The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Dissecting success stories on mathematical problem posing: a case of the Billiard Task
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“The stages by Koichu and Kontorovich (2013) are developed on a small sample of two people and therefore need to be tested for applicability to larger sample groups.”
From The process of problem posing: development of a descriptive phase model of problem posing (2022) · cites this paper as Koichu and Kontorovich, 2013
In the citing paper
“Koichu and Kontorovich (2013) consider spontaneously associated problems related to a given problem-posing situation in their model, yet this is only one aspect of the generation described above.”
From The process of problem posing: development of a descriptive phase model of problem posing (2022) · cites this paper as Koichu and Kontorovich (2013)
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Situated Cognition and the Culture of Learning
Brown, J. S., Collins, A., & Duguid, P. (1989) · Educational Researcher · doi:10.3102/0013189x018001032 · Cited by 13,645
Research works printed but not linked: 36
- Brinkmann, A. (2009). Mathematical beauty and its characteristics. A study of the students' points of view. The Montana Mathematics Enthusiast, 6(3), 365–380. · doi:10.54870/1551-3440.1158
- Brown, S. I., & Walter, M. I. (1983). The art of problem posing. Philadelphia, PA: Franklin Institute Press.
- Carlson, M., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problem-solving framework. Educational Studies in Mathematics, 58, 45–75. · DOI · Paper page
- Cifarelli, V., & Cai, J. (2005). The evolution of mathematical explorations in open ended problem solving situations. The Journal of Mathematical Behavior, 24, 302–324. · DOI
- Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415. · DOI · Paper page
- De Corte, E., & Verschaffel, L. (1996). An empirical test of the impact of primitive intuitive models of operations on solving word problems with a multiplicative structure. Learning and Instruction, 6, 219–243. · doi:10.1016/0959-4752(96)00004-7
- Dreyfus, T., & Eisenberg, T. (1986). On the aesthetics of mathematical thoughts. For the Learning of Mathematics, 6(1), 2–10.
- English, L. D. (1998). Children's problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83–106. · DOI · Paper page
- Goldin, G. A. (2002). Affect, meta-affect, and mathematical belief structures. In G. C. Leder, E. Penkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 59–72). Dordrecht: Kluwer. · DOI
- Harel, G., Koichu, B., & Manaster, A. (2006). Algebra teachers' ways of thinking characterizing the mental act of problem posing. In I. J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (vol. 3, pp. 241–248). Prague, Czech Republic: Charles University.
- Kilpatrick, J. (1982). What is a problem? Problem Solving, 4(2), 1–2. 4-5.
- Kilpatrick, J. (1985). A retrospective account of the past 25 years of research on teaching mathematical problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives. Hillsdale, NJ: Lawrence Erlbaum Associates.
- Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123–147). Hillsdale, NJ: Lawrence Erlbaum Associates.
- Koichu, B., & Berman, A. (2005). When do gifted high school students use geometry to solve geometry problems? Journal of Secondary Gifted Education, 16(4), 168–179. · DOI
- Koichu, B., Katz, E., & Berman, A. (2007). What is a beautiful problem? An undergraduate students' perspective. In J.-H. Woo, H.-C. Lew, K.-S. Park, & D.-Y. Seo (Eds.), Proceedings of the 31th Conference of the International Group for the Psychology of Mathematics Education (vol. 3, pp. 113–120). Seoul, Korea.
- Kontorovich, I., & Koichu, B. (2009). Towards a comprehensive framework of mathematical problem posing. In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (vol. 3, pp. 401–408). Thessaloniki, Greece: PME.
- Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2011). Indicators of creativity in mathematical problem posing: How indicative are they? In M. Avotina, D. Bonka, H. Meissnera, L. Ramana, L. Sheffield, & E. Velikova (Eds.). Proceedings of the 6th International Conference on Creativity in Mathematics Education and the Education of the Gifted Students (pp. 120–125), University of Latvia, Riga, Latvia.
- Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2012). A framework for handling the complexity of students' mathematical problem posing in small groups. The Journal of Mathematical Behavior, 31(1), 149–161. · DOI · Paper page
- Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, NJ: Lawrence Erlbaum. · DOI · Paper page
- Mamona-Downs, J., & Downs, M. (2005). The identity of problem solving. The Journal of Mathematical Behavior, 24, 385–401. · DOI
- Movshovitz-Hadar, N., & Kleiner, I. (2009). Intellectual courage and mathematical creativity. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and education of gifted students (pp. 31–50). Rotterdam, The Netherlands: Sense Publishers. · doi:10.1163/9789087909352_004
- Pelczer, I., & Gamboa, F. (2009). Problem posing: Comparison between experts and novices. In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33th Conference of the International Group for the Psychology of Mathematics Education (vol. 4, pp. 353–360). Thessaloniki, Greece: PME.
- Perrin, J. (2007). Problem posing at all levels in the calculus classroom. School Science and Mathematics, 107(5), 182–192. · doi:10.1111/j.1949-8594.2007.tb17782.x
- Putnam, R., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Researcher, 29(1), 4–15. · doi:10.3102/0013189x029001004 · Paper page
- Ramirez, M. C. (2006). A mathematical problem-formulating strategy. International Journal for Mathematics Teaching and Learning, 79-90. Retrieved from http://www.cimt.plymouth.ac.uk/journal/ramirez.pdf
- Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic.
- Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
- Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM, 29(3), 75–80. · DOI · Paper page
- Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521–539. · DOI · Paper page
- Silver, E. A., Kilpatrick, J., & Schlesinger, B. (1990). Thinking through mathematics: Fostering inquiry and communication in mathematics classrooms. New York: The College Board.
- Silver, E. A., Mamona-Downs, J., Leung, S., & Kenney, P. A. (1996). Posing mathematical problems: An exploratory study. Journal for Research in Mathematics Education, 27(3), 293–309. · doi:10.2307/749366
- Singer, M., Ellerton, N., Silver, E. A., Cai, J., Pelczer, I., Imaoka, M., & Voica, C. (2009). Problem posing in mathematics learning: establishing a theoretical base for research. In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33th Conference of the International Group for the Psychology of Mathematics Education (vol. 1, p. 229). Thessaloniki, Greece: PME.
- Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students' problem posing in school mathematics. In P. Clarkson (Ed.), Technology in Mathematics Education (pp. 518–525). Melbourne: Mathematics Education Research Group of Australasia.
- Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166–175. · DOI · Paper page
- Wells, D. (1990). Are these the most beautiful? The Mathematical Intelligencer, 12(3), 37–41. · doi:10.1007/bf03024015
- Wilson, S. M., & Berne, J. (1999). Teacher learning and the acquisition of professional knowledge: An examination of research on contemporary professional development. In A. Iran-Nejad & P. D. Pearson (Eds.), Review of Research in Education (vol. 24, pp. 173–209). · DOI · Paper page
Cited by
What Research Says About Teaching Mathematics Through Problem Posing
Cai, J. (2022) · Éducation et didactique · doi:10.4000/educationdidactique.10642 · Cited by 114
The process of problem posing: development of a descriptive phase model of problem posing
Baumanns, L., & Rott, B. (2022) · Educational Studies in Mathematics · doi:10.1007/s10649-021-10136-y · Cited by 81
Metadata
- Authors
- Koichu, B., & Kontorovich, I.
- Venue
- Educational Studies in Mathematics
- Published
- 2012-10-03
- Volume
- 83
- Issue
- 1
- Pages
- 71-86
- ISSN
- 0013-1954
- 1573-0816
- Cited by
- 74
- References
- 1
- Language
- en
- Licence
- www.springer.com/tdm (tdm)
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Dissecting success stories on mathematical problem posing: a case of the Billiard Task. https://app.cochat.ai/papers/10.1007/s10649-012-9431-9
- The paper
- Koichu, B., & Kontorovich, I. (2013). Dissecting success stories on mathematical problem posing: a case of the Billiard Task. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-012-9431-9
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.