MATH 5377
Algebraic Reasoning in K-8 Mathematics

For the course syllabus, click here.
For problems worked or assigned in class, click here.
For the supplementary reader, click here.
For links to other online readings, see "Links for specific class meetings" below.
For my math ed web resources page, click here.
For student interviewing tips, click here.
For the sample interview write-up, click here.
For tips on writing papers on math problems, click here.

NOTE: Technical information such as prerequisites, text materials, course format and assignments, and other details can be found in the syllabus, a copy of which is provided in a link at the top of this page.

"College-level" problems

• Session 2: Odd/even arithmetic --- justifications for all four operations.
• Session 2: Odd/even remainders --- justifications for all four cases.
• Session 8: Generalizing factors of factors --- justifications for all four questions.
• Session 9: Clock arithmetic I & II --- definitions and their properties for all four operations (you choose which representation to use).
• Session 10: Clock arithmetic III --- answer all questions in a coherent narrative.
• Session 10: Analyzing operations I or II --- answer all questions in a coherent narrative.
• Session 12: Painting the Cube --- answer all questions in a coherent narrative, with careful attention to mapping among representations.

Links for specific class meetings

• Session 1: Some of the key ideas mentioned in Journal 1
  • to appear following first session
• Session 5: photo of two representations for the integer subtraction problem, from class discussion (thanks to TT, SC, KK)
• Sessions 9, 11: online reading --- Chapter 6 of Algebra and the elementary classroom by Blanton
• Session 9: photo of a clock diagram representation for clock addition, from class discussion (thanks to KG, KK)
• Session 10: online reading --- Chapter 2 of Thinking Mathematically

Links of general interest

• The National Center for Improving Student Learning and Achievement in Mathematics and Science (NCISLA) has a teacher resource web site which includes a list of sample "algebrafied" problems for classroom use, as well as some tips for teachers on bringing algebraic reasoning into class discussions.
• A brief overview of early algebraic reasoning by Carpenter and Levi
• A TCM case study on equality by Falkner et al.
• A recent (2007) report organized by the MAA and funded by the NSF makes recommendations on the teaching of algebra at every level. Participants in this course may be especially interested in the recommendations on "Early Algebra".