Where indicated, a Summary & Review essay (1200 to 3000 words) or an Annotated Bibliographic entry (150 to 500 words) is due. Unless announced otherwise in class or by email, these documents are to be submitted electronically as an attachment in one of the following formats:
(1) .doc (Word 2004 or earlier),
(2) .html (self-contained hyper text markup web page)
(3) .rtf (rich text format)
(4) .txt (plain text).
Send files to Dr. Hauk, hauk@unco.edu by 5pm on the due date (unless otherwise indicated below).

• A set of questions to consider when writing a Summary & Review.
• Examples of student summary and review essays and annotated bibliographies.
• Mathe Ed comprehensive exam rubric — Rubric for grading written work
• Proprosed rubric for presentations
• Writings of interest about purposes and methods used in math ed research:
  • Schoenfeld, A. H., (2007). Method (pdf file of book chapter). In F. Lester (Ed.) Second handbook of research on mathematics teaching and learning. New York: MacMillan.
  • Schoenfeld, A. H. (2000). Purposes and Methods of Research in Mathematics Education (pdf file) Notices of the American Mathematical Society, 47, 641-649.

1. In class introductions
2. Planning for assignments

1. Discussion of key words/concepts in the nature of cognition: think, learn, know, understand, believe, feel, brain, mind.
2. Begin reading and discussion of articles from PME proceedings about technology use in learning mathematics (handed out in class).
3. Choose Team 1 readings.
   • Calculus students and non-routine problem situations (LR, DC, & KR);
   • International comparative studies of student achivement in mathematics (WY & NA);
   • Middle school students and problem-solving (AD & KN).

• Continued discussion in small groups of reading from Wednesday.
• Choose text and presentation dates for Group A book reports.

1. Continue in-class presentations about readings by Team 1 groups (AD & KN).
2. In-class discussion of cultural dichotomies (e.g., right/wrong, good/bad, strong/weak) and alternatives (e.g., simple/complex).

1. First Group A book report.
2. Consider topics for Group B research teams for Research Day projects.

1. Discussion of presentations and the use of the rubric.

1. In-class discussion of cognition key words (see assignment of 1/14).
2. In-class discussion of Cobb (1994).
3. Summary & Review of Team 2 reading (Cobb, 1994) due electronically by 5pm.

1. Decide on Group B research project teams.
2. In-class discussions of philosophical questions from Friday, 30 January (see your class notes for your topics/key words).

HOMEWORK: Read Chapter 3 in How people learn.

1. Second Group A book report presentation.
2. In-class discussions of: Chapter 3 - Learning and Transfer, from How people learn along with more discussion of key words from Friday, 30 January class (see class notes for your topics/key words).

1. Team 3 presentation on article: E. von Glasersfeld (1984). An introduction to radical constructivism.[PDF file] In P. Watzlawick (Ed.), The invented reality (pp. 17-40). New York: Norton.
2. In-class discussions of: article and more key words from Friday, 30 January class.

1. Third Group A report presentation (on PCK).
2. In-class discussions of readings.

1. Team 3 presentation on article: E. von Glasersfeld (1989). Cognition, construction of knowledge, and teaching.[PDF file] Synthese, 80 121-140.
2. In-class discussions of readings.

1. Team 3 presentation on article: E. von Glasersfeld (1995). Sensory experience, abstraction, and teaching. In L. P. Steffe and J. Gale (Eds.). Constructivism in education (pp. 369-384). Hillsdale, NJ: Erlbaum.
2. In-class discussions of readings.

1. Overview of research day projects.
2. In-class discussions of class projects.

1. Discuss working in groups.
2. In-class discussions of four main learning theories and associated theories

HOMEWORK (for 3/2/09): Read orangey pages from Davis, Hauk, & Latiolais (2009), "Culturally responsive college level mathematics" [pages in your box].

1. Review of four approaches to curriculum & instruction from reading (Davis, Hauk, & Latiolais, 2009): transmission, product, process, praxis.
2. In-class discussions of readings to date, particularly of connections among them.

1. In-class discussion of "process" and "procedure" concept maps; connections to existing theories of cognition (e.g., concept image/concept definition of Tall & Vinner (1981), APOS theory (Asiala et al., 1996), cognitive information processing (CIP; Anderson, 1984)).
2. Finalize and submit Research Day poster proposals.

• J. Lobato & D. Siebert (2002). Quantitative reasoning in a reconceived view of transfer. Journal of Mathematical Behavior, 21, 87-116.
• H. L. Kleinert, D. M. Browder, & E. A. Towles-Reeves (2009). Models of cognition for students with significant cognitive disabilities: Implications for assessment. Review of Educational Research, 79, 301-326.

1. In-class discussions of cognitive information processing model of cognition with particular attention to ACT-R theory (Anderson et al., 2004; see below).

1. In-class discussion of Lobato & D. Siebert (2002) and Kleinert, Browder, & Towles-Reeves (2009).
2. S&R essay on the two above articles due Friday, 03 April, 5pm.

1. Continued discussions of readings to date

1. Review poster timeline. See this link for example PowerPoint of a poster (~2.5MB, .PPT file).
2. In-class discussion of Lobato & Siebert (2002).

1. Activity: Situtated cognition from multiple perspectives.
2. In-class discussions of readings - focus on social constructivism.

1. Initial discussion of new reading: Kieren, Davis, Simmt, and Reid (1995).
2. In-class discussions of readings and poster preparation.

1. Poster Due to hauk@unco.edu by 1:20pm as .PPT file (NOT .pptx).
2. In-class discussion of situated cognition.

1. In-class discussions of paper distributed in class on Friday 3/27: Soto-Johnson, Yestness, and Dalton (2007), with focus on social constructivism.
2. In-class review of posters.

1. In-class discussion of readings and timeline for remaining assignments.
2. Draft S&R compare/contrast essay due electronically by 5pm. (see 11 March, above)

1. In-class discussion of bricolage.
2. Activity: Using bricolage idea to design extension of Lobato & Siebert (2002) research.

1. Prepare thesis paragraph for S&R 3, bring to class on Wednesday, 08 April.
2. Teams discuss by email design for extending Lobato & Siebert (2002) [Teams, first listed is team lead: LR-BMS, AD-NA, KN-DC, KR-WY].

1. In-class discussion of readings Kieren et al. (1995) and handout on social constructivism.
2. Discussion of theses for S&R 3. NOTE: Rescheduled to Monday, 13 April
3. Decide next steps for team extensions to Lobato & Siebert (2002).

1. Review social constructivism excerpts handout and Kieren et al. (1995)
2. In-class discussion of: social constructivism

1. In-class sharing of thesis statements for S&R 3
2. In-class discussion of CIP and situated cognition.

1. In-class discussion Anderson et al. (2004) and Kieren et al. (1995).
2. NOTE: S&R 2.1 (revision of S&R 2) due electronically to hauk@unco.edu by 8pm.

Team 4 [WY & KR; NA & AD] Read Miller, G. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. The Psychological Review, 63, 81-97.

1. In-class discussion of Kieren et al. (1995).
2. Activity: What is memory and how does it work?

1. In-class discussion of Miller (1956).
2. Activity: Memory and "chunking."

1. In-class discussion of: Weber & Alcock (2004).
2. Review of the nature of our own understanding of groups and isomorphism; how important is a semantic view for someone earning a PhD in math ed?

1. Activity: Team 4 S&R discussions
2. Bring to class: S&R notes for your Team 4 reading

1. In-class consultation for Team 4 PAIRS.
2. Each team brings DRAFT S&R to class (typed, double spaced).

1. In-class discussion of major cognitive theories.
2. Activity: Knowing or understanding; knowing and understanding?

NOTE: S&R 1.1 (second draft of first S&R) due, on paper, upon arrival at final exam meeting.