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### TIAN Bundle 3 Articles and References (For Teachers) about Positive and Negative Integers

• Ask Dr. Math FAQ: Negative x Negative = Positive from The Math Forum @ Drexel.
Provides several examples of rationale for why multiplying two negatives yields a positive integer.
• Baldwin, J. & Kessel, C. (2000). Concept and Computation: The Role of Curriculum from MER Newsletter.
A look at how and when Chinese and American curricula handle negative numbers.
• Ball, D.L. With an Eye on the Mathematical Horizon: Dilemmas of Teaching Elementary School Mathematics
Based on an earlier version presented at the April 1990 meeting of the American Educational Research Association in Boston. While the dilemmas Ball discusses are about issues much larger than the topic of negative numbers, pages 7-17 and pages 23-31 of the article focus specifically on examples in teaching negative numbers.
• Gregg, J. & Gregg, D. (August 2007). A Context for Integer Computation from Mathematics Teaching in the Middle School, 13(1), 46-50.
Suggests the context of allowance rather than debt or other "contrived" situations for bringing more meaning to integer computation.
• Kent, L.B. (September 2000). Connecting Integers to Meaningful Contexts in Mathematics Teaching in the Middle School, 6(1), 62-66.
This article illustrates how students can begin to intuitively learn the rules for adding and subtracting integers.
• Felder, K. (1997). Negative Times Negative Is What?
This site offers four explanations to the question of why multiplying two negatives gives you a positive number.
• National Research Council (2001). "Number: What Is There to Know?" from Adding It Up: Helping Children Learn (80-83, 244-246).
• Nurnberger-Haag, J. (September 2007). Integers Made Easy: Just Walk It Off in Mathematics Teaching in the Middle School, 13(2), 118-121.
This quick read offers a multisensory method to teach the rules associated with adding, subtracting, multiplying and dividing integers.
• Peled, I., & Carraher, D. (2008). Signed numbers and algebraic thinking. In D.W. Carraher & M.L. Blanton (Eds.), Algebra in the Early Grades (pp. 303-328). New York: NCTM.
Researchers investigate the relationship between algebra and signed numbers and suggest that algebra provides more meaningful models for signed numbers.
• Sfard, A. (2008). Learning Mathematics as Developing a Discourse. In R. Speiser, C. Maher, C. Walter (Eds), Proceedings of 21st Conference of PME-NA (pp. 23-44). Columbus, Ohio: Clearing House for science, mathematics, and Environmental Education.

• While Sfard's key message is the importance of communication in learning mathematics, one of her two examples focuses on students grappling with negative numbers.