MATH 328 Curriculum and Technology in Secondary Mathematics II
Department of Mathematical Sciences Fall 2007
Course Description: This course is designed for students preparing to teach mathematics in grades 7-12. Its focus will be on the teaching of geometry and measurement and connections to other content areas of the secondary mathematics curriculum. A variety of tools including computer software and hands-on manipulatives will be used to develop concepts and generate conjectures.
During the course you will be relearning (or learning for the first time) much of the high school geometry curriculum while you are also learning about teaching geometry.
Prerequisites: This course is intended for students seeking certification to teach mathematics in grades 7-12. You do not have to be admitted to the professional program but should have completed at least two semesters of calculus and a course in discrete mathematics (MATH 221 and MATH 218) or the equivalent.
Instructor: Timothy V. Craine
Contact Information:
Office phone: 860-832-2854
Home phone: 860-688-5418 (up until 10 PM)
Email: crainet@ccsu.edu
Office: Marcus White, Room 108
Office
Hours: Monday 9:00 AM-Noon
Wednesday 9:00 AM-Noon, 2:00-5:00 PM
Thursday 9:00 AM-Noon
Friday 12:00-2:00 PM
Other times by appointment.
Class Meeting Times: Monday and Wednesday 6:45-8:00 PM, Maria Sanford, Room 221.
Required Text: Michael Serra, Discovering Geometry: An Investigative Approach, 4th edition, Key Curriculum Press, 2008.
Software: CCSU has a site license for Geometer’s Sketchpad v. 4.03, which will be used extensively in this course. A special student discount rate is available at the campus bookstore if you wish to install this software on your home computer. Otherwise you may access the software from any computer on campus.
Course Requirements:
· Attend and participate in class regularly.
· Complete homework assignments, assigned on a daily basis.
· Maintain a portfolio of your work to be collected twice during the semester. Instructions and rubrics for each portfolio will be distributed in advance.
· Write a unit plan with your assigned group. Groups will be assigned to write plans for Circles, Similarity, and Trigonometry. Write a plan for a 45 minute lesson that is part of the unit. Present a 20 minute segment of this lesson to the class, which will be video taped to facilitate reflection and feedback.
· Participate in a field experience (in a geometry classroom) and write a report.
· Take midterm and final examinations.
Assessment. Grades for the course will be determined as follows:
Portfolio of assigned problems, sketches from GSP,
report on field experience (October 3 and November 28) 20%
Unit plan (group assignment, due October 31) 10%
Lesson plan (individual assignment, due November 14) 10%
Presentation of Lesson (November 26-December 5) 10%
Reflection on the lesson (due one week after the lesson is presented) 10%
Midterm Exam (October 17) 20%
Final Exam (December 17, 8:30-10:30 PM, note time) 20%
University Policies
1. If you need course adaptations or accommodations because of a disability, if you have emergency medical information to share with us, or if you need special arrangements in case the building must be evacuated, please make an appointment with Prof. Craine as soon as possible. His telephone numbers and office hours are given above.
2. In the event of a weather emergency which requires curtailment or cancellation of classes, listen to WTIC (1080 AM) or call (860) 832-3333 for the “general snow message.”
3. Last day to drop a course Tuesday, October 30. Forms are available in the Enrollment Center, Willard Hall. Cessation of attendance, notice to the instructor, or telephone calls to the Enrollment Center are not considered official notice of a student’s intention to drop the course. Undergraduate full time students for whom dropping a course would reduce their credit load to fewer than 12 credits MUST apply for withdrawal.
4. The final examination has been scheduled by the University and must be taken on the date assigned, Monday, December 17.
Tentative Schedule of Topics (with assignments in bold)
Numbers in Brackets refer to resources on the next page.
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Monday |
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Wednesday |
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9/3 |
No Class—Labor Day |
9/5 |
Introduction to Course Introduction to Geometer’s Sketchpad [1] |
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9/10 |
Van Hiele Levels [7, 9] (Serra: Chapter 1) |
9/12 |
Inductive and Deductive Reasoning (Serra: Chapter 2) |
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9/17 |
Euclid’s Elements Book I Overview [8] |
9/19 |
Euclidean Constructions (Serra: Chapter 3) |
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9/24 |
Forms of proof [5, 6] Triangle Properties (Serra: Chapter 4) |
9/26 |
Polygon Properties (Serra: Chapter 5) |
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10/1 |
Area (Serra: Chapter 8) |
10/3 |
Pythagorean Theorem (Serra: Chapter 9) Portfolio 1 is due |
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10/8 |
Coordinate Geometry [3, 4, 14] |
10/10 |
Transformations (Serra: Chapter 7) |
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10/15 |
Review and Catch up |
10/17 |
Midterm Exam |
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10/22 |
Unit Planning and Lesson Planning |
10/24 |
Work in teams on unit plans |
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10/29 |
Historical Perspectives on Teaching Geometry/NCTM Standards [9, 10, 11] |
10/31 |
CMT and CAPT Unit Plans are due |
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11/5 |
Tessellations (Serra: Chapter 7) |
11/7 |
Matrices and transformations [2] |
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11/12 |
Geoboards and Tangrams [13] |
11/14 |
Three Dimensional Geometry [15] Lesson Plans are due |
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11/19 |
Volume (Serra: Chapter 10) |
11/21 |
No Class—Thanksgiving Break |
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11/26 |
Student Lessons on Serra: Chapters 6, 11, and 12 |
11/28 |
Student Lessons, continued Portfolio 2 is due |
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12/3 |
Student Lessons, continued |
12/5 |
Student Lessons, continued |
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12/10 |
Course Summary and Evaluation |
12/12 |
Review All Lesson Reflections are due |
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12/17 |
Final Exam |
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Additional Resources:
[1] Bennett, Dan. Exploring Geometry with the Geometer's Sketchpad, Key Curriculum Press, 1999.
[2] Coxford, Arthur F., Jr., ed. Geometry from Multiple Perspectives. National Council of Teachers of Mathematics, 1991.
[3] Craine, Timothy V. "Integrating Geometry into the Secondary Mathematics Curriculum," in Hirsch, ed., The Secondary School Mathematics Curriculum, 1985 Yearbook of the National Council of Teachers of Mathematics.
[4] Craine, Timothy V. and Rubenstein, Rheta R. “A Quadrilateral Hierarchy to Facilitate Learning in Geometry,” Mathematics Teacher, 86 (January 1993), pp. 30-36.
[5] Craine, Timothy V. and Rubenstein, Rheta R. "Traveling toward Proof", Mathematics Teacher 93 (April 2000). (“Euclid Airlines”)
[6] DeVilliers, Michael D. Rethinking Proof. Key Curriculum Press, 2003.
[7] Fuys, David; Geddes, Dorothy; and Tischler, Rosamond, The Van Hiele Model of Thinking in Geometry among Adolescents, JRME Monograph Number 3, National Council of Teachers of Mathematics, 1988.
[8] Joyce, David. Euclid’s Elements with commentary. http://aleph0.clarku.edu/~djoyce/java/elements/elements.html
[9] Lindquist, Mary M., ed. Learning and Teaching Geometry, K-12, 1987 yearbook of the National Council of Teachers of Mathematics.
[10] Mamman, Carmelo and Villani, Vinicio. Perspectives on the Teaching of Geometry for the 21st Century, Kluwer Academic Publishers, 1998.
[11] National Council of Teachers of Mathematics, Principles and Standards for School Mathematics, NCTM, 2000. Available online at www.nctm.org.
(Especially Chapter 2. Principles for School Mathematics, and Chapters 6 and 7 as they pertain to geometry, measurement, problem solving, reasoning and proof, communication, connections and representation for grades 6-12.)
[12] NCTM Publications especially Mathematics Teacher and Mathematics Teaching in the Middle School. Also visit www.nctm.org.
[13] Picciotto, Henri. Geometry Labs, Key Curriculum Press, 1999.
[14] Rubenstein, Rheta R.; Craine, Timothy V.; and Butts, Thomas R. Integrated Mathematics 1-3, McDougal Littell, 2002.
[15] Winter, M.; Lappan, G.; Philips, E.; and Fitzgerald, W. Middle Grades Mathematics Project: Spatial Vizualization. Addison-Wesley, 1986.