Critical consciousness in engineering education: going beyond critical thinking in mathematical modeling

References

• Abassian, A., F. Safi, S. Bush, and J. Bostic. 2020. “Five Different Perspectives on Mathematical Modeling in Mathematics Education.” Investigations in Mathematics Learning 12 (1): 53–65. doi:10.1080/19477503.2019.1595360.
   Google Scholar
• Ahern, A., C. Dominguez, C. McNally, J. O’Sullivan, and D. Pedrosa. 2019. “A Literature Review of Critical Thinking in Engineering Education.” Studies in Higher Education 44 (5): 816–828. doi:10.1080/03075079.2019.1586325.
   Web of Science ®Google Scholar
• Andrade, M. O., M. Zurita, I. Burova, and A. Nyamapfene. 2022. “Assessing Higher Levels of Learning Through Real-Life Problems in Engineering Mathematics.” In 2022 IEEE Global Engineering Education Conference (EDUCON), 2002–2006. Tunis, Tunisia: IEEE. doi:10.1109/EDUCON52537.2022.9766484
   Google Scholar
• Anhalt, C., S. Staats, R. Cortez, and M. Civil. 2018. “Mathematical Modeling and Culturally Relevant Pedagogy.” In Cognition, Metacognition, and Culture in STEM Education, edited by Y. J. Dori, Z. Mevarech, and D. Baker, 307–330. South Holland, Netherlands: Springer. doi:10.1007/978-3-319-66659-4_14
   Google Scholar
• Bala, C. O. 2022. The Influence of a Values Affirmation Intervention on Students’ Mathematical, Social, and Epistemological Empowerment. (Doctoral Dissertation, Utah State University). https://digitalcommons.usu.edu/etd/8468.
   Google Scholar
• Banerjee, S. 2021. Mathematical Modeling: Models, Analysis and Applications. 2nd ed. Chapman and Hall/CRC. doi:10.1201/9781351022941
   Google Scholar
• Bardin, L. 1977. Análise de Conteúdo [Content Analysis]. Lisboa: Edições.
   Google Scholar
• Beylefeld, A. A., and A. Le Roux. 2018. “School-visit by pre-Service Teachers: An Insider View on Students’ Experiences and Staff’s Perceptions.” South African Journal of Higher Education 32 (6): 550–569.
   Web of Science ®Google Scholar
• Biembengut, M. S. 2016. Modelagem na Educação Matemática e na Ciência [Modeling in Mathematical Education and Science]. São Paulo: Editora Livraria da Física.
   Google Scholar
• Bissett-Johnson, K., and D. F. Radcliffe. 2021. “Engaging Engineering Students in Socially Responsible Design Using Global Projects.” European Journal of Engineering Education 46 (1): 4–26. doi:10.1080/03043797.2019.1674785.
   Web of Science ®Google Scholar
• Bogdan, R., and S. K. Biklen. 2003. Qualitative Research for Education. 4th ed. London: Pearson Education Group Inc.
   Google Scholar
• Borba, M., and O. Skovsmose. 1997. “The Ideology of Certainty in Mathematics Education.” For the Learning of Mathematics 17 (3): 17–23. https://www.jstor.org/stable/40248248.
   Google Scholar
• Borba, M. C. 1990. “Ethnomathematics in education.” For the Learning of Mathematics 10 (1): 39–43. https://www.jstor.org/stable/40247974.
   Google Scholar
• Børsen, T., Y. Serreau, K. Reifschneider, A. Baier, R. Pinkelman, T. Smetanina, and H. Zandvoort. 2021. “Initiatives, Experiences and Best Practices for Teaching Social and Ecological Responsibility in Ethics Education for Science and Engineering Students.” European Journal of Engineering Education 46 (2): 186–209. doi:10.1080/03043797.2019.1701632.
   Web of Science ®Google Scholar
• Brantlinger, A. 2014. “Critical Mathematics Discourse in a High School Classroom: Examining Patterns of Student Engagement and Resistance.” Educational Studies in Mathematics 85 (2): 201–220. doi:10.1007/s10649-013-9506-2.
   Web of Science ®Google Scholar
• Bryman, A. 2016. Social Research Methods. USA: Oxford University Press.
   Google Scholar
• Burghes, D. N., and M. S. Borrie. 1981. Modelling with Differential Equations, Colston Papers. E. Horwood.
   Google Scholar
• Cevikbas, M., G. Kaiser, and S. Schukajlow. 2022. “A Systematic Literature Review of the Current Discussion on Mathematical Modelling Competencies: State-of-the-art Developments in Conceptualizing, Measuring, and Fostering.” Educational Studies in Mathematics 109 (2): 205–236. doi:10.1007/s10649-021-10104-6.
   Web of Science ®Google Scholar
• Chen, J., A. Kolmos, and X. Du. 2021. “Forms of Implementation and Challenges of PBL in Engineering Education: A Review of Literature.” European Journal of Engineering Education 46 (1): 90–115. doi:10.1080/03043797.2020.1718615.
   Web of Science ®Google Scholar
• Czocher, J., K. Melhuish, S. S. Kandasamy, et al. 2021. “Dual Measures of Mathematical Modeling for Engineering and Other STEM Undergraduates.” International Journal of Research in Undergraduate Mathematics Education 7 (2): 328–350. doi:10.1007/s40753-020-00124-7.
   Google Scholar
• Darlington, E. 2014. “Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Mathematics Examinations.” Teaching Mathematics and Its Applications 33 (4): 213–229. doi:10.1093/teamat/hru021.
   Google Scholar
• Duan, X., D. Wang, and M. Wu. 2015. “Research-based Modelling Teaching Activities: A Case of Mathematical Positioning with GNSS.” In Mathematical Modelling in Educational Research and Practice: Cultural, Social, and Cognitive Influences, edited by G. A. Stillman, W. Blum, and M. S. Biembengut, 523–533. Cham: Springer. doi:10.1007/978-3-319-18272-8_44
   Google Scholar
• Elicer, R., and M. Blomhøj. 2017. “Designing for Students’ Decision-Making and Critical Reflections: A tax Paying Game.” In In Eighth Nordic Conference on Mathematics Education. Stockholm, Sweden: Stockholm University.
   Google Scholar
• Ennis, R. H. 2015. “Critical Thinking: A Streamlined Conception.” In The Palgrave Handbook of Critical Thinking in Higher Education, edited by M. Davies, and R. Barnett, 351–368. New York, NY: Palgrave Macmillan.
   Google Scholar
• Esteves, M. 2006. “Análise de Conteúdo.” In Fazer Investigação: Contributos Para a Elaboração de Dissertações e Teses [Doing Research: Contributions for the Preparation of Dissertations and Theses], edited by J. A. Lima, and J. A. Pacheco, 105–126. Porto: Porto Editora.
   Google Scholar
• Frank, M. 2000. “Engineering Systems Thinking and Systems Thinking.” Systems Engineering 3 (3): 163–168. doi:10.1002/1520-6858(200033)3:3<163::AID-SYS5>3.0.CO;2-T.
   Google Scholar
• Frankenstein, M. 1983. “Critical Mathematics Education: An Application of Paulo Freire’s Epistemology.” Journal of Education 165 (4): 315–339. doi:10.1177/002205748316500403.
   Google Scholar
• Freire, P. 1970. Pedagogy of Oppressed (M.B. Ramos, Trans.). New York: Seabury Press.
   Google Scholar
• Freire, P. 1974. Pedagogia do Oprimido [Pedagogy of the Oppressed]. São Paulo: Paz e Terra.
   Google Scholar
• Frejd, P., and P. Vos. 2022. “A Commentary on the Special Issue “Innovations in Measuring and Fostering Mathematical Modelling Competencies”.” Educational Studies in Mathematics 109 (2): 455–468. doi:10.1007/s10649-021-10122-4.
   Web of Science ®Google Scholar
• Gibbs, A. M., and J. Y. Park. 2022. “Unboxing Mathematics: Creating a Culture of Modeling as Critic.” Educational Studies in Mathematics 110 (1): 167–192. doi:10.1007/s10649-021-10119-z.
   PubMed Web of Science ®Google Scholar
• Große, C. S. 2022. “Multiple Solutions in Dyads or Alone – Fostering the Acquisition of Modeling Competencies in Mathematics.” Learning and Instruction 82: 101683. doi:10.1016/j.learninstruc.2022.101683.
   Web of Science ®Google Scholar
• Gutstein, E. 2006. “"The Real World As We Have Seen It": Latino/a Parents' Voices On Teaching Mathematics For Social Justice.” Mathematical Thinking and Learning 8 (3): 331–358. doi:10.1207/s15327833mtl0803_7.
   Google Scholar
• Hauge, K. H., P. Gøtze, R. Hansen, and L. Steffensen. 2017. “Categories of Critical Mathematics-Based Reflection on Climate Change.” In Mathematics Education and Life at Times of Crisis: Proceedings of the Ninth International Mathematics Education and Society Conference, edited by A. Chronaki, 528–532. Volos, Greece.
   Google Scholar
• Ikeda, T. 2018. “Evaluating Student Perceptions of the Roles of Mathematics in Society Following an Experimental Teaching Program.” ZDM 50: 259–271. doi:10.1007/s11858-018-0927-3.
   Google Scholar
• Jablonka, E., and C. Bergsten. 2021. “Numbers Don’t Speak for Themselves: Strategies of Using Numbers in Public Policy Discourse.” Educational Studies in Mathematics 108 (3): 579–596. doi:10.1007/s10649-021-10059-8.
   PubMed Web of Science ®Google Scholar
• Jemal, A. 2017. “Critical Consciousness: A Critique and Critical Analysis of the Literature.” The Urban Review 49 (4): 602–626. doi:10.1007/s11256-017-0411-3.
   PubMedGoogle Scholar
• Kinnear, G., M. Bennett, R. Binnie, R. Bolt, and Y. Zheng. 2020. “Reliable Application of the MATH Taxonomy Sheds Light on Assessment Practices.” Teaching Mathematics and its Applications: An International Journal of the IMA 39 (4): 281–295. doi:10.1093/teamat/hrz017.
   Web of Science ®Google Scholar
• Kjeldsen, T. H., and M. Blomhøj. 2013. “Developing Students’ Reflections on the Function and Status of Mathematical Modeling in Different Scientific Practices: History as a Provider of Cases.” Science & Education 22 (9): 2157–2171. doi:10.1007/s11191-012-9555-4.
   Web of Science ®Google Scholar
• Kokka, K. 2020. “Social Justice Pedagogy for Whom? Developing Privileged Students’ Critical Mathematics Consciousness.” The Urban Review 52 (4): 778–803. doi:10.1007/s11256-020-00578-8.
   Google Scholar
• Kolovou, M. 2023. “Embracing Culturally Relevant Education in Mathematics and Science: A Literature Review.” The Urban Review, doi:10.1007/s11256-022-00643-4.
   Google Scholar
• Kuntze, S., E. Aizikovitsh-Udi, and D. Clarke. 2017. “Hybrid Task Design: Connecting Learning Opportunities Related to Critical Thinking and Statistical Thinking.” ZDM 49 (6): 923–935. doi:10.1007/s11858-017-0874-4.
   Google Scholar
• Laguador, J., and C. Dotong. 2020. “Engineering Students’ Challenging Learning Experiences and Their Changing Attitude Towards Academic Performance.” European Journal of Educational Research 9 (3): 1127–1140. doi:10.12973/eu-jer.9.3.1127.
   Google Scholar
• Lewis, S. T. 2021. “Theorizing ‘Modelling as Bridge’ Between Content and Vehicle.” In Mathematical Modelling Education in East and West. International Perspectives on the Teaching and Learning of Mathematical Modelling, edited by F. K. S. Leung, G. A. Stillman, G. Kaiser, and K. L. Wong, 45–54. Cham: Springer. doi:10.1007/978-3-030-66996-6_4
   Google Scholar
• Lim, J. H., B. D. Hunt, N. Findlater, et al. 2021. ““In Our Own Little World”: Invisibility of the Social and Ethical Dimension of Engineering Among Undergraduate Students.” Science and Engineering Ethics 27: 74. doi:10.1007/s11948-021-00355-0.
   PubMed Web of Science ®Google Scholar
• Lincoln, S. Y., and E. G. Guba. 1985. Naturalistic Inquiry. Thousand Oaks, CA: Sage.
   Google Scholar
• Liu, X. 2019. A Case Study of University Instructors’ Perceptions and Teaching Practices of Critical Thinking in China (Unpublished doctoral thesis). University of Calgary, Calgary, AB. http://hdl.handle.net/1880/111357.
   Google Scholar
• Lopes, A. P. C. 2022. “Aspects of Attitudes Towards Mathematics in Modeling Activities: Usefulness, Interest, and Social Roles of Mathematics.” International Electronic Journal of Mathematics Education 17 (4): em0711. doi:10.29333/iejme/12394.
   Google Scholar
• Lopes, A. P. C. 2022. “Advanced Algebraic Thinking Processes in Students’ Modelling Activities.” Teaching Mathematics and its Applications: An International Journal of the IMA, hrac024. doi:10.1093/teamat/hrac024.
   Web of Science ®Google Scholar
• Maass, K., S. Zehetmeier, A. Weihberger, et al. 2023. “Analysing Mathematical Modelling Tasks in Light of Citizenship Education Using the COVID-19 Pandemic as a Case Study.” ZDM – Mathematics Education, doi:10.1007/s11858-022-01440-9.
   Google Scholar
• Mayring, P. 2015. “Qualitative Content Analysis: Theoretical Background and Procedures.” In Approaches to Qualitative Research in Mathematics Education. Examples of Methodology and Methods, edited by A. Bikner-Ahsbahs, C. Knipping, and N. Presmeg, 365–380. Dordrecht: Springer. doi:10.1007/978-94-017-9181-6_13
   Google Scholar
• Merck, M. F., M. A. Gallagher, E. Habib, et al. 2021. “Engineering Students’ Perceptions of Mathematical Modeling in a Learning Module Centered on a Hydrologic Design Case Study.” International Journal of Research in Undergraduate Mathematics Education 7 (2): 351–377. doi:10.1007/s40753-020-00131-8.
   Google Scholar
• Niss, M., and W. Blum. 2020. The Learning and Teaching of Mathematical Modelling. London, New York: Routledge.
   Google Scholar
• Rismi, O. D. 2021. “A Learning Design to Improve Higher Order Thinking Skills (HOTS).” Jurnal Riset Pendidikan Matematika Jakarta, doi:10.21009/jrpmj.v3i2.22265.
   Google Scholar
• Rosa, M., and D. C. Orey. 2018. “Reflecting on Glocalization in the Contexts of Local and Global Approaches Through Ethnomodelling.” Educação Matemática Pesquisa 20 (2): 171–201. doi:10.23925/1983-3156.2018v20i2p171-20.
   Google Scholar
• Santos, N. F., and C. M. Cesar. 2021. “Covid and Populism in the News.” Brazilian Journalism Research 17 (3): 536–561. doi:10.25200/BJR.v17n3.2021.1426.
   Web of Science ®Google Scholar
• Shor, I. 1993. “Education is Politics: Paulo Freire’s Critical Pedagogy.” In Paulo Freire: A Critical Encounter, edited by P. Leonard, P. McLaren, P. Leonard, and P. McLaren, 25–35. Routledge Press.
   Google Scholar
• Skovsmose, O. 2021. “Mathematics and Crises.” Educational Studies in Mathematics 108 (1-2): 369–383. doi:10.1007/s10649-021-10037-0.
   PubMed Web of Science ®Google Scholar
• Smith, G., L. Wood, M. Coupland, B. Stephenson, K. Crawford, and G. Ball. 1996. “Constructing Mathematical Examinations to Assess a Range of Knowledge and Skills.” International Journal of Mathematical Education in Science and Technology 27 (1): 65–77. doi:10.1080/0020739960270109.
   Google Scholar
• Souza, D., S. M. Wood, and L. N. 2003. “Designing Assessment Using the MATH Taxonomy.” In In Mathematics Education Research: Innovation, Networking, Opportunity. Proceedings of the 26th Annual Conference of MERGA Inc., 294–301. Geelong, Australia: Deakin University.
   Google Scholar
• Stephan, M., J. Register, L. Reinke, et al. 2021. “People use Math as a Weapon: Critical Mathematics Consciousness in the Time of COVID-19.” Educational Studies in Mathematics 108 (3): 513–532. doi:10.1007/s10649-021-10062-z.
   PubMed Web of Science ®Google Scholar
• Stillman, G. A. 2019. “State of the art on Modelling in Mathematics Education—Lines of Inquiry.” In Lines of Inquiry in Mathematical Modelling Research in Education. ICME-13 Monographs, edited by G. Stillman, and J. Brown. Cham: Springer. doi:10.1007/978-3-030-14931-4_1
   Google Scholar
• Trbušić, H. 2014. “Engineering in the Community: Critical Consciousness and Engineering Education.” Interdisciplinary Description of Complex Systems 12 (2): 108–118. doi:10.7906/indecs.12.2.1.
   Google Scholar
• Veleda, G. G., and D. Burak. 2017. “Mathematical Modelling in Mathematics Education as Way to Develop Critical Consciousness: A Theoretical Study.” Acta Scientiae 19 (2): 211–223.
   Google Scholar
• Watts, R. J., N. C. Williams, and R. J. Jagers. 2003. “Sociopolitical Development.” American Journal of Community Psychology 31: 185–194. doi:10.1023/A:1023091024140.
   PubMed Web of Science ®Google Scholar
• Werpetinski, V. A., and S. R. Lausell. 2017, march. “Developing Critical Consciousness to Promote Engineering for Social Justice: A Pilot Program to Enhance STEM Outreach and Engineering Education Through Service-Learning.” In In American Society for Engineering Education (Ed.) American Society for Engineering Education (ASEE) Zone II Conference. San Juan, Puerto Rico: ASEE.
   Google Scholar
• Wilson, S. 2017. “Maths Anxiety: The Nature and Consequences of Shame in Mathematics Classrooms.” In Proceedings of the 40th Annual Conference of the Mathematics Education Research Group of Australasia, edited by A. Downton, S. Livy, and J. Hall, 562–568. Melbourne: MERGA.
   Google Scholar
• Winberg, C., M. Bramhall, D. Greenfield, P. Johnson, P. Rowlett, O. Lewis, et al. 2020. “Developing Employability in Engineering Education: A Systematic Review of the Literature.” European Journal of Engineering Education 45 (2): 165–180. doi:10.1080/03043797.2018.1534086.
   Web of Science ®Google Scholar
• Zandvoort, H. 2008. “Preparing Engineers for Social Responsibility.” European Journal of Engineering Education 33 (2): 133–140. doi:10.1080/03043790802024082.
   Google Scholar
• Zhao, G. 2020. “STEM Education in the age of “Fake News”: A John Stuart Mill Perspective.” In The Philosophy of Education Society (Org.), The Philosophy of Education 2019 Yearbook, 393–406. Urbana, Illinois: Philosophy of Education Archive.
   Google Scholar
• Zill, D. G. 2016. Differential Equations with Boundary-Value Problems. Boston: Cengage Learning.
   Google Scholar
• Živković, S. 2016. “A Model of Critical Thinking as an Important Attribute for Success in the 21st Century.” Procedia – Social and Behavioral Sciences 232: 102–108. https://doi.org/10.1016/j.sbspro.2016.10.034.
   Google Scholar