Course Identification

This course surveys the main theoretical approaches to cognition, learning and instruction in mathematics and science. Emphasis is placed on the cognitive and socio-cultural approaches with some reference to behaviorism. Within the cognitive approach we discuss Piaget's theory of development and learning - the basis of constructivism; development from an information processing perspective (Neo-Piagetian approaches), issues of memory and learning; the "time" dimension of learning (Ausubel); Metacognition. Within the socio-cultural approach we include Vygotsky's theory of learning and the neo-vygotskian addenda, the cognitive apprenticeship model and references to situated learning.
The themes of concept learning, misconceptions, conceptual change, knowledge integration and problem-solving are discussed from both perspectives. Implications to the design and the practice of instruction are considered throughout the course.
As a routine, in parallel to the lectures teachers will read such articles and will hand in short assignments. The lectures will relate to these assignments. As a midterm the students will carry out a short empirical investigation exploring an important issue that was discussed in class. This investigation will usually replicate a study from the educational literature. In a mini-conference the students will report on their investigation and discuss their findings with the class with special reference to instructional implications. In the final exam each student will get (different) short articles and will critic and discuss them in relation to the different topics that were studied in the course.

Upon successful completion of the course- students should be able to:
1. Describe the main theoretical approaches to cognition, learning and instruction in mathematics and science and how they are related to their practice.
2. Discuss Piaget's theory of development and learning.
3. Explain the Vygotsky's theory of learning as well as the neo-vygotskian addenda - the cognitive apprenticeship model and references to situated learning.
4. Describe the implications of concept learning, misconceptions, conceptual change, knowledge integration and problem-solving to the design and the practice of instruction.
5. Discuss, in a critical manner, central theoretical and empirical articles in relation to the different topics studied in the course.
6. Suggest instructional implications by integrating topics discussed in class.

[1] Arcavi, A., Kessel, C., Meira, L., & Smith, J. P. I. (1998). Teaching mathematical problem solving: A microanalysis of an emergent classroom community. In A. Schoenfeld & E. Dubinsky & J. Kaput (Eds.), Research in Collegiate Mathematics Education III (pp. 1-70). Providence, RI: American Mathematical Society.

[2] Arzi, H. J. (2004). On the time dimension in educational processes and educational research. Canadian Journal of Science, Mathematics and Technology Education, 4(1), 15-21.

[3] Bell, A., & Janvier, C. (1981). The interpretation of graphs representing situations. For the Learning of Mathematics, 2(1), 34-42.

[4] Ben-Zvi, R., Eylon, B., & Silberstein, J. (1986). Is an atom of copper malleable? Journal of Chemical Education, 63(1), 64-66.

[5] Case, R. (1985). Traditional theories of intellectual development, Intellectual Development: Birth to Adulthood (pp. 9-24): Academic Press, Inc.

[6] Chinn, C. A., & Malhotra, B. A. (2002). Epistemologically authentic inquiry in schools: a theoretical framework for evaluating inquiry tasks. Science Education, 86, 175-218.

[7] Clement, J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13(1), 16-30.

[8] Collins, A., Brown, J. S., & Newman, S. E. (1989). Cognitive apprenticeship: Teaching the craft of reading, writing, and mathematics. In L. B. Resnick (Ed.), Knowing, Learning, and Instruction: Essays in Honor of Robert Glaser (pp. 453-493). Hillsdale, NJ: L.E.A.

[9] Dudai, Y. (2002). Memory from A to Z: Keywords, Concepts, and Beyond: Oxford University Press.

[10] Greeno, J. G., Collins, A. M., & Resnick, L. B. (1996). Cognition and learning. In D. C. Berliner & R.

[11] C. Calfee (Eds.), Handbook of Educational Psychology (pp. 15-46). New York: Macmillan Library Reference.

[12] Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235-266.

[13] Hmelo-Silver, C. E., & Barrows, H. S. (2008). Facilitating collaborative knowledge building. Cognition and Instruction, 26, 48-94.

[14] McCloskey, M. (1983). Naive theories of motion. In A. L. Stevens (Ed.), Mental Models (pp. 299-324). Hillsdale, NJ: Lawrence Erlbaum Associates.

[15] Moschkovich, J. N. (2004). Appropriating mathematical practices: A case study of learning to use and explore functions through interaction with a tutor. Educational Studies in Mathematics, 55, 49-80.

[16] Novak, J. D. (2010). Ausubel's assimilation learning theory, Learning, Creating, and Using Knowledge: Concept Maps as Facilitative Tools in Schools and Corporations (2nd ed., pp. 56-89). New York: Routledge.

[17] Posner, G. J., Strike, K. A., Hewson, P. W., & Gertzog, W. A. (1982). Accommodation of a scientific conception: toward a theory of conceptual change. Science Education, 66(2), 211-227.
Schoenfeld, A., & Arcavi, A. (1988). On the meaning of variable. Mathematics Teacher, September, 420-427.

[18] Schoenfeld, A. H. (1985). A framework for the analysis of mathematical behaviour, Mathematical Problem Solving (pp. 11-45). Orlando, FL: Academic Press, Inc. Harcourt Brace Jovanovich, Pub.

[19] Schoenfeld, A. H. (1987). What's all the fuss about metacognition. In A. H. Schoenfeld (Ed.), Cognitive Science and Mathematics Education (pp. 189-216). Hillsdale, NJ: Lawrence Erlbaum Ass.

[20] Shayer, M., & Ginsburg, D. (2010). Thirty years on ? a large anti-Flynn effect/ (II): 13- and 14-year-olds. Piagetian tests of formal operations norms 1976?2006/7. British Journal of Educational Psychology, 77(1), 25-41.

[21] Smith, J. P. I., diSessa, A. A., & Roschelle, J. (1993). Misconceptions reconcieved: A constructivist analysis of knowledge in transition. The Journal of the Learning of Sciences, 3(2), 115-163.

[22] Stewart, J., & Hafner, R. (1994). Reseearch on problem solving in genetics. In D. L. Gabel (Ed.), Handbook of Research on Science Teaching and Learning (pp. 284-300). London: Simon & Schuster and Prentice Hall International.