Abstract
This chapter discusses how modern educational technologies open new opportunities for educating creative and engaging mathematics teachers. In particular, the focus is on using technology to engage mathematics teacher-candidates in exploring how technology can facilitate productive mathematical thinking. The chapter emphasizes the need for viewing mathematics learning as a creative, collaborative and constructive process that sometimes is fraught with inevitable challenges and productive failures, and at other times filled with exhilarating discoveries and new insights. The chapter suggests various ways of implementing digital technologies, such as data collection and analysis tools, electronic response systems, PeerWise, computer simulations, dynamic mathematical software, and Collaborative Learning Annotation System in mathematics teacher education courses in order to inspire teacher-candidates to embrace technology-enhanced creative mathematical thinking. In addition, the importance of technology in scaffolding teacher-candidates and consequently mathematics learners in experiencing and overcoming productive mathematics learning failures is emphasized. The challenge of the implementation of these technologies in mathematics teacher education and the opportunities they offer for embracing creative mathematical thinking are also discussed.
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References
Adams, C. (2001). Overcoming math anxiety. The Mathematical Intelligencer, 23(1), 49–50.
Aralas, D. (2008, July 6–13). Mathematical creativity and its connection with mathematical imagination. Paper presented at the 11th International Congress on Mathematical Education Monterey, Mexico.
Barnes, G. (1989). Physics and size in biological systems. The Physics Teacher, 27(4), 234–253.
Bates, S., & Galloway, R. (2013). PeerWise: Student-generated content for enhanced engagement and learning. Paper presented at the Western Conference on Science Education, London, Ontario. http://ir.lib.uwo.ca/wcse/WCSEThirteen/july11/5/.
Black, K. (2017). The calculated art of quilting. Retrieved from https://www.ualberta.ca/newtrail/featurestories/the-calculated-art-of-quilting.
Bloom, B. S. (1956). Taxonomy of educational objectives: Cognitive domain (Vol. 1). New York, NY: Longman.
Boaler, J. (2010). The elephant in the classroom: Helping children learn and love maths. London, UK: Souvenir Press Ltd.
Bransford, J. D., Brown, A. L., & Cocking, R. R. (2002). How people learn: Brain, mind, experience, and school. Washington, D.C.: The National Academies Press.
British Columbia Ministry of Education. (2013). Defining cross-curricular competencies: Transforming curriculum and assessment. Retrieved from https://curriculum.gov.bc.ca/.
British Columbia Ministry of Education. (2015). Building students success: BC’s new curriculum. Retrieved from https://curriculum.gov.bc.ca/.
Burger, E. B., & Starbird, M. (2000). The heart of mathematics: An invitation to effective thinking. Emeryville, CA: Key College Publishing.
Burridge, P., & Carpenter, C. (2013). Expanding pedagogical horizons: A case study of teacher professional development. Australian Journal of Teacher Education, 38(9), 10–24.
Bursal, M., & Paznokas, L. (2006). Mathematics anxiety and preservice elementary teachers’ confidence to teach mathematics and science. School Science & Mathematics, 106(4), 173–180. https://doi.org/10.2307/749455.
Campbell, P. F., Nishio, M., Smith, T. M., Clark, L. M., Conant, D. L., Rust, A. H. …. Choi, Y. (2014). The relationship between teachers’ mathematical content and pedagogical knowledge, teachers’ perceptions, and student achievement. Journal of Research in Mathematics Education, 45(4).
Carr, J. M. (2012). Does math achievement h’APP’en when iPads and game-based learning are incorporated into fifth-grade mathematics instruction? Journal of Information Technology Education: Research, 11, 269–286.
Chachashvili-Bolotin, S., Milner-Bolotin, M., & Lissitsa, S. (2016). Examination of factors predicting secondary students’ interest in tertiary STEM education. International Journal of Science Education, 38(2), 366–390. http://dx.doi.org/10.1080/09500693.2016.1143137.
Chin, C. (2007). Teacher questioning in science classrooms: Approaches that stimulate productive thinking. Journal of Research in Science Teaching, 44(6), 815–843.
Chinn, S. (2012). Beliefs, anxiety and avoiding failure in mathematics. Child Development Research, vol. 2012, Article ID 396071. http://dx.doi.org/10.1155/2012/396071.
Clement, L. L. (2001). What do students really know about functions? Mathematics Teacher, 94(9), 745–748.
Cole, A. L., & Knowles, J. G. (2000). Researching teaching: Exploring teacher development through reflexive inquiry. Boston, MA: Allyn and Bacon.
Cuban, L. (2001). Oversold and underused: Computers in the classroom. Cambridge, MA: Harvard University Press.
Dang, T (Producer). (2016). Collaborative learning annotation system [Media player]. Retrieved from http://ets.educ.ubc.ca/clas/.
Denny, P. (2016). PeerWise. Retrieved from http://peerwise.cs.auckland.ac.nz/.
Denny, P., Luxton-Reilly, A., & Simon, B. (2009). Quality of student contributed questions using PeerWise. Retrieved from Enschede http://doc.utwente.nl/fid/1445.
Dickinson, M. (2011). Writing multiple-choice questions for higher-level thinking. Learning Solutions. Retrieved from https://www.learningsolutionsmag.com/articles/804/writing-multiple-choice-questions-for-higher-level-thinking.
Dweck, C. S. (2016). Mindset: The new psychology of success. New York, NY: Penguin Random House LLC.
Eijck, M., & Roth, W. M. (2009). Authentic science experiences as a vehicle to change students’ orientations towards science and scientific career choices: Learning from the path followed by Brad. The Culture of Science Education, 4, 611–638.
Erickson, T., & Cooley, B. (2006). A den of inquiry (Vol. 1). Beaverton, OR: Vernier Technology.
Eshach, H. (2014). The use of intuitive rules in interpreting students’ difficulties in reading and creating kinematic graphs. Canadian Journal of Physics, 92(1), 1–8.
Fenyvesi, K., Budinski, N., & Lavicza, Z. (2014). Two solutions to an unsolvable problem: Connecting origami and GeoGebra in a Serbian high school. Paper Presented at the Bridges 2014: Mathematics, Music, Art, Architecture, Culture, Seoul, South Korea.
Feynman, R. P. (1999). The pleasure of finding things out: The best short works of Richard P. Feynman. New York, NY: Helix Books; London, UK: Perseus Books.
Finkelstein, N. D., Adams, W. K., Keller, C. J., Kohl, P. B., Perkins, K. K., Podolefsky, N. S., et al. (2005). When learning about the real world is better done virtually: A study of substituting computer simulations for laboratory equipment. Physical Review Special Topics—Physics Education Research, 1(1), 010103.
Franco-Watkins, A., Derks, P., & Dougherty, M. (2010). Reasoning in the monty hall problem: Examining choice behaviour and probability judgements. Thinking & Reasoning, 9(1), 67–90.
Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational Psychology, 24(5), 645–657. https://doi.org/10.1080/0144341042000262953.
Garforth, L., & Stockelova, T. (2012). Science policy and STS from other epistemic places. Science, Technology and Human Values, 37(2), 226–240.
Ge, X., Ifenthaler, D., & Spector, J. M. (Eds.). (2015). Emerging technologies for STEAM education: Full STEAM ahead. New York, NY: Springer.
Gladwell, M. (2008). Outliers: The story of success (Vol. Spring). New York, NY: Little, Brown and Company.
Goodstein, D. (2000). The coming revolution in physics education. APS News: The American Physical Society, 9(6), 8.
Goth, G. (2009). Physics and size in biological systems. Retrieved from http://www.smccd.net/accounts/goth/MainPages/Scaling/Scaling.htm.
Guerrero, S. (2010). Technological pedagogical content knowledge in the mathematics classroom. Journal of Digital Learning in Teacher Education, 26(4), 132–139.
Hake, R. R. (1998). Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses. American Journal of Physics, 66(1), 64–74.
Hake, R. R. (2012). Helping students to think like scientists in socratic dialogue-inducing labs. The Physics Teacher, 50(1), 48–52. https://doi.org/10.1119/1.3670087.
Harris, J., & Hofer, M. (2011). Technological pedagogical content knowledge (TPACK) in action: A descriptive study of secondary teachers’ curriculum-based, technology-related instructional planning. Journal of Research on Technology in Education, 43(3), 211–229.
Hohenwarter, J., Hohenwarter, M., & Lavicza, Z. (2008). Introducing dynamic mathematics software to secondary school teachers: The case of geogebra. Journal of Computers in Mathematics and Science Teaching, 28(2), 135–146.
Hohenwarter, M. (2014). GeoGebra. www.geogebra.org.
Kastberg, S., & Leatham, K. (2005). Research on graphing calculators at the secondary level: Implications for mathematics teacher education. Contemporary Issues in Technology and Teacher Education, Communication and Information, 5(1), 25–37.
Kay, A. (Producer). (1987). Doing with images makes symbols. The Distinguished Lecture Series: Industry Leaders in Computer Science. Retrieved from https://www.youtube.com/watch?v=0oonXT-gYjU.
Kemmis, S. (2011). A self-reflective practitioner and a new definition of critical participatory action research. In N. Mockler & J. Sachs (Eds.), Rethinking educational practice through reflexive inquiry (pp. 11–29). New York, NY: Springer.
Koehler, M. J., & Mishra, P. (2005). What happens when teachers design educational technology? The development of technological pedagogical content knowledge. Journal of Educational Computing Research, 32(2), 131–152.
Koehler, M. J., & Mishra, P. (2009). What is technological pedagogical content knowledge? Contemporary Issues in Technology and Teacher Education, 9(1), 60–70.
Koehler, M. J., & Mishra, P. (2015). Technological pedagogical content knowledge. In M. J. Spector (Ed.), The SAGE encyclopedia of educational technology (Vol. 2, pp. 782–785). Los Angeles, CA: SAGE.
Kuo, E., & Wieman, C. E. (2016). Toward instructional design principles: Inducing Faraday’s law with contrasting cases. Physical Review Physics Education Research, 12, 0101128.
Lasry, N. (2008). Clickers or flashcards: Is there really a difference? The Physics Teacher, 46(5), 242–244.
Lasry, N., Mazur, E., & Watkins, J. (2008). Peer instruction: From harvard to the two-year college. American Journal of Physics, 76(11), 1066–1069.
Let’s Talk Science. (2013). Spotlight on science learning: The high cost of dropping science and math. Retrieved from http://www.letstalkscience.ca/our-research/spotlight2013.html.
Lewis, S. (2014). The rise: Creativity, the gift of failure, and the search for mastery. New York, NY: Simon & Schuster.
Lingefjärd, T., & Ghosh, J. B. (2016). Learning mathematics as an interplay between internal and external representations. Far East Journal of Mathematical Education, 16(3), 271–297. http://dx.doi.org/10.17654/ME016030271.
Lockhart, P. (2009). A mathematician’s lament: How school cheats us out of our most fascinating and imaginative art form. New York, NY: Bellevue Literary Press.
Luft, J. A., & Hewson, P. W. (2014). Research on teacher professional development knowledge in science. In N. G. Lederman & S. K. Abel (Eds.), Handbook of research on science education (Vol. 2, pp. 889–909). New York, NY: Routledge.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and in the United States. New York, NY : Lawrence Erlbaum Associates, Inc.
Maciel, T. (2015). Smartphones in the classroom help students see inside the black box. APS News, 24(3), 5–6.
Martinovic, D., Karadag, Z., & McDougall, D. (Eds.). (2014). Proceedings of the fifth north american geogebra conference: Explorative learning with technology: GeoGebra-NA 2014. Toronto, Canada: University of Toronto.
Martinovic, D., & Manizade, A. G. (2014). Technology as a partner in geometry classrooms. The Electronic Journal of Mathematics and Technology, 8(2), 69–87.
Mazur, E. (1997a). Moving the mountain: Impediments to change. The Physics Teacher, 35, 1–4.
Mazur, E. (1997b). Peer instruction: User’s MANUAL. Upper Saddle River, NJ: Prentice Hall.
McDemott, L., Rosenquist, M. L., & van Zee, E. H. (1987). Student difficulties in connecting graphs and physics: Examples from kinematics. Americal Journal of Physics, 55(6), 503–513.
McQueen, H. A., Shields, C., Finnegan, D. J., Higham, J., & Simmen, M. W. (2014). PeerWise provides significant academic benefits to biological science students across diverse learning tasks, but with minimal instructor intervention. Biochemistry and Molecular Biology Education, 42(5), 371–381. https://doi.org/10.1002/bmb.20806.
Mesa, V. (2008). Solving problems on functions: Role of the graphing calculator. PNA, 2(3), 109–135.
Milner-Bolotin, M. (2009). Exploring scaling: From concept to applications. Science Education Review, 8, 70–77.
Milner-Bolotin, M. (2012). Increasing interactivity and authenticity of chemistry instruction through data acquisition systems and other technologies. Journal of Chemical Education, 89(4), 477–481.
Milner-Bolotin, M. (2014). Using PeerWise to promote student collaboration on design of conceptual multiple-choice questions. Physics in Canada, 70(3), 149–150.
Milner-Bolotin, M. (2015). Technology-enhanced teacher education for 21st century: Challenges and possibilities. In X. Ge, D. Ifenthaler, & J. M. Spector (Eds.), Emerging technologies for STEAM education (pp. 137–156). Basel, Switzerland: Springer International Publishing.
Milner-Bolotin, M. (2016a). Promoting deliberate pedagogical thinking with technology in physics teacher education: A teacher-educator’s journey. In T. G. Ryan & K. A. McLeod (Eds.), The physics educator: Tacit praxes and untold stories (pp. 112–141). Champaign, IL: Common Ground and The Learner.
Milner-Bolotin, M. (2016b). Rethinking technology-enhanced physics teacher education: From theory to practice. Canadian Journal of Science, Mathematics and Technology Education, 16(3), 284–295. https://doi.org/10.1080/14926156.2015.1119334.
Milner-Bolotin, M., Antimirova, T., & Petrov, A. (2010). Clickers beyond the first year science classroom. Journal of College Science Teaching, 40(2), 18–22.
Milner-Bolotin, M., Fisher, H., & MacDonald, A. (2013). Modeling active engagement pedagogy through classroom response systems in a physics teacher education course. LUMAT: Research and Practice in Math, Science and Technology Education, 1(5), 523–542.
Milner-Bolotin, M., & Nashon, S. (2012). The essence of student visual–spatial literacy and higher order thinking skills in undergraduate biology. Protoplasma, 249(1), 25–30. https://doi.org/10.1007/s00709-011-0346-6.
National Center for Education Statistics. (2011). Trends in international mathematics and science study. Retrieved from Washington, D.C. http://nces.ed.gov/timss/.
National Governors Association Center for Best Practices, & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Retrieved from Washington, D.C. http://www.corestandards.org/wp-content/uploads/Math_Standards1.pdf.
National Numeracy, U. K. (2016). Attitudes towards maths—Research and approach overview. Lewes, UK: National Numeracy.
O’Grady, K., Deussing, M.-A., Scerbina, T., Fung, K., & Muhe, N. (2016). Measuring up: Canadian results of the OECD PISA study: The performance of Canada’s youth in science, reading and mathematics (2015 First Results for Canadians Aged 15). Toronto, Canada: Council of Ministers of Education.
OECD. (2014). PISA 2012 Results: What students know and can do—Student performance in mathematics reading and science. Retrieved from http://www.oecd.org/pisa/keyfindings/pisa-2012-results.htm.
OECD. (2016a). PISA 2015 results: Excellence and equity in education (Vol. I). Paris, France: OECD Publishing.
OECD. (2016b). PISA 2015 results: Policies and practices for successful schools (Vol. II). Paris, France: OECD Publishing.
OECD. (2016c). School leadership for developing professional learning communities. Paris, France: OECD Publishing.
Paul, R., & Elder, L. (2007). Critical thinking: The art of socratic questioning. Journal of Developmental Education, 31(1), 36–37.
Perkins, K., Adams, W., Dubson, M., Finkelstein, N., Reid, S., Wieman, C., et al. (2006). PhET: Interactive simulations for teaching and learning physics. The Physics Teacher, 44(January), 18–23.
Ripley, A. (2013). The smartest kids in the world: And how they got that way. New York, NY: Simon and Schuster.
Rosenhouse, J. (2009). The monty hall problem: The remarkable story of math’s most contentious brain teaser. Oxford, UK: Oxford University Press.
Ruthven, K., Deaney, R., & Hennessy, S. (2009). Using graphing software to teach about algebraic forms: A study of technology-supported practice in secondary-school mathematics. Educational Studies in Mathematics, 71, 279–297.
Salvadori, M. (1980). Why buildings stand up: The strength of architecture. New York, NY: Norton & Company.
Schmidt, W. H., Blömeke, S., Tatto, M. T., Hsieh, F.-J., Cogan, L. S., Houang, R. T., et al. (2011). Teacher education matters: A study of middle school mathematics teacher preparation in six countries. New York, NY: Teachers College Press.
Schoenfeld, A. H. (2014). What makes for powerful classrooms, and how can we support teachers in creating them? A story of research and practice, productively intertwined. Educational Researcher, 43(8), 404–412.
Schuster, D., Undreiu, A., Adams, B., Brookes, D., & Milner-Bolotin, M. (2009). Motion-matching: A challenge game to generate motion concepts. The Physics Teacher, 47(7), 381–385.
Sfard, A. (2012). New clothes—and no emperor. For the Learning of Mathematics, 32(2, July), 2–4.
Shahrill, M. (2013). Review of effective teacher questioning in mathematics classrooms. International Journal of Humanities and Social Science, 3(17), 224–231.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from world’s teachers for improving education in the classroom. New-York, NY: The Free Press.
Tobias, S. (1993). Overcoming math anxiety: Revised and expanded. New York, NY: W.W. Norton and Company.
Troen, V., & Boles, K. C. (2003). Who’s teaching your children?: Why the teacher crisis is worse than you think and what can be done about it. New Haven, CT: Yale University Press.
UMass Donahue Institute Research and Evaluation Group. (2011). Increasing student interest in science, technology, engineering, and math (STEM): Massachusetts STEM pipeline fund programs using promising practices (M. D. o. H. Education, Trans.). Boston, MA: University of Massachusetts Donahue Institute. Retrieved from http://www.mass.edu/stem/documents/Student%20Interest%20Summary%20Report.pdf
USA National Research Council. (2013). Next generation science standards: For states, by states. Washington, D.C.: The National Academies Press.
Vernier-Technology. (2016). Logger pro (Version 3.6.1). Portland, OR: Vernier Technology. Retrieved from www.vernier.com.
Vickrey, T., Rosploch, K., Rahmanian, R., Pilarz, M., & Stains, M. (2015). Research-based implementation of peer instruction: A literature review. CBE—Life Science Education, 14(Spring), 1–11.
Watson, A., & Harel, G. (2013). The role of teachers’ knowledge of functions in their teaching: A conceptual approach with illustrations from two cases. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 154–168.
Wieman, C. E., Adams, W. K., Loeblein, P., & Perkins, K. K. (2010). Teaching physics using PhET simulations. The Physics Teacher, 48(April), 225–227.
Acknowledgements
The use of educational technologies in the courses described in this chapter became possible thanks to the support of the Teaching and Learning Enhancement Fund and the Faculty of Education at the University of British Columbia. We also would like to thank Davor Egersdorfer (a Teaching and Research Assistant for the project) for his contributions to the project and for providing valuable feedback on this chapter. In addition, we would like to acknowledge the book editors for their valuable, thoughtful and productive feedback on this chapter. Lastly, we would like to express our gratitude to the mathematics and science teacher-candidates at the University of British Columbia for their participation, feedback and encouragement for this project. Their enthusiasm for creative use of technology in mathematics and science education served the continuous motivation and inspiration for us .
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Milner-Bolotin, M. (2018). Nurturing Creativity in Future Mathematics Teachers Through Embracing Technology and Failure. In: Freiman, V., Tassell, J. (eds) Creativity and Technology in Mathematics Education. Mathematics Education in the Digital Era, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-72381-5_10
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