A Comparative Study of Proportional reasoning of Costa Rican and Spanish students in ratio comparison problems
DOI:
https://doi.org/10.15359/ru.37-1.21Keywords:
Evaluation, Level of reasoning, Proportionality, Comparative study, comparison of ratiosAbstract
Abstract
[Objective] This study seeks to evaluate the level of proportional reasoning and strategies in ratio comparison problems of Costa Rican and Spanish students between 11 and 16 years old. [Methodology] Using an interpretative research approach, 704 students were given one of two questionnaires with three items on ratio comparison (a total of six different levels of proportional reasoning, according to Noelting). The percentage of correct answers and levels of proportional reasoning, and the result of a content analysis of correct and incorrect strategies are presented. [Results] The majority of students correctly answered the problems with the lowest Noelting proportional reasoning level (IA to IIA), with this proportion decreasing in grades 6 to 8 of General Basic Education as the proportional reasoning level of the problem increased. Similar results were obtained with respect to correct strategies. The most frequent incorrect strategies were the comparison of the first terms of ratios and additive comparisons. Virtually all students reached the first two proportional reasoning levels of Noelting, and as the course progressed, a higher proportion attained the following levels of reasoning, but few students achieved level IIIA, corresponding to formal operations, even in the highest grade (grade 10). [Conclusions] It was concluded that it is necessary to reinforce the teaching of reasoning about comparison of ratios, and to take it into account in the mathematical topics based on this reasoning.
References
Behr, M. J., Harel, G., Post, T. R., y Lesh, R. (1992). Rational number, ratio, and proportion. En D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296–333). Macmillan.
Behr, M., Lesh, R., Post, T., y Silver E. (1983). Rational number concepts. En R. Lesh y M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 91-125). Academic Press.
Ben-Chaim, D., Keret, Y. e Ilany, B. S. (2012). Ratio and proportion: Research and teaching in mathematics teachers’ education. Sense Publisher. https://doi.org/10.1007/978-94-6091-784-4_2
Boyer, T. W. y Levine, S. C. (2015). Prompting children to reason proportionally: Processing discrete units as continuous amounts. Developmental Psychology, 51(5), 615–620. https://doi.org/10.1037/a0039010.
Burgos, M. y Godino, J. D. (2020). Modelo ontosemiótico de referencia de la proporcionalidad. Implicaciones para la planificación curricular en primaria y secundaria. Avances de Investigación en Educación Matemática, 18, 1-20. https://doi.org/10.35763/aiem.v0i18.255
Burgos, M., y Godino, J. D. (2019). Emergencia de razonamiento proto-algebraico en tareas de proporcionalidad en estudiantes de primaria. Educación Matemática, 31(3), 117-150.
Butto, C. M., Fernández, J. D., Araujo, D. C. y Ramírez, A. B. (2019). El razonamiento proporcional en educación básica. Horizontes Pedagógicos, 21(2), 39-52. https://doi.org/10.33881/0123-8264.hop.21204
Carpenter, T. P., Fennema, E., y Romberg, T. A. (Eds.). (1993). Rational numbers: An integration of research. Routledge. https://doi.org/10.4324/9780203052624
Cerrón, W. (2019). La investigación cualitativa en educación. Horizonte de la Ciencia, 9(17), 1-8.
Fernández, C., y Llinares, S. (2012). Características del desarrollo del razonamiento proporcional en la educación primaria y secundaria. Enseñanza de las Ciencias, 30(1), 129-142. https://doi.org/10.5565/rev/ec/v30n1.596
Gil, J., León, J. y Morales, M. (2017). Los paradigmas de investigación educativa, desde una perspectiva crítica. Conrado, 13(58), 72-74. https://conrado.ucf.edu.cu/index.php/conrado/article/view/476
Gómez, D. y Dartnell, P. (2019). Middle schoolers’ biases and strategies in a fraction comparison task. International Journal of Science and Mathematics Education, 17(6), 1233-1250. https://doi.org/10.1007/s10763-018-9913-z
González-Forte, J. M., Fernández, C., Van Hoof, J., y Van Dooren, W. (2022). Profiles in understanding operations with rational numbers. Mathematical Thinking and Learning, 24(3), 230-247. https://doi.org/10.1080/10986065.2021.1882287
He, W., Yang, Y., y Gao, D. (2018). Proportional reasoning in 5- to 6-year-olds. Journal of Cognition and Development, 19(4), 389–412. https://doi.org/10.1080/15248372.2018.1495218
Inhelder, B. y Piaget, J. (1958). The growth of logical thinking from childhood to adolescence. Basic Books. https://doi.org/10.1037/10034-000
Karplus, R., Pulos, S., y Stage, E. K. (1983). Early adolescents' proportional reasoning on ‘rate’problems. Educational Studies in Mathematics, 14(3), 219-233. https://doi.org/10.1007/BF00410539
Kieren, T. E. (2020). Rational and fractional numbers as mathematical and personal knowledge: Implications for curriculum and instruction. En G. Leinhardt, R. Putnam, y R. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 323-371). Routledge. https://doi.org/10.4324/9781315044606
Krippendorff, K. (2013). Content analysis: An introduction to its methodology. SAGE.
Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. En F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (V. 1, pp. 629-667). Information Age.
Ministerio de Educación Pública (MEP) (2012). Programas de Estudio de Matemáticas. I, II Y III Ciclos de la Educación General Básica y Ciclo Diversificado. MEP.
Ministerio de Educación, Cultura y Deporte (MECD) (2014). Real Decreto 126/2014, de 28 de febrero, por el que se establece el currículo básico de la Educación Primaria. MECD.
Ministerio de Educación, Cultura y Deporte (MECD) (2015). Real decreto 1105/2014, de 26 de diciembre, por el que se establece el currículo básico de la educación secundaria obligatoria y del bachillerato. MECD.
Noelting, G. (1980a). The development of proportional reasoning and the ratio concept. Part I. Diferentiation of stages. Educational Studies in Mathematics, 11 (2), 217-253. https://doi.org/10.1007/BF00304357
Noelting, G. (1980b). The development of proportional reasoning and the ratio concept. Part II. Problem structure at succesive stages: Problem solving strategies and the mechanism of adaptive restructuring. Educational Studies in Mathematics, 11(3), 331-363. https://doi.org/10.1007/BF00697744
Obando, G., Vasco, C. E. y Arboleda, L. C. (2014). Enseñanza y aprendizaje de la razón, la proporción y la proporcionalidad: Un estado del arte. Revista Latinoamericana de Matemática Educativa,17(1), 59-81. https://dx.doi.org/10.12802/relime.13.1713
Otzen, T. y Manterola, C. (2017). Técnicas de muestreo sobre una población a estudio. Int. J. Morphol, 35(1), 227-232. https://doi.org/10.4067/S0717-95022017000100037
Pérez-Echeverría, M. P., Carretero, M. y Pozo, J. I. (1986). Los adolescentes ante las matemáticas: Proporción y probabilidad. Cuadernos de Pedagogía, 133, 9-13.
Post, T., Behr, M. y Lesh, R. (1988). Proportionality and the development of pre-algebra understandings. En A. Coxford, A. Shulte (Eds.), The idea of algebra, K-12 (pp. 78-90), National Council of Teachers of Mathematics.
Tourniare, F. y Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational Studies in Mathematics, 16(2), 181-204. https://doi.org/10.1007/PL00020739
Van Dooren, W., Vamvakoussi, X. y Verschaffel, L. (2018). Proportional reasoning. International Academy of Education (IAE).
Vanluydt, E., Verschaffel, L., y Van Dooren, W. (2022a). The early development of proportional reasoning: A longitudinal study of 5- to 8-year-olds. Journal of Educational Psychology, en prensa. https://doi.org/10.1037/edu0000734
Vanluydt, E., Verschaffel, L., y Van Dooren, W. (2022b). The role of relational preference in early proportional reasoning. Learning and Individual Differences, 93, 102108. https://doi.org/10.1016/j.lindif.2021.102108
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
1. Authors guarantee the journal the right to be the first publication of the work as licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
2. Authors can set separate additional agreements for non-exclusive distribution of the version of the work published in the journal (eg, place it in an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
3. The authors have declared to hold all permissions to use the resources they provided in the paper (images, tables, among others) and assume full responsibility for damages to third parties.
4. The opinions expressed in the paper are the exclusive responsibility of the authors and do not necessarily represent the opinion of the editors or the Universidad Nacional.
Uniciencia Journal and all its productions are under Creative Commons Atribución-NoComercial-SinDerivadas 4.0 Unported.
There is neither fee for access nor Article Processing Charge (APC)
