Pesquisa sobre Proposição de Problemas Matemáticos: Trinta Anos de Avanços a partir da Publicação “On Mathematical Problem Posing”
DOI:
10.37084/REMATEC.1980-3141.2024.n52.e2024010.id737Palavras-chave:
Problemas MatemáticosResumo
Em 1994, Ed Silver publicou um artigo original intitulado “On Mathematical Problem Posing”. Silver tanto ajudou a estabelecer as bases para a pesquisa de proposição de problemas como apontou direções-chave que a pesquisa de proposição de problemas poderia explorar. Este artigo fornece uma breve revisão da literatura sobre proposição de problemas nas últimas três décadas, mostrando que houve avanços marcantes na pesquisa de proposição de problemas. Fornecemos não apenas uma revisão dos avanços na pesquisa de proposição de problemas, mas também do impacto do artigo original de Silver na pesquisa de proposição de problemas. O artigo termina com uma discussão de três áreas específicas de pesquisa sobre a proposição de problemas matemáticos (uma dessas áreas é a Aprendizagem Baseada em Proposição de Problemas [P-PBL]) que estão prontas para o progresso e podem significativamente avançar todo o campo.
Downloads
Métricas
Referências
Akay, H.,; Boz, N. (2010). The effect of problem posing oriented analyses-II course on the atti¬tudes toward mathematics and mathematics self-efficacy of elementary prospective math-emat¬ics teachers. Australian Journal of Teacher Education, 35(1), 6. DOI: https://doi.org/10.14221/ajte.2010v35n1.6
Baumanns, L.,; Rott, B. (2021). Rethinking problem-posing situations: A review. Investiga-tions in Mathematics Learning, 13(2), 59–76. DOI: https://doi.org/10.1080/19477503.2020.1841501
Brown, S. I.,; Walter, M. I. (1983). The art of problem posing. The Franklin Institute Press.
Butts, T. (1980). Posing problems properly. In S. Krulik; R. Reys (Eds.), Problem solving in school mathematics (pp. 23–33). National Council of Teachers of Mathematics.
Cai, J. (1998). An investigation of U.S. and Chinese students’ mathematical problem posing and problem solving. Mathematics Education Research Journal, 10, 37–50. DOI: https://doi.org/10.1007/BF03217121
Cai, J. (2003). Singaporean students’ mathematical thinking in problem solving and problem pos¬ing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719–737. DOI: https://doi.org/10.1080/00207390310001595401
Cai, J. (2022). What research says about teaching mathematics through problem posing. Edu-cation; Didactique, 16, 31–50. DOI: https://doi.org/10.4000/educationdidactique.10642
Cai, J.,; Cifarelli, V. V. (2005). Exploring mathematical exploration: How two college stu-dents formulated and solved their own mathematical problems. Focus on Learning Problems in Mathematics, 27(3), 43–72.
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: https://doi.org/10.1016/S0732-3123(02)00142-6
Cai, J.,; Hwang, S. (2020). Learning to teach through mathematical problem posing: Theoreti-cal considerations, methodology, and directions for future research. International Journal of Educational Research, 102, 101391. DOI: https://doi.org/10.1016/j.ijer.2019.01.001
Cai, J.,; Hwang, S. (2021). Teachers as redesigners of curriculum to teach mathematics through problem posing: Conceptualization and initial findings of a problem-posing project. ZDM–Mathematics Education, 53, 1–14. DOI: https://doi.org/10.1007/s11858-021-01252-3
Cai, J.,; Hwang, S. (2022). Making mathematics challenging through problem posing in the class¬room. In R. Leikin, C. Christou, A. Karp, D. Pitta-Pantazi,; R. Zazkis (Eds.), Mathemati-cal challenges for all. Springer. DOI: https://doi.org/10.1007/978-3-031-18868-8_7
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. DOI: https://doi.org/10.1007/s10763-016-9758-2
Cai, J.,; Leikin, R. (2020). Affect in mathematical problem posing: Conceptualization, advanc-es, and future directions for research. Educational Studies in Mathematics, 105(3), 287–301. DOI: https://doi.org/10.1007/s10649-020-10008-x
Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B.,; Garber, T. (2013). Mathematical prob¬lem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathe-matics, 83, 57–69. DOI: https://doi.org/10.1007/s10649-012-9429-3
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. DOI: https://doi.org/10.1007/978-1-4614-6258-3_1
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’ concep-tions on problem posing and lesson design. International Journal of Educational Research, 102, 101404. DOI: https://doi.org/10.1016/j.ijer.2019.02.004
Cai, J., Muirhead, F., Cirillo, M.,; Hwang, S. (2021). Supporting teachers to teach mathematics through problem posing: An early-stage longitudinal study [NSF Grant Proposal]. University of Delaware.
Cai, J., Koichu, B., Rott, B., Zazkis, R.,; Jiang, C. (2022). Mathematical problem posing: Task variables, processes and products. In C. Fernández, S. Llinares, A. Gutiérrez,; N. Planas (Eds.), Proceedings of the 45th conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 119–145). PME.
Cai, J., Hwang, S., Melville, M.,; Robison, V. (2023). 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 (Eds.), Theorizing teaching. Springer. DOI: https://doi.org/10.1007/978-3-031-25613-4_8
Chen, T.,; Cai, J. (2020). An elementary mathematics teacher learning to teach using prob¬lem posing: A case of the distributive property of multiplication over addition. International Jour-nal of Educational Research, 102, 101420. DOI: https://doi.org/10.1016/j.ijer.2019.03.004
Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D.,; Sriraman, B. (2005). An empiri-cal taxonomy of problem posing processes. ZDM, 37(3), 149–158. DOI: https://doi.org/10.1007/s11858-005-0004-6
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. DOI: https://doi.org/10.1016/j.jmathb.2005.09.007
Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52(3), 243–270. DOI: https://doi.org/10.1023/A:1024364304664
Crespo, S.,; Harper, F. (2020). Learning to pose collaborative mathematics problems with sec-ondary prospective teachers. International Journal of Educational Research, 102, 101430. DOI: https://doi.org/10.1016/j.ijer.2019.05.003
Crespo, S.,; Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting pro¬spective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415. DOI: https://doi.org/10.1007/s10857-008-9081-0
Doig, B.,; Groves, S. (2011). Japanese lesson study: Teacher professional development through communities of inquiry. Mathematics Teacher Education and Development, 13(1), 77–93.
Ellerton, N. F. (1986). Children’s made-up mathematics problems – A new perspective on talented mathematicians. Educational Studies in Mathematics, 17, 261–271. DOI: https://doi.org/10.1007/BF00305073
English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83–106. DOI: https://doi.org/10.5951/jresematheduc.29.1.0083
Fan, L., Chen, J., Zhu, Y., Qiu, X.,; Hu, Q. (2004). Textbook use within and beyond Chinese mathematics classrooms: A study of 12 secondary schools in Kunming and Fuzhou of China. In L. Fan, N. Y. Wong, J. Cai,; S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 228–261). World Scientific. DOI: https://doi.org/10.1142/9789812562241_0009
Garofalo, J.,; Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical per¬formance. Journal for Research in Mathematics Education, 16(3), 163–176. DOI: https://doi.org/10.5951/jresematheduc.16.3.0163
Guo, Y., Yan, J.,; Men, T. (2021). Chinese junior high school students’ mathematical problem-posing performance. ZDM–Mathematics Education, 53, 1–13. DOI: https://doi.org/10.1007/s11858-021-01240-7
Guskey, T. R.,; Yoon, K. S. (2009). What works in professional development? Phi Delta Kap-pan, 90(7), 495–500. DOI: https://doi.org/10.1177/003172170909000709
Hart, K. M. (Ed.). (1981). Children’s understanding of mathematics (pp. 11–16). John Murray.
Healy, C. C. (1993). Creating miracles: A story of student discovery. Key Curriculum Press.
Hwang, S.,; Cai, J. (2003). A perspective for examining the link between problem solving and problem posing. In N. A. Pateman, B. J. Dougherty,; J. Zilliox (Eds.), Proceedings of the 27th conference of the International Group for the Psychology of Mathematics Education held joint-ly with the 25th conference of PME-NA (Vol. 3, pp. 103–110). Center for Research and Devel-opment Group, University of Hawai’i.
Illustrative Mathematics. (n.d.). Supporting English-language learners. https://curriculum.illustra¬tivemathematics.org/HS/teachers/supporting_ell.html
Jiang, C.,; Cai, J. (2014). An analysis of mathematical problem-posing tasks in Chinese and US reform textbooks. In S. Oesterle, P. Liljedahl, C. Nicol,; D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 3, pp. 393–400). PME.
Jiang, C.,; Cai, J. (2015). An investigation of questions on the sixth grade students’ mathemat-ical problem posing. In K. Beswick, T. Muir,; J. Fielding-Wells (Eds.), Proceedings of the 39th conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 113–120). PME.
Kar, T., Özdemir, E., İpek, A. S.,; Albayrak, M. (2010). The relation between the problem posing and problem solving skills of prospective elementary mathematics teachers. Procedia-Social and Behavioral Sciences, 2(2), 1577–1583. DOI: https://doi.org/10.1016/j.sbspro.2010.03.239
Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123–147). Erlbaum.
Koichu, B. (2020). Problem posing in the context of teaching for advanced problem solving. International Journal of Educational Research, 102, 101428. DOI: https://doi.org/10.1016/j.ijer.2019.05.001
Koichu, B.,; Kontorovich, I. (2013). Dissecting success stories on mathematical problem pos-ing: A case of the Billiard Task. Educational Studies in Mathematics, 83(1), 71–86. DOI: https://doi.org/10.1007/s10649-012-9431-9
Kotsopoulos, D.,; Cordy, M. (2009). Investigating imagination as a cognitive space for learn-ing mathematics. Educational Studies in Mathematics, 70, 259–274. DOI: https://doi.org/10.1007/s10649-008-9154-0
Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Lei-kin, A. Berman,; B. Koichu (Eds.), Creativity in mathematics and the education of gifted stu-dents (pp. 129–145). Sense. DOI: https://doi.org/10.1163/9789087909352_010
Leikin, R.,; Sriraman, B. (2017). Creativity and giftedness: Interdisciplinary perspectives from mathematics and beyond. Springer. DOI: https://doi.org/10.1007/978-3-319-38840-3
Lesh, R. (1981). Applied mathematical problem solving. Educational Studies in Mathematics, 12(2), 235–264. DOI: https://doi.org/10.1007/BF00305624
Lesh, R., Landau, M.,; Hamilton, E. (1983). Conceptual models and applied mathematical problem-solving research. In R. Lesh; M. Landau (Eds.), Acquisition of mathematics con¬cepts and processes (pp. 264–343). Academic Press.
Leung, S. S.,; Silver, E. A. (1997). The role of task format, mathematics knowledge, and cre-ative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9(1), 5–24. DOI: https://doi.org/10.1007/BF03217299
Lewis, W. M.,; Colonnese, M. W. (2021). Fostering mathematical creativity through problem posing and three-act tasks. Gifted Child Today, 44(3), 141–150. DOI: https://doi.org/10.1177/10762175211008502
Li, X., Song, N., Hwang, S.,; Cai, J. (2020). Learning to teach mathematics through prob¬lem posing: Teachers’ beliefs and performance on problem posing. Educational Studies in Mathe-matics, 105(3), 325–347. DOI: https://doi.org/10.1007/s10649-020-09981-0
Lubinski, D.,; Benbow, C. P. (2006). Study of mathematically precocious youth after 35 years: Uncovering antecedents for the development of math-science expertise. Perspectives on Psychological Science, 1(4), 316–345. DOI: https://doi.org/10.1111/j.1745-6916.2006.00019.x
Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 30, 520–540. DOI: https://doi.org/10.2307/749772
McLeod, D. B.,; Adams, V. M. (1989). Affect and mathematical problem solving: A new per-spec¬tive. Lawrence Erlbaum Associates. DOI: https://doi.org/10.1007/978-1-4612-3614-6
Melville, M.,; Corey, D. L. (2021). Kyouzaikenkyuu: An exploration of Japanese mathemat¬ics teachers’ daily planning practices. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-021-09493-5 DOI: https://doi.org/10.1007/s10857-021-09493-5
Moses, B., Bjork, E.,; Goldenberg, E. P. (1990). Beyond problem solving: Problem posing. In T. J. Cooney; C. R. Hirsch (Eds.), Teaching and learning mathematics in the 1990s (pp. 82–91). National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Journal for Research in Mathematics Education. https://doi.org/10.2307/749544 DOI: https://doi.org/10.2307/749544
Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester Jr. (Ed.), Sec-ond handbook of research on mathematics teaching and learning (pp. 257–315). Information Age.
Polya, G. (1957). How to solve it: A new aspect of mathematical method. Princeton University Press.
Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula (Ed.), Handbook of research on teacher education (2nd ed., pp. 102–119). Macmillan.
Rott, B., Specht, B.,; Knipping, C. (2021). A descriptive phase model of problem-solving pro-cesses. ZDM. https://doi.org/10.1007/s11858-021-01244-3 DOI: https://doi.org/10.1007/s11858-021-01244-3
Schindler, M.,; Bakker, A. (2020). Affective field during collaborative problem posing and prob¬lem solving: A case study. Educational Studies in Mathematics, 105, 303–324. https://doi.org/10.1007/s10649-020-09973-0 DOI: https://doi.org/10.1007/s10649-020-09973-0
Schoenfeld, A. H. (1985). Making sense of “out loud” problem-solving protocols. The Journal of Mathematical Behavior, 4(2), 171–191.
Schroeder, T. L.,; Lester, F. K. (1989). Developing understanding in mathematics via problem solving. New Directions for Elementary School Mathematics, 31, 42.
Silber, S.,; Cai, J. (2017). Pre-service teachers’ free and structured mathematical problem pos-ing. International Journal of Mathematical Education in Science and Technology, 48(2), 163–184. DOI: https://doi.org/10.1080/0020739X.2016.1232843
Silber, S.,; Cai, J. (2021). Exploring underprepared undergraduate students’ mathematical prob¬lem posing. ZDM–Mathematics Education, 53, 1–13. DOI: https://doi.org/10.1007/s11858-021-01272-z
Silver, E. A. (1985). Research on teaching mathematical problem solving: Some underrepre-sented themes and needed directions. In Teaching and learning mathematical problem solv-ing: Multiple research perspectives. Lawrence Erlbaum Associates.
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–Mathematics Education, 97(3), 75–80. DOI: https://doi.org/10.1007/s11858-997-0003-x
Silver, E. A. (Ed.). (2013). Teaching and learning mathematical problem solving: Multiple research perspectives. Routledge.
Silver, E. A.,; Cai, J. (1996). An analysis of arithmetic problem posing by middle school stu-dents. Journal for Research in Mathematics Education, 27(5), 521–539. DOI: https://doi.org/10.5951/jresematheduc.27.5.0521
Silver, E. A., Mamona-Downs, J., Leung, S. S.,; Kenney, P. A. (1996). Posing mathematical problems: An exploratory study. Journal for Research in Mathematics Education, 27, 293–309. DOI: https://doi.org/10.5951/jresematheduc.27.3.0293
Singer, F. M., Ellerton, N.,; Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1–7. DOI: https://doi.org/10.1007/s10649-013-9478-2
Singer, F. M., Sheffield, L. J.,; Leikin, R. (2017). Advancements in research on creativity and giftedness in mathematics education: Introduction to the special issue. ZDM, 49(1), 5–12. DOI: https://doi.org/10.1007/s11858-017-0836-x
Smith, M. S.,; Friel, S. N. (Eds.). (2015). Cases in mathematics teacher education: Tools for developing knowledge needed for teaching. Information Age. DOI: https://doi.org/10.1007/978-3-319-04993-9_18
Stanic, G. M. A.,; Kilpatrick, J. (1988). Historical perspectives on problem solving in math-ematics curriculum. In R. I. Charles; E. A. Silver (Eds.), Research agenda for mathematics education: The teaching and assessing of mathematical problem solving (pp. 1–22). National Council of Teachers of Mathematics.
Stein, M. K., Smith, M. S., Henningsen, M. A.,; Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. Teachers College Press.
Stoyanova, E.,; Ellerton, N. F. (1996). A framework for research into students’ problem pos-ing in school mathematics. In P. C. Clarkson (Ed.), Technology in mathematics education (pp. 518–525). Mathematics Education Research Group of Australasia.
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.
Tichá, M.,; Hošpesová, A. (2013). Developing teachers’ subject didactic competence through problem posing. Educational Studies in Mathematics, 83(1), 133–143. DOI: https://doi.org/10.1007/s10649-012-9455-1
Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through prob¬lem posing. Teaching and Teacher Education, 25(1), 166–175. DOI: https://doi.org/10.1016/j.tate.2008.08.003
Van Harpen, X. Y.,; Sriraman, B. (2013). Creativity and mathematical problem posing: An analy¬sis of high school students’ mathematical problem posing in China and the USA. Educa-tional Studies in Mathematics, 82(2), 201–221. DOI: https://doi.org/10.1007/s10649-012-9419-5
Voica, C.,; Singer, F. M. (2012). Creative contexts as ways to strengthen mathematics learn-ing. Procedia-Social and Behavioral Sciences, 33, 538–542. DOI: https://doi.org/10.1016/j.sbspro.2012.01.179
Williams, S. R.,; Leatham, K. R. (2017). Journal quality in mathematics education. Journal for Research in Mathematics Education, 48(4), 369–396. DOI: https://doi.org/10.5951/jresematheduc.48.4.0369
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. DOI: https://doi.org/10.1007/s10649-017-9760-9
Xu, H.,; Cai, J. (2020). Fostering the development of students’ thinking in teaching “Using let¬ters to represent quantitative relationship” through collaborative learning and problem pos-ing. Elementary Mathematics Teachers, 2020(2), 14–16. [in Chinese].
Yao, Y., Hwang, S.,; Cai, J. (2021). Preservice teachers’ mathematical understanding exhibit-ed in problem posing and problem solving. ZDM–Mathematics Education, 53, 1–13. DOI: https://doi.org/10.1007/s11858-021-01277-8
Yoon, K. S., Duncan, T., Lee, S. W.-Y., Scarloss, B.,; Shapley, K. (2007). Reviewing the evi-dence on how teacher professional development affects student achievement (Issues; Answers Report, REL 2007–No. 033). U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Southwest.
Zhang, H.,; Cai, J. (2021). Teaching mathematics through problem posing: Insights from an analysis of teaching cases. ZDM–Mathematics Education, 53, 1–13. DOI: https://doi.org/10.1007/s11858-021-01260-3
Zhang, L., Cai, J., Song, N., Zhang, H., Chen, T., Zhang, Z.,; Guo, F. (2022). Mathematical problem posing of elementary school students: The impact of task format and its relationship to problem solving. ZDM–Mathematics Education, 54, 497–512. DOI: https://doi.org/10.1007/s11858-021-01324-4
Downloads
Publicado
- Visualizações do Artigo 117
- PDF downloads: 127
Como Citar
Edição
Seção
Português (Brasil)
Español (España)
English
