Rethinking Problem-Posing Situations: A Review

References

• Arıkan, E. E. (2019). Comparison of mathematical problem-posing skills of university students in the context of critical thinking dispositions. Istanbul Sabahattin Zaim University Journal of Faculty of Education, 1(1), 51–66. https://dergipark.org.tr/en/pub/izujed/issue/42924/492065
   Google Scholar
• Arıkan, E. E., & Ünal, H. (2015). Investigation of problem-solving and problem-posing abilities of seventh-grade students. Educational Sciences – Theory & Practice, 15(5), 1403–1416. https://doi.org/10.12738/estp.2015.5.2678
   Google Scholar
• Baumanns, L., & Rott, B. (2019). Is problem posing about posing „problems“? A terminological framework for researching problem posing and problem solving. In I. Gebel, A. Kuzle & B. Rott (Eds.), Proceedings of the 2018 Joint Conference of ProMath and the GDM Working Group on Problem Solving (pp. 21–32). WTM. https://doi.org/10.37626/GA9783959871167.0.02
   Google Scholar
• Becker, J. P., & Shimada, S. (1997). The open-ended approach: A new proposal for teaching mathematics. National Council of Teachers of Mathematics.
   Google Scholar
• Bowen, G. A. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27–40. https://doi.org/10.3316/QRJ0902027
   Google Scholar
• Brown, S. I., & Walter, M. I. (1983). The art of problem posing. Franklin Institute Press.
   Google Scholar
• Bruder, R. (2000). Akzentuierte Aufgaben und heuristische Erfahrungen – Wege zu einem anspruchsvollen Mathematikunterricht für alle. In L. Flade & W. Herget (Eds.), Mathematik. Lehren und lernen nach TIMSS. Anregungen für die Sekundarstufen (pp. 69–78). Volk und Wissen.
   Google Scholar
• Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem-posing research in mathematics education: Some answered and unanswered questions. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing. From research to effective practice (pp. 3–34). Springer.
   Google Scholar
• Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21(4), 401–421. https://doi.org/10.1016/S0732-3123(02)00142-6
   Google Scholar
• Cai, J., & Hwang, S. (2020). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research, 20, 1–8. https://doi.org/10.1016/j.ijer.2019.01.001
   Web of Science ®Google Scholar
• Cai, J., & Jiang, C. (2017). An analysis of problem-posing tasks in Chinese and US elementary mathematics textbooks. International Journal of Science and Mathematics Education, 15(8), 1521–1540. https://doi.org/10.1007/s10763-016-9758-2
   Web of Science ®Google Scholar
• Cambridge Dictionary. (2020). Pose. https://dictionary.cambridge.org/de/worterbuch/englisch/pose
   Google Scholar
• Cantor, G. (1966/1932). Gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Mit erläuternden Anmerkungen sowie mit Ergänzungen aus dem Briefwechsel Cantor-Dedekind. Georg Olms.
   Google Scholar
• Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM Mathematics Education, 37(3), 149–158. https://doi.org/10.1007/s11858-005-0004-6
   Google Scholar
• Cifarelli, V. V., & Cai, J. (2005). The evolution of mathematical explorations in open-ended problem-solving situations. The Journal of Mathematical Behavior, 24(3–4), 302–324. https://doi.org/10.1016/j.jmathb.2005.09.007
   Google Scholar
• Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20(1), 37–46. https://doi.org/10.1177/001316446002000104
   Web of Science ®Google Scholar
• Dickman, B. (2014). Problem posing with the multiplication table. Journal of Mathematics Education at Teachers College, 5(1), 47–50. https://doi.org/10.7916/jmetc.v5i1.643
   Google Scholar
• Díez, F., & Moriyón, R. (2004). Solving mathematical exercises that involve symbolic computations. Computing in Science & Engineering, 6(1), 81–84. https://doi.org/10.1109/MCISE.2004.1255826
   Web of Science ®Google Scholar
• Doyle, W. (1988). Work in mathematics classes: The context of students’ thinking during instruction. Educational Psychologist, 23(2), 167–180. https://doi.org/10.1207/s15326985ep2302_6
   Web of Science ®Google Scholar
• English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34(3), 183–217. https://doi.org/10.1023/A:1002963618035
   Google Scholar
• Felmer, P., Pehkonen, E., & Kilpatrick, J. (Eds.). (2016). Posing and solving mathematical problems. Advances and new perspectives. Springer.
   Google Scholar
• Fleiss, J. L., Levin, B., & Paik, M. C. (2003). Statistical methods for rates and proportions (3rd ed.). John Wiley & Sons.
   Google Scholar
• Groetsch, C. W. (2001). Inverse problems: The other two-thirds of the story. Quaestiones Mathematicae, 24 (Supplement 1), 89–94.
   Google Scholar
• Halmos, P. R. (1980). The heart of mathematics. The American Mathematical Monthly, 87(7), 519–524. https://doi.org/10.1080/00029890.1980.11995081
   Web of Science ®Google Scholar
• Jiang, C., & Cai, J. (2014). Collective problem posing as an emergent phenomenon in middle school mathematics group discourse. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of the 38th conference of the international group for the psychology of mathematics education and the 36th conference of the north American chapter of the psychology of mathematics education (Vol. 3, pp. 393–400). PME.
   Google Scholar
• Kinda, S. (2013). Generating scenarios of division as sharing and grouping: A study of japanese elementary and university students. Mathematical Thinking and Learning, 15(3), 190–200. https://doi.org/10.1080/10986065.2013.794256
   Web of Science ®Google Scholar
• Koichu, B., Berman, A., & Moore, M. (2007). Heuristic literacy development and its relation to mathematical achievements of middle school students. Instructional Science, 35(2), 99–139. https://doi.org/10.1007/s11251-006-9004-3
   Web of Science ®Google Scholar
• Koichu, B., & Kontorovich, I. (2013). Dissecting success stories on mathematical problem posing: A case of the billiard task. Educational Studies in Mathematics, 83(1), 71–86. https://doi.org/10.1007/s10649-012-9431-9
   Web of Science ®Google Scholar
• Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2012). An exploratory framework for handling the complexity of mathematical problem posing in small groups. The Journal of Mathematical Behavior, 31(1), 149–161. https://doi.org/10.1016/j.jmathb.2011.11.002
   Google Scholar
• Lang, S. (1989). Faszination Mathematik – Ein Wissenschaftler stellt sich der Öffentlichkeit. Vieweg.
   Google Scholar
• Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference? ZDM Mathematics Education, 45(2), 183–197. https://doi.org/10.1007/s11858-012-0460-8
   Google Scholar
• Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (2nd ed., pp. 763–804). NCTM.
   Google Scholar
• Leuders, T. (2015). Aufgaben in Forschung und Praxis. In R. Bruder, L. Hefendehl-Hebeker, B. Schmidt-Thieme, & H.-G. Weigand (Eds.), Handbuch der Mathematikdidaktik (pp. 435–460). Springer.
   Google Scholar
• Leung, S.-K. S. (2013). Teachers implementing mathematical problem posing in the classroom: Challenges and strategies. Educational Studies in Mathematics, 83(1), 103–116. https://doi.org/10.1007/s10649-012-9436-4
   Web of Science ®Google Scholar
• Lowrie, T. (2002). Young children posing problems: The influence of teacher intervention on the type of problems children pose. Mathematics Education Research Journal, 14(2), 87–98. https://doi.org/10.1007/BF03217355
   Google Scholar
• Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (2nd ed.). Pearson.
   Google Scholar
• Moher, D., Liberati, A., Tetzlaff, J., & Altman, D. G. (2009). Preferred reporting items for systematic reviews and meta-analyses: The prisma statement. PLoS Medicine, 6(7). https://doi.org/10.1371/journal.pmed.1000097
   Web of Science ®Google Scholar
• Newell, A., & Simon, H. A. (1972). Human problem solving. Prentice-Hall.
   Google Scholar
• Pehkonen, E. (1995). Introduction: Use of open-ended problems. ZDM Mathematics Education, 27(2), 55–57.
   Google Scholar
• Pelczer, I., & Gamboa, F. (2009). Problem posing: Comparison between experts and novices. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33th conference of the international group for the psychology of mathematics education (Vol. 4, pp. 353–360). PME.
   Google Scholar
• Pólya, G. (1945). How to solve it. University Press.
   Google Scholar
• Pólya, G. (1966). On teaching problem solving. In The Conference Board of the Mathematical Sciences (Ed.), The role of axiomatics and problem solving in mathematics (pp. 123–129). Ginn.
   Google Scholar
• Posamentier, A. S., & Krulik, S. (2008). Problem-solving strategies for efficient and elegant solutions, grades 6-12: A resource for the mathematics teacher (2nd ed.). Corwin.
   Google Scholar
• Rott, B. (2014). Mathematische Problembearbeitungsprozesse von Fünftklässlern – Entwicklung eines deskriptiven Phasenmodells. Journal für Mathematik-Didaktik, 35(2), 251–282. https://doi.org/10.1007/s13138-014-0069-2
   Google Scholar
• Ruthven, K. (2020). Problematising learning to teach through mathematical problem posing. International Journal of Educational Research, 20, 1–7. https://doi.org/10.1016/j.ijer.2019.07.004
   Web of Science ®Google Scholar
• Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.
   Google Scholar
• Schoenfeld, A. H. (1989). Teaching mathematical thinking and problem solving. In L. B. Resnick & L. E. Klopfer (Eds.), Toward a thinking curriculum: Current cognitive research (pp. 83–103). Association for Supervisors and Curriculum Developers.
   Google Scholar
• Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition and sense-making in mathematics. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). MacMillan.
   Google Scholar
• Silber, S., & Cai, J. (2017). Pre-service teachers’ free and structured mathematical problem posing. International Journal of Mathematical Education in Science and Technology, 48(2), 163–184. https://doi.org/10.1080/0020739X.2016.1232843
   Web of Science ®Google Scholar
• Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
   Google Scholar
• Silver, E. A. (1995). The nature and use of open problems in mathematics education: Mathematical and pedagogical perspectives. ZDM Mathematics Education, 27(2), 67–72.
   Google Scholar
• Singer, F. M., Ellerton, N. F., & Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1–7. https://doi.org/10.1007/s10649-013-9478-2
   Web of Science ®Google Scholar
• Singer, F. M., Ellerton, N. F., & Cai, J. (Eds.). (2015). Mathematical problem posing. From research to effective practice. Springer.
   Google Scholar
• Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488. https://doi.org/10.3102/00028312033002455
   Web of Science ®Google Scholar
• Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. C. Clarkson (Ed.), Technology in mathematics education (pp. 518–525). Mathematics Education Research Group of Australasia.
   Google Scholar
• Stoyanova, E. (1997). Extending and exploring students’ problem solving via problem posing [Doctoral dissertation, Edith Cowan University]. http://ro. ecu.edu.au/cgi/viewcontent.cgi?article=1886&context=theses
   Google Scholar
• Stoyanova, E. (1999). Extending students’ problem solving via problem posing. Australian Mathematics Teacher, 55(3), 29–35.
   Google Scholar
• Sullivan, P., & Clarke, D. (1991). Catering to all abilities through ‘good’ questions. Arithmetic Teacher, 39(2), 14–18. https://doi.org/10.5951/AT.39.2.0014
   Google Scholar
• Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2(1), 59–89. https://doi.org/10.1207/s1532690xci0201_3
   Google Scholar
• Tao, T. (2006). Solving mathematical problems: A personal perspective. Oxford University Press.
   Google Scholar
• Tichá, M., & Hošpesová, A. (2013). Developing teachers’ subject didactic competence through problem posing. Educational Studies in Mathematics, 83(1), 133–143. https://doi.org/10.1007/s10649-012-9455-1
   Web of Science ®Google Scholar
• Törner, G., & Azarello, F. (2012). Grading mathematics education research journals. EMS Newsletter, 10, 52–54.
   Google Scholar
• Van Gog, T., Paas, F., & Van Merriënboer, J. J. G. (2006). Effects of process-oriented worked examples on troubleshooting transfer performance. Learning and Instruction, 16(2), 154–164. https://doi.org/10.1016/j.learninstruc.2006.02.003
   Web of Science ®Google Scholar
• Wickelgren, W. A. (1974). How to solve problems. W. H. Freeman und Company.
   Google Scholar
• Williams, S. R., & Leatham, K. R. (2017). Journal quality in mathematics education. Journal for Research in Mathematics Education, 48(4), 369–396. https://doi.org/10.5951/jresematheduc.48.4.0369
   Web of Science ®Google Scholar
• Xie, J., & Masingila, J. O. (2017). Examining interactions between problem posing and problem solving with prospective primary teachers: A case of using fractions. Educational Studies in Mathematics, 96(1), 101–118. https://doi.org/10.1007/s10649-017-9760-9
   Web of Science ®Google Scholar
• Yeo, J. B. W. (2017). Development of a framework to characterize the openness of mathematical tasks. International Journal of Science and Mathematics Education, 15(1), 175–191. https://doi.org/10.1007/s10763-015-9675-9
   Web of Science ®Google Scholar