

MATH 520 - Functions and Equations
MATH 521 - Vectors and Matrices
MATH 529 - Mathematical Problem Solving
MATH 537 - Mathematical Modeling
MATH 591 - Abstract Algebra and Number Theory.

Group B:

MED 528 - Teaching of Discrete Mathematics
MED 534 - Teaching Algebra and Trigonometry
MED 543 - Teaching Geometry
MED 550 - Teachng Applied Probability and Statistics
MED 595 - Teaching Advanced Topics in Secondary School Mathematics

Course Description

A focus on current research on instruction in algebra and trigonometry and issues related to their curriculum. The course also contains approaches to the teaching and learning of algebra and trigonometry from conceptual and problem solving points of view.

Course Objectives

Study appropriate content for teachers of high school algebra and trigonometry along with appropriate instructional and assessment techniques.
Include mathematical concepts, such as those contained in the NCTM and Coloradoís Content Standards in Mathematics, into the course.
Include the use computers and graphics calculators as tools for teaching and learning mathematics.
Provide both content and pedagogical content so that participating teachers are able to not only learn new content but are able to use appropriate tools and instructional methods in their classrooms.
Provide opportunities to develop curriculum materials for your classes.

Pedagogical Content

In small "chat" groups or as a class, we will discuss reading assignments, problem assignments and various techniques that might be appropriate for student understanding of mathematics. Two projects will be required. The first is an individual project and the second is a project in which you will work with one or two other members of our class. Keeping in line with new instructional roles in the teaching of mathematics, a variety of instructional methods will be adopted, including the use of technology. In particular, we will refer to graphic technology via both computer and calculator. I see myself taking on such roles as facilitator, coach, resource person, moderator, as well as presenter of new materials at various times during the semester.

Online discussions and curriculum projects will ensue related to the integration of appropriate content into the secondary mathematics classroom. You are recommended to choose projects that you expect to use in your classrooms this semester or next.
Online time will be devoted mainly to discussions and presentations.

Part of the semester will be devoted to discussion of common assignment and readings. All will participate as one group.
Part of the semester will be devoted to one individual report, individual presentation, and/or activity for all to participate - led by various class members
Each of you will be responsible to develop and organize an activity that you will describe and present online. This can go into a portfolio, it can be associated with your project(s), and it will counts as credit toward the course grade.

Content of Course

The following content, as related the NCTM and State Standards, will be addressed in some form in this course: function concepts and difficulties that students have with them, problem solving and its significance in mathematics instruction, spreadsheet use for solving problems, use of graphic calculators and computer graphics software, common mistakes make by students in algebra, differences between equation-function-formula, concept development within algebra and trigonometry, and real world applications of mathematics.

Assessment

A letter grade will be assigned based on the following:

A portfolio - containing mathematical writings, resource materials, project write-ups, etc.
Project (1 single, and 1 small group)
Online presentation of project(s)
Online discussions (quality and quantity)

Research Reference

Kieran, C. Chapter 17, "The Learning and Teaching of School Algebra", Handbook of Research on Mathematics Teaching and Learning, NCTM: 1992

Tall, D. Chapter 20, "The Transition to Advanced Mathematical Thinking: Functions, Limits, Infinity and Proof", Handbook of Research on Mathematics Teaching and Learning, NCTM: 1992

Bibliography

1. Primary Referenced Materials

Coxford, A. F. & Shulte, A. P. (eds) , The Ideas of Algebra, K-12 (1988 Yearbook) Reston, VA: The Council, 1992.

Glatzer, D. J. & Choate, S. A., Algebra for Everyone: Inservice Handbook, Reston, VA.: The Council.

Murdock, J., & Kamischke, E. Advanced Algebra Through Data Exploration: A Graphing Calculator Approach &, Key Curriculum Press, 1996.

National Council of Teachers of Mathematics, Algebra for the Twenty-first Century: Proceedings of the August 1992 Conference, Reston, VA: The Council, 1989.

National Council of Teachers of Mathematics, Curriculum and Evaluation STANDARDS for School Mathematics, Reston, VA: The Council, 1989.

National Council of Teachers of Mathematics, Professional Standards for Teaching Mathematics, Reston, VA: The Council, 1991.

National Council of Teachers of Mathematics, Assessment Standards for School Mathematics, Reston, VA: The Council, 1995.

National Council of Teachers of Mathematics, Principles and Standards for School Mathematics, Reston, VA: The Council, 2000.

National Council of Teachers of Mathematics, Patterns and Functions, NCTM Addenda Series: Grades 5-8.

National Council of Teachers of Mathematics, Connecting Mathematics , NCTM Addenda Series: Grades 9-12.

Wagner, S. & Keiran, C. (eds) Research Issues in the Learning and Teaching of Algebra, Reston, VA: The National Council, of Teachers of Mathematics, Inc, 1989.

2. Secondary Referenced Materials

Cooney, T. J. & Hirsch, C. R. (eds), Teaching and Learning Mathematics in the 1990's (1990 Yearbook) Reston, VA: The Council, 1992.

Eckert P., Kitchen, G. et al., Graphing Calculators in the Secondary Mathematics Classroom, Michigan Council of Teachers of Mathematics, 1989.

Fetta, I. B., Explorations in Algebra, Precalculus, Statistics (A Manual for the TI-81 Graphing Calculator), Orlando, FL: HBJ College Publishers, 1992.

Hirsch, C. R. (Ed), A Core Curriculum: Making Mathematics. Count for Everyone, Reston, VA: National Council of Teachers of Mathematics, 1993.

Hyde, N., Explorations for the TI-81 and TI-82 Graphics Calculator (College Algebra and Trigonometry), B., Boston: MA, PWS Publishing Company, 1994.

Kelley, B., Using the TI-81 Graphics Calculator to Explore Functions, Burlington, Ontario, Brendan Kelley Publishing Co, 1991.

National Research Council, Everybody Counts: A Report to the Nation on the Future of Mathematics Education, Washington, DC: National Academy Press, 1989.

National Research Council, Reshaping School Mathematics: A Philosophy and Framework for Curriculum, Washington, DC: National Academy Press, 1990.

Wilson P. S. (Ed.) Research Ideas from the Classroom: High School Mathematics , Reston, VA.: National Council of Teachers of Mathematics, 1993.

Course Relationship to Standards

Applicability of the Course Objectives to Recommendations of Professional Organizations and Associations

We will address recommendations that relate to the National Council of Teachers of Mathematics as standards of Algebra, Functions, and Trigonometry for grades 9-12, as well as standards of Patterns and Functions, and Algebra for grades 5-8. In particular in helping students to: Algebra (a) represent situations that involve variable quantities with expressions, equations, inequalities, and matrices; and (b) use tables and graphs as tools to interpret expressions, equations, and inequalities. Functions (a) model real-world phenomena with a variety of functions; (b) translate among tabular, symbolic, and graphical representations of functions; (c) recognize that a variety of problem situations can be models by the same type of function. Trigonometry (a) apply trigonometry to problem situations, involving triangles; (b) understand the connection between trigonometry and circular functions, and (c) apply graphing techniques to trigonometry functions. Patterns and Function (a) describe and represent relationships with tables, graphs, and rules; and (b) use patters and functions to represent and solve problems. Algebra (a) apply algebraic methods to solve a variety of real-world and mathematical problems; and (b) solving linear equations using concrete, informal, and formal methods.

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