Spring 2002

This information effective for Spring 2002.
Check with instructor the first day of class for any changes.

Education

[EDUC 185B]

185B. Introduction to Teaching Mathematics

Spring 2002
Instructor: Dr. Judit Moschkovich
MW 5:30–7:15 p.m.
Crown 202

Office: Crown 232
Office hours: Tuesdays 1:00–3:00 p.m. and by appointment
Phone: 459-2004
E-mail: jmoschko@cats

Course Description

This course provides an introduction to different views of learning and teaching mathematics, the principles in the national and state mathematics teaching standards, and teaching practices in secondary mathematics classrooms. This course is intended for undergraduate mathematics or science majors who are considering becoming mathematics teachers.

Students will explore the connections between research and practice in mathematics education and different perspectives on mathematics learning and teaching. Students will also examine their own mathematical learning, their own beliefs about learning and teaching mathematics, and participate in discussions of content and pedagogy. These discussions will be grounded in direct experience (their own learning, relevant readings, observations in secondary mathematics classrooms, interviews with students, or written cases) and in classroom data (videotapes, audiotapes, transcripts, interviews, and written student work). Students will be required to observe a mathematics classrooms for at least one class period each week.

The course is part of the Secondary Mathematics Subject Matter Program and the minor program in Education. Students participating in the Community Teaching Fellowship in math and Science are required to take either this course or EDUC 185C Science Teaching in Spring 01. For more information contact Dr. Judit Moschkovich jmoschko@cats or 459-2004.

The course will address the following topics:

Course Requirements

Class-work will include working on mathematics problems, discussion of readings, analysis and discussion of classroom data (video or audio tapes of classrooms, student work, etc.), and reflections on classroom observations. Homework is central to the course and includes problems, readings, summaries of readings, reflections on classroom observations, cases, and essays.

Required work:

1. Participation in class discussions of readings and data.
2. Observing one period of a math class per week for 6 weeks total, starting around Week 2 of the Quarter, ending when testing begins in schools. You will only be observing, not tutoring or teaching.
3. Written reflections on classroom observations (1–2 pages, 1 per week starting Week 2 or later depending on classroom placements, due on Wednesdays).
4. Written reactions for readings from the required list (1 page maximum, 1 per week, due Mondays, 8 total).
5. Two short essays (3–4 pages, due Week 6 and Week 8).
6. One written review of 3 math textbooks (2 pages, due Week 4).
7. One written report on an interview with a student (3–4 pages, due Finals Week). This will be the final assignment. If for any reason you cannot interview a student for this report, you can turn in “Essay 3: Teaching Division of Fractions” instead.

The course is Writing intensive and it fulfills a W requirement. What does this mean?

• The course requires about 25 pages of writing per quarter.
• But not all writing will be in the form of a formal essay. Only 2 short essays are required.
• Reactions to readings can be written in a personal reflection style.
• Classroom observations are in response to specific questions and can be written as notes and thoughts you have as you observe.
• You can choose the final assignment

  Fractions Interview Report or
  Essay 3: Teaching Division of Fractions.

Most importantly:

• You will have the opportunity to revise any written assignment.
• Support for working on your writing skills will be provided by the instructor and writing staff on campus.

Attendance is required. No more than 3 absences. Passing requires completing the work at a satisfactory (75% or C) level.

• Required Book for the course (Available at the bookstore)
  Corwin, R., Storeygard, J., and Price, S. (1996). Talking Mathematics. Portsmouth, NH: Heinemann.
• Required Reader for the course (Available at Slug Books)
  (readings may change, final reading list will be available by first day of class)

1. Schoenfeld A. (2001) Mathematics education in the 20th Century. In Education across a century: The centennial volume, 100th Yearbook of the National Society for the Study of Education, p. 239–278.
2. Borasi, R. The invisible hand in mathematics instruction. In Cooney, T. and Hirsch, C. (1990). Teaching and Learning Mathematics in the 1990s. Reston, VA: NCTM. Pages 174–182.
3. Dossey, (1997). Appendix: Defining and measuring quantitative literacy. In L.A. Steen Why Numbers Count. NY, NY: College Entrance Examination Board. Pages 173–186.
4. Cooney, T., Brown, S., Dossey, J., Schrage, G., and Wittmann, E. (1996). Mathematics, pedagogy ands teacher education. Chapter 1: Thinking about being a mathematics teacher (pages 1–27) and Chapter 6: Posing Mathematically: A Novelette (pages 306–315). Portsmouth, NH: Heinemann.
5. Carraher, D. (1989). Mathematics learned in and out of school. In Harris M. (Ed), Schools, Mathematics and Work. Bristol, PA: The Falmer Press. Chapter 16.
6. Moschkovich, J (in press). An introduction to everyday and academic mathematical practices in the classroom. To appear in M. Brenner and J. Moschkovich (Eds.) Everyday and Academic Mathematics in the Classroom. Journal for Research in Mathematics Education monograph.
7. Saxe, G. (1999). Cognition, development, and cultural practices. In E. Turiel (Ed.), Development and Cultural Change: Reciprocal Processes (pp. 19–36). SF: Jossey-Bass.
8. Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27 (1), 29–64.
9. Van Oers B. (1996). Learning mathematics as a meaningful activity. In Steffe, Nesher, Cobb, Goldin, and Greer (Eds.) Theories of mathematical learning, pp. 91–113.
10. Donovan, M.S., Bransford, J., Pellegrino (1999.). How people learn: Bridging research and practice. Washington, DC: National Academy Press. Chapters 1 and 2.
11. Moschkovich, (1999) Students’ use of the x-intercept as an instance of a transitional conception. Educational Studies in Mathematics, 37: 169–197.
12. Stiff, Johnson and Johnson (1993). Cognitive issues in mathematics education. In Research Ideas for the Classroom, edited by P. Wilson. NY: Macmillan.
13. Stigler, J. and Hiebert, J. (1999). Teaching is a cultural activity. In The Teaching Gap. (Chapter 6 pages 85–101). The Free Press.
14. Ball, D.L. (1993) With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal.
15. Thompson, A., Philipp, R., Thompson, P., and Boyd, B. (1994). Calculational and Conceptual Orientations in teaching mathematics. In Professional Development for Teachers of Mathematics.
16. Schoenfeld, A. (1988). When good teaching leads to bad results. Educational Psychologist, 23, 145–166.
17. Ma, L. (1999). Knowing and teaching elementary mathematics. Chapter 3: Generating representations: Division by fractions.
18. Hiebert, J. (1990). The role of routine procedures in the development of mathematical competence. In Cooney, T. and Hirsch, C. (1990). Teaching and Learning Mathematics in the 1990s. Reston, VA: NCTM. Pages 31–40.
19. Ball, D.L. (1991). What's all this talk about “Discourse”? The Arithmetic Teacher, November 1991, 44–47.
20. Moschkovich, J.N. (1999) Supporting the participation of English language learners in mathematical discussions. For the Learning of Mathematics 19(1), 11–19.
21. Delpit, L. (1995). Skills and other dilemmas of a progressive black educator. In Other People’s Children, Cultural Conflict in the Classroom. New York: The New Press, pp. 11–20.
22. McDiarmid, G.W. (1991). What teachers need to know about cultural diversity: restoring subject matter to the picture. In M. Kennedy (Ed.), Teaching academic subjects to diverse learners. New York: Teachers College Press.
23. Silva, C., Moses, R. (1990). The Algebra Project: Making middle school mathematics count. Journal of Negro Education, Vol. 59, No. 3, pp. 375–391.
24. Secada, W. (1990). The challenges of a changing world for mathematics education. In Cooney and C. Hirsch (Eds.), Teaching and learning mathematics. Reston, VA: NCTM. Pages 135–143.
25. Escalante, J. and Dirmann (1990). The Jaime Escalante math program. The Journal of Negro Education.
26. Riordan, J. and Noyce, P. (2001). The impact of two standards-based mathematics curricula on student achievement in Massachusetts. Journal for Research in Mathematics Education, Vol. 32, No. 4, 368–398.
27. Jacob, B. (2001). Implementing standards: The California mathematics textbook debacle. Phi Delta Kappan, Vol. 83, No. 3, 264–272.

Cases

26. Mathematics Teaching Cases: Fractions, decimals, ratios, and percents. Edited by C. Barnett, D. Goldstein, and B. Jackson. Why Isn’t it one less? Pages 77–79. I still Don’t See Why May Way Doesn’t work. Pages 28–29.

Narrative Evaluation Template

1. Overall, this student's participation and written assignments indicated

• Excellent/outstanding
• Very good/above average
• Satisfactory/a good working/passing
• Marginal/uneven/below average
• Poor/minimal/unsatisfactory understanding of the ideas in the course.

2. Class participation

• made strong contributions to class meetings
• was clearly engaged during class meetings
• contributed insightful ideas and supported other students’ learning
• listened actively and contributed to the classroom dynamics
• attended class regularly
• was usually present
• attended irregularly
• was often absent

3. Written assignments
Of the ____ writing assignments_____ were late or missing
The required 2–4 page essays (2) were usually:

• Excellent: Extraordinary, with coherent analysis that integrated ideas and evidence in well-developed and eloquent reflections
• Very good: Very well developed, with clear connections between ideas and evidence to support the arguments
• Passing: Of good sound quality, reflecting active engagement with the topic, though in places the work would have benefited from being pushed further
• Marginal: Uneven quality, at times sketchy and not sufficiently grounded in the course materials or not addressing the topic fully
• Unsatisfactory: Poor quality, either showing a lack of adequate engagement with the topic or not turned in at all.

The required written summaries of a reading (8) showed:

• Extremely thoughtful engagement with the ideas
• Thoughtful engagement with the ideas
• Satisfactory engagement with the ideas
• Uneven engagement with the ideas

The required written reflections on classroom observations (6) showed:

• Extremely thoughtful engagement with the ideas
• Thoughtful engagement with the ideas
• Satisfactory engagement with the ideas
• Uneven engagement with the ideas

The required written review of textbooks showed:

• Extremely thoughtful engagement with the ideas
• Thoughtful engagement with the ideas
• Satisfactory engagement with the ideas
• Uneven engagement with the ideas

The required final assignment (a written report on an interview with a student or an essay) showed:

• Extremely thoughtful engagement with the ideas
• Thoughtful engagement with the ideas
• Satisfactory engagement with the ideas
• Uneven engagement with the ideas

Items below apply to only some students:
I observed impressive progress in____________ understanding of the course material, as evidenced by improvements in

• understanding of the readings and class material, or depth of analysis of ideas and evidence, or coherence and organization of ideas expressed.

_____ went beyond the assigned work in class by _____(extra presentation, optional rewrite, optional reading annotation).

This was clearly honors quality work.

This student demonstrates great potential for graduate work.