Mathematics Seminar

MATH 4000

1 semester hour

 

(Please note that in some communications, this course has been listed as TEAM 4000 and been called Capstone Math.  I prefer what is listed above.)

 

Course Information

 

Course Description:

This capstone course integrates mathematics concepts from a variety of fields, such as geometry, algebra, linear algebra, calculus, and probability.  Graphing calculators, software such as Geometer’s Sketchpad, and spreadsheets, are incorporated in the course.

 

Course Objectives:

  1. Students will be able to demonstrate understanding of the real and complex number systems, their operations, and properties.
  2. Students will be able to construct geometric interpretations of algebraic principles.
  3. Students will be able to solve problems involving Euclidean and transformational geometry.
  4. Students will be able to solve problems involving trigonometric functions.
  5. Students will be able to model problems and demonstrate the difference between an approximation and an “exact” answer.
  6. Students will be able to describe fundamental concepts underlying various mathematical ideas, e.g. rate of change underlies the concept of slope.

 

Prerequisites and Co-requisites:

 

15 semester hours of mathematics coursework from either the RODP add-on endorsement program or from a mathematics major program

 

It is assumed that students will have a working knowledge of algebra, geometry, probability, trigonometry, and calculus.

 

Course Topics:

The various content topics listed in the course objectives are interwoven within a problem-solving environment.  Effective teaching of mathematics is built upon a thorough understanding of the mathematics.  The ability to recognize a mathematical concept in various forms and to analyze its underlying properties is fundamental to excellent pedagogy.  Therefore, this course has as its focus in depth explorations of familiar topics.

 

Specific Course Requirements:

Best practice recommendations for high school mathematics include use of graphing calculators and appropriate software, such as spreadsheets and geometry utilities.  Therefore, working knowledge of a graphing calculator and spreadsheet is expected.  (All references in coursework will  be for the TI-83+.)    Students will also learn to use Geometer’s Sketchpad.

 

Textbook, Supplementary Materials, Hardware, and Software Requirements

 

Required Textbook:

Mathematics for High School Teachers An Advanced Perspective, Usiskin, Peressini, Marchisotto, & Stanley.  Pearson,

ISBN 0-13-044941-5

 

Readings:

Warrington, M., “How Children Think about Division with Fractions,”  Mathematics Teaching in the Middle School, May, 1997.

Thorton, S. “New Approaches to Algebra:  Have We Missed the Point?” Mathematics Teaching in the Middle School, March, 2001.

 

Software and Hardware:

Microsoft Word with Equation Editor (The Equation Editor comes with Word, but is not part of the standard Install procedure.  It might be necessary to get the Word CD and install Equation Editor.)

Geometer’s Sketchpad, student version, Key Curriculum Press

Graphing calculator with computer connection (e.g., TI-83+ with Graph-link)

 

Instructor Information:

Please see the separate page inside the course to find instructor contact information as well as a statement of virtual office hours and other communication information.

 

Assessment and Grading

 

Testing Procedure:

There will be one on-line final.  Students will need to arrange for a proctor for the final.

 

Grading Procedure

The point value and rubric for grading each assignment will be attached to the assignment.  Students will be expected to discuss mathematical ideas using appropriate language and symbols. In this course, simply arriving at the correct solution will not be sufficient.  Often, more than one solution path will be required.  All explanations should be clearly stated so that another person can follow the logic.  Success in this course will require thoughtfulness and flexible thinking.

 

Grading  Scale:

The following percents of total points possible will earn the given grade:

90-100         A

80-89          B

70-79          C

60-69          D

Below 60     F

 

Assignments and Participation

 

Assignments and Projects:

1.          Representing Fractions and their Operations (based on Warrinton article):  There will be two submission dates for this assignment.  The first submission will receive feedback, but no grade.  The student should modify the work in response to feedback and submit this assignment again.  The second submission will be graded.

2.          Representing Algebraic Concepts (based on Thornton article):  Again, there will two submissions for this assignment—the first for feedback and the second for a grade.

3.          Functions and their representations (Chapter 1):  Responses to Problems 9 and 10 will be graded.

4.          Functions and their representations (Section 3.1.2):  Responses to Problem 6a-c, f.

5.          Functions and their representations (Section 3.3.1)

6.          Operations and their properties (Section 4.1.1)

7.          Operations and their properties (Section 4.1.2)

8.          Operations and their properties (Section  4.2.1)

9.          Operations and their properties (Section 4.3.3)

10.      Transformational geometry (Section 7.1.4)

11.      Distance (Section 8.1.2)

12.      Similarity (Section 8.2.1)

13.      Trigonometry (Chapter 9)

 

Class Participation:

Students are expected to make contributions to the discussion board.  Students are expected to communicate with the instructor as a resource.  Check the course bulletin board often.

Punctuality:

Due dates are important!