The Role of Intra-mathematical Connections in Learning Decimal Numbers
DOI:
https://doi.org/10.35763/aiem25.6399Keywords:
Mathematical connections, Rational numbers, Decimal numbers, Number sense, Secondary educationAbstract
Several characterizations proposed for number sense coincide in the need to promote the establishment of connections for the strategic use of rational numbers by students. This study follows a case study design for the analysis of eight class sessions of a group of 12–13-year-old students who study decimal numbers. Results show a relationship between the emergence of specific types of mathematical connections and the possible development of specific components of number sense in students. A special relevance of “justification” type connections is pointed out in the construction of fundamental aspects of number sense. Opportunities to refine reference models of mathematical connections are also discussed.
Downloads
References
Bryman, A. (2009). Social Research Methods. Oxford.
Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections. Dissertation [Doctoral dissertation]. Simon Fraser University.
Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293–316. https://doi.org/10.1007/s10649-006-9036-2
Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education. Routledge. https://doi.org/10.4324/9780203029053
De Gamboa, G., Badillo, E., & Font, V. (2023). Meaning and Structure of Mathematical Connections in the Classroom. Canadian Journal of Science, Mathematics and Technology Education, 23(2), 241-261. https://doi.org/10.1007/s42330-023-00281-2
De Gamboa, G., Badillo, E., Ribeiro, M., Montes, M., & Sánchez-Matamoros, G. (2020). The role of teachers’ knowledge in the use of learning opportunities triggered by mathematical connections. En S. Zehetmeier, D. Potari, & M. Ribeiro (Eds.), Professional development and knowledge of mathematics teachers (pp. 24-43). Routledge. https://doi.org/10.4324/9781003008460-3
De Gamboa, G., & Figueiras, L. (2014). Conexiones en el conocimiento matemático del profesor: propuesta de un modelo de análisis. En M. González, M. Codes, D. Arnau, & T. Ortega (Eds.), Investigación en Educación Matemática XVIII. (pp. 337-344). SEIEM.
Dolores-Flores, C., & García-García, J. (2017). Conexiones intramatemáticas y extramatemáticas que se producen al resolver problemas de Cálculo en contexto: un estudio de casos en el nivel superior. Bolema, 31(57), 158-180. https://doi.org/10.1590/1980-4415v31n57a08
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103-131. https://doi.org/10.1007/s10649-006-0400-z
Eli, J. A., Mohr-Schroeder, M. J., & Lee, C. W. (2011). Exploring mathematical connections of prospective middlegrades teachers through card-sorting tasks. Mathematics Education Research Journal, 23(3), 297-319. https://doi.org/10.1007/s13394-011-0017-0
Font, V., Godino, J. D., & Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82, 97-124. https://doi.org/10.1007/s10649-012-9411-0
Gay, A. S., & Aichele, D. B. (1997). Middle school students' understanding of number sense related to percent. School Science and Mathematics, 97(1), 27 36. https://doi.org/10.1111/j.1949-8594.1997.tb17337.x
González-Forte, J. M., Fernández, C., Van Hoof, J., & Van Dooren, W. (2022). Profiles in understanding the density of rational numbers among primary and secondary school students. AIEM - Avances de investigación en educación matemática, 22, 47-70. https://doi.org/10.35763/aiem22.4034
Ghazali, M., Mohamed, R., & Mustafa, Z. (2021). A Systematic Review on the Definition of Children's Number Sense in the Primary School Years. Eurasia Journal of Mathematics, Science and Technology Education, 17(6), 1-12. https://doi.org/10.29333/ejmste/10871
Hatisaru, V. (2023) Mathematical connections established in the teaching of functions. Teaching Mathematics and its Applications: An International Journal of the IMA, 42(3) 207-227. https://doi.org/10.1093/teamat/hrac013
Hiebert, J., & Wearne, D. (1986). Procedures over concepts: the acquisition of decimal number knowledge. En J. Hiebert (Ed.), Conceptual and procedural knowledge: the case for mathematics (pp. 199-223). Laurence Erlbaum.
Isotani, S., Adams, D., Mayer, R.E., Durkin, K., Rittle-Johnson, B., & McLaren, B.M. (2011). Can erroneous examples help middle-school students learn decimals? Sixth European Conference on Technology Enhanced Learning: Towards Ubiquitous Learning (pp. 1-14). EC-TEL. https://doi.org/10.1007/978-3-642-23985-4_15
Lachance, A., & Confrey, J. (2001). Helping students build a path of understanding from ratio and proportion to decimal notation. The Journal of Mathematical Behavior, 20(4), 503-526. https://doi.org/10.1016/S0732-3123(02)00087-1
McIntosh, A., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining basic number sense. For the learning of mathematics, 12(3), 2-44.
Nickerson, S. D., & Whitacre, I. (2010). A local instruction theory for the development of number sense. Mathematical Thinking and Learning, 12(3), 227-252. https://doi.org/10.1080/10986061003689618
Resnick, L. B., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual Bases of Arithmetic Errors: The Case of Decimal Fractions. Journal for Research in Mathematics Education, 20(1), 8-27. https://doi.org/10.2307/749095
Rathouz, M. (2011). Visualizing Decimal Multiplication with Area Models: Opportunities and Challenges. Issues in the Undergraduate Mathematics Preparation of School Teachers, 2, 1-12.
Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & Font, V. (2023). Combined use of the extended theory of connections and the onto-semiotic approach to analyze mathematical connections by relating the graphs of f and f’. Educational Studies in Mathematics, 114, 63-88. https://doi.org/10.1007/s10649-023-10246-9
Schneider, S. B., & Thompson, C. S. (2000). Incredible equations develop incredible number sense. Teaching Children Mathematics, 7(3), 146-148. https://doi.org/10.5951/TCM.7.3.0146
Şengül, S., & Gülbağcı, H. (2012). An investigation of 5th grade Turkish students' performance in number sense on the topic of decimal numbers. Procedia-Social and Behavioral Sciences, 46, 2289-2293. https://doi.org/10.1016/j.sbspro.2012.05.472
Sowder, J. (1992). Estimation and number sense. In D. A. Grouw (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 245-275). MacMillan Publishing Company.
Tian, J., & Siegler, R. S. (2018). Which type of rational numbers should students learn first? Educational Psychology Review, 30, 351-372. https://doi.org/10.1007/s10648-017-9417-3
VanHoof, J., Verschaffel, L., & VanDooren, W. (2015). Inappropriately applying natural number properties in rational number tasks: characterizing the development of the natural number bias through primary and secondary education. Educational Studies in Mathematics, 90(1),39-56. https://doi.org/10.1007/s10649-015-9613-3
Verschaffel, L., Greer, B., & De Corte., E. (2007). Whole number concepts and operations. En F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557-628). Information Age.
Yang, D. C., Hsu, C. J., & Huang, M. C. (2004) A Study of Teaching and Learning Number Sense for Sixth Grade Students in Taiwan. International Journal of Science and Mathematics Education, (2), 407-430 https://doi.org/10.1007/s10763-004-6486-9
Yin, R. (2014). Case Study Research. Sage.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Genaro De Gamboa, Sofía Caviedes, Edelmira Badillo Jiménez
This work is licensed under a Creative Commons Attribution 4.0 International License.
The articles published in this journal are under a license Creative Commons: By 4.0 España from number 21 (2022).
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and keep the acknowledgement of authorship.
- The texts published in this journal are – unless indicated otherwise – covered by the Creative Commons Attribution 4.0 international licence. You may copy, distribute, transmit and adapt the work, provided you attribute it (authorship, journal name, publisher) in the manner specified by the author(s) or licensor(s). The full text of the licence can be consulted here: http://creativecommons.org/licenses/by-nc/4.0.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
