• https://theoejwilson.com/
  • mariatogel
  • santuy4d
  • garuda slot
  • garudaslot
  • https://edujournals.net/
  • nadimtogel
  • https://mitrasehatjurnal.com/
  • slot gacor hari ini
  • g200m
  • 55kbet
  • slot gacor
  • garudaslot
  • link slot gacor
    • DIGITAL TOOLS AND PAPER-AND-PENCIL IN SOLVING-AND-EXPRESSING: HOW TECHNOLOGY EXPANDS A STUDENT’S CONCEPTUAL MODEL OF A COVARIATION PROBLEM | Jacinto | Journal on Mathematics Education

    DIGITAL TOOLS AND PAPER-AND-PENCIL IN SOLVING-AND-EXPRESSING: HOW TECHNOLOGY EXPANDS A STUDENT’S CONCEPTUAL MODEL OF A COVARIATION PROBLEM

    Hélia Jacinto, Susana Carreira

    Abstract


    This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (MPST) model to analyze the processes of solving-and-expressing-problems. Resorting to qualitative methods for data collection and analysis, we report on the case of an 8th grader working on a covariation problem to examine the role that paper-and-pencil and digital tools play in the development of a conceptual model of the situation. We found that the resources used throughout the solving-and-expressing activity influenced the depth of the conceptual model developed, within a process of progressive mathematization. Whereas paper-and-pencil led to the emergence of a conceptual model based on exploring particular cases, the digital transformation of the solution was triggered by the process of communicating its mathematical justification and expanded the previous model. Moreover, the complexity of this activity is evidenced by its multiple sequences of processes. Finally, the integration process seems crucial as the concomitant use of technological and mathematical resources precedes major advancements in the expansion of the conceptual model.


    Keywords


    mathematical problem-solving; conceptual model; covariation; paper-and-pencil; digital technology; techno-mathematical fluency

    Full Text:

    PDF

    References


    Bairral, M., Arzarello, F. & Assis, A. (2017). Domains of Manipulation in Touchscreen Devices and Some Didactic, Cognitive, and Epistemological Implications for Improving Geometric Thinking. In G. Aldon, F. Hitt, L. Bazzini, & U. Gellert (Eds.), Mathematics and Technology: A C.I.E.A.E.M. Sourcebook (pp. 113-142). Cham: Springer Nature.

    Barrera-Mora, F., & Reyes-Rodríguez, A. (2013). Cognitive processes developed by students when solving mathematical problems within technological environments. The Mathematics Enthusiast, 1&2, 109-136.

    Borba, M., & Villarreal, M. (1998). Graphing calculators and reorganization of thinking: the transition from functions to derivative. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd International Conference for the Psychology of Mathematics Education, (vol 2, pp. 136-143). Stellenbosch, South Africa: IGPME.

    Brady, C., Eames, C., & Lesh, R. (2015). Connecting Real-World and In-School Problem-Solving Experiences. Quadrante, 24(2), 5-38.

    Carlson, M., & Bloom, I. (2005). The cyclic nature of problem solving: An emergent problem-solving framework. Educational Studies in Mathematics, 58, 45-75. https://doi.org/10.1007/s10649-005-0808-x

    Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events. Journal for Research in Mathematics Education, 33(5), 352-378. https://doi.org/10.2307/4149958

    Carreira, S. & Jacinto, H. (2019). A model of mathematical problem solving with technology: the case of Marco solving-and-expressing. In P. Liljedahl & M. Santos Trigo (Eds.), Mathematical Problem solving, (pp. 41-62). Cham: Springer. https://doi.org/10.1007/978-3-030-10472-6_3

    Carreira, S., Jones, K., Amado, N., Jacinto, H., & Nobre, S. (2016). Youngsters solving mathematics problems with technology. New York: Springer. https://doi.org/10.1007/978-3-319-24910-0

    Chan, K., & Leung, S. (2014). Dynamic Geometry Software Improves Mathematical Achievement: Systematic Review and Meta-Analysis. Journal of Educational Computing Research, 51(3), 311–325. https://doi.org/10.2190/EC.51.3.c

    Dooley, L. (2002). Case Study Research and Theory Building. Advances in Developing Human Resources, 4(3), 335-354. https://doi.org/10.1177/1523422302043007

    Ekawati, R., Kohar, A. W., Imah, E. M., Amin, S. M., & Fiangga, S. (2019). Students’ cognitive processes in solving problem related to the concept of area conservation. Journal on Mathematics Education, 10(1), 21–36. https://doi.org/10.22342/jme.10.1.6339.21-36

    Geraniou, E. & Jankvist, U. T. (2019). Towards a definition of “mathematical digital competency”. Educational Studies in Mathematics, 102, 29–45. https://doi.org/10.1007/s10649-019-09893-8

    Gravemeijer, K. (2005). What makes mathematics so difficult, and what can we do about it? In L. Santos, A. P. Canavarro & J. Brocardo (Eds.), Educação matemática: Caminhos e encruzilhadas – Encontro de homenagem a Paulo Abrantes (pp. 83-101). Lisbon, Portugal: APM.

    Halamish, V. & Elbaz, E. (2020). Children's reading comprehension and metacomprehension on screen versus on paper. Computers & Education, 145. https://doi.org/10.1016/j.compedu.2019.103737

    Hoyles, C., & Noss, R. (2009). The technological mediation of mathematics and its learning. Human Development, 52(2), 129–147. https://doi.org/10.1159/000202730

    Hoyles, C., Noss, R., Kent, P., & Bakker. A. (2010). Improving mathematics at work: The need for techno-mathematical literacies. London, UK: Routledge.

    Jacinto, H., & Carreira, S. (2017a). Mathematical Problem Solving with Technology: the Techno-Mathematical Fluency of a Student-with-GeoGebra. International Journal of Science and Mathematics Education, 15(6), 1115–1136. https://doi.org/10.1007/s10763-016-9728-8

    Jacinto, H., & Carreira, S. (2017b). Different ways of using GeoGebra in Mathematical Problem-Solving beyond the Classroom: evidences of Techno-mathematical Fluency. Bolema, 31(57), (pp. 266-288). https://doi.org/10.1590/1980-4415v31n57a13

    Jones, K. (2000). Providing a foundation for deductive reasoning: Students’ interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44, 55-85. https://doi.org/10.1023/A:1012789201736

    Jupri, A., Drijvers, P., & van den Heuvel-Panhuizen, M. (2016). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal, 26, 683-710. https://doi.org/10.1007/s13394-013-0097-0

    Komatsu, K., & Jones, K. (2020). Interplay between Paper-and-Pencil Activity and Dynamic-Geometry-Environment Use during Generalisation and Proving. Digital Experiences in Mathematics Education, 6(2), 123–143. https://doi.org/10.1007/s40751-020-00067-3

    Koyuncu, I., Akyuz, D., & Cakiroglu, E. (2015). Investigating plane geometry problem-solving strategies of prospective mathematics teachers in technology and paper-and-pencil environments. International Journal of Science and Mathematics Education, 13(4), 837-862. https://doi.org/10.1007/s10763-014-9510-8

    Kurniati, D., Purwanto, P., As'ari, A., & Dwiyana, D. (2018). Exploring the mental structure and mechanism: how the style of truth-seekers in mathematical problem-solving? Journal on Mathematics Education, 9(2), 311-326. https://doi.org/10.22342/jme.9.2.5377.311-326

    Lesh, R. (2000). Beyond constructivism: identifying mathematical abilities that are most needed for success beyond school in an age of information. Mathematics Education Research Journal, 12(3), 177-195.

    Lesh, R., & Doerr, H. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: models and modeling perspectives on mathematics problem solving, learning, and teaching, (pp. 3-33). Mahwah, NJ: Erlbaum Associates.

    Lesh, R. & Harel, G. (2003). Problem Solving, Modeling, and Local Conceptual Development. Mathematical Thinking and Learning, 5(2-3), 157–189. https://doi.org/10.1080/10986065.2003.9679998

    Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning, (pp. 763-804). Charlotte, NC: Information Age Publishing and NCTM.

    Martin, A., & Grudziecki, J. (2006). DigEuLit: Concepts and tools for digital literacy development. Innovation in Teaching and Learning in Information and Computer Sciences, 5(4), 249-267.

    Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco, CA: Jossey-Bass.

    Montague, M., & Applegate, B. (1993). Mathematical problem-solving characteristics of middle school students with learning disabilities. The Journal of Special Education, 27(2), 175–201.

    Noss, R., Healy, L., & Hoyles, C. (1997). The construction of mathematical meanings: Connecting the visual with the symbolic. Educational Studies in Mathematics, 33(2), 203-233.

    Pugalee, D. (2004). A comparison of verbal and written descriptions of students’ problem solving processes. Educational Studies in Mathematics, 55, 27-47. https://doi.org/10.1023/B:EDUC.0000017666.11367.c7

    Santia, I., Purwanto, Sutawidjadja, A., Sudirman, & Subanji. (2019). Exploring Mathematical Representations in Solving Ill-Structured Problems: The Case of Quadratic Function. Journal on Mathematics Education, 10(3), 365-378. https://doi.org/10.22342/jme.10.3.7600.365-378

    Santos-Trigo, M., & Camacho-Machín, M. (2013). Framing the use of computational technology in problem solving approaches. The Mathematics Enthusiast, 1&2, 279-302.

    Schoenfeld, A. (1985). Mathematical problem solving. New York: Academic Press.

    Treffers, A. (1987). Three dimensions: a model of goal and theory description in mathematics education. Dordrecht, The Netherlands: Reidel.

    Usiskin, Z. (2018). Electronic vs. paper textbook presentations of the various aspects of mathematics. ZDM Mathematics Education, 50, 849-861. https://doi.org/10.1007/s11858-018-0936-2

    Wollscheid, S., Sjaastad, J. & Tømte, C. (2016). The impact of digital devices vs. pen(cil) and paper on primary school students’ writing skills – A research review. Computers & Education, 95, 19-35. https://doi.org/10.1016/j.compedu.2015.12.001

    Yao, X., & Manouchehri, A. (2019). Middle school students’ generalizations about properties of geometric transformations in a dynamic geometry environment. The Journal of Mathematical Behavior, 55, 1-19. https://doi.org/10.1016/j.jmathb.2019.04.002

    Zawojewski, J., & Lesh, R. (2003). A models and modeling perspective on problem solving. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 317-336). Mahwah, NJ: Erlbaum.




    DOI: https://doi.org/10.22342/jme.12.1.12940.113-132

    Refbacks

    • There are currently no refbacks.


    Creative Commons License
    This work is licensed under a Creative Commons Attribution 4.0 International License.

    Journal on Mathematics Education
    Doctoral Program on Mathematics Education
    Faculty of Teacher Training and Education, Universitas Sriwijaya
    Kampus FKIP Bukit Besar
    Jl. Srijaya Negara, Bukit Besar
    Palembang - 30139
    email: jme@unsri.ac.id
    p-ISSN: 2087-8885 | e-ISSN: 2407-0610

    Creative Commons License
    Journal on Mathematics Education (JME) is licensed under a Creative Commons Attribution 4.0 International License.


    View My Stats