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Course Objectives: The primary objective of this course is to
develop a deep, articulate, understanding of the background, development, and
directions in research on mathematical cognition, broadly defined. Students
will be able to evaluate, summarize, and review ideas about cognition put
forward by researchers, practitioners, historians, and policy-makers. Successful
students will also demonstrate, by the end of the course, a capacity for
analysis and synthesis of the nature and questions of mathematics cognition
for at least one "grade band" (K-8, 6-12, college), Moreover, successful students
will explore issues in cognition and the preparation of teachers. Finally,
the course will help prepare students to assess the applications of cognitive
theories in research, practice, history, and policy and the restrictions on
their precision and applicability.
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Instructional Strategies: There
are three major instructional strategies for the course: a focus on effective
writing about mathematics education, appropriate use of research and policy
documents, and expanding graduate students' lived-experience of research on
cognition.
- Written assignments in the course:
- regular Summary and Review or Annotated Bibliography assignments on the course readings,
- short expository and comparative essays,
- exam questions that require explanation,
application of theories to new situations, analysis, synthesis, and
evaluation of knowledge gained from readings and observations,
- Research and policy documents (the NCTM Principles and Standards document in particular) are used to help each
student think about and analyze school mathematics teaching and
learning. Students are helped to master the appropriate use of research,
history, and policy in bolstering arguments for any changes in practice
(e.g., in the teaching and learning of mathematics or in the
preparation of school teachers).
- In order to better understand practice, students will: complete,
reflect, and report on observation of mathematics teachers and learners
(in person or on video) and participate in a case-study research project.
Methods of Evaluation: Assessment of student learning is accomplished
through at least two in-class examinations (with an oral component to at
least one of these exams), regular (and increasingly sophisticated) writing
assignments, and an in-class written final exam.
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Bibliography - Required materials for the
course:
- Text, e-book, or CD-ROM: National Council of Teachers of Mathematics
(2000). Principles
and Standards for School Mathematics
(PSSM). Reston, VA: Author.
If you have not already done so, join
the National Council of Teachers of Mathematics [PDF application form].
For your $39 you get e-access to one journal and the PSSM.
- Buy the paperback: Rodriguez, A. J., & Kitchen, R. S. (Eds.) (2005). Preparing
mathematics and science teachers for diverse classrooms: Promising
strategies for transformative pedagogy. Mahwah, NJ: Erlbaum.
ISBN 0805846808, $27.50.
The book is a collection of chapters written by different authors
offering theoretical and practical arguments for helping prospective
teachers learn to meet the needs of the diverse demographics they will
encounter among students in their future teaching.
- Buy the IMAP CD: Integrating mathematics and pedagogy to illustrate children's
reasoning. (2005) CD-ROM, ISBN: 0131198548. Cost: about
$18.00
This professional development CD-ROM for teachers of grades 1-5 offers
video clips and other tools designed to help teachers understand student
thinking about mathematics. Twenty-five video clips cover place value,
subtraction, and fractions.
See: http://www.allynbaconmerrill.com/title/0131198548.
- Available e-book follow this link: for the electronic edition [PDF file] or buy it for about $25 through the National Research Council: How
people learn: Brain, mind, experience, and school (Expanded edition) (2000).
Additional
research, practice, and policy documents chosen each semester:
Articles provided in-class or online:
Cobb, Paul (1994). Where is
the mind? Constructivist and sociocultural perspectives on mathematical
development. Educational Researcher, 23(7).
(Oct., 1994), pp. 13-20. [PDF]
http://calteach.ucsc.edu/aboutus/documents/Cobb-construcandsocdevinmath.pdf
Glasersfeld, Ernst von (2001)
Constructivisme radical et enseignement. In: Revue Canadienne de
l'enseignement des sciences, des mathématiques et des technologies 1 (2): 211-222.
L'apprendre sera défini en tant qu'activité conceptuelle et l'enseignement
distingué de l'instruction. On analysera le rôle de la langue dans ces
processus. L'auteur soutient qu'il ne peut y avoir aucune compréhension sans
réflexion. La réflexion est induite par la verbalisation et peut donc être
encouragée en stimulant la conversation. On montrera que la notion développée
par Ceccato de "conscience opérationnelle" s'avère appropriée à
l'enseignement et compatible avec le modèle théorique de Piaget.
English: Learning will be defined as a conceptual activity and teaching
distinguished from training. The role of language in these processes will be
examined. The author maintains that there can be no understanding without
reflection. Reflection is induced by verbalization and can therefore be encouraged
by fostering conversation. Ceccato's notion of "operational awareness" will
be shown to be relevant to teaching and compatible with Piaget's theoretical
model.
Reprinted in: Perspectives
31(2): 191-204.
English translation: Radical Constructivism and Teaching [PDF]
Click here for PDF
Gottfredson, Linda (submitted
2003 paper, online) Neo-Eugenics
Click here for draft or
Click here to go to partial text in Google books
Discusses fundamental flaws in the assumptions behind the reported research
(namely, that IQ tests are valid; that IQ tests are not culturally biased;
that IQ exists.
McLeod, D. B. (1989). The
role of affect in mathematical problem solving. In D. B. McLeod and V. M.
Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 20-36). New York: Springer-Verlag.
The purpose of this chapter was to propose a theoretical framework for
investigating the affective factors that help or hinder performance in
mathematical problem solving. In motivating a need for this framework, McLeod
summarized how affect influences several major categories of the mathematical
problem solving process. These processes included the ability to retrieve
information from the long-term memory, representational styles of solvers,
the roles of the solvers' conscious and unconscious mental processes, the
role of metacognition (knowledge about cognition and the regulation of
cognition), and the role of automaticity. In addition, McLeod stated that
affective influences on problem solving would vary according to the kind of
heuristic strategy that the problem required and according to the phases
through which the problem solver moved in addressing the problem.
Moschkovich, J. & Brenner, M. E. (2000). Using a Naturalistic Lens on Mathematics and Science
Cognition and Learning. In A. E. Kelly & R. Lesh (Eds.), Research
Design in Mathematics and Science Education
(pp. 457-486). Mahwah, NJ: Erlbaum. Available through Net Library
Any paper by Frank Pajares
and/or Dale H. Schunk and/or Barry J. Zimmerman would be a good start. There
are lots of things available on Frank Pajares' web site:
http://www.emory.edu/EDUCATION/mfp/self-efficacy.html
Selections from books:
Supplemental text: Gay, G. (2000). Culturally
responsive teaching: Theory, research, and practice. New York:
Teachers College.
Supplemental text: Stanic, G. M. A.,
& Kilpatrick, J. (2003). A history of school mathematics.Reston,
VA: National Council of Teachers of Mathematics.
Supplemental e-books available through UNCo Net Library:
- +
Inquiry and the National Science Education Standards: A Guide for
Teaching and Learning
Publication: Washington, D.C.
National Academies Press, 2000.
- + Strengthening the Linkages between the
Sciences and the Mathematical Sciences
Compass Series (Washington, D.C.)
Publication: Washington, D.C. National Academy Press, 2000.
- + Innovations in Science and Mathematics
Education: Advanced Designs for Technologies of Learning
by Jacobson, Michael J.
Publication: Mahwah, N.J. Lawrence Erlbaum Associates, Inc., 2000.
- +
Beyond Modularity: A Developmental Perspective On Cognitive Science
Learning, Development, and Conceptual Change
by Karmiloff-Smith, Annette.
Publication: Cambridge, Mass. MIT Press, 1995.
- + Distance Learning Technologies: Issues,
Trends, and Opportunities
by Lau, Linda K.
Publication: Hershey, Pa. Idea Group Publishing, 2000.
- + Mathematics Success and Failure Among
African-American Youth: The Roles of Sociohistorical Context, Community
Forces, School Influence, and Individual Agency
Studies in Mathematical Thinking
and Learning
by Martin, Danny Bernard.
- +
An Invitation to Cognitive Science. Vol. 3, Thinking
by Osherson, Daniel N.; Gleitman,
Lila R.
Publication: Cambridge, Mass. MIT Press, 1995.
- + Words On the Web: Computer Mediated
Communication
by Pemberton, Lyn
Publication: Exeter, England ; Portland, OR, USA Intellect Books, 2000.
- + Grading the Nation's Report Card: Evaluating
NAEP and Transforming the Assessment of Educational Progress
by Pellegrino, James W.
Publication: Washington, D.C. National Academies Press, 1999.
- + Word Problems: Research and Curriculum
Reform Studies in Mathematical Thinking and Learning
by Reed, Stephen K.
Publication: Mahwah, N.J. Lawrence Erlbaum Associates, Inc., 1999.
- + Improving Statistical Reasoning: Theoretical
Models and Practical Implications
by Sedlmeier, Peter.
Publication: Mahwah, N.J. Lawrence Erlbaum Associates, Inc., 1999.
- +
The Mind Within the Net: Models of Learning, Thinking, and Acting
by Spitzer, Manfred.
Publication: Cambridge, Mass MIT Press, 1999.
- +
The Nature of Cognition
by Sternberg, Robert J.
Publication: Cambridge, Mass. MIT Press, 1999.
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