Fall 2004 Advance Course Information

This information effective for Fall 2004. Check with instructor the first day of class for any changes.

Education

[EDUC-213B]

213B. Research and Practice in Mathematics Education

Instructor: Judit Moschkovich
Office: Crown 232
Phone: 459-2004
E-mail: jmoschko@ucsc.edu

Course Description

The course focuses on understanding how students learn mathematics. The course provides an introduction to theoretical approaches to learning mathematics in secondary classrooms and to the research that is the basis for national and state mathematics teaching standards. The course provides a) a survey of current theories of mathematical thinking, cognition, and learning and b) an introduction to current research on student learning for two secondary topics, proportional reasoning and algebraic thinking. In their final papers for the course, students review research on student learning for one other topic selected from the following list: rational number operations, geometry and spatial reasoning, probability and statistics; functions, calculus (especially limits), or proof. Students apply the theories and research discussed in class by writing essays, conducting and analyzing interviews with students, and writing a final paper.

[This course is required for the single-subject secondary mathematics MA/credential program and is part of a two-quarter sequence required for MA students. The second quarter (EDUC 213C) focuses on approaches and methods for teaching secondary mathematics].

Doctoral students in mathematics education are required to take this course.
Graduate students outside of the Education Department are welcome to register for this course.

The course will address the following topics:

Course Requirements and Evaluation

Class-work includes discussing readings, analyzing and discussing interviews, and making two presentations. Homework is central to the course and includes completing written summaries of readings (4), interview(s) with a student (1 or 2), essays (2 or 3), and one final paper.

Attendance is required. No more than 3 absences. No late work accepted.
Passing (P) is equivalent to a B grade for graduate courses (70-80% of all points)

Evaluation will be on the basis of participation, presentations, and written work:

Required Readings

1. Reader is available at Slug Books.
2. Required text for Week 6:

Fostering Algebraic Thinking: A Guide for Teachers Grades 6-10. Mark Driscoll (1999). Portsmouth, NH: Heinemann. (Available at UCSC Bookstore).
*Please make sure that you buy this book at the beginning of the quarter or the bookstore will return all copies still on the shelf after the 4th week.

EDUC 213B. Research and Practice in Mathematics Education
Fall 2003 Reader

1. Schoenfeld, A. (2000) Purposes and methods of research in mathematics education. Notices of the American Mathematical Society, June/July 2000, pages 641-649.
2. Battista, M. (1999). The mathematical mis-education of America's youth: Ignoring research and scientific study in education.
3. Schoenfeld, A. (1987) Cognitive science and mathematics education: An overview. In A. Schoenfeld (Ed.) Cognitive science and mathematics education. Hillsdale, NJ: Erlbaum.
4. Erlwanger, S. (1973). Benny's conception of rules and answers in IPI mathematics. JCMB, Vol. 1, No. 2, Autumm 1973.
5. Hughes, M. (1986). Piaget under attack. Chapter 2 in Children and Number: Difficulties in learning mathematics, pages 12-23.
6. Confrey, J. (1990). What constructivism implies for teaching. In R. Davis, C. Maher, and N. Noddings (Eds.) Constructivist views on the teaching and learning of mathematics. Reston, VA: NCTM. Pages 108-122.
7. Yackel, E., Cobb, P., Wood, T., Wheatly, G, and Merkel, G. (1990). The importance of social interaction in children's construction of mathematical knowledge. In Cooney, T. and Hirsch, C. (1990). Teaching and Learning Mathematics in the 1990s. Reston, VA: NCTM. Pages 12-21.
8. Forman, E. (1996). Learning mathematics as participation in classroom practice: Implications of Sociocultural theory. In Steffe, Nesher, Cobb, Goldin, and Gree (Eds.) Theories of mathematical learning, pages 115-130.
9. 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.
10. Goos, M. (2004) Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, Vol. 35, No. 4, 258-291.
11. Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning. New York: Macmillan, pp. 334-370.
12. Hiebert, J. and Carpenter, T. (1992). Learning and teaching with understanding. In D. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning. New York: Macmillan, pp. 65-97.
13. 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.
14. Lamon, S. (1999) Teaching fractions and ratios for understanding, Chapter 1 pages 1-9 and Chapter 2 pages 11-14.
15. Kieran, C. (1992). The learning and teaching of school algebra. . In D. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning. New York: Macmillan, pages 390-419.
16. Chazan, D (2000). Beyond formulas in mathematics and teaching. Chapter 3: Towards a "conceptual understanding" of school algebra, pages 59-110. NY: Teachers College Press.
17. Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of mathematics 14 (3): 24-35.
18. Schoenfeld, A. H. & Arcavi, A. (1988). On the meaning of variable. Mathematics Teacher, 81, 420-427.
19. Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In A. F. Coxford & A. P. Schulte (Eds.), The ideas of algebra. Reston, VA: National Council of Teachers of Mathematics. Pages 8-19.
20. Moschkovich, J.N, Schoenfeld, A., and Arcavi, A. (1993). Aspects of understanding: On multiple perspectives and representations of linear relations, and connections among them. In T.A. Romberg, E. Fennema and T.P. Carpenter (Eds.), Integrating Research on the Graphical Representation of Function. Hillsdale, NJ: Erlbaum. Pages 69-100.
21. Moschkovich, J.N. (2000) Learning mathematics in two languages: Moving from obstacles to resources. In W. Secada (Ed.), Changing Faces of Mathematics (Vol. 1): Perspectives on multiculturalism and gender equity. Reston, VA: NCTM. Pages 85-93.
22. Moschkovich, J.N. (1999) Supporting the participation of English language learners in mathematical discussions. For the Learning of Mathematics 19(1), 11-19.
23. Brenner, M. (1994). A communication framework for mathematics classrooms: Exemplary instruction for culturally and linguistically diverse students. In Language and Learning: Educating linguistically diverse students, B. McLeod (Ed.), pages 233-268. Albany: SUNY.

Readings for Interviews

24. Lowery, L. (1974). Proportional reasoning. In Lowery, Learning About Learning Series. Berkeley, CA: Univ. of California. Pages 17-20 and 37-38.
25. Cramer, K., Post, T., Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. Owens (Ed.) Research ideas for the classroom: Middle grades mathematics. NY, NY: Macmillan Publishing Company.
26. Understanding ratio and proportion. Chapter 13 in G. Cathcart, Y. Pothier, J. Vance, and N. Bezuk (Eds.) Learning mathematics in elementary and middle schools.

Readings for research paper

Chapters from D. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning. New York: Macmillan.

27. Rational number: Behr, M., Harel, G., Post, T., and Lesh, R. (1992) Rational number, ratio, and proportion (pages 296-333).
28. Geometry: Clements, D. and Battista, M (1992). Geometry and spatial reasoning (pages 420-464).
29. Probability and statistics: Shaughnessy, M. (1992). Research on Probability and statistics: Reflections and directions (pages 465-494).
30. Functions, calculus, limits, proof: Tall, D. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity and proof (pages 420-464).

Readings for research paper

As part of the course requirements you will write a 10- to 15-page research paper.

1. The first step in planning the research paper is to pick a topic from the five topics below.
2. The second step in planning the research paper is to read one of the chapters listed below. These readings are in the reader.

Rational number and ratio
Behr, M., Harel, G., Post, T., and Lesh, R. (1992) Rational number, ratio, and proportion. In D. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning. New York: Macmillan. Pages 296-333.

Geometry
Clements, D. and Battista, M (1992). Geometry and spatial reasoning. In D. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning. New York: Macmillan, pages 420-464.

Probability and statistics
Shaughnessy, M. (1992). Research on Probability and statistics: Reflections and directions. In D. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning. New York: Macmillan, pages 465-494.

Functions
Tall, D. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity and proof. In D. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning. New York: Macmillan, pages 495-511.

Functions, calculus, limits, proof:
Tall, D. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity and proof. In D. Grouws (Ed.), Handbook of Research in Mathematics Teaching and Learning. New York: Macmillan, pages 495-511.

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