Archives
Current issue
About
About us
Aims and Scope
Abstracting and Indexing
Editorial Office
Open Access Policy
Publication Ethics
Journal History
Publisher
Follow us: Twitter
Contact
For Authors
Editorial Policy
Peer Review Policy
Manuscript Preparation Guidelines
Copyright & Licencing
Publication Fees
Fee Waiver Policy for Doctoral Students
EJMSTE Language Editing Service
More
Statistics
Special Issues
Special Issue Announcements
Published Special Issues
RESEARCH PAPER
Strategies and representations used by early childhood education students in a functional thinking task: A case study
1
Universidad Católica del Maule, Talca, CHILE
2
Colegio Santo Tomas, Curicó, CHILE
3
Universidad Metropolitana de Ciencias de la Educación, Santiago, CHILE
Online publication date: 2023-10-27
Publication date: 2023-12-01
EURASIA J. Math., Sci Tech. Ed 2023;19(12):em2363
KEYWORDS
ABSTRACT
This article presents a study that addressed the functional relationships that two early childhood education students (five-six years old) evidenced, as well as the representations they used when solving a functional thinking task. The proposed task involved the function f(x)=2x, with six questions on particular cases and one on generalization. The data was collected through a semi-structured interview to each of the students and a qualitative analysis of their answers was carried out in each of the questions of the task. The results suggest that the two students are capable of approaching the proposed task through different strategies, such as additive and multiplicative correspondence relationship, and covariation. Also, it was found that they use systems of varied representations, being the verbal representation to express the generalization of the functional relationship one that stands out. It is concluded that early childhood education students may be able to tackle tasks that involve algebraic notions that focus on functional thinking.
REFERENCES (38)
1.
Alsina, A. (2020). Itinerario de enseñanza para el álgebra temprana [Teaching itinerary for early algebra]. Revista Chilena de Educación Matemática [Chilean Magazine of Mathematics Education], 12(1), 5-20. https://doi.org/10.46219/rechi....
2.
Azcárate, C., & Deulofeu, J. (1990). Funciones y gráficas [Functions and graphics]. Síntesis [Synthesis].
3.
Blanton, M. (2008). Algebra and the elementary classroom: Transforming thinking, transforming practice. Heinemann.
4.
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/jresem....
5.
Blanton, M., & Kaput, J. (2004). Elementary grades students’ capacity for functional thinking. In M. Johnsen, & A. Berit (Eds.), Proceedings of the 28th International Group of the Psychology of Mathematics Education (pp. 135-142). Bergen University College.
6.
Blanton, M., & Kaput, J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412-446.
7.
Blanton, M., Levi, L., Crites, T., & Dougherty, B. (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3-5. National Council of Teachers of Mathematics.
8.
Brizuela, B., & Blanton, M. (2014). El desarrollo del pensamiento algebraico en niños de escolaridad primaria [The development of algebraic thinking in primary school children]. Revista de Psicología [Psychology Magazine], 14, 37-57.
9.
Cañadas, M. C., & Castro, E. (2007). A proposal of categorization for analyzing inductive reasoning. PNA, 1(2), 69-81. https://doi.org/10.30827/pna.v....
10.
Cañadas, M. C., & Figueiras, L. (2011). Uso de representaciones y generalización de la regla del producto [Use of representations and generalization of the product rule]. Infancia y Aprendizaje [Childhood and Learning], 34(4), 409-425. https://doi.org/10.1174/021037....
11.
Cañadas, M. C., & Molina, M. (2016). Una aproximación al marco conceptual y principales antecedentes del pensamiento funcional en las primeras edades [An approach to the conceptual framework and main antecedents of functional thinking in the early ages]. In E. Castro, E. Castro, J. L. Lupiáñez, J. F. Ruíz, & M. Torralbo (Eds.), Investigación en educación matemática. Homenaje a Luis Rico [Research in mathematics education. Tribute to Luis Rico] (pp. 209-218). Comares.
12.
Cañadas, M., Brizuela, B. M., & Blanton, M. (2016). Second graders articulating ideas about linear functional relationships. Journal of Mathematical Behavior, 41, 87-103. https://doi.org/10.1016/j.jmat....
13.
Castro, E., Cañadas, M. C., & Molina, M. (2017). Pensamiento funcional mostrado por estudiantes de educación infantile [Functional thinking shown by early childhood education students]. Educación Matemática en la Infancia [Mathematics Education in Childhood], 6(2), 1-13. https://doi.org/10.24197/edmai....
14.
Cetina-Vázquez, M., & Cabañas-Sánchez, G. (2022). Estrategias de generalización de patrones y sus diferentes formas de uso en quinto grado [Pattern generalization strategies and their different forms of use in fifth grade]. Enseñanza de las Ciencias [Science Teaching], 40(1), 65-86. https://doi.org/10.5565/rev/en....
15.
Clapham, C. (1998). Diccionario de matemáticas [Mathematics dictionary]. Complutense.
16.
Clements, D. H., & Sarama, J. (2007). Early childhood mathematics. In F. K. Lester (Ed.), Second handbook of mathematics teaching and learning (pp. 461-556). Information Age.
17.
Clements, D. H., Baroody, A. J., & Sarama, J. (2013). Background research on early mathematics. National Governor’s Association.
18.
Confrey, J., & Smith, E. (1991). A framework for functions: Prototypes, multiple representations and transformations. In R. Underhill (Ed.), Proceedings of the 13th Annual Meeting of the North American Chapter of The International Group for the Psychology of Mathematics Education (pp. 57-63). PME.
19.
Gómez, B. (2016). Sobre el análisis didáctico de la razón [On the didactic analysis of reason]. In E. Castro, E. Castro, J. L. Lupiáñez, J. F. Ruíz., & M. Torralbo (Eds.), Investigación en educación matemática. Homenaje a Luis Rico [Research in mathematics education. Tribute to Luis Rico] (pp. 165-174). Comares.
20.
Hernández, R., Fernández, C., & Baptista, P. (2007). Fundamentos de metodología de la investigación [Fundamentals of research methodology]. McGraw-Hill.
21.
Kaput, J. (2000). Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying” the K-12 curriculum. National Center for Improving Student Learning and Achievement in Mathematics and Science.
22.
Mason, J. (1996). Expressing generality and roots of algebra. In N. Bernarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 65-86). Springer. https://doi.org/10.1007/978-94....
23.
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 [Use of representations and patterns by fifth grade primary school students in a generalization task]. Educación Matemática en la Infancia [Mathematics Education in Childhood], 2(1), 24-40. https://doi.org/10.24197/edmai....
24.
MINEDUC. (2012). Bases curriculares de matemática educación básica [Basic education mathematics curricular bases]. Unidad de Currículum y Evaluación [Curriculum and Assessment Unit].
25.
MINEDUC. (2018). Bases curriculares de la educación parvularia [Curriculum bases of nursery education]. Unidad de Currículum y Evaluación [Curriculum and Assessment Unit].
26.
Molina, M. (2009). Una propuesta de cambio curricular: Integración del pensamiento algebraico en educación primaria [A proposal for curricular change: Integration of algebraic thinking in primary education]. PNA, 3(3), 135-156. https://doi.org/10.30827/pna.v....
27.
Morales, R., & Parra, J. (2022). Estrategias que emplean futuros profesores de educación primaria en una tarea de relación funcional [Strategies used by future primary school teachers in a functional relationship task]. Acta Scientiae [Journal of Science], 24(3), 32-62. https://doi.org/10.17648/acta.....
28.
Morales, R., Cañadas, M., Brizuela, B., & Gómez, P. (2018). Relaciones funcionales y estrategias de alumnos de primero de educación primaria en un contexto funcional [Functional relationships and strategies of first-year primary education students in a functional context]. Enseñanza de las Ciencias [Science Teaching], 36(3), 59-78. https://doi.org/10.5565/rev/en....
29.
Pinto, E., & Cañadas, M. C. (2018). Generalization in fifth graders within a functional approach. PNA, 12(3), 173-184. https://doi.org/10.30827/pna.v....
30.
Rico, L. (1997). Consideraciones sobre el currículo de matemáticas para educación secundaria [Considerations on the mathematics curriculum for secondary education]. In L. Rico (Ed.), La educación matemática en la enseñanza secundaria [Mathematics education in medium school] (pp. 15-38). Horsori.
31.
Rico, L. (2006). La competencia matemática en PISA [Mathematical competence in PISA]. PNA, 1(2), 47-66. https://doi.org/10.30827/pna.v....
32.
Rico, L. (2009). Sobre las nociones de representación y comprensión en la investigación en educación matemática [On the notions of representation and understanding in mathematics education research]. PNA, 4(1), 1-14. https://doi.org/10.30827/pna.v....
33.
Smith, E. (2008). Representational thinking as a framework for introducing functions in the elementary curriculum. In J. Kaput, W. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 133-160). Routledge. https://doi.org/10.4324/978131....
34.
Soares, J., Blanton, M. L., & Kaput, J. (2005). Thinking Algebraically across the elementary school curriculum. Teaching Children Mathematics, 2(5), 228-235. https://doi.org/10.5951/TCM.12....
35.
Stake, R. (1999). Investigación con estudio de casos [Research with case studies]. Morata.
36.
Strachota, S. (2016). Conceptualizing generalization. Open Mathematical Education Notes, 6, 41-55.
37.
Torres, M., Cañadas, M., Moreno, A., & Gómez, P. (2021). Estructuras en las formas directa e inversa de una función por estudiantes de 7-8 años [Structures in the direct and inverse forms of a function by 7-8 year old students]. Uniciencia [Unscience], 35(2), 1-16. https://doi.org/10.15359/ru.35....
38.
Warren, E., Miller, J., & Cooper, T. (2013). Exploring young students’ functional thinking. PNA, 7(2), 75-84. https://doi.org/10.30827/pna.v....
Share
RELATED ARTICLE
| eISSN: | 1305-8223 |
| ISSN: | 1305-8215 |
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
