Conceptual understanding

Goal: Submit a manuscript to Wisconsin Teacher of Mathematics based on the research we read this semester on the topic of "conceptual understanding".

Course structure

Each week a student will:

  1. Lead class discussion based on an article of his/her choosing.
  2. Another student will serve as "secretary" by:
    1. recording important aspects of the class discussion,
    2. choosing the article for the class to read next, and
    3. preparing to lead class discussion the following week.

As a class collectively complete manuscript.

Calendar

Week 1

  1. Discuss "Strands of Mathematical Proficiency" (Adding It Up, 2001, pg. 115-145)
  2. Discuss how to read research
  3. Make leader & secretary schedule

Weekly assignments

Date Leader Secretary Article
Jan. 25 Hlas n/a Strands of Mathematical proficiency
Feb. 1 Hlas Krystal Transfer of Mathematical Knowledge
(Kaminsky, Sloutsky, & Heckler, 2009)
Feb. 8 Krystal Lindsey Developing conceptual understanding and procedural skill in mathematics: An iterative process.
(Rittle-Johnson, Siegler & Alibali, 2001)
Feb. 15 Lindsey Kaya Using Evidence-Based Practices to Build Mathematics Competence Related to Conceptual, Procedural, and Declarative Knowledge (Miller & Hudson, 2007)
Feb. 22 Kaya Rosie An Alternative Reconceptualization of Procedural and Conceptual Knowledge (Baroody, Feil & Johnson, 2007)
Mar. 1 Rosie Krystal Role of Conceptual Knowledge in Mathematical Procedural Learning (Byrnes & Wasik, 1991)
Mar. 8 Krystal Lindsey Reconceptualizing procedure knowledge (Star, 2005)
Mar. 15 Lindsey Kaya Using prediction to promote mathematical understanding and reasoning (Kasmer & Kim, 2011)
Mar. 29 Kaya Rosie Examining the effects of writing on conceptual and procedural knowledge in calculus (Porter & Masingila, 2000)
Apr. 5 Rosie Hlas Cconceptual knowledge of preservice secondary mathematics teachers: How well do they know the subject matter they will teach? (Bryan, 1999)
Apr. 12 Hlas ? Profound understanding of fundamental mathematics (Ma, 1999)

Scoring

Class leader #1

Discussion leader was …

  • well prepared as shown by fluid discussion and staying on task (10 pts)
  • mostly prepared, but noticeable discussion stagnation or noticeably off task (9 pts)
  • somewhat prepared, but often discussion stagnated and was off task (7 pts)

Chosen article is _____ relevant

  • highly (5 pts)
  • somewhat (4 pts)
  • barely (3 pts)

Discussion should last for at least 30 minutes. (start at 5 pts)

  • Each minute below 30. (-0.5 pts)
20 pts

Class leader #2

Discussion leader was …

  • well prepared as shown by fluid discussion and staying on task (10 pts)
  • mostly prepared, but noticeable discussion stagnation or noticeably off task (9 pts)
  • somewhat prepared, but often discussion stagnated and was off task (7 pts)

Chosen article is _____ relevant

  • highly (5 pts)
  • somewhat (4 pts)
  • barely (3 pts)

Discussion should last for at least 30 minutes. (start at 5 pts)

  • Each minute below 30. (-0.5 pts)
20 pts

Secretary #1

Records class discussion on the manuscript template in a …

  • accurate and complete manner (10 pts)
  • mostly accurate or complete manner but something is missing (9 pts)
  • somewhat accurate or complete but missing many important details (7.5 pts)
  • nonexistent manner (0 pts)

    Updated notes in timely manner (-1 per extra week)
10 pts

Secretary #2

Records class discussion on the manuscript template in a …

  • accurate and complete manner (10 pts)
  • mostly accurate or complete manner but something is missing (9 pts)
  • somewhat accurate or complete but missing many important details (7.5 pts)
  • nonexistent manner (0 pts)

    Updated notes in timely manner (-1 per extra week)
10 pts

Collaboration

This instructor will assign a score based on classroom observations and classmate feedback regarding participation and contributions to the manuscript.

20 pts

Manuscript

Manuscript is submitted to the Wisconsin Mathematics Teacher journal

20 pts

Grading scale with required points:

A (93), A- (90); B+ (87), B (83), B- (80); C+ (77), C (73), C- (70); D (60 pts)