Problem Solving

Handbooks, special collections, etc.

• Brown, S. I.: M.I. Walter (1990). The Art of Problem Posing. Hillsdale, New Jersey, Hove and London: Lawrence Erlbaum Associates, Publishers
• Karp, A., & Wasserman, N. (2015). Mathematics in Middle and Secondary School. A problem solving approach. Charlotte, NC: Information Age.
• Krulik, S. & Reys, R. E. (1980).  Problem Solving in School Mathematics, 1980 Yearbook of the National Council of Teachers of Mathematics, Reston, VA:  NCTM.
• Liljedahl. P., Santos-Trigo, M., Malaspina, U., Bruder, R. (2016).   Problem Solving in Mathematics Education. Springer.                                                                            
• Newell, A; H. Simon (1972). Human problem solving. Englewood Cliffs, NJ: Prentice Hall.
• Polya, G. (1973). How to solve it. Princeton, NJ: Princeton University Press.
• Polya, G. (1981). Mathematical discovery. New York: John Wiley & Sons.
• Polya, G. (1954). Mathematics and plausible reasoning; Vol. 1. Introduction and analogy in mathematics; Vol. 2. Patterns of plausible inference. Princeton, NJ: Princeton University Press.
• Schoenfeld, A. (1985). Mathematical problem solving. New York, NY: Academic Press.
• Schoenfeld, A. (1992). Learning to think mathematically: problem solving, metacognition, and sense-making in mathematics. In D. A. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334-370). Reston, VA: NCTM.
• Watson, A., Mason, J. (2005). Mathematics as a constructive activity. Learners Generating examples. Mahwah, NJ – London: Lawrence Erlbaum Associates, Publishers.
• Watson, A., Ohtani, M. (2015). Task design in mathematics education. Springer.

Papers and chapters

• Bernardo, A. B. (2001). Analogical problem construction and transfer in mathematical problem solving. Educational Psychology, 21(2), 137-150. 
• Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem posing research in mathematics: Some answered and unanswered questions. In F.M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 3–34). Springer.
• Cooney, Thomas J. (1985). A Beginning Teacher's View of Problem Solving. Journal for Research in Mathematics Education, Vol. 16, No. 5,  324-336.
• English, L. D. & Gainsburg, J. (2016). Problem solving in a 21st- Century mathematics education.In L. D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (pp. 313–335). NY: Routledge.                        
• Kilpatrick, J. (1978) Variables and methodologies in research on problem solving. In L. Hartfield (Ed.), Mathematical problem solving. Columbus, OH: ERIC, 7-20.
• Kilpatrick, J. (1985) A retrospective account of the past twenty-five years of research on teaching mathematical problem solving. In E.A.Silver (ed), Teaching and learning mathematical problem solving: Multiple research perspectives (1-16). Hillsdale, NJ: Lawrence Erlbaum.
• Kilpatrick, J. (1987). Problem formulating: Where do good problem come from? In A.H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123–147). Hillsdale,NJ: Erlbaum.
• Novick, L., & Holyoak, K. (1991). Mathematical problem solving by analogy. Journal of Experimental Psychology, 17(3), 398–415.
• Santos-Trigo, M. (2007). Mathematical problem solving: An evolving research and practice domain. ZDM—The International Journal on Mathematics Education, 39(5, 6): 523–536.
• Schoenfeld, A. H. (1982). Some thoughts on problem-solving research and mathematics education. In F. K. Lester & J. Garofalo (Eds.), Mathematical problem solving: Issues in research (pp. 27–37). Philadelphia: Franklin Institute Press.
• Schoenfeld, A. (1987). What’s all the fuss about metacognition. In Cognitive Science and Mathematics Education /edited by A.Schoenfeld. New Jersey-London: Lawrence Erlbaum Associates, Publishers.
• Schoenfeld, A. (1989).Explorations of Students' Mathematical Beliefs and Behavior Journal for Research in Mathematics Education, Vol. 20, No. 4, 338-355.
• Silver, E. (1982). Knowledge organization and mathematical problem solving. In F. K. Lester &J. Garofalo (Eds.), Mathematical problem solving: Issues in research (pp. 15–25).Philadelphia: Franklin Institute Press.
• Silver, E.; J. Mamona-Downs, S. Leung; P. Kenney (1996). Posing mathematical problems: an exploratory study. Journal for Research in Mathematics Education, 27 (3), 293-309.
• Singer, F., Ellerton, N., & Cai, J. (2013). Problem posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 9–26.
• Stanic G; J. Kilpatrick (1989). Historical Perspectives on problem solving in the mathematics curriculum. In R. Charles & E. Silver (Eds.), The teaching and assessing of mathematical problem solving. Reston, VA: National Council of Teachers of Mathematics, 1-22.

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Faculty publications

• Karp, A. (2002). Math problems in blocks: How to write them and why.  PRIMUS, 12(4), 289-304.
• Karp, A. (2006). And now put aside your pens and calculators...:  On mental problem solving in the high school mathematics lesson. Focus on Learning Problems in Mathematics, 28(1), 23-36.
• Karp, A., & Marcantonio, N.  (2010). “The number which is always positive, even if it is negative” (On studying the concept of absolute value). Investigations in Mathematics Learning, 2(3), 43-68.
• Karp, A. (2015). Problems in old Russian textbooks: How they were selected In K. Bjarnadottir et al. (Eds.) “Dig where you stand” 3 (pp. 203-218). Uppsala: Uppsala University

A few TC dissertations

• DeGraaf, E. (2015). What makes a good problem? Perspectives of students, teachers, and mathematicians.
• McCarron, Craig S. (2011). Comparing the Effects of Metacognitive Prompts and Contrasting Cases on Transfer in Solving Algebra Problems.
• Nahornick, Ashley. (2014). The effect of group dynamics on high-school students' creativity and problem-solving strategies with investigative open-ended non-routine problems.
• Smith, J.P. (1973). The effect of general versus specific heuristics in mathematical problem solving tasks.
• Tjoe, Hartono Hardi (2011).Which approaches do students prefer? Analyzing the mathematical problem solving behavior of mathematically gifted students.

Members of the TSG

Alexander Karp

Philip Smith