University of Texas at El Paso
College of Education
Department of Teacher Education

MTED 3330
"Integration and Alternative Representation of Basic Mathematical Principles"

Instructor: Dr. Mourat A. Tchoshanov Office: EDUC 603 Phone: (915) 747-7668 Fax: (915) 747-7441 E-mail: mouratt@utep.edu

Semester: Sections: Room: Office hours:

Required Text

Course Package (selected articles on multiple representations and connections in teaching and learning of school mathematics)

Krulick, S., & J. Rudnick (2000). Teaching Middle School Mathematics: Activities, Materials, and Problems. – Boston, MA: Allyn and Bacon

Course Objectives

Main intention of the course is to explore the relationship between “hands-on” (learning) and “minds-on” (cognition) mathematics. Therefore, the course is designed around ideas of multiple connections and representations which are fundamental issues in developing students’ conceptual understanding of school mathematics. This course is aimed to achieve several objectives:

1. To examine the role of multiple connections and representations in teaching and learning of school mathematics

2. To understand the relationships between the abstract or symbolic (e.g., math statements, expressions, formulas,…), the pictorial or semi-concrete (e.g., diagrams, sketches, graphs,…) and the concrete (e.g., manipulative materials, physical objects, models,…) representations to support math learning and cognition

3. To study the impact of multiple connections and representations on the development of students’ conceptual understanding

4. To practice on using multiple connections and representations in teaching and learning school mathematics through projects, activities, games, and problems.

Course Syllabus

Course Requirements

1. It is expected that students will attend all classes and actively participate in class discussions and activities. Students are expected to prepare for each class session. If a student misses a session, it is the responsibility of the student to make up for it.

2. Group presentations to be discussed in class - each group must distribute an outline of their presentation.

3. Teaching Micro-activity in class (15 min): each student will present 3-4 activities to their peers.

4. Problem Solving Interviews and Protocols: each student will have opportunity to interview peers using concrete, pictorial, and abstract representations and complete protocols of problem solving process. Two exemplary protocols (1-2 pages each) will be turned in to instructor.

5. Reflection-paper (8-10 pages) on using multiple connections and representations in teaching and learning of school mathematics. This paper might include reflections on readings, class discussions and conducted activities and presentations.

Grade Distribution

Classroom participation/preparation/discussion	15%
Group Presentation	15%
Teaching micro-activities	20%
Two Exemplary Problem Solving Protocols	20%
Reflection-Paper	30%

Grading Scale:

90 - 100 = A (Excellent - 4.0)	80 - 89 = B (Good - 3.0)
70 - 79 = C (Average - 2.0)	60 - 69 = D (Passing - 1.0)
0 - 59 = F (Failure - 0.0)

Deadlines
Course drop -
Complete Portfolio -

Notes

• Lateness to class is strongly discouraged. Many classes will begin with a group activity or presentation. Your group will depend upon you to be present and prepared for class. Missed assignments must be completed.

• The schedule of topics and reading assignments may change over the course of the semester. Any changes to the syllabus will be announced in class. Every student is responsible for these changes whether or not he or she is present in class. It is recommended that students exchange telephone numbers &/or e-mail addresses with a few of their colleagues.

• Please hand in all written assignments on the date they are due. One-half of a letter grade will be deducted for late assignments.

• Please feel free to speak to me regarding any questions or concerns. You can reach me during office hours (by appointment), speak to me after class, call or e-mail me.

Bibliography

• Ball, D. L. (1993). Halves, pieces, and twoths: Constructing and using representational contexts in teaching fractions. In: T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.). Rational numbers: An integration of research. Hillsdale, NJ: Lawrence Erlbaum Associates. - Pp. 157-195.

• Cai, J., Lane, S., & Jacabcsin, M. (1996). The role of open-ended tasks and holistic scoring rubrics: Assessing students’ mathematical reasoning and communication. In: Communication in Mathematics. K-12 and Beyond. Edited by P. Elliott, & M. Kenney. Reston, VA: NCTM. - Pp. 137-145.

• Clements, D., & McMillen, S. (1996). Rethinking "concrete" manipulatives. Teaching children mathematics. Jan., 1996. - Pp. 270-279.

• Davis, R. B., & Maher, C. A. (1997). How students think: The role of representations. In L. D. English (Ed.). Mathematical reasoning: Analogies, metaphors, and images (pp. 93-116). Mahwah, NJ: Lawrence Erlbaum Associates. - Pp. 93-115.

• Demana, F., & Waits, B. (1990). Enhancing mathematics teaching and learning through technology. In: T. Cooney, C. Hirsch (Eds.). Teaching and learning mathematics in the 1990s. Reston, VA; NCTM. Pp.212-222.

• Dufour-Janvier, B., Bednarz, N., & Belanger, M. (1987). Pedagogical consideration concerning the problem of representation. In: C. Janvier (Ed.) Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates. - Pp. 109-122.

• Greeno, J. G., & Hall, R. P. (1997). Practicing representation: Learning with and about representational forms. Phi Delta Kappan, 78, 361-367.

• Hodgson, T. (1995). Connections as problem-solving tools. In: Connecting mathematics across the curriculum. Edited by P. House, & A. Coxford. Reston, VA: NCTM. - Pp. 13-21.

• Schultz, J., & Waters, M. (2000). Why Representations? Mathematics Teacher, V.93, #6. Pp. 448-453

• Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In: C. Janvier (Ed.) Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates. - Pp. 33-40.

• Lesh, R., Behr, M., & Post, T. (1987). Rational number relations and proportions. In: C. Janvier (Ed.) Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates. - Pp. 41-58.

• Seeger, F. (1998). Representations in the mathematics classroom: Reflections and constructions. Seeger, F., Voigt, J., Werschescio, V. (Eds.). The culture of the mathematics classroom. Cambridge, MA: Cambridge University Press. - Pp. 308-343.

• Silver, E., Kilpatric, J., & Schlesinger, B. (1990). Communicating mathematical ideas: Private and public discourse. In: Thinking through mathematics: Fostering inquiry and communication in mathematics classroom. -Reston, VA: NCTM. - Pp. 15-24.

• Wheatley, G., & R. Shumway (1992). The Potential for calculators to transform elementary school mathematics. In: Calculators in mathematics education. Edited by J. Fey, & C. Hirsch. Reston, VA: NCTM. - Pp. 1-8.