The collection of articles in this special issue highlights the importance of problem posing from both teachers' and students' perspectives. Considerable research has been conducted across several decades on students' problem posing, as the authors of the articles indicate. In contrast, studies of teachers' knowledge of their students' thinking as they engage in mathematical problem-posing and their capabilities in posing problems have been limited. Because research on teachers' problem posing has not been proli'c, the current articles raise more issues and questions than they can answer. I explore some of these issues and the challenges they present.
Cai, J., & Hwang, S. (2019). Learning to teach through mathematical 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.
Carpenter, T. P., & Romberg, T. A. (2004). Powerful PRACTICES in MATHEMATICS & science: RESEARCH-BASED PRACTICES for TEACHING AND LEARNING. Madison: University of Wisconsin.
Chen, T., & Cai, J. (2019). An elementary mathematics teacher learning to teach using problem posing: A case of the distributive property of multiplication over addition. INTERNATIONAL JOURNAL of EDUCATIONAL RESEARCH. https://doi.org/10.1016/j.ijer.2019.03.004.
Crespo, S., & Harper, F. K. (2019). Learning to pose collaborative mathematics problems with secondary prospective teachers. INTERNATIONAL JOURNAL of EDUCATION RESEARCH. https://doi.org/10.1016/j.ijer.2019.05.003.
Doerr, H. M., & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. JOURNAL for RESEARCH in MATHEMATICS EDUCATION, 34(2), 110–136.
English, L. D. (2010). Modeling with complex data in the primary school. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.). Modeling students’ MATHEMATICAL modeling competencies (pp. 287–300). Dordrecht: Springer.
English, L. D. (2012). Data modelling with ﬁrst-grade students. EDUCATIONAL Studies in MATHEMATICS EDUCATION, 81(1), 15–30.
English, L. D., & King, D. T. (2019). STEM integration in 6th grade: Designing and constructing paper bridges. INTERNATIONAL JOURNAL of Science AND MATHEMATICS EDUCATION, 17(5), 863–884. https://doi.org/10.1007/s10763-018-9912-0https://link.springer.com/journal/10763.
English, L. D., & Watson, J. M. (2015). STATISTICAL LITERACY in the ELEMENTARY school: Opportunities for problem posing. MATHEMATICAL problem posing. Springer. English, L. D., & Watters, J. J. (2005). Mathematical modelling in the early school years. MATHEMATICS EDUCATION RESEARCH JOURNAL, 16(3), 59–80.
Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. INTERNATIONAL STATISTICAL Review, 70, 1–51.
Horn, I. (2012). Strength in numbers: COLLABORATIVE LEARNING in SECONDARY MATHEMATICS. Reston, VA: National Council of Teachers of Mathematics.
Koichu, B. (2019). Problem posing in the context of teaching for advanced problem posing. INTERNATIONAL JOURNAL of EDUCATIONAL RESEARCH. https://doi.org/10.1016/j.ijer.
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, 149–161.
Lehrer, R., & English, L. D. (2018). Introducing children to modeling variability. In D. Ben-Zvi, K. Makar, & J. Garﬁeld (Eds.). INTERNATIONAL HANDBOOK of RESEARCH in STATISTICS EDUCATION. Springer INTERNATIONAL HANDBOOKS of EDUCATION (pp. 229–260). Cham: Springer. https://doi.org/10.1007/978-3-319-66195-7_7.
Lehrer, R., & Schauble, L. (2012). Seeding evolutionary thinking by engaging children in modeling its foundations. Science EDUCATION, 96(4), 701–724.
Leikin, R., & Elgrably, H. (2019). Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers. INTERNATIONAL JOURNAL of EDUCATIONAL RESEARCH. https://doi.org/10.1016/j.ijer.2019.04.002.
Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H. M. Doerr (Eds.). Beyond constructivism: Models AND modeling perspectives on MATHEMATICS problem solving, LEARNING, AND TEACHING (pp. 3–33). Mahwah, NJ: Erlbaum.
Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.). Second HANDBOOK of RESEARCH on MATHEMATICS TEACHING AND LEARNING (pp. 763–804).
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Lotan, R. A. (2003). Group-worthy tasks. EDUCATIONAL LEADERSHIP, (March), 72–75.
McKenna, A. F. (2014). Adaptive expertise and knowledge ﬂuency in design and innovation. In A. A. Johri, & B. M. Olds (Eds.). CAMBRIDGE HANDBOOK of engineering EDUCATION RESEARCH (pp. 227–242). New York: Cambridge University Press.
Reiser, B. J. (2004). Scaﬀolding complex learning: The mechanisms of structuring and problematizing student work. JOURNAL of the LEARNING Sciences, 13(3), 273–304.
Silver, E. A. (1994). On mathematical problem posing. For the LEARNING of MATHEMATICS, 14(1), 19–28.
Singer, F. M., Ellerton, N. F., & Cai, J. (2015). MATHEMATICAL problem posing: From RESEARCH to eﬀective PRACTICE. Springer.
Wendell, K. B., & Lee, H. S. (2010). Elementary students’ learning of materials science practices through instruction based on engineering design tasks. JOURNAL of Science EDUCATION AND Technology, 19(6), 580–601. https://doi.org/10.1007/s10956-010-9225-8.
Xu, B., Cai, J., Liu, Q., & Hwang, S. (2019). Teachers’ predictions of students’ mathematical thinking related to problem posing. INTERNATIONAL JOURNAL of EDUCATIONAL RESEARCH. https://doi.org/10.1016/j.ijer.2019.04.005.