# Preparing Teachers to Use Excelets: Developing Creative Modeling Experiences for Secondary Mathematics Students

## Abstract

There are many challenges in preparing mathematics teachers for today’s classrooms including content, pedagogy, technology, and creativity. This qualitative study was designed to examine how pre-service mathematics teachers solve modeling tasks using Excelets, an interactive form of an Excel spreadsheet that allows for the manipulation of data and the visualization of changes in numeric, graphic, and symbolic form (Sinex in Developer’s guide to Excelets: dynamic and interactive visualization with “Javaless” applets or interactive Excel spreadsheets, 2005). Specific emphasis was given to how such experiences translate into providing creative learning environments in future teaching. The study focused on four specific participants and analyzed their Technological Pedagogical Content Knowledge (TPACK) scores (AMTE, 2009), “think-alouds”, and written work to assess their understanding of modeling tasks that integrated technology as a tool for learning. Top-tier participants demonstrated abilities to recognize, accept, adapt, and explore mathematics creatively when using and integrating mathematical modeling tools while bottom-tier participants failed to exhibit these skills. Top-tier participants demonstrated high levels of creativity and TPACK yet rated themselves low in these skills while bottom-tier participants provided little creativity and TPACK yet rated themselves extremely high. These results indicate that there is more work to be done in preparing teachers to provide students with stimulating mathematics problems and explorations while scaffolding their integration of technological tools such as Excel.

## Keywords

Secondary preservice teachers Modeling Creativity Excelets TPACK## References

- Abramovich, S. (1995). Technology-motivated teaching of advanced topics in discrete mathematics.
*Journal of Computers in Mathematics and Science Teaching,**14*(3), 391–418.Google Scholar - Applebaum, M., & Saul, M. (2009). Anecdotes and assertions about creativity in the working mathematics classroom. In R. Leikin et al. (Eds.),
*Creativity in mathematics and the education of gifted students*(pp. 271–284). Rotterdam, The Netherlands: Sense Publishers.Google Scholar - Arganbright, D. (2005). Developing mathematics creativity with spreadsheets.
*Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education,**9*(3), 187–201.Google Scholar - Association of Mathematics Teacher Educators. (2006).
*Preparing teachers to use technology to enhance the learning of mathematics: A position of the association of mathematics teacher educators*. San Diego, CA: Author.Google Scholar - Association of Mathematics Teacher Educators. (2009).
*Mathematics TPACK (Technological Pedagogical Content Knowledge) Framework*. San Diego, CA: Author.Google Scholar - Ball, D., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide?
*American Educator,**29*(3), 14–22.Google Scholar - Beck, J. A., & Wynn, H. C. (1998).
*Technology in teacher education: Progress along the continuum.*ERIC Document Reproduction No. ED 424 212.Google Scholar - Bolden, D. S., Harries, A. V., & Newton, D. P. (2010). Pre-service primary teachers’ conceptions of creativity in mathematics.
*Educational Studies in Mathematics,**73*(2), 143–157.CrossRefGoogle Scholar - Borko, H., & Putnam, R. T. (1996). Learning to teach. In D. C. Berliner & R. C. Calfee (Eds.),
*Handbook of educational psychology*(pp. 673–708). New York, NY: Macmillan.Google Scholar - Brown, P. S., & Gould, J. D. (1987). An experimental study of people creating spreadsheets.
*ACM Transactions on Office Information Systems,**5*(3), 258–272.CrossRefGoogle Scholar - Conference Board of the Mathematical Sciences. (2001).
*The mathematical education of teachers*. Providence, RI American Mathematical Society. Washington D.C.: Mathematical Association of America.CrossRefGoogle Scholar - Conference Board of the Mathematical Sciences. (2012).
*The mathematical education of teachers II*. Providence, RI: American Mathematical Society. Washington D.C.: Mathematical Association of America.CrossRefGoogle Scholar - Davis, G. A., & Rimm, S. B. (2004).
*Education of the gifted and talented*(5th ed.). Boston, MA: Pearson Education Press.Google Scholar - Doerr, H. M. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum et al. (Eds.),
*Modelling and applications in mathematics education: The 14th ICMI study*(pp. 69–78). New York, NY: Springer.CrossRefGoogle Scholar - Drier, H. S. (2001). Teaching and learning mathematics with interactive spreadsheets.
*School Science and Mathematics,**10*(4), 170–179.CrossRefGoogle Scholar - Fischer, G., & Nakakoji, K. (1994). Amplifying designers’ creativity with domain-oriented design environments. In T. Dartnall (Ed.),
*Artificial intelligence and creativity, Part V*(pp. 343–364). Dordrecht, The Netherlands: Kluwer Academic Publishers.CrossRefGoogle Scholar - Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking “pedagogical content knowledge”: Conceptualizing and measuring teachers’ topic-specific knowledge of students.
*Journal for Research in Mathematics Education,**39*(4), 372–400.Google Scholar - Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement.
*American Educational Research Journal,**42*(2), 371–406.CrossRefGoogle Scholar - International Society for Technology in Education. (2008).
*National educational technology standards for teachers.*Retrieved from http://www.iste.org/standards/standards/standards-for-teachers. - Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman, & B. Koichu (Eds.),
*Creativity in mathematics and the education of gifted students*(pp. 129–145). Rotterdam, The Netherlands: Sense Publishers.Google Scholar - Lev-Zamir, H. (2008). Can an algorithm be a way to elevate the development of creativity in mathematics teachers? In R. Leikin (Ed.),
*Proceedings of the 5th International Conference on Creativity in Mathematics and the Education of Gifted Students*(pp. 444–446). Haifa, Israel.Google Scholar - Lin, Y. S. (2011). Fostering creativity through education: A conceptual framework of creative pedagogy.
*Creative Education,**2*(3), 149–155.CrossRefGoogle Scholar - Lortie, D. C. (1975).
*School teacher: A sociological study*. Chicago, IL: University of Chicago Press.Google Scholar - Mann, E. (2006). Creativity: The essence of mathematics.
*Journal for the Education of the Gifted,**30*(2), 236–260.CrossRefGoogle Scholar - Martin, T. S. (Ed.). (2007).
*Mathematics teaching today: Improving practice, improving student learning*. Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Milgram, R., & Hong, E. (2009). Talent loss in mathematics: Causes and solutions. In R. Leikin, A. Berman, & B. Koichu (Eds.),
*Creativity in mathematics and the education of gifted students*(pp. 149–163). Rotterdam, The Netherlands: Sense Publishers.Google Scholar - Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge.
*Teachers College Record,**108*(6), 1017–1054.CrossRefGoogle Scholar - National Governors Association Center for Best Practices, Council of Chief State School Officers. (2010).
*Common core state standards (Mathematics)*. Washington, D.C.: National Governors Association Center for Best Practices, Council of Chief State School Officers. Retrieved from http://www.corestandards.org/Math/ - Niess, M. L. (2005). Preparing teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge.
*Teaching and Teacher Education,**21,*509–523.CrossRefGoogle Scholar - Niess, M. L. (2008). Knowledge needed for teaching with technologies—Call it TPACK.
*AMTE Connections,**17*(2), 9–10.Google Scholar - Niess, M. L., Sadri, P., & Lee, K. H. (2007).
*Dynamic spreadsheets as learning technology tools: Developing teachers’ technology pedagogical content knowledge (TPCK)*. Paper Presented at the Meeting of the American Educational Research Association Annual Conference, Chicago, IL.Google Scholar - Niess, M. L., Ronau, R. N., Shafer, K. G., Driskell, S. O., Harper, S. R., Johnston, C., et al. (2009). Mathematics teacher TPACK standards and development model.
*Contemporary Issues in Technology and Teacher Education,**9*(1), 4–24.Google Scholar - Pead, D., & Ralph, B. (with Muller, E.). (2007). Uses of technologies in learning mathematics through modelling. In W. Blum et al. (Eds.),
*Modelling and applications in mathematics education: The 14th ICMI study*(pp. 309–318). New York, NY: Springer.Google Scholar - Polly, D., Mims, C., Shepherd, C. E., & Inan, F. (2010). Evidence of impact: Transforming teacher education with preparing tomorrow’s teachers to teach with technology (PT3) grants.
*Teaching and Teacher Education,**26,*863–870.CrossRefGoogle Scholar - Safuanov, I. S. (2008). Fostering creativity of prospective teachers in Tatarstan. In R. Leikin (Ed.),
*Proceedings of the 5th international conference on creativity in mathematics and the education of gifted students*(pp. 449–451). Haifa, Israel.Google Scholar - Shriki, A. (2009). Developing prospective teachers’ awareness of mathematical creativity through generating new concepts.
*Educational Studies in Mathematics,**73*(2), 159–179.CrossRefGoogle Scholar - Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching.
*Educational Researcher,**15*(2), 4–14.CrossRefGoogle Scholar - Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing.
*ZDM—The International Journal on Mathematics Education,**29*(3), 75–80.CrossRefGoogle Scholar - Sinex, S. A. (2005).
*Developer’s guide to Excelets: Dynamic and interactive visualization with “Javaless” applets or interactive excel spreadsheets*. Retrieved from http://academic.pgcc.edu/~ssinex/excelets. - Sinex, S. A. (2006).
*Exploring cyclic data in nature*. Retrieved from http://academic.pgcc.edu/~ssinex/excelets/periodic_data.xls. - Sinex, S. A. (2011a).
*Cookies stack*. Retrieved from http://academic.pgcc.edu/~ssinex/cookies_stack.xls. - Sinex, S. A. (2011b
*). Investigating the height of a stack of cookies*. Retrieved from http://academic.pgcc.edu/~ssinex/cast/cookies_stack.pdf. - Sinex, S. A. (2011c).
*Kinetics of cancer cell growth*. Retrieved from http://academic.pgcc.edu/~ssinex/excelets/Kinetics_cancer_cells.xls. - Sinex, S. A. (2012).
*What are the odds? Using probably in mathematical models*. Retrieved from http://academic.pgcc.edu/~ssinex/excelets/Probability.xls. - Subotnik, R. F., Pillmeier, E., & Jarvin, L. (2009). The psychosocial dimensions of creativity in mathematics: Implications for gifted education policy. In R. Leikin, A. Berman, & B. Koichu (Eds.),
*Creativity in mathematics and the education of gifted students*(pp. 165–179). Rotterdam, The Netherlands: Sense Publishers.Google Scholar - Thomas, M. O. J., & Palmer, J. M. (2014). Teaching with digital technology: Obstacles and opportunities. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.),
*The mathematics teacher in the digital era*(pp. 71–89). Dordrecht, the Netherlands: Springer.CrossRefGoogle Scholar - Thompson, A. D., & Mishra, P. (2007). Breaking news: TPCK becomes TPACK!
*Journal of Computing in Teacher Education,**24*(2), 38–64.Google Scholar - Yerushalmy, M. (2009). Educational technology and curricular design: Promoting mathematical creativity for all students. In R. Leikin, A. Berman, & B. Koichu (Eds.),
*Creativity in mathematics and the education of gifted students*(pp. 101–113). Rotterdam, The Netherlands: Sense Publishers.Google Scholar - Zelkowski, J., Gleason, J., Cox, D. C., & Bismarck, S. (2013). Developing and validating a reliable TPACK instrument for secondary mathematics preservice teachers.
*Journal of Research on Technology in Education,**46*(2), 173–206.CrossRefGoogle Scholar