CHARACTERIZING STUDENT EXPERIENCE OF VARIATION WITHIN A STEM CONTEXT: IMPROVING CATAPULTS
Keywords:Statistics education research, Variation, Students’ experiences, Practice of statistics, STEM education, TinkerPlots
STEM learning experiences at the school level provide both opportunities and challenges for exploring students’ understanding of statistical concepts. This report focuses on data handling and informal inference embedded in a STEM context, that is, of testing, adjusting, and retesting catapults. In particular, the learning goal was for Grade 4 (aged 9–10 years) students to build on their developing understanding of variation while learning about the science topic of force as demonstrated by two configurations of catapults causing ping pong balls to be launched different distances. This report focuses on the students’ experiences of variation that were associated with the activity from a structural perspective during implementation. The analysis, employing various aspects of the Structure of Observed Learning Outcomes, points to the potential contribution of multimodal functioning in identifying and characterizing understanding of variation in a new context. The activity took place with 50 students in two classes with data collected from student workbooks. Results suggest that meaningful engagement with context can provide support for developing understanding of the concept of variation.
Ainley, J., Pratt, D., & Hansen, A. (2006). Connecting engagement and focus in pedagogic task design. British Educational Research Journal, 32(1), 23–38. https://doi.org/10.1080/01411920500401971
Australian Curriculum, Assessment and Reporting Authority. (2019). Australian Curriculum. https://www.australiancurriculum.edu.au/
Bargagliotti, A., Franklin, C., Arnold, P., Gould, R., Johnson, S., Perez, L., & Spangler, D.A. (2020). Pre-K-12 Guidelines for Assessment and Instruction in Statistics Education II (GAISE II). American Statistical Association and National Council of Teachers of Mathematics. https://www.amstat.org/asa/files/pdfs/GAISE/GAISEIIPreK-12_Full.pdf
Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of learning: The SOLO taxonomy. Academic Press.
Biggs, J., & Collis, K. (1989). Towards a model of school-based curriculum development and assessment using the SOLO taxonomy. Australian Journal of Education, 33(2), 151–163. https://doi.org/10.1177%2F168781408903300205
Biggs, J. B., & Collis, K. F. (1991). Multimodal learning and the quality of intelligent behaviour. In H. A. H. Rowe (Ed.), Intelligence: Reconceptualization and measurement (pp. 57–76). Lawrence Erlbaum.
Chick, H., Watson, J., & Fitzallen, N. (2018). “Plot 1 is all spread out and Plot 2 is all squished together”: Exemplifying statistical variation with young students. In J. Hunter, P. Perger, & L. Darragh (Eds.), Making waves, opening spaces. Proceedings of the 41st annual conference of the Mathematics Education Research Group of Australasia, Auckland, July 1–5 (pp. 218–225). https://merga.net.au/Public/Publications/Annual_Conference_Proceedings/2018-MERGA-CP.aspx
Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. American Mathematical Monthly, 104, 801–823. https://doi.org/10.1080/00029890.1997.11990723
Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13. https://doi.org/10.3102%2F0013189X032001009
Collis, K.F., & Romberg, T.A. (1991). Assessment of mathematical performance: An analysis of open-ended test items. In M.C. Wittrock & E.L. Baker (Eds.), Testing and cognition. Prentice Hall.
Creswell, J. W. (2013). Research design: Quantitative, qualitative and mixed method approaches (2nd ed.). SAGE Publications.
Engler, J. (2012, June 15). STEM education is the key to the U.S.’s economic future. U.S. News and World Report Civic. https://www.usnews.com/opinion/articles/2012/06/15/stem-education-is-the-key-to-the-uss-economic-future
English, L. D., Hudson, B., & Dawes, L. (2013). Engineering based problem solving in the middle school: Design and construction with simple machines. Journal of Pre-college Engineering Education Research, 3(2), 1–13. https://doi.org/10.7771/2157-9288.1081
Finzer, W. (2013). The data science education dilemma. Technology Innovations in Statistics Education, 7(2). http://escholarship.org/uc/item/7gv0q9dc#page-1
Fitzallen, N., & Watson, J. (2020). Using the practice of statistics to design students’ experiences in STEM. In B. Shelley, K. te Riele, N. Brown, & T. Crellin (Eds.), Harnessing the transformative power of education (pp. 74–99). Koninklijke Brill. http://dx.doi.org/10.1163/9789004417311
Fitzallen, N., Watson, J., Wright, S., & Duncan, B. (2018). Data representation in a STEM context: The performance of catapults. In M. A. Sorto & E. Paparistodemou (Eds.), Looking back, looking forward. Proceedings of the 10th International Conference on the Teaching of Statistics, Kyoto, Japan, July 8–14. https://iase-web.org/icots/10/proceedings/pdfs/ICOTS10_4B2.pdf?1531364264
Fitzgerald, M. (2001). Katapultos: Teaching basic statistics with ballistics. Tech Directions, 61(4), 20–23.
François, K., & Monteiro, C. (2018). Big data literacy. In M. A. Sorto & E. Paparistodemou (Eds.), Looking back, looking forward. Proceedings of the 10th International Conference on the Teaching of Statistics, Kyoto, Japan, July 8–14. International Statistical Institute. https://iase-web.org/icots/10/proceedings/pdfs/ICOTS10_7F1.pdf?1531364287
Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A pre-K-12 curriculum framework. American Statistical Association. http://www.amstat.org/education/gaise/
Green, D. (1993). Data analysis: What research do we need? In L. Pereira-Mendoza (Ed.), Introducing data analysis in the schools: Who should teach it? (pp. 219-239). International Statistical Institute.
Groth, R. E., Austin, J. W., Naumann, M., & Rickards, M. (2021). Toward a theoretical structure to characterize early probabilistic thinking. Mathematics Education Research Journal, 33, 241-261. https://doi.org/10.1007/s13394-019-00287-w
Jacobbe, T. (2012). Elementary school teachers’ understanding of the mean and median. International Journal of Science and Mathematics Education, 10, 1143–1161. https://doi.org/10.1007/s10763-011-9321-0
Kader, G., & Mamer, J. (2008). Statistics in the middle grades: Understanding center and spread. Teaching Mathematics in the Middle School, 14(1), 38–43. https://doi.org/10.5951/MTMS.14.1.0038
Konold, C., & Miller, C. D. (2015). TinkerPlots: Dynamic data exploration. [Computer software, Version 2.3.2]. Learn Troop.
Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105. http://iase-web.org/documents/SERJ/SERJ8(1)_Makar_Rubin.pdf
Moore, D. S. (1990). Uncertainty. In L. A. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 95–137). National Academy Press. https://doi.org/10.17226/1532
Moore, D. S., & McCabe, G. P. (1989). Introduction to the practice of statistics. W. H. Freeman.
National Research Council. (2013). Next generation science standards: For states, by states. National Academy Press. https://doi.org/10.17226/18290
Noll, J., & Shaughnessy, J. M. (2012). Aspects of students’ reasoning about variation in empirical sampling distributions. Journal for Research in Mathematics Education, 43(5), 509–556. https://doi.org/10.5951/jresematheduc.43.5.0509
Office of the Chief Scientist. (2013). Science, technology, engineering and mathematics in the national interest: A strategic approach. Australian Government.
Petrosino, A. J., Lehrer, R., & Schauble, L. (2003). Structuring error and experimental variation as distribution in the fourth grade. Mathematical Thinking and Learning, 5(2&3), 131–156. https://doi.org/10.1080/10986065.2003.9679997
Reading, C. (2004). Student description of variation while working with weather data. Statistical Education Research Journal, 3(2), 84–105. https://iase-web.org/documents/SERJ/SERJ3(2)_Reading.pdf?1402525005
Ridgway, J., Ridgway, R., & Nicholson, J. (2018). Data Science for all: A stroll in the foothills. In M. A. Sorto & E. Paparistodemou (Eds.), Looking back, looking forward. Proceedings of the 10th International Conference on the Teaching of Statistics, Kyoto, Japan, July 8–14. https://iase-web.org/icots/10/proceedings/pdfs/ICOTS10_3A1.pdf?1531364253
Shaughnessy, J. M. (1997). Missed opportunities in research on the teaching and learning of data and chance. In F. Biddulph & K. Carr (Eds.), People in mathematics education. Proceedings of the 20th annual Conference of the Mathematics Education Research Group of Australasia, Aotearoa (Vol. 1, pp. 6–22). https://www2.merga.net.au/documents/Keynote_Shaughnessy_1997.pdf
Shaughnessy, J. M., Watson, J., Moritz, J., & Reading, C. (1999, April). School mathematics students’ acknowledgment 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.
Surles, W., Crosby, J., McNeil, J., Zarske, M. S., & Samson, C. (2011). Launch into learning: Catapults! College of Engineering and Applied Science, University of Colorado. https://www.teachengineering.org/lessons/view/cub_catapult_lesson01
Watson, J. M. (2005). Variation and expectation as foundations for the chance and data curriculum. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce & A. Roche (Eds.), Building connections: Theory, research and practice. Proceedings of the 28th Annual Conference of the Mathematics Education Research Group of Australasia, Melbourne (pp. 35–42). MERGA.
Watson, J.M. (2007). Inference as prediction. Australian Mathematics Teacher, 63(1), 6–11.
Watson, J.M. (2009). The development of statistical understanding at the elementary school level. Mediterranean Journal for Research in Mathematics Education, 8(1), 89–109.
Watson, J.M., & Callingham, R.A. (2003). Statistical literacy: A complex hierarchical construct. Statistics Education Research Journal, 2(2), 3–46. http://iase-web.org/documents/SERJ/SERJ2(2)_Watson_Callingham.pdf
Watson, J.M., Callingham, R.A., & Kelly, B.A. (2007). Students’ appreciation of expectation and variation as a foundation for statistical understanding. Mathematical Thinking and Learning, 9, 83–130. https://doi.org/10.1080/10986060709336812
Watson, J. M., Campbell, K. J., & Collis, K. F. (1993). Multimodal functioning in understanding fractions. Journal of Mathematical Behavior, 12(1), 45–62.
Watson, J. M., & Collis, K. F. (1994). Multimodal functioning in understanding chance and data concepts. In J. P. da Ponte & J. F. Matos (Eds.), Proceedings of the Eighteenth International Conference for the Psychology of Mathematics Education, Lisbon (Vol. 4, pp. 369–376).
Watson, J. M., Collis, K. F., Callingham, R. A., & Moritz, J. B. (1995). A model for assessing higher order thinking in statistics. Educational Research and Evaluation, 1(3), 247–275. https://doi.org/10.1080/1380361950010303
Watson, J.M., Collis, K.F., & Moritz, J.B. (1997). The development of chance measurement. Mathematics Education Research Journal, 9, 60–82. http://dx.doi.org/10.1007/BF03217125
Watson, J., Fitzallen, N., & Chick, H. (2020a). What is the role of statistics in integrating STEM education? In J. Anderson & Y. Li (Eds.), Integrated approaches to STEM education: An international perspective (pp. 91–116). Springer. https://doi.org/10.26181/601cd997becd5
Watson, J., Fitzallen, N., English, L., & Wright, S. (2020b). Introducing statistical variation in year 3 in a STEM context: Manufacturing licorice. International Journal of Mathematical Education in Science and Technology, 51(3), 354–387. https//doi.org/10.1080/0020739X.2018.1562117
Watson, J., Fitzallen, N., Fielding-Wells, J., & Madden, S. (2018). The practice of statistics. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 105–137). Springer. https://doi.org/10.1007/978-3-319-66195-7_4
Watson, J. M., & Kelly, B. A. (2002a). Can grade 3 students learn about variation? In B. Phillips (Ed.), Developing a statistically literate society. Proceedings of the Sixth International Conference on Teaching Statistics, Cape Town. International Statistical Institute. https://iase-web.org/documents/papers/icots6/2a1_wats.pdf?1402524960
Watson, J. M., & Kelly, B. A. (2002b). Grade 5 students’ appreciation of variation. In A. Cockburn & E. Nardi (Eds), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education, Norwich, July 21–26 (Vol. 4, pp. 385–392). University of East Anglia.
Watson, J. M., & Kelly, B. A. (2002c). Variation as part of chance and data in grades 7 and 9. In B. Barton, K.C. Irwin, M. Pfannkuch, & M. O. J. Thomas (Eds.), Mathematics education in the South Pacific. Proceedings of the 25th Annual Conference of the Mathematics Education Research Group of Australasia, Auckland (Vol. 2, pp. 682–289). MERGA.
Watson, J. M., & Kelly, B. A. (2004). Statistical variation in a chance setting: A two-year study. Educational Studies in Mathematics, 57, 121–144. https://doi.org/10.1023/B:EDUC.0000047053.96987.5f
Watson, J. M., & Kelly, B. A. (2005). The winds are variable: Student intuitions about variation School Science and Mathematics, 105(5), 252–269. https://doi.org/10.1111/j.1949-8594.2005.tb18165.x
Watson, J. M., Kelly, B. A., Callingham, R. A., & Shaughnessy, J. M. (2003). The measurement of school students’ understanding of statistical variation. International Journal of Mathematical Education in Science and Technology, 34(1), 1–29. https://doi.org/10.1080/0020739021000018791
Watson, J.M., & Moritz, J.B. (1998). Longitudinal development of chance measurement. Mathematics Education Research Journal, 10(2), 103–127.
Watson, J.M., & Moritz, J.B. (2001). Development of reasoning associated with pictographs: representing, interpreting, and predicting. Educational Studies in Mathematics, 48, 47–81. https://doi.org/10.1023/A:1015594414565
Wild, C. (2006). The concept of distribution. Statistics Education Research Journal, 5(2), 10–26. http://iase-web.org/documents/SERJ/SERJ5(2)_Wild.pdf