Towards posing and answering questions about bar graphs
DOI:
https://doi.org/10.52041/iase24.601Abstract
Posing questions about categorical variables and answering them using representations is a neglected area of research. A small exploratory study was conducted with 13-14-year-old Pasifika and Māori students using culturally appropriate data and pedagogy. Data collection included pre and post-tests and a video-record of a 10-lesson implementation. The findings indicated novice students could learn to pose quantitative questions about categorical variables but struggled to deconstruct questions and to decode representations to answer simple, conditional, and joint questions. The implications of the findings are discussed.References
Arnold, P. (2013). Statistical investigative questions: An enquiry into posing and answering investigative questions from existing data. (Doctoral thesis.) The University of Auckland, New Zealand. http://hdl.handle.net/2292/21305
Arnold, P. (2022). Statistical investigations | Te Tūhuratanga Tauanga: Understanding progressions in The New Zealand curriculum and Te Marautanga o Aotearoa. NZCER Press. https://www.nzcer.org.nz/nzcerpress/statistical-investigations-te-tuhuratanga-tauanga
Arnold, P., & Franklin, C. (2021). What makes a good statistical question? Journal of Statistics and Data Science Education, 29(1), 122–130. https://doi.org/10.1080/26939169.2021.1877582
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 II (GAISE II). ASA. https://www.amstat.org/asa/files/pdfs/GAISE/GAISEIIPreK-12_Full.pdf
Batanero, C., & Álvarez-Arroyo, R. (2024). Teaching and learning probability. ZDM – Mathematics Education, 56(1), 5–17. https://doi.org/10.1007/s11858-023-01511-5
Böcherer-Linder, K., Eichler, A., & Vogel, M. (2018). Visualizing statistical information with unit squares. In M. A. Sorto, A. White, & L. Guyot (Eds.), Looking back, looking forward. Proceedings of the Tenth International Conference on Teaching Statistics (ICOTS10), International Statistical Institute. https://iase-web.org/icots/10/proceedings/pdfs/ICOTS10_7C1.pdf?1531364285
Ben-Zvi, D., Gravemeijer, K., & Ainley, J. (2018). Design of statistics learning environments. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education, Springer. https://doi.org/10.1007/978-3-319-66195-7_16
Budgett, S., & Puloka, M. (2019). Making sense of categorical data–Question confusion. In S. Budgett (Ed.), Decision making based on data. Proceedings of the Satellite Conference of the International Association for Statistical Education, International Statistical Institute. https://iase- web.org/documents/papers/sat2019/IASE2019%20Satellite%20114_BUDGETT.pdf?1569666564
Budgett, S., Pfannkuch, M., & Puloka, M. (2022). Extracting conditional proportions from bar graphs. In S. Peters & L. Zapata-Cardona, F. Bonafini, & A. Fan (Eds.), Bridging the gap: Empowering and educating today’s learners in statistics. Proceedings of the Eleventh International Conference on Teaching Statistics (ICOTS11), International Statistical Institute. https://doi.org/10.52041/iase.icots11.T6E2
Casey, S., Hudson, R., & Ridley, L. (2018). Students’ reasoning about association of categorical variables. In M.A. Sorto, A. White, & L. Guyot (Eds.), Looking back, looking forward. Proceedings of the Tenth International Conference on Teaching Statistics (ICOTS10), International Statistical Institute. https://iase-web.org/icots/10/proceedings/pdfs/ICOTS10_2E2.pdf?1531364243
Gould, R., Bargagliotti, A., & Johnson, T. (2017). An analysis of secondary teachers' reasoning with participatory sensing data, Statistics Education Research Journal, 16(2), 305–334. https://doi.org/10.52041/serj.v16i2.194
Hunter, R. (2023). Tracing the threads of research to establish equitable and culturally appropriate pedagogical practices within mathematical interactions and discourse for all learners. Theory into Practice, 62(1), 79–89. https://doi.org/10.1080/00405841.2022.2135903
Hunter, R., & Hunter, J. (2017). Maintaining a cultural identity while constructing a mathematical disposition as a Pasifika learner. In E.A. McKinley & L.T. Smith (Eds.), Handbook of Indigenous education (pp. 423–441). Springer. https://doi.org/10.1007/978-981-10-1839-8_14-1
Konold, C., Pollatsek, A., Well, A., & Gagnon, A. (1997). Students analyzing data: Research of critical barriers. In J. Garfield & G. Burrill (Eds.), Research on the role of technology in teaching and learning statistics. Proceedings of IASE Roundtable Conference, (pp. 151–167). International Statistical Institute. https://iase-web.org/documents/papers/rt1996/13.Konold.pdf?1402524984
Lumley, T. (2022). Statistics in the media: Learning and teaching. Keynote Speaker Eleventh International Conference on Teaching Statistics (ICOTS11). IASE Webinar YouTube. https://www.youtube.com/watch?v=NKxbSe3JqTw
Ministry of Education (2020). Pacific values framework: Designing for Pacific learners and contexts. Author. https://ncea.education.govt.nz/pacific-values-framework
Morris, N. (2021). Learning probability in the Kingdom of Tonga: The influence of language and culture. Educational Studies in Mathematics, 107, 111–134. https://doi.org/10.1007/s10649-020- 10022-z
Puloka, M. & Pfannkuch, M. (2023). What’s in a Pasifika name? Constructing a name dataset. Statistics and Data Science Educator. https://sdse.online/lessons/SDSE23-001/SDSE23-001.pdf
Puloka, M. S. (2016). Exploring Year 13 students’ probabilistic reasoning from an eikosogram (Master’s thesis, Auckland University). https://researchspace.auckland.ac.nz/handle/2292/33551
Puloka, M., Budgett, S., & Pfannkuch, M. (2021). What questions do novices pose about categorical data? In R. Helenius & E. Falck (Eds.), Statistics education in the era of data science: Proceedings of the Satellite conference of the International Association for Statistical Education. IASE. https://doi.org/10.52041/iase.lciru
Vaioleti, T. M. (2006). Talanoa research methodology: A developing position on Pacific research. Waikato Journal of Education, 12, 21-34. https://doi.org/10.15663/wje.v12i1.296
Watson, J. M., & Callingham, R. (2015). Lung disease, indigestion and two-way tables. Investigations in Mathematics Learning, 8(2), 1–16. https://files.eric.ed.gov/fulltext/EJ1090075.pdf
Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical inquiry. International Statistical Review, 67(3), 223–248. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x
Xiong, C., Setlur, V., Bach, B., Lin, K., Koh, E., & Franconeri, S. (2022). Visual arrangements of bar charts influence comparisons in viewer takeaways. IEEE Transactions on Visualization and Computer Graphics, 28(1), 955–965. https://doi.org/10.1109/TVCG.2021.3114823