Designing Interactive Dynamic Technology Activities to Support the Development of Conceptual Understanding
Technology can make a difference in teaching and learning mathematics when it serves as a vehicle for learning and not just as a tool to crunch numbers and to draw graphs. This paper discusses a technology leveraged program to develop student understanding of core mathematical concepts. A sequence of applet-like dynamically linked documents allows students to take a meaningful mathematical action, immediately see the consequences, and then reflect on those consequences in content areas associated with the middle grades U.S. Common Core State Standards. The materials are based on the research literature about student learning, in particular enabling students to confront typical misconceptions, and designed to support carefully thought out mathematical progressions within and across the grades.
KeywordsConceptual understanding Learning progressions Interactive dynamic technology Action consequence principle
I wish to thank Thomas Dick and Wade Ellis, my collaborators on Building Concepts, Becky Byer, who develops all of the interactive dynamic files and Dan Ilaria, for his comments on the manuscript and support for the project.
- Baumgartner, L.M. (2001). An update on transformational learning. In S.B. Merriam (Ed.), New directions for adult and continuing education: No. 89. The new update on adult learning theory (pp. 15–24). San Francisco: Jossey-Bass.Google Scholar
- Ben-Zvi, D., & Friedlander, A. (1997). Statistical thinking in a technological environment. In J. B. Garfield & G. Burrill (Eds.), Research on the role of technology in teaching and learning statistics (pp. 45–55). Voorburg: International Statistical Institute.Google Scholar
- Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80(2), 139–144.Google Scholar
- Budgett, S., Pfannkuch, M., Regan, M., & Wild, C. (2013). Dynamic visualizations and the randomization test. Technology Innovations in Statistics Education, 7(2).Google Scholar
- Building Concepts: Fractions (2014). Texas Instruments Education Technology. http://education.ti.com/en/us/home.
- Building Concepts: Ratios and Proportional Relationships (2015). Texas Instruments Education Technology. http://education.ti.com/en/us/home.
- Building Concepts: Statistics and Probability (2016). Texas Instruments Education Technology. http://education.ti.com/en/us/home.
- Burrill, G., & Dick, T. (2008). What state assessments tell us about student achievement in algebra. Paper presented at National Council of Teachers of Mathematics 2008 Research Presession, Salt Lake City UT.Google Scholar
- Chance, B., Ben-Zvi, D., Garfield, J., & Medina, E. (2007). The role of technology in improving student learning in statistics. Technology Innovations in Statistics Education 1, 1–26. Retrieved from http://eschlarship.org/uc/item/8sd2t4rr.
- Common Core State Standards (2010). College and career standards for mathematics. Council of Chief State School Officers (CCSSO) and National Governor’s Association (NGA).Google Scholar
- Cranton, P. (2002). Teaching for transformation. In J. M. Ross-Gordon (Ed.), New directions for adult and continuing education: No. 93. Contemporary viewpoints on teaching adults effectively (pp. 63–71). San Francisco: Jossey-Bas.Google Scholar
- del Mas, R., Garfield, J., & Chance, B. (1999) A model of classroom research in action: Developing simulation activities to improve students’ statistical reasoning. Journal of Statistics Education, 7(3), www.amstat.org/publications/jse/secure/v7n3/delmas.cfm.
- Dick, T. (2008). Tackling tough to learn/ tough to teach mathematics: A conceptual framework. Unpublished paper prepared for Designing Professional Development Experiences Using Interactive Dynamic Technology.Google Scholar
- Dick, T., & Burrill, G. (2009). Shaping teacher attitudes toward technology from “tools for doing” to “tools for learning”. Presentation at the Association of Mathematics Teacher Educators, Orlando, FL.Google Scholar
- Drijvers, P. (2012). Digital technology in mathematics education: Why it works (or doesn’t). Paper presented for Technology Topic Study Group at the Twelfth International Congress on Mathematical Education, Seoul, Korea.Google Scholar
- Empson, S., & Knudsen, J. (2003). Building on children’s thinking to develop proportional reasoning. Texas Mathematics Teacher, 2, 16–21.Google Scholar
- Fazio, L. K., Thompson, C. A., & Siegler, R. S. (2012, November). Relations of symbolic and non-symbolic fraction and whole number magnitude representations to each other and to mathematics achievement. Talk presented at the Annual Meeting of the Psychonomic Society, Minneapolis, MN.Google Scholar
- Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., et al. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A preK–12 curriculum framework. Alexandria, VA: American Statistical Association.Google Scholar
- Ginsburg, A., & Leinwand, S. (2009). Informing grades 1–6 mathematics standards development: What can be learned from high performing Hong Kong, Korea and Singapore. Washington DC: American Institutes for Research.Google Scholar
- Gould, R. (2011). Statistics and the modern student. Department of statistics papers. Department of Statistics, University of California Los Angeles.Google Scholar
- Heid, M. K. (1995). The interplay of mathematical understanding, facility with a computer algebra program, and the learning of mathematics. In Proceedings of the 17th Annual Meeting of the North American Chapter of PME (pp. 221–225). Columbus: Program Committee.Google Scholar
- Hodgson, T. (1996). The effects of hands-on activities on students’ understanding of selected statistical concepts. In E. Jakbowski, D. Watkins & H. Biske (Eds.), Proceedings of the Eighteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 241–246). ERIC Clearing House for Science, Mathematics, and Environmental Education.Google Scholar
- Japanese Ministry of Education (MoE) (2008). Elementary School Teaching Guide for the Japanese Course of Study: Mathematics.Google Scholar
- 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, 5(1), 25–37.Google Scholar
- Kennedy, M. M. (1991). Policy issues in teacher education. Phi Delta Kappan, 72, 658–665.Google Scholar
- Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up. Washington DC: National Research Council, National Academy Press.Google Scholar
- Kolb, D. (1984). Experiential learning: Experience as the source of learning and development. Englewood Cliffs: Prentice-Hall.Google Scholar
- Lamon, S. (1999). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Hillsdale: Erlbaum.Google Scholar
- Lamon, S. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–667). Charlotte: Information Age Publishing.Google Scholar
- Lane, D. M., & Peres, S. C. (2006). Interactive simulations in the teaching of statistics: Promise and pitfalls. In A. Rossman and B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics [CD-ROM]. Voorburg: International Statistical Institute.Google Scholar
- Mack, N. K. (1995). Critical ideas, informal knowledge, and understanding fractions. In J. T. Sowder & B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 67–84). Albany: SUNY Press.Google Scholar
- Mathematics Education of Teachers II (2012). Conference Board of the Mathematical Sciences. Providence, Washington DC: American Mathematical Society, Mathematical Association of America.Google Scholar
- Mezirow, J. (1997). Transformative learning: Theory to practice. In P. Cranton (Ed.), New directions for adult and continuing education: No. 74. Transformative learning in action: Insights from practice (pp. 5–12). San Francisco: Jossey-Bass.Google Scholar
- Mezirow, J. (2000). Learning to think like an adult: Core concepts of transformation theory. In J. Mezirow & Associates (Eds.), Learning as transformation: Critical perspectives on a theory in progress (pp. 3–34). San Francisco: Jossey-Bass.Google Scholar
- Michael, J., & Modell, H., 2003. Active learning in secondary and college science classrooms: A working model of helping the learning to learn. Mahwah: Erlbaum http://nces.ed.gov/nationsreportcard/itmrlsx/search.aspx?subject=mathematics.
- National Research Council (1999). In J. D. Bransford, A. L. Brown & R. R. Cocking (Eds.), How people learn: brain, mind, experience, and school. Washington, DC: National Academy Press.Google Scholar
- National Research Council (2012). In S. Singer, N. Nielsen & H. Schweingruber (Eds.), Discipline-based education research: Understanding and improving learning in undergraduate science and engineering. Washington, DC: The National Academies Press.Google Scholar
- Progressions for the Common Core Standards in Mathematics (2011). Draft 3–5 Progression on Number and Operations—Fractions; Draft 6–8 Progression on Statistics and Probability; Draft 6–8 Progression on Expressions and Equations; Draft 6–7 Progression on Ratios and Proportional Relationships Common Core State Standards Writing Team. Retrieved January 15, 2015 from http://ime.math.arizona.edu/progressions/.
- Roschelle, J., Shechtman, N., Tatar, D., Hegedus, S., Hopkins, B., Empson, S., et al. (2010). Integration of technology, curriculum, and professional development for advancing middle school mathematics: Three large-scale studies. American Educational Research Journal, 47(4), 833–878.CrossRefGoogle Scholar
- Sacristan, A., Calder, N., Rojano, T., Santos-Trigo, M., Friedlander, A., & Meissner, H. (2010). The influence and shaping of digital technologies on the learning—and learning trajectories—of mathematical concepts. In C. Hoyles & J. Lagrange (Eds.), Mathematics education and technology—rethinking the terrain: The 17th ICMI study (pp. 179–226). New York: Springer.Google Scholar
- Schwier, R. A., & Misanchuk, E. R. (1993). Interactive multimedia instruction (Chap. 9, pp. 155–192). Englewood Cliffs: Educational Technology Publications.Google Scholar
- Shaughnessy, J. M., Watson, J., Moritz, J., & Reading, C. (1999). School mathematics students’ acknowledgement of statistical variation. In C. Maher (Chair), There’s More to Life than Centers. Presession Research Symposium, 77th Annual National Council of Teachers of Mathematics Conference, San Francisco, CA.Google Scholar
- Siegler, R. S., & Pyke, A. A. (2012). Developmental and individual differences in understanding of fractions. Developmental Psychology. Advance online publication. doi: 10.1037/a0031200.
- Sowder, J. T. (1992). Estimation and number sense. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 371–389). New York: Macmillan.Google Scholar
- Statkey (2012). Lock, R., Lock, P., Lock, K., Lock, E., & Lock, D. Companion materials for Statistics: Unlocking the power of data. www.lock5stat.com/statkey/sampling_1_cat/sampling_1_cat.html.
- Suh, J. M. (2010). Tech-knowledgy for diverse learners [Technology Focus Issue]. Mathematics Teaching in the Middle School, 15(8), 440–447.Google Scholar
- Suh, J., & Moyer, P. S. (2007). Developing students’ representational fluency using virtual and physical algebra balances. Journal of Computers in Mathematics and Science Teaching, 26(2), 155–173.Google Scholar
- Thompson, P. (2002). Didactic objects and didactic models in radical constructivism. In K. Gravemeijer, R. Lehrer, B.v Oers, & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 191–212). Dordrecht: Kluwer Academic.Google Scholar
- Zehavi, N., & Mann, G. (2003). Task design in a CAS environment: Introducing (In) equations. In J. Fey, A. Cuoco, C. Kieran, L. McMullin, & R. Zbiek (Eds.), Computer algebra systems in secondary school mathematics education (pp. 173–191). Reston: NCTM.Google Scholar
- Zull, J. (2002). The art of changing the brain: Enriching the practice of teaching by exploring the biology of learning. Alexandria: Association for Supervision and Curriculum Development.Google Scholar