Skip to main navigation menu Skip to main content Skip to site footer
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 24 No. 1 (2021): March

RELATIONAL THINKING IN THE SCHOOLING OF THE HIERARCHY OF OPERATIONS AND EARLY ALGEBRA IN ELEMENTARY

DOI
https://doi.org/10.12802/relime.21.2411
Submitted
November 7, 2022
Published
2021-03-15

Abstract

The general objective of this study was to promote relational thinking in the analysis of numerical expressions, using the hierarchy of operations, in third grade students. A psychoeducational sequence was designed based on the representation of numerical properties and expressions of equality by equivalence, based on phenomenal activities (phenomenological didactics) and on the application of the hierarchy of operations. Thirty students were evaluated through multiple indicators of their performance in both procedural and conceptual domains. 71.43% of the students reached a very high or high level of achievement in tasks of the application of the hierarchy of operations. The results are discussed in terms of the relationship between relational thinking and phenomenal activities with the level of achievement of the hierarchy of operations.

References

  1. Blanton, M., Brizuela, B. M., Stephens, A., Knuth, E., Isler, I., Gardiner, A. M., … Stylianou, D. (2017). Implementing a Framework for Early Algebra. In C. Kieran (Ed.), Teaching and Learning Algebraic Thinking with 5 – to 12-Years-Olds (pp. 79-105) Montreal: Springer.
  2. Blanton, M. y Kaput, J. J. (2005). Characterizing a classroom practice that promotes Algebraic reasoning. Journal for Research in Mathematics Education, 36 (5), 412-446.
  3. Bourbaki, N. (1963). Essays on the History of Mathematics. Moscú: IL.
  4. Carpenter, T. P., Franke, M. L., y Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in the elementary school. Portsmouth, NH: Heinemann.
  5. Carpenter, T. P., Levi, L., Franke, M. L., y Zeringue, J. K. (2005). Algebra in elementary school: Developing relational thinking, ZDM, 37(1), 53-59.
  6. Carraher, D. W., y Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 669–705). Charlotte, NC: Information Age Publishing. Common Core State Standards Initiative [CCSSM] (2010). Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
  7. Davydov, V. V. (1962). An experiment in introducing elements of algebra in elementary school. Soviet Education, 8, 27-37.
  8. Dupree, K. M. (2016). Questioning the Order of Operations. Mathematics teaching in the Middle School, 22 (3), 152-159.
  9. Freudenthal, H. (1971). Geometry between the devil and the deep sea. In The teaching of geometry at the pre-college level (pp. 137-159). Springer, Dordrecht.
  10. Freudenthal, H. (1974). Soviet research on teaching algebra at the lower grades of elementary school. Educational Studies in Mathematics, 5, 391-412.
  11. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Reidel Publishing, Dordrecht.
  12. Glidden, P. L. (2008). Prospective Elementary Teachers’ Understanding of Order of Operations. School Science and Mathematics, 108 (4), 130-137.
  13. Gravemeijer, K. y Doorman, M. (1999) Context problems in realistic mathematics education: a calculus course as an example. Educational Studies in Mathematics 39 (1–3), 111–129.
  14. Gunnarsson, R. Sönnerhed, W. W. y Hernell, B. (2016). Does it help to use mathematically superfluous brackets when teaching the rules for the order of operations? Educational Studies of Mathematics, 92, 91-105.
  15. Headlam, C. (2013). An investigation into children understanding of the order of operations. Tesis Doctoral. Plymouth: Plymouth University.
  16. Herscovics, N. y Kieran, C. (1980). Constructing meaning for the concept of equation, Mathematics Teacher, 73, 572-580.
  17. Johnson, D., y Johnson, R. (2014). La evaluación en el aprendizaje cooperativo. Cómo mejorar la evaluación individual a través del grupo, Madrid, Ediciones SM.
  18. Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher, y M. L. Blanton (Eds.), Algebra in the early grades (pp. 5–17). Mahwah, NJ: Lawrence Erlbaum.
  19. Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390–419). New York: Macmillan.
  20. Kieran, C. (1996). The changing face of school algebra. In: C. Alsina, J. Alvarez, B. Hodgson, C. Laborde, y A. Pérez (Eds.), 8th International Congress on Mathematical Education: Selected lectures (271-290). Seville, Spain: S. A. E. M. Thales.
  21. Kieran, C. (2004). Algebraic Thinking in the Early Grades: What Is It? The Mathematics Educator, 8 (1), 139-151.
  22. Kieran, C. (2017). Seeking, Using, and Expressing Structure in Numbers and Numerical Operations: A Fundamental Path to Developing Early Algebraic Thinking. In C. Kieran (Ed.), Teaching and Learning Algebraic Thinking with 5 – to 12-Years-Olds (pp. 79-105) Montreal: Springer.
  23. Kieran, C. y Chalouh, L. (1993). The transition from arithmetic to algebra. In T. D. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (179-198). New York: Macmillan Publishing Company.
  24. Kieran, C., Pang, J. S., Ng, S. F., Schifter, D., y Steinweg, A. S. (2017). Topic Study Group 10: Teaching and learning of early algebra. In G. Kaiser (Ed.), The Proceedings of the 13th International Congress on Mathematical Education. New York: Springer.
  25. Knuth, E. J., Stephens, A. C., McNeil, N. M., y Alibali, M. W. (2006). Does Understanding the Equal Sign Matter? Evidence from Solving Equations. Journal for Research in Mathematics Education, 37 (4), 297-312.
  26. Kvale, S. (2008). Qualitative inquiry between scientistic evidentialism, ethical subjectivism and the free market. International Review of Qualitative Research, 1(1), 5-18.
  27. Larsen, S. (2013) A local instructional theory for the guided reinvention of the group and isomorphism concepts. Journal of Mathematical Behavior, 32 (4), 712–725.
  28. Linchevski, L., y Livneh, D. (1999). Structure sense: The relationship between algebraic and numerical contexts. Educational Studies in Mathematics, 40, 173–196.
  29. Liebenberg, R., Sasman, M. y Olivier, A. (1999). From numerical equivalence to algebraic equivalence. Proceedings of the Fifth Annual Congress of the Association for Mathematics Education of South Africa, 2, 173-183.
  30. Miller, S. P., y Mercer, C. D. (1993). Using data to learn Concrete-Semiconcrete-Abstract instruction for students with math disabilities. Learning Disabilities Research and Practice, 8, 89–96.
  31. Molina, M. (2006). Desarrollo de pensamiento relacional y comprensión del signo igual por alumnos de tercero de educación primaria. Tesis doctoral. Granada: Departamento de Didáctica de la Matemática, Universidad de Granada.
  32. Molina, M. (2009). Una propuesta de cambio curricular: integración del pensamiento algebraico en educación primaria, PNA, 3 (3), 135-156.
  33. Molina, M., Castro, E., y Ambrose, R. (2006). Trabajo con igualdades numéricas para promove pensamiento relacional. PNA, 1(1), 31-46.
  34. National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  35. Papadopoulos, I., y Gunnarsson, R. (2020). Exploring the way rational expressions trigger the use of “mental” brackets by primary school students. Educational Studies in Mathematics, 103(2), 191-207.
  36. Riadi, A., Atini, N. L., y Ferita, R. A. (2019). Thinking Skills of Junior High School Students Related to Gender. International Journal of Trends in Mathematics Education Research, 2(3), 112-115.
  37. Slavin, R. E. (1995). Cooperative learning: Theory, research, and practice. (2a edición). Boston: Allyn y Bacon.
  38. Stephens, M. (2007). Students’ emerging algebraic thinking in the middle school years. Mathematics: Essential research, essential practice, 2, 678-687.
  39. Stephens, M., y Ribeiro, A. (2012). Working towards algebra: The importance of relational thinking. Revista Latinoamericana de Investigación en Matemática Educativa, 15(3), 373-402.
  40. Taff, J. (2017). Rethinking order of operations (or what is the matter with Dear Aunt Sally). Mathematics Teacher, 111 (2), 126-132.
  41. Venenciano, L.C., Yagi, S.L., y Zenigami, F.K. (2021). The development of relational thinking: a study of Measure Up first-grade students’ thinking and their symbolic understandings.Educational Studies in Mathematics, 1-16.
  42. Warren, E., y Cooper, T. J. (2009). Developing Mathematics Understanding and Abstraction: The case of Equivalence in the Elementary Years. Mathematics Education Research Journal, 21 (2), 76-95.
  43. Witzel, B. S., Mercer, C. D., y Miller, M. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research & Practice, 18(2), 121-131.
  44. Zorin, B. y Carver, D. (2015). Operation: Save Aunt Sally. Mathematics Teaching in the Middle School. National Council of Teachers of Mathematics, 20 (7), 438.443.

Downloads

Download data is not yet available.

Similar Articles

1 2 3 4 5 6 7 8 9 10 > >> 

You may also start an advanced similarity search for this article.