EDUC 5840/MATH 5840 Mathematics Learning Environments

 

 

Faculty of Graduate Studies

Graduate Program in Education

Graduate Program in Mathematics and Statistics

Summer 2007 Course Outline

 

Course Director: Professor Margaret Sinclair

Office: 3159 TEL Bldg.  – enter through 3150

Phone: 416 736 2100 (20344) 

E-mail: msinclair@edu.yorku.ca          

Course Website: http://www.yorku.ca/sinclair

 

Class meetings: (Tentative) Wednesday, 6 p.m. to 9 p.m.- April 18 to June 27. There will be a discussion about the remaining class.

Course Location: TEL 3069

 

Course Description

This course explores issues in mathematics education in light of new developments in cognitive theory, in order to characterize environments for learning mathematics that are both learner centered and knowledge centered. Topics include: mathematics learning as a social/cultural experience, mathematics as sense making, the impact of technology on mathematics learning environments. A specialized mathematics background is not a prerequisite for the course. (Same as Math & Statistics 5840 3.0)

 

Evaluation

Evaluation for the course will be based on:

Reading-related assignments (30%)

Reflection narrative (15%)

Final project (55%) – paper and presentation

 

Presentation of Submitted Work

Please use APA style for submitted papers.

-          Refer to the style guides found at:

 http://info.library.yorku.ca/depts/ref/refweb.htm

-         When citing internet-based sources, please refer to: http://info.library.yorku.ca/internet/citing.htm

 

Academic Conduct

Academic honesty is of the utmost importance in any learning environment. Please familiarize yourself with the regulations on plagiarism and cheating on the FGS website.

 

Online Participation

 

There will be a conference set up on First Class. Through the conference you can share ideas with other participants in the class. I will use the conference to post any notices about the classes or assignments.

 

How class will be conducted: 

We will be involved in discussing course readings, listening to and viewing examples of students’ mathematics learning, and engaging in exploratory activities. We will also have individual and group presentations on topics related to the themes of the course.

 

Assignments – Evaluation for the course will be based on:

1.      Reading Reports: 30% Each participant will prepare 3 papers (4-5 pgs, double-spaced, APA 5th style). The first paper will be on one of the readings for the week of April 25th. The next two may be on a weekly reading or may be chosen from the course references, or from a recent volume (after 2000) of one of the following math education journals: ESM, JMB, CJSMTE, JRME. Expectations – Discuss the main ideas in the article. If it is a research article include (briefly) information about the methodology as well as results and implications. “A” papers will include: strong writing, correct use of references, analysis that brings in ideas or theories from one or more other articles. Paper due dates: April 25, May 9, May 23.  Note: papers on weekly readings cannot be handed in after the class.

2.      Presentation: 25% Individual or group presentation based on topics/issues discussed during the course. Approximately 20 minutes.

3.      Research paper. (30%) An academic paper (10-12 pages, including references, 12 point type, double spaced) on a course related topic. Papers can be based on the research used for the presentation. A one-page proposal for the paper is to be submitted on June 6th. Two students may collaborate on a paper. The length will then be 16-20 pages. Due date – July 4th

4.       Reflection and Report. (15%) Because class discussion and in-class activities are key components of this course, regular attendance, and active, informed participation are expected. One of the course meetings will be replaced by attendance at a meeting or conference related to mathematics education, e.g., the YSIMSTE Technology and Equity Conference, a Fields Mathematics Forum meeting, the OAME conference.  A reflection (approx 3 pages) on course discussions and activities, plus a report (approx 3 pages) on the meeting attended, will form the basis for this section of the evaluation. Due Date: Reports/reflection will be due at the last class.

 

Required textbooks:There will be no required text for the course, although a number of books will be recommended and some will be available for short term loan.  

 

Suggested Readings and Resources

 

Anderson, J. R., Reder, L. M., & Simon, H. A. (1996). Applications and misconceptions of cognitive psychology to mathematics education.Unpublished manuscript.

 

Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7, 245-274.

 

Baker, D., Street, B., & Tomlin, A. (2003). Mathematics as social: Understanding relationships between home and school numeracy practices. For the Learning of Mathematics, 23(3), 11-15.

Ball, D. L. (2000). Bridging practices: Intertwining content and pedagogy in teaching and learning to teach. Journal of Teacher Education, 51(3), 241 - 247.

 

Becker, J. R. (1995). Women's ways of knowing in mathematics. In P. Rogers & G. Kaiser (Eds.), Equity in mathematics education: Influences of feminism and culture. London: The Falmer Press.

Boaler, J. (2002). Learning from teaching: Exploring the relationship between reform curriculum and equity. Journal for Research in Mathematics Education, 33(4), 239-258.

 

Bransford, J. D., Brown, A. L., Cocking, R. R., Donovan, M. S., & Pellegrino, J. W. (Eds.). (2000). How people learn: Brain, mind, experience, and school. Expanded edition. Washington, DC: National Academy Press, Chapter 6: The design of learning environments, pp 131-154.

Burton, L. (2004). Mathematicians as enquirers: Learning about learning mathematics. New York: Springer-Verlag.

 

Burton, L. (Ed.). (2003). Which Way Social Justice in Mathematics Education? Westport, Conn: Praeger.

 

Butterworth, B. (1999). The Mathematical Brain. London: MacMillan. Ch. 7: Good and bad at numbers, pp 273 – 318.

Civil, M., & Planas, N. (2004). Participation in the mathematics classroom: Does every student have a voice? For the Learning of Mathematics, 24(1), 7-12.

Clements, D. H., & Sarama, J. (Eds.). (2004). Hypothetical Learning Trajectories. Special Issue: Mathematical Thinking and Learning 6(2).

 

Cobb, P., Yackel, E., & McClain, K. (Eds.). (2000). Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design. Mahwah, NJ: Lawrence Erlbaum Associates.

 

Collins, A., Brown, J. S., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational researcher, 18(1), 32-42.

Collins, A., Brown, J. S., & Newman, S. E. (1989). Cognitive apprenticeship: Teaching the crafts of reading, writing and mathematics. In Lauren B. Resnick (Ed.), Knowing, learning, and Instruction: Essays in honor of Robert Glaser (pp. 453-494). Hillsdale, NJ: Lawrence Erlbaum Associates.

Davis, B., & Simmt, E. (in press). Mathematics for teaching: An ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics.

 

Davis, B., & Simmt, E. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education, 34(2), 137-167.

Eisenberg, T., & Dreyfus, T. (1991). On the reluctance to visualize in mathematics. In W. Zimmermann & S. Cunningham (Eds.), Visualization in teaching and learning mathematics (pp. 25-38). Washington, DC: Mathematical Association of America.

Ellington, A. J. (2003). A meta-analysis of the effects of calculators on students' achievement and attitude levels in precollege mathematics classes. Journal for Research in Mathematics Education, 34(5).

Even, R., & Schwarz, B. B. (2003). Implications of competing intrepretations of practice for research and theory in mathematics education. Educational Studies in Mathematics, 54, 283-313.

Flores, A., & Perkins, I. (2002). Mathematical notations and procedures of recent immigrant students. Mathematics Teaching in the Middle School, 7(6), 346-351.

Glaser, R. (1992). Expert knowledge and processes of thinking. In D. F. Halpern (Ed.), Enhancing thinking skills in the sciences and mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.

Goldenberg, E. P., Cuoco, A. A., & Mark, J. (1998). A role for geometry in general education. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 3-44). Mahwah, NJ: Lawrence Erlbaum.

Gordon Calvert, L. M. (2001). Mathematical Conversations within the Practice of Mathematics. New York: Peter Lang.

 

Hadas, N., Hershkowitz, R., & Schwarz, B. B. (2000). The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments. Educational Studies in Mathematics, 44(127-150).

Hewitt, D. (1999). Arbitrary and necessary part 1: a way of viewing the mathematics curriculum. For the learning of mathematics, 19(3), 2-9.

Honebein, P. C., Duffy, T. M., & Fishman, B. J. (1993). Constructivism and the design of learning environments: Context and authentic activities for learning. In T. M. Duffy, J. Lowyck & D. Honassen (Eds.), Designing environments for constructive learning (pp. 1-22). Heidelberg: Springer Verlag.

Laborde, Collette (1998). Visual phenomena in the teaching/learning of geometry in a computer-based environment. In Mammana, C., & Villani, V. (Eds.). (1998) Perspectives on the teaching of geometry for the 21st century: An ICMI study. Dordrecht: Kluwer Academic Publishers.

Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven: Yale University Press.

 

Leder, G. C., Pehkonen, E., & Torner, G. (Eds.). (2003). Beliefs: A hidden variable in mathematics education? Dordrecht: Kluwer Academic Publishers.

Noddings, N. (1997). Rethinking the benefits of the college-bound curriculum: Escaping academic captivity. Retrieved October 16, 2002, from http://www.pdkintl.org/kappan/noddings.htm

Norman, D. A. (1993). Things that make us smart: Defending human attributes in the age of the machine. Toronto, ON: Addison Wesley Publishing Company. Chapter 2: Experiencing the world, pp. 19-41.

Page, M. S. (2002). Technology-enriched classrooms: Effects on students of low socioeconomic status. Journal of Research on Technology in Education, 34(4), 389-409.

Pijls, M., Dekker, R., & Van Hout-Wolters, B. (2003). Mathematical level raising through collaborative investigations with the computer. International Journal of Computers for Mathematical Learning, 8, 191-213.

Presmeg, N. C. (1986). Visualisation in high school. For the Learning of Mathematics, 6(3), 42-46.

 

Resnick, L. B. (1988). Treating mathematics as an ill-structured discipline. In R. I. Charles and E. A. Silver (Eds.), The teaching and assessing of mathematical problem solving. (pp. 32-60). Hillsdale, NJ: Lawrence Erlbaum Associates

Romberg, T. A., Carpenter, T. P., & Dremock, F. (Eds.). (2005). Understanding mathematics and science matters. Mahwah, NJ: Lawrence Erlbaum Associates.

 

Schoenfeld, A. H. (1994). Reflections on doing and teaching mathematics. In A. H. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 53-70). Hillsdale, NJ: Lawrence Erlbaum Associates.

Skemp, R. S. (1987). The psychology of learning mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates. Ch: 12 – Relational understanding and instrumental understanding, pp. 152 – 163; Ch: 16 – Emotions and survival in the classroom, 189

 

Sierpinska, A. (2004). Research in mathematics education through a keyhole: Task problematization. For the Learning of Mathematics, 24(2), 7-15.

 

Sinclair, N. (2006). Mathematics and Beauty: Aesthetic Approaches to Teaching Children: Teachers College Press.

 

Tellent-Runnels, M. J., Thomas, J. A., Lan, W. Y., & Cooper, S. (2006). Teaching courses online: A review of the research. Review of Educational Research, 76(1), 93-135.

 

Verschaffel, L., Greer, B., & De Corte, E. (2002). Everyday knowledge and mathematical modeling of school word problems. In K. Gravemeijer, R. Lehrer, B. Van Oers & L. Verschaffel (Eds.), Symbolizing, Modeling and Tool Use in Mathematics Education. Dordrecht, The Netherlands: Kluwer Academic Publishers.

 

Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. USA: Cambridge University Press.

 

 

 

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