Annotated Bibliography
Baroody, Arthur J., and Herbert P. Ginsburg. "The Effect of Instruction on Children's Understanding." The Elementary School Journal. 84:2 (November 1983), 198-212 (http://www.jstor.org).This article provides examples and research on the effect of teaching mathematics in certain ways and they ways in which that effects the students genuine understanding.
Boyer, Carl B. The History of Mathematics. New York: Wiley, 1968. This is a very informative book recounting the history of mathematics.
CME Development Team. Algebra 1. Boston: Pearson, 2009. This textbook has very thoughtful explanations, example and problems covering all Algebra 1 topics.
Howe, Roger, and Susanna Epp. "PMET - Resources: Taking Place Value Seriously."Mathematical Association of America. N.p., n.d. Web. 21 July 2011. http://www.maa.org/pmet/resources/PVHoweEpp-Nov2008.pdf. This article breaks down place value and emphasizes its importance in many contexts.
Howe, Roger. "From Arithmetic to Algebra." Mathematics Bulletin. May 2010. This article emphasized the importance of making the connections between algebra and arithmetic and provides many concrete examples.
Kuchemann, Dietmar. "Children's Understanding of Numerical Variables." Mathematics in School. 7:4 (September 1978), 23-26 (http://www.jstor.org). This article delves into research on what students understand about variables and common misconceptions.
MacNeal, Edward. Mathsemantics: Making Numbers Talk Sense. New York: Viking, 1994. This book gives very detailed examples of why the wording of math problems is imperative.
McNeil, Nicole M., Laura Grandau, Eric J. Knuth, Martha W. Alibali, Ana C. Stephens, Shanta Hattikudur and Daniel E. Krill. "Middle-School Students' Understanding of the Equal Sign: The Book They Can't Read Can't Help." Cognition and Instruction 24:3 (2006), 367-385, accessed July 12, 2011, www.nd.edu/~nmcneil/mcneiletal06.pdf. This article gives a very thorough analysis of the many causes of students misunderstandings of the equals sign.
Philipp, Randolph A. "The Many Uses of Algebraic Variables," Mathematics Teacher 55 (1992):157-161, accessed July 13, 2011, www.education.indiana.edu. This article gives interesting information about variables and their different uses.
Tirosh, Dina., Ruhama Even, and Naomi Robinson."Simplifying Algebraic Expression: Teacher Awareness and Teaching Approaches. Educational Studies in Mathematics 35:1(1998), 51-64 (http://www.jstor.org). This article provides a study of students' tendencies to solve expressions as well as the teachers awareness of the students misconceptions.
Usiskin, Zalman. "Conceptions of School Algebra and Uses of Variables." Algebraic Thinking, Grades K-12: Readings from NCTM's School Based Journals and Other Publications (1999), 7-13, www.octm.org, accessed July 13, 2011. This article discusses students misunderstandings that students have of variables and their representations.
Comments: