Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 59

The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.

Teaching mathematics through problem posing: insights from an analysis of teaching cases

Zhang, Huirong, Cai, Jinfa·2021·ZDM – Mathematics Education
DOI 10.1007/s11858-021-01260-3
Open this paper in CoChat — free account

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.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1007/s11858-021-01260-3

Cites

1 of 1 references verified0 citation errors · 0 not checkable

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.

A few free checks a day · papers already verified open instantly · results are public

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?

9 more claims about this paper

Create a free account to see every claim other papers make about this one.

See all claims — free account

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

Show all 1 references

Research works printed but not linked: 60

  1. Australian Education Council. (1991). A national statement on mathematics for Australian schools: A jointproject of the States, Territories and the Commonwealth of Australia initiated by the Australian Education Council. . Curriculum Corporation.
  2. Bryk, A. S., Gomez, L. M., Grunow, A., & LeMahieu, P. G. (2015). Learning to improve: How America’s schools can get better at getting better. . Harvard Education Press.
  3. Cai, J. (2003). What research tells us about teaching mathematics through problem solving. In F. Lester (Ed.), Research and issues in teaching mathematics through problem solving. (pp. 241–254). National Council of Teachers of Mathematics.
  4. Cai, J., Chen, T., Li, X., Xu, R., Zhang, S., Hu, Y., Zhang, L., & Song, N. (2020). Exploring the impact of a problem-posing workshop on elementary school mathematics teachers’ problem posing and lesson design. International Journal of Educational Research, 102, 101404. · DOI
  5. Cai, J., & Hwang, S. (2002). Generalized and generative thinking in U.S. and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21, 401–421. · DOI · Paper page
  6. Cai, J., & Hwang, S. (2020). Learning to teach mathematics through problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research. https://doi.org/10.1016/j.ijer.2019.01.001. · DOI · Paper page
  7. Cai, J., & Hwang, S. (2021). Teachers as re-designers of curriculum to teach mathematics through problem posing: Conceptualization and initial findings of a problem-posing project. ZDM-Mathematics Education.
  8. 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. Springer.
  9. Cai, J., Hwang, S., Melville, M. & Robison, V. (in press). Theories for teaching and teaching for theories: Artifacts as tangible entities for storing and improving professional knowledge for teaching. In A. Praetorius & C. Y. Charalambous (Ed), Theorizing teaching. Springer.
  10. Cai, J., & Jiang, C. (2017). An analysis of problem-posing tasks in Chinese and U.S. elementary mathematics textbooks. International Journal of Science and Mathematics Education, 15(8), 1521–1540. · DOI · Paper page
  11. Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83, 57–69. · DOI
  12. Cai, J., Wang, N., Moyer, J. C., Wang, C., & Nie, B. (2011). Longitudinal investigation of the curriculum effect: An analysis of student learning outcomes from the LieCal Project. International Journal of Educational Research, 50, 117–136. · DOI
  13. Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1998). A longitudinal study of invention and understanding in children’s multidigit addition and subtraction. Journal for Research in Mathematics Education, 29, 3–20. · DOI · Paper page
  14. Cazden, C. B. (1986). Classroom discourse: The language of teaching and learning. . Heinemann.
  15. Chinese Ministry of Education. (2001a). Curriculum standards for school mathematics of nine-year compulsory education (Trial version). . Beijing Normal University Press.
  16. Chinese Ministry of Education. (2001b). Guidelines for curriculum reform of elementary education (Trial version). . Beijing Normal University Press.
  17. Chinese Ministry of Education. (2003). Curriculum standards of high school mathematics (Trial version). People’s Education Press.
  18. Chinese Ministry of Education. (2011). Mathematics curriculum standard of compulsory education (2011 version). . Beijing Normal University Press.
  19. Cobb, P., & Bauersfeld, H. (1995). The emergence of mathematical meaning: Interaction in classroom cultures. . Lawrence Erlbaum.
  20. Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B., & Perlwitz, M. (1991). Assessment of a problem-centered second-grade mathematics project. Journal for Research in Mathematics Education, 22, 3–29. · DOI · Paper page
  21. Doyle, W. (1983). Academic work. Review of Educational Research, 53, 159–199. · DOI · Paper page
  22. Doyle, W. (1988). Work in mathematics classes: The context of students’ thinking during instruction. Educational Psychologist, 23, 167–180. · DOI · Paper page
  23. Ellerton, N. F. (2013). Engaging pre-service middle-school teacher-education students in mathematical problem posing: Development of an active learning framework. Educational Studies in Mathematics, 83(1), 87–101. · DOI · Paper page
  24. Forman, E., & Cazden, C. B. (1985). Exploring Vygotskian perspectives in education: The cognitive value of peer interaction. In J. V. Wertsch (Ed.), Culture, communication, and cognition: Vygotskian perspectives. (pp. 323–347). Cambridge University Press.
  25. Fuson, K. C., Carroll, W. M., & Drueck, J. V. (2000). Achievement results for second and third graders using the standards-based curriculum everyday mathematics. Journal for Research in Mathematics Education, 31, 277–295. · DOI
  26. Goldin, A. G., & Mcclintock, E. C. (1984). Task variables in mathematical problem solving. . Franklin Institute Press.
  27. Hembree, R., & Marsh, H. (1993). Problem solving in early childhood: Building foundations. In R. J. Jenson (Ed.), Research ideas for the classroom: Early childhood mathematics. (pp. 151–170). National Council of Teachers of Mathematics.
  28. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A., & Human, P. (1997). Making sense: Teaching and learning mathematics with understanding. . Heinemann.
  29. Hiebert, J., & Wearne, D. (1993). Instructional task, classroom discourse, and students’ learning in second grade. American Educational Research Journal, 30, 393–425. · doi:10.3102/00028312030002393 · Paper page
  30. Hillen, A. F., & Hughes, E. K. (2008). Developing teachers’ abilities to facilitate meaningful classroom discourse through cases: The case of accountable talk. In M. S. Smith & S. Friel (Eds.), Cases in mathematics teacher education: Tools for developing knowledge needed for teaching. AMTE Fourth monograph of the Association of Mathematics Teacher Educators.
  31. Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education. (pp. 123–147). Lawrence Erlbaum Associates.
  32. 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. · DOI · Paper page
  33. Kroll, D. L., & Miller, T. (1993). Insights from research on mathematical problem solving in the middle grades. In D. T. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics. (pp. 58–77). National Council of Teachers of Mathematics.
  34. Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27, 29–63. · doi:10.3102/00028312027001029 · Paper page
  35. Leinhardt, G. (1989). Math lessons: A contrast of novice and expert competence. Journal for Research in Mathematics Education, 20(1), 52–75. · DOI · Paper page
  36. Lloyd, G. M., Cai, J., & Tarr, J. E. (2017). Issues in curriculum studies: Evidence-based insights and future directions. In J. Cai (Ed.), Compendium for research in mathematics education. National Council of Teachers of Mathematics.
  37. Lu, C., & Wang, B. (2006). Research on mathematics teaching through using mathematical situations and posing problems in high school and primary school [in Chinese]. . Guizhou People’s Publishing House.
  38. Matsko, V. J., & Thomas, J. (2015). Beyond routine: Fostering creativity in mathematics classrooms. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing. (pp. 125–139). Springer. · DOI
  39. Merseth, K. K. (2003). Windows on teaching math: Cases of middle and secondary classrooms. . Teachers College Press.
  40. Merseth, K. K. (2016). The early history of case-based instruction: Insights for teacher education today. Journal of Teacher Education, 42(4), 243–249. · DOI · Paper page
  41. Ministry of Education (Singapore). (2012). Primary mathematics teaching and learning Syllabus. . Author.
  42. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. . Author.
  43. National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. . Author.
  44. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. . Author.
  45. Perry, M., VanderStoep, S. W., & Yu, S. L. (1993). Asking questions in first-grade mathematics classes: Potential influences on mathematical thought. Journal of Educational Psychology, 85, 31–40. · DOI
  46. Resnick, L. B. (1989). Developing mathematical knowledge. American Psychologist, 44, 162–169. · DOI · Paper page
  47. Ridgeway, J., Zawojewski, J. S., Hoover, M. N., & Lambdin, D. (2002). Student attainment in the connected mathematics curriculum. In S. Senk & D. Thompson (Eds.), Standards-oriented school mathematics curricula: What are they? What do students learn? Lawrence Erlbaum Associates.
  48. Romberg, T. A., & Shafer, M. (2002). Mathematics in Context (MiC): Preliminary evidence about student outcomes. In S. Senk & D. Thompson (Eds.), Standards-oriented school mathematics curricula: What are they? What do students learn? Lawrence Erlbaum Associates.
  49. Schroeder, T. L., & Lester, F. K., Jr. (1989). Developing understanding in mathematics via problem solving. In P. R. Trafton (Ed.), New directions for elementary school mathematics. (pp. 31–42). National Council of Teachers of Mathematics.
  50. 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. · DOI
  51. 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
  52. Singer, F. M., Ellerton, N., & Cai, J. (Eds.). (2015). Mathematical problem posing: From research to effective practice. . Springer.
  53. Singer, F. M., & Moscovici, H. (2008). Teaching and learning cycles in a constructivist approach to instruction. Teaching and Teacher Education, 24(6), 1613–1634. · DOI
  54. Smith, M. S., Boyle, J., Arbaugh, F., Steele, M. D., & Stylianides, G. (2014). Cases as a vehicle for developing knowledge needed for teaching. In Y. Li, E. A. Silver, & S. Li (Eds.), Transforming mathematics instruction: Multiple approaches and practices. Cham: Springer.
  55. Stein, M. K., Grover, B. W., & Henningsen, M. A. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33, 455–488. · doi:10.3102/00028312033002455 · Paper page
  56. Stein, M. K., Henningsen, M. A., Smith, M. S., & Silver, E. A. (2009). Implementing standards-based mathematics instruction: A casebook for professional development. (2nd ed.). Teachers College Press.
  57. Stein, M. K., Smith, M. S., & Silver, E. A. (1999). The development of professional developers. Harvard Educational Review, 69, 237–269. · DOI · Paper page
  58. Tarr, J. E., Reys, R. E., Reys, B. J., Chavez, O., Shih, J., & Osterlind, S. J. (2008). The impact of middle-grades mathematics curricula and the classroom learning environment on student achievement. Journal for Research in Mathematics Education, 39(3), 247–280.
  59. Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning. (pp. 127–146). Macmillan.
  60. Williams, S. M. (1992). Putting case-based instruction into context: Examples from legal and medical education. The Journal of the Learning Sciences, 2(4), 367–427. · DOI · Paper page

Cited by

See all 59

Metadata

Authors
Zhang, H., & Cai, J.
Venue
ZDM – Mathematics Education
Publisher
Springer Science and Business Media LLC
Published
2021-04-12
Volume
53
Issue
4
Pages
961-973
ISSN
  • 1863-9690
  • 1863-9704
DOI
10.1007/s11858-021-01260-3
Cited by
59
References
1
Language
en
Licence

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: Teaching mathematics through problem posing: insights from an analysis of teaching cases. https://app.cochat.ai/papers/10.1007/s11858-021-01260-3
The paper
Zhang, H., & Cai, J. (2021). Teaching mathematics through problem posing: insights from an analysis of teaching cases. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-021-01260-3

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.