Education 62.03: Curriculum and Teaching in the Middle School (Mathematics and Science)

**Course Topics Outline**

*1. Curriculum and Teaching: Resources for Critical
Reflection *

- The objectives of the science curriculum: beyond the merely practical
- The objectives of the mathematics curriculum: math as an art form
- Quality of life and the humanistic values of a middle-school curriculum
- Pausing to smell the flowers: is there more to life than knowing and having?
- Education for a life worth living: the role of mathematics and science

*2. Standards vs. Values: from Mass Production to Education
for being Human *

- How do we define the highest possible standards for math and science education?
- What could "high standards for all students" really mean?
- Higher, faster, longer ... the fast track to narrow specialized skills?
- What are the highest human values that are embodied in math and science?
- How can students be empowered to participate in these aspects of math and science?

*3. Esthetics and the Humanities as Explorations in Human
Values *

- Nil humani alienum: math and science as part of the humanities
- Theories of Being Human vs. the Experience of Being Human
- Highest Esthetic Values: On the Sublime
- Alternative Views on Esthetics: Expressivism/Romanticism, Formalism, Functionalism, Modernisms, and Postmodernisms

*4. The Two Cultures and their Dialogue *

Why Math/Science and Arts/Humanities went their separate ways

- The historical paths
- Snow's Two Cultures
- The situation today
What Math/Science has to say to Arts/Humanities

- materialism vs. idealism
- systematic analysis vs. holistic experience
- the esthetics of mathematics
- the esthetics of science, theory and experiment
What Arts/Humanities has to say to Math/Science

- the phenomenology of experience
- rationality and other affective modes
- performance and choice
- the esthetics of teaching
- the esthetics of learning

*5. Experiential Models for Learning Science and
Mathematics *

- the need for direct participation in the contexts where scientific and mathematical concepts and practices are used
- simulations and facsimiles vs. authentic experience
- participant observation, legitimate peripheral participation, and apprenticeship
- re-contextualizing the learning of science and mathematics

6. Esthetic Models of Learning and Teaching for Mathematics and Science

- the esthetic function in teaching mathematics and science
- the artful performance of teaching
- esthetics and motivation
- esthetics and intuition, esthetics and judgment
- the esthetic function in learning mathematics and science
- pattern recognition in a fuzzy world
- creating fluid organizations of knowledge
- the uses and values of ambiguity

7. Design as the Meeting Place of Mathematics, Science, and Esthetics

- the esthetics of art and architecture
- the esthetics of engineering
- the esthetics of mathematical modelling and scientific representations
- the esthetics of experimental design

*8. The Role of the Visual in Mathematics and Science *

- the visual semiotics of mathematics: algebras and geometries
- the visual representations of scientific concepts and relationships
- the logic of esthetic order in the representation of mathematics and science

*9. Esthetics in the Languages of Mathematics, Science,
Teachers, and Students *

- Elegant mathematics and interesting textbooks
- Fascination with science and boredom in science class
- Narrative and persuasion in scientific and mathematical writing and teaching
- Speaking and writing for teachers: communication and motivation
- Speech and writing for students: dialects, genres, and style

**Course Readings: **[1-7 are in Course Packet,
Part I; the others will be distributed separately]

1. Wechsler, J. Ed. 1978. On aesthetics in science. Introduction

2. Einstein, A. 19 . Letter to Jacques Hadamard.

3. Poincare, H. 1908. "Mathematical reasoning" in The Foundations of Science.

4. Papert, S. 1978. "The Mathematical unconscious" in Wechsler, Ed.

5. Gruber, H. 1978. "Darwin's Tree of Nature" in Wechsler, Ed.

6. Kohn, D. 1996. "The Aesthetic Construction of Darwin's Theory" in Tauber, Ed.

7. John-Steiner, V. 1985. "Visual Thinking" in Notebooks of the Mind.

8. Root-Bernstein, R. 1996. "The sciences and arts share a common creative aesthetic" in Tauber, ed., pp. 49-82.

9. Faxon, A. 1996. "Intersections of art and science to create aesthetic perception" in Tauber, ed., pp. 251-266.

10. Ulam, S. From: Adventures of a Mathematician, pp. 18-55.

11. Lemke, J.L. 1990. Talking Science: Language, Learning, and Values. Norwood, NJ: Ablex Publishing. 1990. [ pp. 129-137, on the norms of science discourse]

12. Lemke, J.L. 1994. "The Missing Context in Science Education: Science." [available on this website]

We will also read a selection from CP Snow's *The Two
Cultures, *on the lack of communication between math/science
vs. arts/humanities