Bibliography
Bednarz, Nadine, and Bernadette Janvier. “Emergence and Development of Algebra as a Problem-Solving Tool: Continuities and Discontinuities with Arithmetic.” Approaches to Algebra, 1996, 115–36. https://doi.org/10.1007/978-94-009-1732-3_8. This article worked well in conjunction with the ones that focused on schema development.
Carpenter, Thomas P., James M. Moser, and James Hiebert. “Problem Structure and First-Grade Children’s Initial Solution Processes for Simple Addition and Subtraction Problems.” Journal for Research in Mathematics Education 12, no. 1 (1981): 27–39. https://doi.org/10.5951/jresematheduc.12.1.0027. This article was helpful particularly in the beginning of my research. It provided insight into problem solving with young children.
Chen, Zhe. “Schema Induction in Children’s Analogical Problem Solving.” Journal of Educational Psychology 91, no. 4 (1999): 703–15. https://doi.org/10.1037/0022-0663.91.4.703. This article discussed transfer regarding problem solving. It was useful.
Fuchs, Lynn S., Douglas Fuchs, Karin Prentice, Mindy Burch, Carol L. Hamlett, Rhoda Owen, Michelle Hosp, and Deborah Jancek. “Explicitly Teaching for Transfer: Effects on Third-Grade Students’ Mathematical Problem Solving.” Journal of Educational Psychology 95, no. 2 (2003): 293–305. https://doi.org/10.1037/0022-0663.95.2.293. This article was useful to explain the effect of explicitly teaching transfer and the role transfer plays in problem solving.
Fuchs, Lynn S., Douglas Fuchs, Robin Finelli, Susan J. Courey, and Carol L. Hamlett. “Expanding Schema-Based Transfer Instruction to Help Third Graders Solve Real-Life Mathematical Problems.” American Educational Research Journal 41, no. 2 (2004): 419–45. https://doi.org/10.3102/00028312041002419. This article discussed schema-based transfer and explained how developing schemas and successful transfer increases success with problem solving.
Moses, Barbara. “Algebra for a New Century.” Teaching Children Mathematics 3, no. 6 (February 1997). This short article explains why it is important to stress the generalizations of patterns.
National Research Council (1989). Everybody Counts: A report on the nations of the future of mathematics education. Washington, DC. This report discusses the importance of mathematical literacy in a technological world.
Polya, George. How to solve it: a new aspect of mathematical method. (s.l.): Princeton U.P., 1945. This book is the original publication of Polya’s steps.
https://www.nctm.org/flipbooks/standards/pssm/html5/index.html (Pg 29) This online resource discusses the NCTM process standards.
Schoenfeld, Alan H. “Making Mathematics Work for All Children: Issues of Standards, Testing, and Equity.” Educational Researcher 31, no. 1 (2002): 13–25. https://doi.org/10.3102/0013189x031001013. This article shared how mathematics is a barrier for students’ success.
Wang, Jian, and Emily Lin. “Comparative Studies on U.S. and Chinese Mathematics Learning and the Implications for Standards-Based Mathematics Teaching Reform.” Educational Researcher 34, no. 5 (2005): 3–13. https://doi.org/10.3102/0013189x034005003. This study addressed differences between mathematics learning in the U.S. and China from textbooks to instruction and culture.
Xin, Yan Ping. “The Effect of Schema-Based Instruction in Solving Mathematics Word Problems: An Emphasis on Prealgebraic Conceptualization of Multiplicative Relations.” Journal for Research in Mathematics Education 39, no. 5 (2008): 526–51. https://doi.org/10.5951/jresematheduc.39.5.0526. This article was useful to build understanding about schemas in word problems.
Xin, Yan Ping. “Word Problem Solving Tasks in Textbooks and Their Relation to Student Performance.” The Journal of Educational Research 100, no. 6 (2007): 347–60. https://doi.org/10.3200/joer.100.6.347-360. This article offered additional insight into the differences between the U.S. and China.
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