Metacognitive Strategies for Mathematical Modeling with Engineering Groups of Students: Adaptation and Validation of a Questionnaire

Автор: Noemí Cárcamo-Mansilla, María D. Aravena-Díaz

Журнал: International Journal of Cognitive Research in Science, Engineering and Education @ijcrsee

Рубрика: Original research

Статья в выпуске: 1 vol.12, 2024 года.

Бесплатный доступ

A sequential exploratory mixed-methods study is implemented to develop an instrument that allows for the evaluation of the metacognitive strategies used by engineering groups of students when solving mathematical modeling problems. The findings of the qualitative study guided by observations and interviews reveal the use of metacognitive strategies of ‘planning’, ‘monitoring and, if necessary, regulation’, and ‘evaluation’. In this article, we present the final categories of the qualitative analysis and discuss how these data were shaped into a theoretical construct and items of an instrument to measure metacognitive strategies. The psychometric properties of the instrument are analyzed, and it is argued that it has a similar interpretation among males and females, as there are no significant differences in these results. The development of the present study demonstrates how the qualitative method can support the adaptation of an instrument to measure metacognitive strategies, thus contributing to validity and applicability.

Еще

Modeling, metacognitive strategies, Engineering Education, questionnaire, Gender Invariance

Короткий адрес: https://sciup.org/170202068

IDR: 170202068   |   DOI: 10.23947/2334-8496-2024-12-1-41-55

Список литературы Metacognitive Strategies for Mathematical Modeling with Engineering Groups of Students: Adaptation and Validation of a Questionnaire

  • ABET. (2017). Engineering Accreditation Commission Criteria for Accrediting. Engineerings programs. ABET. http://www.abet.org
  • Allen, K., Reed-Rhoads, T., Terry, R. A., Murphy, T. J., & Stone, A. D. (2008). Coefficient alpha: An engineer’s interpretation of test reliability. Journal of Engineering Education, 97, 87-94. https://doi.org/10.1002/j.2168-9830.2008.tb00956.x DOI: https://doi.org/10.1002/j.2168-9830.2008.tb00956.x
  • Alpers, B. (2021). Making Sense of Engineering Workplace Mathematics to Inform Engineering Mathematics Education. A Report for the Mathematics Interest Group. European Society for Engineering Education (SEFI). https://www.sefi.be/wp-content/uploads/2021/04/Workplace_Mathematics_SEFI_final.pdf
  • Aravena Díaz, M. D., Díaz Levicoy, D., Rodríguez Alveal, F., & Cárcamo Mansilla, N. (2022). Case study and mathematical modeling in the training of engineers. Characterization of STEM skills. Ingeniare. Revista chilena de ingeniería, 30(1), 37-56. http://dx.doi.org/10.4067/S0718-33052022000100037. DOI: https://doi.org/10.4067/S0718-33052022000100037
  • Aravena-Díaz, M. D., Sanhueza Henríquez, S., Rodriguez Gallardo, M., & Cárcamo Mansilla, N. (in press). Mathematical modeling to reduce gender gaps in STEM: characterization of STEM skills in high school students. In V. Geiger, G. Kaiser & H. Siller (Eds.), Researching Mathematical Modelling Education in Disruptive Times, International Perspectives on the Teaching and Learning of Mathematical Modelling.
  • Assis Gomes, C., Almeida, L. S., & Núñez, J. C. (2017). Rationale and Applicability of Exploratory Structural Equation Modeling (ESEM) in psychoeducational contexts. Psicothema, 29(3), 396–401. https://doi.org/10.7334/psicothema2016.369
  • Bembenutty, H. (2007). Self-Regulation of Learning and Academic Delay of Gratification: Gender and ethnic differences among college students. Journal of Advanced Academics, 18(4), 586–616. https://doi.org/10.4219/jaa-2007-553 DOI: https://doi.org/10.4219/jaa-2007-553
  • Bidjerano, T. (2005). Gender differences in self-regulated learning [Paper presentation]. Annual Meeting of the Northeastern Educational Research Association, Kerhonkson, New York. https://eric.ed.gov/?id=ED490777
  • Blum, W. (2011). Can Modelling Be Taught and Learnt? Some Answers from Empirical Research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 15–30). https://doi.org/10.1007/978-94-007-0910-2_3 DOI: https://doi.org/10.1007/978-94-007-0910-2_3
  • Borromeo, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM - International Journal on Mathematics Education, 38(2), 86–95. https://doi.org/10.1007/BF02655883 DOI: https://doi.org/10.1007/BF02655883
  • Cardella, M. E. (2008). Which mathematics should we teach engineering students? An empirically grounded case for a broad notion of mathematical thinking. Teaching Mathematics and Its Applications, 27(3), 150–159. https://doi.org/10.1093/teamat/hrn008 DOI: https://doi.org/10.1093/teamat/hrn008
  • Cárcamo Mansilla, N., Aravena-Díaz, M. D., & Berres, S. (in press). Metacognitive Strategies in Mathematical Modelling with Groups of Engineering Students. In V. Geiger, G. Kaiser & H. Siller (Eds.), Researching Mathematical Modelling Education in Disruptive Times, International Perspectives on the Teaching and Learning of Mathematical Modelling.
  • Cech, E., Rubineau, B., Silbey, S., & Seron, C. (2011). Professional role confidence and gendered persistence in engineering. American sociological review, 76(5), 641-666. https://doi.org/10.1177/0003122411420815 DOI: https://doi.org/10.1177/0003122411420815
  • Charles, M., & Bradley, K. (2009). Indulging our gendered selves? Sex segregation by field of study in 44 countries. American journal of sociology, 114(4), 924-976. https://doi.org/10.1086/595942 DOI: https://doi.org/10.1086/595942
  • Cheryan, S. (2012). Understanding the paradox in math-related fields: Why do some gender gaps remain while others do not?. Sex roles, 66, 184-190. https://doi.org/10.1007/s11199-011-0060-z DOI: https://doi.org/10.1007/s11199-011-0060-z
  • Ciascai, L., & Lavinia, H. (2011). Gender differences in metacognitive skills. A study of the 8th grade pupils in Romania. Procedia - Social and Behavioral Sciences, 29, 396–401. https://doi.org/10.1016/j.sbspro.2011.11.255 DOI: https://doi.org/10.1016/j.sbspro.2011.11.255
  • Correll, S. J. (2004). Constraints into preferences: Gender, status, and emerging career aspirations. American sociological review, 69(1), 93-113. DOI: https://doi.org/10.1177/000312240406900106
  • Creswell, J. (2009). Research Design Qualitative, Quantitative and Mixed Methods Approaches. SAGE Publications.
  • Creswell, J., & Plano, V. (2018). Designing and Conducting Mixed Methods Research. SAGE Publications.
  • Dirksen, U. (2019). Trabajo del fututo y futuro del trabajo. Nueva Sociedad, 279. https://static.nuso.org/media/articles/downloads/3.TC_Dirksen_279.pdf
  • Escobar-Pérez, J., & Cuervo-Martínez, Á. (2008). Validez de contenido y juicio de expertos: Una aproximación a su utilización. Avances En Medición, 6(1), 27–36. http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1665-61802017000300042
  • Ferrando, P. J., & Anguiano-Carrasco, C. (2010). El análisis factorial como técnica de investigación en psicología. Papeles del psicólogo, 31(1), 18–33. https://www.papelesdelpsicologo.es/pdf/1793.pdf
  • Fitzpatrick, C. (1994). Adolescent Mathematical Problem Solving: The Role of Metacognition, Strategies and Beliefs [paper presentation]. Annual Meeting of the American Educational Research Association. New Orleans. https://files.eric.ed.gov/fulltext/ED374969.pdf
  • Flores-Ruiz, E., Miranda-Novales, M. G., & Villasís-Keever, M. A. (2017). The research protocol VI: How to choose the appropriate statistical test. Inferential statistics. Revista Alergia México, 64(3), 364-370. https://doi.org/10.29262/ram.v64i3.304 DOI: https://doi.org/10.29262/ram.v64i3.304
  • Gainsburg, J. (2013). Learning to Model in Engineering. Mathematical Thinking and Learning, 15(4), 259–290. https://doi.org/10.1080/10986065.2013.830947 DOI: https://doi.org/10.1080/10986065.2013.830947
  • Garofalo, J., & Lester, F. (1985). Metacognition, Cognitive Monitoring, and Mathematical Performance. Journal for Research in Mathematics Education, 16(3), 163. https://doi.org/10.2307/748391 DOI: https://doi.org/10.2307/748391
  • Gläser-Zikuda, M., Hagenauer, G., & Stephan, M. (2020). The potential of qualitative content analysis for empirical educational research. Forum Qualitative Sozialforschung, 21(1), 35–61. https://doi.org/10.17169/fqs-21.1.3443
  • Hegedus, S. J. (2001). Problem Solving in Integral Calculus: One Role of Metacognitive Thinking. In R. Speiser, C. A. Maher, & C. N. Walter (Eds.), Proceedings of the 23rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. (pp. 491–500). ERIC Clearinghouse for Science, Mathematics and Environmental Education. https://files.eric.ed.gov/fulltext/ED476613.pdf
  • Hidayat, R., Zamri, S., & Zulnaidi, H. (2018). Does Mastery of Goal Components Mediate the Relationship between Metacognition and Mathematical Modelling Competency?. Educational Sciences: Theory & Practice, 18(3). https://doi.org/10.12738/estp.2018.3.0108 DOI: https://doi.org/10.12738/estp.2018.3.0108
  • Hidayat, R., Zulnaidi, H., & Zamri, S. (2018). Roles of metacognition and achievement goals in mathematical modeling competency: A structural equation modeling analysis. PLoS ONE, 13(11). https://doi.org/10.1371/journal.pone.0206211 DOI: https://doi.org/10.1371/journal.pone.0206211
  • Hong, E., O’Neil, H. F., Jr., & Feldon, D. (2005). Gender effects on mathematics achievement: Mediating role of state and trait self-regulation. In A. M. Gallagher, & J. C. Kaufman (Eds.), Gender differences in mathematics (pp. 264–293). New York, NY: Cambridge University Press. http://ndl.ethernet.edu.et/bitstream/123456789/16205/1/4.pdf#page=281 DOI: https://doi.org/10.1017/CBO9780511614446.014
  • Humberto, J., & Rojas, C. (2017). La Cuarta Revolución Industrial o Industria 4.0 y su Impacto en la Educación Superior en Ingeniería en Latinoamérica y el Caribe. 15 Th LACCEI International Multi-Conference for Engineering, Education, and Technology. http://www.laccei.org/LACCEI2017-BocaRaton/work_in_progress/WP386.pdf
  • International Engineering Alliance. (2014). 25 years of the Washington Accord. International Engineering Alliance. http://www.ieagreements.org/25_years/
  • Johanson, G. A., & Brooks, G. P. (2010). Initial scale development: Sample size for pilot studies. Educational and Psychological Measurement, 70(3), 394–400. https://doi.org/10.1177/0013164409355692 DOI: https://doi.org/10.1177/0013164409355692
  • Jonassen, D., Strobel, J., & Lee, C. (2006). Everyday Problem Solving in Engineering: Lessons for Engineering Educators. Journal of Engineering Education, 9(2), 139–151. https://doi.org/https://doi.org/10.1002/j.2168-9830.2006.tb00885.x DOI: https://doi.org/10.1002/j.2168-9830.2006.tb00885.x
  • Kaiser, G., & Schwarz, B. (2010). Authentic Modelling Problems in Mathematics Education-Examples and Experiences. J Math Didakt, 31, 51–76. https://doi.org/10.1007/s13138-010-0001-3 DOI: https://doi.org/10.1007/s13138-010-0001-3
  • Kent, P., & Noss, R. (2003). Mathematics in the University Education of Engineers A Report to the Ove Arup Foundation. The Ove Arup Foundation. https://www.ovearupfoundation.org/library/media-reports
  • Kohlbacher, F. (2006). The use of qualitative content analysis in case study research. Forum Qualitative Sozialforschung, 7(1). https://doi.org/10.17169/fqs-7.1.75
  • Kuckartz, U. (2019). Qualitative Text Analysis: A Systematic Approach. In: Kaiser, G., Presmeg, N. (Eds.) Compendium for Early Career Researchers in Mathematics Education. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-030-15636-7_8 DOI: https://doi.org/10.1007/978-3-030-15636-7_8
  • Li, T. (2013). Mathematical Modeling Education is the Most Important Educational Interface Between Mathematics and Industry. In A. Damlamian, J. Rodrigues, & R. Sträßer (Eds.), New ICMI Study Series (pp. 51–58). Springer. https://doi.org/10.1007/978-3-319-02270-3_5 DOI: https://doi.org/10.1007/978-3-319-02270-3_5
  • Lyon. J. A., & Magana, A. J. (2020). A Review of Mathematical Modeling in Engineering Education. International Journal of Engineering Education, 36(1), 101–116. https://www.ijee.ie/1atestissues/Vol36-1A/09_ijee3860.pdf
  • Mann, A., & DiPrete, T. A. (2013). Trends in gender segregation in the choice of science and engineering majors. Social science research, 42(6), 1519-1541. https://doi.org/10.1016/j.ssresearch.2013.07.002 DOI: https://doi.org/10.1016/j.ssresearch.2013.07.002
  • Maaß, K. (2006). What are modelling competencies?, ZDM, 38(2), 113–142. https://doi.org/10.1007/BF02655885 DOI: https://doi.org/10.1007/BF02655885
  • Mayring, P. (2014). Qualitative Content Analysis. Theoretical Foundation, Basic Procedures and Software Solution. https://www.ssoar.info/ssoar/handle/document/39517 DOI: https://doi.org/10.1007/978-94-017-9181-6_13
  • Muthén, L. K., & Muthén, B. O. (2017). Mplus User’s Guide. Muthén & Muthén.
  • National Center for Science and Engineering Statistics (NCSES). 2023. Diversity and STEM: Women, Minorities, and Persons with Disabilities 2023. National Science Foundation. https://ncses.nsf.gov/wmpd
  • Newell, J., Dahm, K., Harvey, R., & Newell, H. (2004). Development metacognitive engineering teams. Chemical Engineering Education, 38(4), 106–129. https://doi.org/10.4018/978-1-5225-2212-6.ch006 DOI: https://doi.org/10.4018/978-1-5225-2212-6.ch006
  • Oliden, P. E., & Zumbo, B. D. (2008). Coeficientes de fiabilidad para escalas de respuesta categórica ordenada. Psicothema, 20(4), 896–901. http://www.psicothema.com/psicothema.asp?id=3572
  • Palmer, A., Amat, S., Busquier, S., Romero, P., & Tejada, J. (2013). Mathematics for Engineering and Engineering for Mathematics. In A. Damlamian, J. Rodrigues, & R. Sträßer (Eds.), New ICMI Study Series (pp. 185–198). Springer. https://doi.org/10.1007/978-3-319-02270-3_17 DOI: https://doi.org/10.1007/978-3-319-02270-3_17
  • Penagos, H. P. (2011). How can metacognition be developed through problem-solving in higher education?. Ingeniería e Investigación, 31(1), 213-223. https://repositorio.unal.edu.co/handle/unal/33495 DOI: https://doi.org/10.15446/ing.investig.v31n1.20557
  • Preacher, K., & Coffman, D. (2006). Computing power and minimum sample size for RMSEA. http://quantpsy.org/
  • Rakoczy, K., Buff, A., & Lipowsky, F. (2005). Dokumentation der Erhebungs-und Auswertungsinstrumente zur schweizerisch-deutschen Videostudie.” Unterrichtsqualität, Lernverhalten und mathematisches Verständnis”. 1. Frankfurt: Main: GFPF ua.
  • Richert, A., Shehadeh, M., Willicks, F., & Jeschke, S. (2016). Digital Transformation of Engineering Education - Empirical Insights from Virtual Worlds and Human-Robot-Collaboration. International Journal of Engineering Pedagogy (IJEP), 6(4), 23. https://doi.org/10.3991/ijep.v6i4.6023 DOI: https://doi.org/10.3991/ijep.v6i4.6023
  • Riegle-Crumb, C. (2006). The path through math: Course sequences and academic performance at the intersection of race-ethnicity and gender. American Journal of Education, 113(1), 101-122. https://doi.org/10.1086/506495 DOI: https://doi.org/10.1086/506495
  • Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334–370). New York: MacMillan. http://hplengr.engr.wisc.edu/Math_Schoenfeld.pdf
  • Schukajlow, S., & Krug, A. (2013). Planning, monitoring and multiple solutions while solving modeling problems. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th Conference of the International 4 - 177 Group for the Psychology of Mathematics Education (pp. 177–184). Kiel, Germany: PME. https://www.researchgate.net/publication/274257874_PLANNING_MONITORING_AND_MULTIPLE_SOLUTIONS_WHILE_SOLVING_MODELLING_PROBLEMS
  • Sanabria, T., & Penner, A. (2017). Weeded out? Gendered responses to failing calculus. Social Sciences, 6(2), 47. https://doi.org/10.3390/socsci6020047 DOI: https://doi.org/10.3390/socsci6020047
  • Simons, H. (2013). El estudio de caso: Teoría y práctica. Ediciones Morata, S. L. Madrid
  • Smith-Doerr, L., Alegria, S. N., & Sacco, T. (2017). How diversity matters in the US science and engineering workforce: A critical review considering integration in teams, fields, and organizational contexts. Engaging Science, Technology, and Society, 3, 139-153. https://doi.org/10.17351/ests2017.142 DOI: https://doi.org/10.17351/ests2017.142
  • Soon, W., Lioe, L. T., & McInnes, B. (2011). Understanding the difficulties faced by engineering undergraduates in learning mathematical modelling. International Journal of Mathematical Education in Science and Technology, 42(8), 1023–1039. https://doi.org/10.1080/0020739X.2011.573867 DOI: https://doi.org/10.1080/0020739X.2011.573867
  • Stillman, G. (2011). Applying Metacognitive Knowledge and Strategies in Applications and Modelling Tasks at Secondary School. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 165–180). https://doi.org/10.1007/978-94-007-0910-2_18 DOI: https://doi.org/10.1007/978-94-007-0910-2_18
  • Stillman, G., & Galbraith, P. (1998). Applying mathematics with real world connections: metacognitive characteristics of secondary students. Educational Studies in Mathematics, 36(2), 157–194. https://doi.org/10.1023/A:1003246329257 DOI: https://doi.org/10.1023/A:1003246329257
  • Tashakkori, A., & Teddlie, C. (2003). Handbook of mixed methods in social and behavioral research. Thousand Oaks, CA: Sage. https://doi.org/10.4135/9781506335193 DOI: https://doi.org/10.4135/9781506335193
  • Tristán-López, a. (2008). Modificación al modelo de Lawshe para el dictamen cuantitativo de la validez de contenido de un instrumento objetivo. Avances En Medición, 6, 37–48. https://dialnet.unirioja.es/servlet/articulo?codigo=2981185
  • Tzohar-Rozen, M., & Kramarski, B. (2014). Metacognition, Motivation and Emotions: Contribution of Self-Regulated Learning to Solving Mathematical Problems. Global Education Review, 1(4), 76–95. http://ger.mercy.edu/index.php/ger/article/view/63
  • Vorhölter, K. (2017). Measuring Metacognitive Modelling Competencies. In G Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical Modelling and Applications. International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 175–185). Springer, Cham DOI: https://doi.org/10.1007/978-3-319-62968-1_15
  • Vorhölter, K. (2018). Conceptualization and measuring of metacognitive modelling competencies: empirical verification of theoretical assumptions. ZDM Mathematics Education, 50(1), 343–354. https://doi.org/10.1007/s11858-017-0909-x DOI: https://doi.org/10.1007/s11858-017-0909-x
  • Vorhölter, K. (2019). Enhancing metacognitive group strategies for modelling. ZDM Mathematics Education, 51, 703–716. https://doi.org/10.1007/s11858-019-01055-7 DOI: https://doi.org/10.1007/s11858-019-01055-7
  • Vorhölter, K., Krüger, A., & Wendt, L. (2019). Chapter 2: Metacognition in Mathematical Modeling – An Overview. In S. Chamberlin & B. Sriraman (Eds.), Affect in Mathematical Modeling. Advances in Mathematics Education (pp. 29–51). Springer. https://doi.org/10.1007/978-3-030-04432-9_3 DOI: https://doi.org/10.1007/978-3-030-04432-9_3
  • Vorhölter, K., & Krüger, A. (2021). Metacognitive strategies in modeling: Comparison of the results achieved with the help of different methods. Quadrante, 30(1), 178-197. https://doi.org/10.48489/quadrante.23653
  • Wang, M. T., & Degol, J. L. (2017). Gender gap in science, technology, engineering, and mathematics (STEM): Current knowledge, implications for practice, policy, and future directions. Educational psychology review, 29, 119-140. https://doi.org/10.1007/s10648-015-9355-x DOI: https://doi.org/10.1007/s10648-015-9355-x
  • Wedelin, D., Adawi, T., Jahan, T., & Andersson, S. (2015). Investigating and developing engineering students’ mathematical modelling and problem-solving skills. European Journal of Engineering Education, 40(5), 557–572. https://doi.org/10.1080/03043797.2014.987648 DOI: https://doi.org/10.1080/03043797.2014.987648
  • Weller, J., Gontero, S., & Campbell, S. (2019). Cambio tecnológico y empleo: una perspectiva latinoamericana. Riesgos de la sustitución tecnológica del trabajo humano y desafíos de la generación de nuevos puestos de trabajo. Macroeconomía del Desarrollo, N° 201 (LC/TS.2019/37), Santiago, Comisión Económica para América Latina y el Caribe (CEPAL). www.cepal.org/apps
  • Wengrowicz, N., Dori, Y. J., & Dori, D. (2018). Metacognition and Meta-assessment in Engineering Education. In Y. J. Dori, Z. R. Mevarech, & D. R. Baker (Eds.), Cognition, Metacognition, and Culture in STEM Education. Innovations in Science Education and Technology (pp. 191–216). Springer, Cham. https://doi.org/10.1007/978-3-319-66659-4_9 DOI: https://doi.org/10.1007/978-3-319-66659-4_9
  • World Economic Forum, (2020). The Future of Jobs Report 2020. https://www.weforum.org/reports/the-future-of-jobs-report-2020
  • Woetzel, J., Madgavkar, A., Ellingrud, K., Labaye, E., Devillard, S., Kutcher, E., Manyika, J., Dobbs, R., & Krishnan, M. (2015). The power of parity: How advancing women’s equality can add $12 trillion to global growth. McKinsey Global Institute. https://www.mckinsey.com/featured-insights/employment-and-growth/how-advancing-womens-equality-can-add-12-trillion-to-global-growth
  • Yin, R. K. (2014). Case study research design and methods (5th ed.). Thousand Oaks, CA: Sage.
  • Yildirim, T. Pinar. (2010). Understanding the modelling skills shift in engineering: The impact of self-efficacy, epistemology, and metacognition [Master’s thesis, University of Pittsburgh]. University of Pittsburgh ProQuest Dissertations Publishing. https://www.proquest.com/docview/858073953
Еще
Статья научная