Examination of technology-enhanced statistical problem-solving tasks designed by pre-service teachers
Keywords:task design, technology, pre-service teachers, statistical problem solving
In this study, technology-enhanced statistical problem-solving tasks designed by pre-service teachers (PTs) were examined. The PTs designed 28 tasks. The designed tasks were analyzed within the context of the Considerations for Design and Implementation of Statistics Tasks (C-DIST) components. It was revealed that the tasks were mostly designed within the framework of the learning goal of “statistical questions-making interpretations based on the measures that serve to represent the data and the forms of representation” and that mostly real, multivariate and large data sets were used. In addition, it was observed that the context was employed in order to complete the prepared tasks and the tasks mostly included the entire investigation cycle. It was determined that the prepared tasks were mostly at Level B, followed by the tasks at Level A and Level C. In light of the results obtained, inferences were made for preparing PTs to teach statistics.
Australian Curriculum, Assessment and Reporting Authority (ACARA) (2015) Australian curricu-lum: Mathematics: Sequence of content. https://australiancurriculum.edu.au/media/3680/mathematics_-_sequence_of_content.pdf
Bakogianni, D. (2015). Studying the process of transforming a statistical inquiry-based task in the context of a teacher study group. In K. Krainer & N. Vondrova (Eds.), Proceedings of the 9th Conference of the European Society for Research in Mathematics Education (CERME9). (pp. 615–621). Charles University.
Balcı, M. (2023). Teaching statistics in middle school mathematics: Investigation of the curricu-lum and course materials. [Unpublished master dissertation]. Hacettepe University.
Bargagliotti, A., Franklin, C., Arnold, P., Gould, R., Johnson, S., Perez, L., & Spangler, D. (2020). Pre-K-12 Guidelines for Assessment and Instruction in Statistics Education (GAISE) report II. VA: American Statistical Association.
Batur, A., Özmen, Z. M., Topan, B., Akoğlu, K., & Güven, B. (2021). A cross-national comparison of statistics curricula. Turkish Journal of Computer and Mathematics Education (TUR-COMAT), 12(1), 290–319. https://doi.org/10.16949/turkbilmat.793285 DOI: https://doi.org/10.17762/turcomat.v12i1.278
Ben-Zvi, D. (2011). Statistical reasoning learning environment. Revista de Educação Matemática e Tecnológica Iberoamericana, 2, 1–13. https://doi.org/10.36397/emteia.v2i2.2152.
Boaler, J., & Levitt, S. (2019, October 23). Modern high school math should be about data science-not Algebra 2. Los Angeles Times. https://www.latimes.com/opinion/story/2019-10-23/math-high-school-algebra-data-statistics
Braswell, J. S., Dion, G. S., Daane, M. C., & Jin, Y. (2005). The Nation’s Report Card [TM]: Mathematics, 2003. NCES 2005-451. National Center for Education Statistics.
Burgess, T. (2007). Investigating the nature of teacher knowledge needed and used in teaching statistics. [Unpublished doctoral dissertation]. Massey University.
Burgess, T. A. (2011). Teacher knowledge of and for statistical investigations. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics – Challenges for teaching and teacher education (pp. 259–270). Springer. DOI: https://doi.org/10.1007/978-94-007-1131-0_26
Carver, R., Everson, M., Gabrosek, J., Horton, N., Lock, R., Mocko, M., ... & Wood, B. (2016). Guidelines for Assessment and Instruction in Statistics Education (GAISE) college report 2016. American Statistical Association.
Casey, S. A., Harrison, T., & Hudson, R. (2021). Characteristics of statistical investigations tasks created by preservice teachers. Investigations in Mathematics Learning, 13(4), 303–322. https://doi.org/10.1080/19477503.2021.1990659 DOI: https://doi.org/10.1080/19477503.2021.1990659
Casey, S., Hudson, R., Harrison, T., Barker, H. & Draper, J. (2020). Preservice Teachers’ Design of Technology-Enhanced Statistical Tasks. Contemporary Issues in Technology and Teacher Education, 20(2), 269–292.
Casey, S. A., & Wasserman, N. H. (2015). Teachers’ knowledge about informal line of best fit. Statistics Education Research Journal, 14(1), 8–35. DOI: https://doi.org/10.52041/serj.v14i1.267
Chick, H., & Beswick, K. (2018). Teaching teachers to teach Boris: A framework for mathematics teacher educator pedagogical content knowledge. Journal of Mathematics Teacher Educa-tion 21(5), 475–499. https://doi.org/10.1007/s10857-016-9362-y DOI: https://doi.org/10.1007/s10857-016-9362-y
Chick, H. L. & Pierce, R. U. (2008). Teaching statistics at the primary school level: Beliefs, af-fordances, and pedagogical content knowledge. In C. Batanero, G. Burrill, C. Reading & A. Rossman (Eds.), Joint ICMI/IASE study: Teaching statistics in School mathematics. Chal-lenges for teaching and teacher education. Proceedings of the ICMI Study 18 and 2008 IASE round table conference. ICMI/IASE. DOI: https://doi.org/10.52041/SRAP.08303
Cobb, P & McClain, K. (2004). Principles of Instructional design for supporting the development of students’ statistical reasoning, In D Ben-Zvi & J. Garfield (Ed.) The challenge of develop-ing statistical literacy, reasoning and thinking (pp.375–396), Kluwer. DOI: https://doi.org/10.1007/1-4020-2278-6_16
Cobb, G. W. & Moore, D. S. (1997). Mathematics, statistics, and teaching, The American mathe-matical monthly, 104(9), 801–823. DOI: https://doi.org/10.1080/00029890.1997.11990723
Concord Consortium (2019). Common online data analysis platform (CODAP) [computer soft-ware]. https://codap. concord.org/
Curcio, F. R. (1989). Developing graph comprehension. Elementary and middle school activities. National Council of Teachers of Mathematics.
Curcio, F. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18(5), 382–393. https://doi.org/10.2307/749086 DOI: https://doi.org/10.5951/jresematheduc.18.5.0382
da Ponte, J. P. (2011). Preparing teachers to meet the challenges of statistics education. In C. Ba-tanero, G. Burill, C. Reading (Eds.), Teaching statistics in school mathematics-Challenges for teaching and teacher education (pp. 299–309). Springer. DOI: https://doi.org/10.1007/978-94-007-1131-0_29
delMas, R. (2004). A comparison of mathematical and statistical reasoning. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 79–95). Kluwer Academic Publishers. DOI: https://doi.org/10.1007/1-4020-2278-6_4
Dierdorp, A., Bakker,A. Eijkelhof, H. & Maanen, J. (2011). Authentic practices as contexts for learning to draw inferences beyond correlated data, Mathematical Thinking and Learning, 13(1–2), 132-151. https://doi.org/10.1080/10986065.201 1 .53829 DOI: https://doi.org/10.1080/10986065.2011.538294
Franklin C., Bargagliotti A. E., Case C. A., Kader G. D., Schaeffer R. L., Spangler D. A. (2015). The statistical education of teachers. VA: American Statistical Association. DOI: https://doi.org/10.1080/09332480.2015.1099362
Franklin, C., Kader, G., Mewborn, D., et al. (2005) Guidelines for Assessment and Instruction in Statistics Education. (GAISE) Report: A pre-k-12 Curriculum Framework. American Statis-tical Association.
Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Schaeffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) Report: A Pre-K-12 curriculum framework. American Statistical Association, Alexandria.
Friel, S., Bright, G., and Curcio, F. (1997). Understanding Students' Understanding of Graphs. Mathematics Teaching in the Middle School, 3(3), 224–227. DOI: https://doi.org/10.5951/MTMS.3.3.0224
Gorman, N. (2017, February 7). Survey finds teachers spend 7 hours per week searching for in-structional materials. Education World. Retrieved from www.educationworld.com.
Groth, R. E. (2007). Toward a conceptualization of statistical knowledge for teaching. Journal for Research in Mathematics Education, 38(5), 427–437. https://www.jstor.org/stable/30034960
Groth, R. E. (2013). Characterizing key developmental understandings and pedagogically power-ful ideas within a statistical knowledge for teaching framework. Mathematical Thinking and Learning, 15, 121–145. https://doi.org/10.1080/10986065.2013.770718 DOI: https://doi.org/10.1080/10986065.2013.770718
Hannigan, A., Gill, O., & Leavy, A. M. (2013). An investigation of prospective secondary mathe-matics teachers’ conceptual knowledge of and attitudes towards statistics. Journal of Math-ematics Teacher Education, 16(6), 427–449. https://doi.org/10.1007/s10857-013-9246-3 DOI: https://doi.org/10.1007/s10857-013-9246-3
Jones, D. L., & Jacobbe, T. (2014). An analysis of the statistical content of textbooks for prospec-tive elementary teachers. Journal of Statistics Education, 22(3), 22–40 https://doi.org/10.1080/10691898.2014.11889713 DOI: https://doi.org/10.1080/10691898.2014.11889713
Jones, D. L., Brown, M., Dunkle, A., Hixon, L., Yoder, N., & Silbernick, Z. (2015). The statistical content of elementary school mathematics textbooks. Journal of Statistics Education, 23(3), 1–22. https://doi.org/10.1080/10691898.2015. 11889748 DOI: https://doi.org/10.1080/10691898.2015.11889748
Langrall, C. W., Makar, K., Nilsson, P., & Shaughnessy, J. M. (2017). Teaching and learning prob-ability and statistics: An integrated perspective. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 490–525). VA: National Council of Teachers of Mathematics.
Leavy, A. & Frischemeier, D. (2022). Developing the statistical problem posing and problem refin-ing skills of prospective teachers. Statistics Education Research Journal, 21(1), 1–27. https://doi.org/10.52041/serj.v21i1.226 DOI: https://doi.org/10.52041/serj.v21i1.226
Lee, H. S. (2019, May 16). Data science education in 6-12 classrooms: What should a coulda woulda, but often ain’t there. Presentation at the United States Conference on Teaching Sta-tistics, State College, PA. Retrieved from: https://www.youtube.com/watch?v=53WuS5z3oPY&feature=youtu.be&t=596
Lee, H. S., Kersaint, G., Harper, S. R., Driskell, S. O., Jones, D. L., Leatham, K. R., Angotti, R. L. & Adu-Gyamfi, K. (2014). Teachers’ use of transnumeration in solving statistical tasks with dynamic statistical software, Statistics Education Research Journal, 13(1), 25–52. DOI: https://doi.org/10.52041/serj.v13i1.297
Lovett, J.N. & Lee, H.S. (2018) Preservice Secondary Mathematics Teachers’ Statistical Knowledge: A Snapshot of Strengths and Weaknesses, Journal of Statistics Education, 26(3), 214–222. https://doi.org/10.1080/10691898.2018.1496806 DOI: https://doi.org/10.1080/10691898.2018.1496806
McClain, K., & Cobb, P. (2001). Supporting studentsí ability to reason about data. Educational Studies in Mathematics, 45(1/3), 103–129. https://doi.org/10.1023/A:10138745 14650 DOI: https://doi.org/10.1023/A:1013874514650
Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. Wiley Publi-cations.
Ministry of National Education [MoNE], (2018). Middle school mathematics curriculum (Elemen-tary and middle schools 1,2,3,4,5,6,7 and 8 grades). [Matematik dersi öğretim programı (il-kokul ve ortaokul 1,2,3,4,5,6,7 and 8. Sınıflar]. Ankara.
Neto, S. C. (2017). Combining distance and traditional learning: A study of the use of virtual learn-ing environment objects and massive online open courses in statistics class. International Journal of Information and Education Technology, 7(1), 1–5. https://doi.org/10.18178/ijiet.2017.7.1.831 DOI: https://doi.org/10.18178/ijiet.2017.7.1.831
Peck, R., Gould, R., Miller, S., & Zbiek, R. (2013). Developing essential understanding of statistics for teaching mathematics in grades 9-12. VA: National Council of Teachers of Mathematics.
Perkowski, D. A., & Perkowski, M. (2007). Data and probability connections: Mathematics for middle school teachers. NJ: Pearson Prentice Hall.
Prodromou, T. (2015). Teaching statistics with technology, Australian Mathematics Teacher, 71(3), 32–40.
Putney, L. G. (2010). Case study. In N. Salkind (Ed.) Encyclopedia of research design. (pp. 89–103). Thousand Oaks, CA: Sage Publications.
Rossman, A., Chance, B., & Medina, E. (2006). Some important comparisons between statistics and mathematics, and why teachers should care. In G. F. Burrill, & P. C. Elliott (Eds.), Thinking and reasoning about data and chance: Sixty eighth year book (pp. 323–333). VA: NCTM.
Scheaffer, R. L. (2006). Statistics and mathematics: On making a happy marriage. In G. F. Burrill, & P. C. Elliott (Eds.), Thinking and reasoning about data and chance: Sixty eighth year book (pp. 309–322). VA: NCTM.
Shaughnessy, J. M. (2007). Research on statistical learning and reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 957–1009). NC: Information Age Publishing.
Shaughnessy, J. M., Garfield, J. & Greer, B. (1996). Data handling. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Ed.), International handbook of mathematics educa-tion (pp. 205–237). Kluwer Academic Publishers. DOI: https://doi.org/10.1007/978-94-009-1465-0_8
Shapiro, E. J., Sawyer, A. G., Dick, L. K., & Wismer, T. (2019). Just what online resources are el-ementary mathematics teachers using? Contemporary Issues in Technology and Teacher Education, 19(4), 670–686.
Suhermi, S. & Widjajanti, D. B. (2020). What are the roles of technology in improving student statistical literacy?. Journal of Physics: Conference Series, 1581(1), 012067. https://doi.org/10.1088/1742- 6596/1581/1/012067 DOI: https://doi.org/10.1088/1742-6596/1581/1/012067
Tishkovskaya, S. & Lancaster, G. A. (2012). Statistical education in the 21st century: A review of challenges, teaching innovations and strategies for reform. Journal of Statistics Education, 20(2), 1–56. https://doi.org/10691898.2012.11889641 DOI: https://doi.org/10.1080/10691898.2012.11889641
Tran, D., & Lee, H. S. (2015). Considerations for design and implementation of statistics tasks. In Teaching statistics through data investigations MOOC-Ed, Friday Institute for Educational Innovation: NC State University, Raleigh, NC. Retrieved from http://ficourses.s3.amazonaws.com/tsdi/unit_3/CDIST.pdf
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Sta-tistical Review, 67(3), 223–265. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x DOI: https://doi.org/10.2307/1403699
Wild, C. J., Utts, J. M., & Horton, N. J. (2018). What is statistics? In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International Handbook of Research in Statistics Education (pp. 5–36). Springer. DOI: https://doi.org/10.1007/978-3-319-66195-7_1
Weiland, T. (2019). The contextualized situations constructed for the use of students by school mathematics textbooks. Statistics Education Research Journal, 18(2), 18–38. https://doi.org/10.52041/serj.v18i2.138 DOI: https://doi.org/10.52041/serj.v18i2.138
How to Cite
Copyright (c) 2023 Nadide Yılmaz
This work is licensed under a Creative Commons Attribution 4.0 International License.