skip to main content
10.1145/3362789.3362828acmotherconferencesArticle/Chapter ViewAbstractPublication PagesteemConference Proceedingsconference-collections
research-article

Theoretical and Methodological Proposal on the Development of Critical Thinking through Mathematical Modeling in the Training of Engineers

Authors Info & Claims
Published:16 October 2019Publication History

ABSTRACT

The present work constitutes a research advance, which takes up previous work where the teaching of Mathematics in higher education is modified through experimentation in the classroom using the modeling of real phenomena and / or simulation. The idea is to rethink Mathematical modeling as a didactic strategy that aims to develop not only disciplinary but also transversal competencies such as Critical Thinking. A review of ideas around Critical Thinking is shown, and this is intended to show that Mathematical modeling can help develop this competency in the Mathematics classroom. A theoretical proposal of how we conceive Mathematical modeling and methodological proposals is presented along with elements to look at these processes in the classroom. Considering that this study focuses on the study of the articulation of mathematical modeling as a didactic strategy and on critical thinking, based on mathematical modeling activities, the level of critical thinking of engineering students who perform these modeling activities in a Differential Equations course will be evaluated.

References

  1. UN DESA. 2013. World Population Prospects: The 2012 Revision, Highlights and Advance Tables. ONU, United Nations Department of Economic and Social Affairs/Population Division. New York: United Nations. Retrieved from http://esa.un.org/unpd/wpp/Documentation/pdf/WPP2012_HIGHLIGHTS.pdfGoogle ScholarGoogle Scholar
  2. T. R. Kelley and J. G. Knowles. 2016. A conceptual framework for integrated STEM education. International Journal of STEM Education, 3--11. DOI 10.1186/s40594-016-0046-zGoogle ScholarGoogle Scholar
  3. F. M. Esteve and M. Gisbert. 2013. Explorando el potencial educativo de los entornos virtuales 3D. Teoría de la Educación. Educación y cultura en la era de la información. 14(3), 5--327.Google ScholarGoogle Scholar
  4. L. M. Murawski. 2014. Critical Thinking in the Classroom...and Beyond. Journal of Learning in Higher Education, 10(1), pp. 25--30.Google ScholarGoogle Scholar
  5. R. Rodríguez. 2017. Repensando la enseñanza de las matemáticas para futuros ingenieros: actualidades y desafíos. Revista de Investigación Educativa de la REDIECH, 8(15), 69--85.Google ScholarGoogle Scholar
  6. A. Arseven, 2015. Mathematical modeling Approach in Mathematics Education. Universal Journal of Educational Research, 3(12), 973--980. DOI: 10.13189/ujer.2015.031204Google ScholarGoogle ScholarCross RefCross Ref
  7. H. Coskun. 2017. Mathematical modeling research in Turkey: A content analysis study. Educational Research and Reviews, 12(1), 19--27. DOI: 10.5897/ERR2016.3077Google ScholarGoogle ScholarCross RefCross Ref
  8. Ciltas and A. Isik. 2013. The Effect of Instruction through Mathematical modeling on modeling Skills of Prospective Elementary Mathematics Teachers. Educational Sciences: Theory & Practice, 13(2), 1187--1192.Google ScholarGoogle Scholar
  9. L. D. English. 2009. Promoting interdisciplinarity through mathematical modeling. ZDM Mathematics Education, 41, 161--181 DOI 10.1007/s11858-008-0106-zGoogle ScholarGoogle ScholarCross RefCross Ref
  10. M. Kertil and C. Gure.l 2016. Mathematical modeling: A bridge to STEM education. International Journal of Education in Mathematics, Science and Technology, 4(1), 44--55. DOI:10.18404/ijemst.95761Google ScholarGoogle ScholarCross RefCross Ref
  11. C.-H. Huang. 2012. Investigating engineering students' mathematical modeling competency. World Transactions on Engineering and Technology Education, 10(2), 99--104.Google ScholarGoogle Scholar
  12. S. Dundar, B. Gokkurt and Y. Soylu. 2012. Mathematical modeling at a glance: a theoretical study. Social and Behavioral Sciences, 46, 3465--3470.Google ScholarGoogle Scholar
  13. S. Maričič, K. Špijunović and B. Lazic. 2016. The Influence of Content on the Development of Students' Critical Thinking in the Initial Teaching of Mathematics. Croatian Journal of Education. 18(1/), 11--40. DOI: 10.15516/cje. v18i1.1325Google ScholarGoogle Scholar
  14. G. Aksu and N. Koruklu. 2015. Determination the effects of vocational high school students' logical and critical thinking skills on mathematics success. Eurasian Journal of Educational Research, 59, 181.Google ScholarGoogle Scholar
  15. S. Osman et al. 2016. Identifying Pertinent Elements of Critical Thinking and Mathematical Thinking Used in Civil Engineering Practice in Relation to Engineering Education. The Qualitative Report 2016, 21(2), 212--227.Google ScholarGoogle Scholar
  16. M. P. Kindelán and A. M. Martín. 2008. Ingenieros del siglo XXI: importancia de la comunicación y de la formación estratégica en la doble esfera educativa y profesional del ingeniero. ARBOR Ciencia, Pensamiento y Cultura, CLXXXIV (732), 731--742.Google ScholarGoogle Scholar
  17. J. A. Villa-Ochoa, M. Rosa and M. E. Gavarrete. 2018. Aproximaciones socioculturales a la modelación en Educación Matemática. Aportes de una comunidad latinoamericana. Revista Latinoamericana de Etnomatemática, 11(1), 4--12.Google ScholarGoogle Scholar
  18. P. Camarena. 2009. La matemática en el contexto de las ciencias. Innovación Educativa, 9(6), 15--25. http://www.redalyc.org/pdf/1794/179414894003.pdfGoogle ScholarGoogle Scholar
  19. J. F. Molina-Toro, J. A. Villa-Ochoa and L. Suárez Téllez. 2018. La modelación en el aula como un ambiente de experimentación-con-graficación-y-tecnología. Un estudio con funciones trigonométricas. Revista Latinoamericana de Etnomatemática, 11(1), 87--115.Google ScholarGoogle Scholar
  20. M. Brito-Vallina, L. Alemán-Romero, E. Fraga-Guerra, J. Para-García and R. Arias-deTapia. 2011. Papel de la modelación matemática en la formación de los ingenieros. Ingeniería Mecánica, 14(2), 129--139.Google ScholarGoogle Scholar
  21. R. G. Jacobs. and Durandt. J. 2017. Attitudes of Pre-Service Mathematics Teachers towards modeling: A South African Inquiry. EURASIA Journal of Mathematics Science and Technology Education, 13(1), 61--84. DOI 10.12973/eurasia.2017.00604aGoogle ScholarGoogle ScholarCross RefCross Ref
  22. S. Aztekin and T. Zehra. 2015. The content analysis of mathematical modeling studies in Turkey: a meta-synthesis study. Education and Science. 40(178), 139--161Google ScholarGoogle Scholar
  23. W. Blum and R. Borromeo. 2009. Mathematical modeling: Can It Be Taught And Learnt? Journal of Mathematical modeling and Application, 1(1), 45--58.Google ScholarGoogle Scholar
  24. N. Mousoulides, C. Christou and B. Sriraman. 2008. A Modeling Perspective on Teaching and Learning of Mathematical Problem Solving. Mathematical Thinking and Learning, 10(3), 293--304 DOI: 10.1080/1098606080221813Google ScholarGoogle ScholarCross RefCross Ref
  25. Association of American Colleges and Universities (AAC&U). 2009. Critical Thinking VALUE rubric. https://www.aacu.org/value/rubrics/inquiry-analysisGoogle ScholarGoogle Scholar
  26. GAIMME: Guidelines for Assessment and Instruction in Mathematical Modeling Education, Second Edition. 2019. Sol Garfunkel and Michelle Montgomery, editors, COMAP and SIAM, Philadelphia. https://www.siam.org/Publications/Reports/Detail/guidelines-for-assessment-and-instruction-in-mathematical-modeling-educationGoogle ScholarGoogle Scholar
  27. L. Albarracín and N. Gorgorió. 2013. Problemas de estimación de grandes cantidades: modelización e influencia del contexto. Revista Latinoamericana de Investigación en Matemática Educativa, 16 (3), 289--315.Google ScholarGoogle Scholar
  28. A. Carberry and A. Mc Kenna. 2014. Exploring student conceptions of modeling and modeling uses in engineering design. Journal of Engineering Education. 103(1), 77--90.Google ScholarGoogle ScholarCross RefCross Ref
  29. J. Cozcher. 2017. How can emphasizing mathematical modeling principles benefits students in a traditionally taught differential equations course? Journal of Mathematical Behavior, 45, 78--94.Google ScholarGoogle ScholarCross RefCross Ref
  30. L. Plaza. 2016. Obstáculos presentes en modelación matemática. Caso ecuaciones diferenciales en la formación de ingenieros. Revista científica, 25, 176--187.Google ScholarGoogle Scholar
  31. A. Aydogan., A. K. Erbas, E. Cakiroglu and C. Alacaci 2017. Developing teachers' models for assessing students' competence in mathematical modeling through lesson study. International Journal of Mathematical Education in Science and Technology, 48(6), 895--912.Google ScholarGoogle ScholarCross RefCross Ref
  32. C. Paolucci and H. Wessels, H. 2017. An Examination of Preservice Teachers' Capacity to Create Mathematical Modeling Problems for Children. Journal of Teacher Education, 68(3), 330--344.Google ScholarGoogle ScholarCross RefCross Ref
  33. J. A. Shahbari and M. Tabach. 2016. Developing modeling lenses among practicing. International Journal of Mathematical Education in Science and Technology, 47(5), 717--732.Google ScholarGoogle ScholarCross RefCross Ref
  34. A. S. Zeytun, B. Cetinkaya, and A. K. Erbas. 2017. Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course. EURASIA Journal of Mathematics Science and Technology Education, 13(3), 691--722.Google ScholarGoogle ScholarCross RefCross Ref
  35. M. Fahim and N. S. Masouleh (2012). Critical Thinking in Higher Education: A Pedagogical Look. Theory and Practice in Language Studies, 2(7), 1370--1375.Google ScholarGoogle ScholarCross RefCross Ref
  36. A. M. S. Atabaki, N. Keshtiaray and M. H. Yarmohammadian, (2015). Scrutiny of Critical Thinking Concept. International Education Studies, 8(3), 93--102.Google ScholarGoogle ScholarCross RefCross Ref
  37. C. Poondej and T. Lerdpornkulrat, (2015). The reliability and construct validity of the critical thinking disposition scale. Journal of Psychological and Educational Research, 23 (1), 23--36.Google ScholarGoogle Scholar
  38. R. H. Ennis (1985). A Logical Basis for Measuring Critical Thinking Skills. Educational Leadership, 43(2) p44--48.Google ScholarGoogle Scholar
  39. D. Vargas (2015). Evidence of Critical Thinking in High School Humanities Classrooms. Gist Education and Learning Research Journal, (11), 26--44Google ScholarGoogle Scholar
  40. H. Bie, H. P. Wilhelm and H. Van der Meij (2015). The Halpern Critical Thinking Assessment: Toward a Dutch appraisal of critical thinking. Thinking Skills and Creativity, 17, 33--44.Google ScholarGoogle ScholarCross RefCross Ref
  41. S. Cargas, S. Williams and M. Rosenberg (2017). An approach to teaching critical thinking across disciplines using performance tasks with a common rubric. Thinking Skills and Creativity, 26, 24--37.Google ScholarGoogle ScholarCross RefCross Ref
  42. L. Elder and R. Paul (2010). Critical Thinking: Competency Standards Essential for the Cultivation of Intellectual Skills, Part 1. Journal of Developmental Education, 34(2), 38--39.Google ScholarGoogle Scholar
  43. L. Bigozzi. et al. (2018) The Influence of Teaching Approach on Students' Conceptual Learning in Physics. Frontiers in Psychology. 9, (2474). DOI: 10.3389/fpsyg.2018.02474Google ScholarGoogle Scholar
  44. JobTestPrep (2019). https://www.jobtestprep.com/watson-glaser-test?utm_source=wikijob&utm_medium=nav-link&utm_content=watson-glaser&utm_campaign=jobtestprep-comGoogle ScholarGoogle Scholar
  45. The Halpern Critical Thinking Assessment. 2016. https://sites.google.com/site/dianehalperncmc/home/research/halpern-critical-thinking-assessmentGoogle ScholarGoogle Scholar
  46. R. H. Ennis, J. Millman and T. N. Tomko. 1985. Cornell critical thinking tests level X & level Z: Manual. Boise, ID: Midwest Publications.Google ScholarGoogle Scholar
  47. A. Villa and M. Poblete, M. 2007. Aprendizaje basado en Competencias. Una propuesta para la evaluación de las competencias genéricas. Bilbao, España: Ediciones Mensajero.Google ScholarGoogle Scholar
  48. J. R. Valenzuela and. M Flores (2012). Fundamentos de investigación educativa. Monterrey, México: Editorial Digital del Tecnológico de Monterrey.Google ScholarGoogle Scholar
  49. T. J. Kennedy and M. R. L. Odell. 2014. Engaging Students In STEM Education Science Education International, 25(3), 246--258.Google ScholarGoogle Scholar
  50. P. R. Hernández, et al. (2014). Connecting the STEM dots: measuring the effect of an integrated engineering design intervention. International Journal of STEM Education, 24, 107--120. DOI 10.1007/s10798-013-9241-0Google ScholarGoogle Scholar
  51. D. Bell. 2016. The reality of STEM education, design and technology teachers' perceptions: a phenomenographic study. International Journal of Technology and Design Education (2016) 26, 61--79. DOI 10.1007/s10798-015-9300-9Google ScholarGoogle Scholar

Index Terms

  1. Theoretical and Methodological Proposal on the Development of Critical Thinking through Mathematical Modeling in the Training of Engineers

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in
      • Published in

        cover image ACM Other conferences
        TEEM'19: Proceedings of the Seventh International Conference on Technological Ecosystems for Enhancing Multiculturality
        October 2019
        1085 pages
        ISBN:9781450371919
        DOI:10.1145/3362789

        Copyright © 2019 ACM

        Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 16 October 2019

        Permissions

        Request permissions about this article.

        Request Permissions

        Check for updates

        Qualifiers

        • research-article
        • Research
        • Refereed limited

        Acceptance Rates

        Overall Acceptance Rate496of705submissions,70%

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader