Annotated Bibliography
Roger Howe, "Arithmetic to Algebra," Mathematics Bulletin, Chinese Mathematical Society and Beijing Normal University, (May 2010): 13 - 22.
The juxtaposition of different solution paths has been an essential tool for my instruction of algebra for years, the additional juxtaposition of arithmetic methods makes for a much stronger and comprehensive learning opportunity for students entering secondary study.
Roger Howe, "Developing and Interpreting Multiplication and Division with the Number Line," course bibliography of readings, Yale National Initiative, (June 2011)
This short paper (2 page) on number line modeling of multiplicative operations is not publicly available, the strategies above, using number line models, reflect main ideas.
Glenda Lappan, et al., Michgan State University, Connected Mathematics 2. Boston: Pearson, 2009.
This text series, designed for the 6 th, 7 th, and 8 th grades, uses significant methodology akin to Singapore Mathematics. I believe it is invaluable for secondary teachers to be aware of the jargon, content, and format students have used in prior study.
Susan J. Lamon, Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers. New Jersey: Lawrence Erlbaum Associates, 2 nd Edition, 2005.
Lamon's text for teachers is a very comprehensive, robust taxonomy of pedagogy of fractions. It can be valuable for high school teachers working with struggling students.
Liping Ma, "Three approaches to one-place addition and subtraction: Counting strategies, memorized facts, and thinking tools," Carnegie Foundation for the Advancement of Teaching, draft, June 21, 2011
Ma's work is focused on the content of early primary education, however the pedagogical observations she makes have ramifications that are enlightening for teachers at any level.
Ivan Niven, Numbers: Rational and Irrational. Washington, DC: The Mathematical Association of America, 1961
I found this book very helpful for an Algebra 2 curriculum that will have some focus on group theory and the taxonomy of numbers. Niven introduces rational numbers well.
John Allen Paulos, Innumeracy: Mathematical Illiteracy and Its Consequences. New York: Hill & Wang, 2001
I recommend the book more as a generally beneficial reading for math teachers than as a primer or guide specific to fractions.
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