Master of Education, Summer, 1998

Department of Mathematics Education

Comprehensive Examination

INSTRUCTIONS: Respond to one question in Section 1, one question in Section 2, and the only question in Section 3. Consider that the examination will place 50 percent on the response to Section 3 and 50 percent to Sections 1 and 2 combined.

Return the examination to J. Wilson on Monday, June 29. You man consult any books, technology, journals, reports, and notes but do not discuss with other people. Responses should be typed but may use any electronic format, including HTML.

Section 1.

1. Recent statements of standards for school mathematics include an emphasis on applications of mathematics.

a) Identify some goals relating to applications that you would adopt as a teacher of school mathematics. Explain why you would adopt these goals as opposed to others.

b) Describe the features (e.g., content, organization, teaching methods, activities) of a secondary school curriculum that emphasizes the goals you have identified.

2. Your department head has asked you to prepare a position paper for your department as you plan changes in the geometry curriculum. (OPTION: Substitute a different content for geometry, e.g., algebra, statistics, consumer mathematics, probability, etc.)

a) What are the main goals of the high school geometry curriculum?

b) To what extent do you agree with the NCTM Standards regarding geometry topics that should receive increased or decreased attention?

c) What roles will technology play in your revised curriculum?

d) What forms of assessment, if any, should your department be using to assess geometry learning?


Section 2.

1. All three of the NCTM Standards documents challenge teachers to make connections in their mathematics classes. The 1995 NCTM yearbook was Connecting Mathematics across the Curriculum. Discussions of connections encourage connections within mathematics as well as interdisciplinary connections.

a) Why does the NCTM advocate the use of connections? What are the costs or problems with making connections? What do YOU advocate and why?

b) Describe the components of a "good" use of connections in the mathematics classroom.

c) Choose a topic from Algebra II, Advanced Geometry, or Calculus and illustrate how you would make 10 a mathematical connection and 2) an interdisciplinary connection.

2. Technology tools in mathematics instruction.

a) Select a topic in the school mathematics that you teach (or might teach). Describe how you would use technology tools to teach the topic. Discuss how technology tools would enable you to change the coverage of the content in the topic.

b) Select a topic not now included in the school curriculum that you feel technology tools would allow you to teach. Discuss the topic, how you would teach it, and why you would introduce it.


Section 3.

Discuss the potential of the Internet for mathematics instruction in the secondary school. Assume, and describe, the adequate and satisfactory access and connectivity. Your response should deal with the potential you can identify in this resource rather than dwell on limitations of currently available materials and access. The focus of your discussion should be on mathematics teaching and learning.