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Articles

Generalization strategies and representations used by final-year elementary school students

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Pages 23-43 | Received 24 Aug 2020, Published online: 28 Apr 2022

References

  • Amit, M., & Neria, D. (2008). “Rising to the challenge”: Using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM, 40(1), 111–129. https://doi.org/10.1007/s11858-007-0069-5
  • Barbosa, A., Vale, I., & Palhares, P. (2012). Pattern tasks: Thinking processes used by 6th grade students. Revista Latinoamericana de Investigación en Matemática Educativa, 15(3), 273–293.
  • Blanton, M. L., Brizuela, B. M., Gardiner, A., Sawrey, K., & Newman-Owens, A. (2015). A learning trajectory in 6-year-olds’ thinking about generalizing functional relationships. Journal for Research in Mathematics Education, 46(5), 511–558. https://doi.org/10.5951/jresematheduc.46.5.0511
  • Blanton, M. L., & Kaput, J. J. (2004). Elementary grades students’ capacity for functional thinking. In M. J. Hoines, & A. B. Fugslestad (Eds.), Proceedings of the 28th international group for the psychology of mathematics education (Vol. 2) (pp. 135–142). PME.
  • Blanton, M. L., & Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 3(5), 412–446. https://doi.org/10.2307/30034944
  • Blanton, M. L., Levi, L., Crites, T., & Dougherty, B. J. (Eds.). (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3-5. NCTM.
  • Cañadas, M. C., Blanton, M. L., & Brizuela, B. M. (2019). Special issue on early algebraic thinking. Infancia y Aprendizaje, 42(3), 469–478. https://doi.org/10.1080/02103702.2019.1638569
  • Carraher, D. W., Martinez, M. V., & Schliemann, A. D. (2008). Early algebra and mathematical generalization. ZDM, 40(1), 3–22. https://doi.org/10.1007/s11858-007-0067-7
  • Common Core State Standards Initiative (CCSSI). (2010). Common core state standards for mathematics. National Governors Association Center for Best Practices and the Council of Chief State School Officers.
  • El Mouhayar, R., & Jurdak, M. (2015). Variation in strategy use across grade level by pattern generalization types. International Journal of Mathematical Education in Science and Technology, 46(4), 553–569. https://doi.org/10.1080/0020739X.2014.985272
  • Hitt, F., & González-Martín, A. S. (2016). Generalization, covariation, functions, and calculus. In Á Gutiérrez, G. C. Leder, & P. Boero (Eds.), The second handbook of research on the psychology of mathematics education (pp. 3–38). Sense Publishers.
  • Kaput, J. J. (1999). Teaching and learning a new algebra. In E. Fennema, & T. A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133–155). Lawrence Erlbaum Associates.
  • Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 5–17). Lawrence Erlbaum Associates.
  • Lannin, J., Barker, D., & Townsend, B. (2006). Algebraic generalisation strategies: Factors influencing student strategy selection. Mathematics Education Research Journal, 18(3), 3–28. https://doi.org/10.1007/BF03217440
  • Lepak, J. R., Wernet, J. L., & Ayieko, R. A. (2018). Capturing and characterizing students’ strategic algebraic reasoning through cognitively demanding tasks with focus on representations. The Journal of Mathematical Behavior, 50, 57–73. https://doi.org/10.1016/j.jmathb.2018.01.003
  • Mason, J., Burton, L., & Stacey, K. (1989). Pensar matemáticamente [Thinking mathematicaly]. Labor.
  • Mason, J., Graham, A., & Johnston-Wilder, S. (2005). Developing thinking in algebra. The Open University y Paul Chapman Publishing.
  • Merino, E., Cañadas, M. C., & Molina, M. (2013). Uso de representaciones y patrones por alumnos de quinto de educación primaria en una tarea de generalización [Representations and patterns used by fifth grade students in a generalization task]. Edma 0-6, 2(1), 24–40. https://doi.org/10.24197/edmain.1.2013.24-40
  • Ministerio de Educación, Cultura y Deporte. (2014). Real decreto 126/2014, de 28 de febrero, por el que se establece el currículo básico de la educación primaria [royal decree 126/2014, of February 28, which establishes the basic curriculum of primary education] (Vol. 52, pp. 1–58).
  • Ministry of Education Singapore. (2012). Mathematics syllabus: Primary one to six. Curriculum Planning and Development Division.
  • Molina, M., Ambrose, R., & del Río, A. (2018). First encounter with variables by first and third grade Spanish students. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5- to 12-year-olds (pp. 261–280). Springer.
  • Morales, R., Cañadas, M. C., Brizuela, B. M., & Gómez, P. (2018). Relaciones funcionales y estrategias de alumnos de primero de Educación primaria en un contexto funcional [Functional relationships and strategies of first graders in a functional context]. Enseñanza de las Ciencias, 36(3), 59–78. https://doi.org/10.5565/rev/ensciencias.2472
  • Moss, J., & Beatty, R. (2006). Knowledge building in mathematics: Supporting collaborative learning in pattern problems. International Journal of Computer-Supported Collaborative Learning, 1(4), 441–465. https://doi.org/10.1007/s11412-006-9003-z
  • Pinto, E., & Cañadas, M. C. (2017). Estructuras y generalización de estudiantes de tercero y quinto de primaria: Un estudio comparativo [Structures and generalisation in third and fifth year of primary school: A comparative study]. In J. M. Muñoz-Escolano, A. Arnal-Bailera, P. Beltrán-Pellicer, M. L. Callejo, & J. Carrillo (Eds.), Investigación en Educación Matemática XXI (pp. 407–416). SEIEM.
  • Pinto, E., & Cañadas, M. C. (2021). Generalizations of third and fifth graders within a functional approach to early algebra. Mathematics Education Research Journal, 33, 113–134. https://doi.org/10.1007/s13394-019-00300-2
  • Pólya, G. (1989). ¿Cómo plantear y resolver problemas? [How to solve it?]. Trillas.
  • Radford, L. (2010). Layers of generality and types of generalization in pattern activities. PNA, 4(2), 37–62.
  • Radford, L. (2018). The emergence of symbolic algebraic thinking in primary school. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5- to 12-year-olds (pp. 3–25). Springer.
  • Ramírez-Uclés, R., & Cañadas, M. C. (2018). Nominación y atención del talento matemático por parte del docente [nomination and attention to mathematical talent by the teacher]. UNO. Revista de Didáctica de las Matemáticas, 79, 23–30.
  • Rico, L. (1997). Consideraciones sobre el currículo de matemáticas para educación secundaria [considerations about secondary education mathematics curriculum]. In L. Rico (Coord.) (Ed.), La Educación Matemática en la enseñanza secundaria (pp. 15–38). Horsori.
  • Rico, L. (2007). La competencia matemática en PISA [The mathematical competence in PISA]. PNA, 1(2), 47–66.
  • Rico, L., Castro, E., Castro, E., Coriat, M., Marín, A., & Puig, L. (1997). La educación matemática en la enseñanza secundaria [Mathematical education in secondary education]. Editorial Horsori.
  • Smith, E. (2008). Representational thinking as a framework for introducing functions in the elementary curriculum. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 133–160). Lawrence Erlbaum Associates.
  • Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20(2), 147–164. https://doi.org/10.1007/BF00579460
  • Stephens, A., Ellis, A., Blanton, M. L., & Brizuela, B. M. (2017). Algebraic thinking in the elementary and middle grades. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 386–420). NCTM.
  • Torres, M. D., Cañadas, M. C., & Moreno, A. (2019). Estructuras y representaciones de alumnos de 2° de primaria en una aproximación funcional del pensamiento algebraico [Second graders’ structures and representations used in a functional approach of algebraic thinking]. In J. M. Marbán, M. Arce, A. Maroto, J. M. Muñoz-Escolano, & Á Alsina (Eds.), Investigación en Educación Matemática XXIII (pp. 573–582). SEIEM.
  • Ureña, J., Ramírez-Uclés, R., & Molina, M. (2019). Representations of the generalization of a functional relationship and the relation with the interviewer’s mediation. Infancia y Aprendizaje, 42(3), 570–614. https://doi.org/10.1080/02103702.2019.1604020
  • Warren, E., & Cooper, T. (2005). Introducing functional thinking in year 2: A case study of early algebra teaching. Contemporary Issues in Early Childhood, 6(2), 150–162. https://doi.org/10.2304/ciec.2005.6.2.5
  • Warren, E., & Cooper, T. (2008). Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking. Educational Studies in Mathematics, 67(2), 171–185. https://doi.org/10.1007/s10649-007-9092-2
  • Warren, E., Trigueros, M., & Ursini, S. (2016). Research on the learning and teaching of algebra. In A. Gutierrez, G. C. Leder, & P. Boero (Eds.), The second handbook of research on the psychology of mathematics education (pp. 73–108). Sense Publishers.
  • Zapatera Llinares, A. (2018). Cómo alumnos de educación primaria resuelven problemas de generalización de patrones. Una trayectoria de aprendizaje [How primary education students solve problems of generalization of patterns. A learning trajectory]. Revista Latinoamericana de Investigación en Matemática Educativa, 21(1), 87–114. https://doi.org/10.12802/relime.18.2114

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