Experiencing teaching and learning quantitative reasoning in a project-based context
Abstract
This paper presents the findings of a small-scale study that investigated the issues and challenges of teaching and learning about quantitative reasoning (QR) within a project-based learning (PjBL) context. Students and teachers were surveyed and interviewed about their experiences of learning and teaching QR in that context in contrast to teaching and learning mathematics in more traditional settings. The grade 9–12 student participants were characterised by a history of disengagement with mathematics and school in general, and the teacher participants were non-mathematics specialist teachers. Both students and teachers were new to the PjBL situation, which resulted in the teaching/learning relationship being a reciprocal one. The findings indicated that students and teachers viewed QR positively, particularly when compared with traditional mathematics teaching, yet tensions were identified for aspects such as implementation of curriculum and integration of relevant mathematics into projects. Both sets of participants identified situations where learning QR was particularly successful, along with concerns or difficulties about integrating QR into project work. The findings have implications for educators, who may need to examine their own approaches to mathematics teaching, particularly in terms of facilitating student engagement with the subject.
Keywords
Project-based learning Quantitative reasoning Big Picture Engagement MotivationNotes
Compliance with ethical standards
Following ethical approval from the researchers’ institution and the Department of Education, all students were invited to participate in a survey and interview. Informed consent was obtained from the students and their parents.
References
- ACARA. (2015a). Australian curriculum: general capabilities. Retrieved from: http://www.australiancurriculum.edu.au/generalcapabilities/numeracy/introduction/introduction.
- ACARA. (2015b). Australian curriculum: mathematics. Retrieved from: http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1.
- Attard, C. (2011). The influence of teachers on student engagement with mathematics during the middle years. Paper presented at the AAMT23/MERGA34 combined conference, 7–9 July 2011. Northern Territory, Australia: Alice Springs.Google Scholar
- Bartscher, K., Gould, B., & Nutter, S. (1995). Increasing student motivation through project-based learning. Master’s research project, Saint Xavier and IRI Skylight. (ED 392549).Google Scholar
- Bell, S. (2010). Project-based learning for the 21st century: skills for the future. The Clearing House: A Journal of Educational Strategies, Issues and Ideas, 83(2), 39–43.CrossRefGoogle Scholar
- Beswick, K., Callingham, R., & Muir, T. (2012). Teaching mathematics in a project-based learning context: initial teacher knowledge and perceived needs. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Mathematics education: expanding horizons (Proceedings of the 35th annual conference of the Mathematics Research Group of Australasia (pp. 114–121). Singapore: MERGA.Google Scholar
- Beswick, K., Muir, T., Jade, K., Farrington, L., & Callingham, R. (2013). Increasing the LD50 of mathematics: re-engaging students in mathematics learning. In S. Herbert, J. Tillyer, & T. Spencer (Eds.), Mathematics: launching futures (Proceedings of the 24th annual biennial conference of the Australian Association of Mathematics Teachers (pp. 55–64). Melbourne: AAMT.Google Scholar
- Beswick, K., Watson, J., & Brown, N. (2006). Teachers’confidence and beliefs and their students’ attitudes towards mathematics. In P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities, cultures and learning spaces (Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia (pp. 68–75). Adelaide: MERGA.Google Scholar
- Big Picture Education Australia. (2011). The learning goals: keys for successful learning. Strawberry Hills, NSW: Author.Google Scholar
- Big Picture Education Australia. (2013). About us. Retrieved from http:www.bigpicture.org.au/about-us/big-picture-education-australia.
- Blumenfeld, P. C., Soloway, E., Marx, R. W., Krajcik, J. S., Guzdial, M., & Palincsar, A. (1991). Motivating project-based learning: sustaining the doing, supporting the learning. Educational Psychologist, 26(3 and 4), 369–398.CrossRefGoogle Scholar
- Creswell, J. W. (2003). Research design: qualitative, quantitative, and mixed methods approaches (2nd ed.). Thousand Oaks: Sage Publications, Inc.Google Scholar
- Diehl, W., Grobe, T., Lopez, H., & Cabral, C. (1999). Project-based learning: a strategy for teaching and learning. Boston: Center for Youth Development and Education, Corporation for Business, Work, and Learning.Google Scholar
- Doppelt, Y. (2009). Assessing creative thinking in design-based learning. International Journal of Technology and Design Education, 19(1), 55–65.CrossRefGoogle Scholar
- Down, B., & Hogan, J. (2010). Big Picture Education Australia: the school and network research framework. Retrieved from http://www.bigpicture.org.au/files/BP_SNRF_10May_new1.pdf.
- Fredricks, J., Blumenfeld, P., & Paris, A. (2004). School engagement: potential of the concept, state of the evidence. Review of Educational Research, 74, 59–109.CrossRefGoogle Scholar
- Hmelo-Silver, C. E., Golan Duncan, R., & Chinn, C. A. (2007). Scaffolding and achievement in problem-based and inquiry learning: a response to Kirschner, Sweller, and Clark. Educational Psychologist, 42(2), 99–107.CrossRefGoogle Scholar
- Hogan, J., & Hogan, L. (2011). Learning goals: keys for successful learners. Sydney: Big Picture Australia.Google Scholar
- Ingram, N. (2013). Mathematical engagement skills. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: yesterday, today and tomorrow (Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 402–409). Melbourne: MERGA.Google Scholar
- Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: an analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41, 75–86.CrossRefGoogle Scholar
- Krajik, J.S., & Blumenfeld, P. (2006). Project-based learning. In R. K. Sawyer (Ed.). The Cambridge handbook of the learning sciences. New York: Cambridge.Google Scholar
- Krajik, J. S., Blumenfeld, P. C., Marx, R. W., Bass, K. M., Fredricks, J., & Soloway, E. (1998). Inquiry in project-based science classrooms: initial attempts by middle school students. The Journal of the Learning Sciences, 7, 313–350.CrossRefGoogle Scholar
- Ladewski, B. G., Krajcik, J., & Harvey, C. L. (1994). A middle grade teacher’s emerging understanding of project-based instruction. The Elementary School Journal, 94(5), 498–515.CrossRefGoogle Scholar
- Lattimer, H., & Riordan, R. (2011). Project-based learning engages students in meaningful work. Middle School Journal, 43(2), 18–23.CrossRefGoogle Scholar
- Lee, H. K., & Breitenberg, M. (2010). Education in the new millennium: the case for design-based learning. International Journal of Art and Design Education, 29(1), 54–60.CrossRefGoogle Scholar
- Luke, A., Elkins, J., Weir, K., Land, R., Carrington, V., Dole, S., …Stevens, L.. (2003). Beyond the middle: a report about literacy and numeracy development of target group students in the middle years of schooling. Canberra: Commonwealth of Australia.Google Scholar
- Martin, A. J. (2006). The relationship between teachers’ perceptions of student motivation and engagement and teachers’ enjoyment of and confidence in teaching. Asia-Pacific Journal of Teacher Education, 34(1), 73–93.CrossRefGoogle Scholar
- Marx, R. W., Blumenfeld, P. C., Krajcik, J. S., & Soloway, E. (1997). Enacting project-based science: challenges for practice and policy. Elementary School Journal, 97, 341–358.CrossRefGoogle Scholar
- Mayes, R., Peterson, F., & Bonilla, R. (2012). Quantitative reasoning: current state of understanding. In R. Mayes & L. Hatfield (Eds.), WISDOM: quantitative reasoning and mathematical modelling: a drive for STEM integrated education and teaching in context (pp. 7–38). Laramie: University of Wyoming.Google Scholar
- Munns, G., & Martin, A. J. (2006). It’s all about MeE: a motivation and engagement framework. Annual Conference of the Australian Association for Research in Education (AARE, 2005), UWS Parramatta Campus, NSW.Google Scholar
- O’Leary, Z. (2010). The essential guide to doing your research project. Thousand Oaks: Sage Publications Inc.Google Scholar
- Park Rogers, M. A., Cross, D. L., Sommerfeld Gresalfi, M., Trauth-Nare, A. E., & Buck, G. A. (2011). First year implementation of a project-based learning approach: the need for addressing teachers’ orientations in the era of reform. International Journal of Science and Mathematics Education, 9, 893–917.CrossRefGoogle Scholar
- Ryan, R. M., & Deci, E. L. (2000). Intrinsic and extrinsic motivations: classic definitions and new directions. Contemporary Educational Psychology, 25, 54–67.CrossRefGoogle Scholar
- Shavelson, R. (2008). Reflections on quantitative reasoning: an assessment perspective. In B. L. Madison & L. A. Steen (Eds.), Calculation vs context: quantitative literacy and its implications for teacher education (pp. 22–47). Washington, DC: Mathematical Association of America.Google Scholar
- Srivastava, P. (2009). A practical iterative framework for qualitative data analysis. International Journal of Qualitative Methods, 8(1), 76–84.Google Scholar
- Stafford, R. E. (1972). Hereditary and environmental components of quantitative reasoning. Review of Educational Research, 42(2), 183–201.CrossRefGoogle Scholar
- Tadich, B., Deed, C., Campbell, C., & Prain, V. (2007). Student engagement in the middle years: a year 8 case study. Issues in Educational Research, 17(2), 256–271.Google Scholar
- Thomas, J. W. (2000). A review of research on project-based learning. Retrieved from: http://www.bie.org/index.php/site/RE/pbl_research/29.
- Toolin, R. E. (2004). Striking a balance between innovation and standards: a study of teachers implementing project-based approaches to teaching science. Journal of Science Education and Technology, 13(2), 179–187.CrossRefGoogle Scholar
- Tseng, K.-H., Chang, C.-C., Lou, S.-J., & Chen, W.-P. (2013). Attitudes towards science, technology, engineering and mathematics (STEM) in a project-based learning (PjBL) environment. International Journal of Technology Design Education, 23, 87–102.CrossRefGoogle Scholar
- Yetkiner, Z. E., Anderoglu, H., & Capraro, R. M. (2008). Research summary: project-based learning in middle school mathematics. Retrieved from: http://www.nmsa.org/Research/ResearchSummaries/ProjectBasedLearningMath/tabid/1570/Default.aspx.