THE DEVELOPMENT OF INFORMAL STATISTICAL THINKING IN YOUNG STUDENTS


Published: Jul 24, 2017
Keywords:
Statistics education research TinkerPlots® Informal statistical inference
Έφη Παπαριστοδήμου (Efi Paparistodimou)
Μαρία Μελετίου - Μαυροθέρη
Abstract

This paper focuses on developing students’ informal inference skills, reporting on how a group of third grade students formulated and evaluated data-based inferences using the dynamic statistics data-visualization environment Tinker Plots® (Konold & Miller, 2005), software specifi cally designed to meet the learning needs of students in the early grades. Children analyzed collected data using TinkerPlots® as an investigation tool, and made a presentation of their fi ndings to the whole school. Findings from the study support the view that statistics instruction can promote the development of learners’ inferential reasoning at an early age, through an informal, data-based approach. These also suggest that the use of dynamic statistics software has the potential to enhance statistics instruction by making inferential reasoning accessible to young learners.

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References
Australian Education Council (1991). A national statement on mathematics for Australian
schools. Melbourne: Author.
Bakker, A. (2004). Reasoning about shape as a pattern in variability. Statistics Education
Research Journal, 3 (2), 64-83.
Ben-Zvi, D. (2000). Toward Understanding the Role of Technological Tools in Statistical
Learning. Mathematical Thinking and Learning, 2 , 127-155.
Ben-Zvi, D. (2006). Scaffolding students’ informal inference and argumentation. In
A. Rossman & B. Chance (Eds.), Working Cooperatively in Statistics Education:
Proceedings of the Seventh International Conference of Teaching Statistics
(ICOTS-7) , Salvador, Brazil. Voorborg, The Netherlands: International Statistical
Institute.
Common Core State Standards Initiative (2010). Mathematics. Washington, DC: Council
of Chief State School Offi cers & National Governors Association Center for Best
Practices.
GAISE Report (2005). Guidelines for assessment and instruction in statistics education:
A Pre-K-12 Curriculum Framework . Alexandria, VA: The American Statistical
Association. [Online: http://www.amstat.org/education/gaise]
Garfi eld, J., & Ahlgren, A. (1998). Diffi culties in learning basic concepts in probability
and statistics: Implications for research. Journal for Research in Mathematics
Education, 19 , 44-63.
Gil, E., & Ben-Zvi, D. (2011). Explanations and Context in the Emergence of Students’
Informal Inferential Reasoning. Mathematical Thinking and Learning , 13 (1), 87-
Gordon, F. S., & Gordon, S. P. (1992). Sampling + Simulation = Statistical Understanding. In
F. S. Gordon (Ed.), Statistics for the twenty-fi rst century (pp. 207-216). Washington,
DC: The Mathematical Association of America.
Green, D. G. (1982). A survey of probability concepts in 3000 students aged 11-16. In
D. V. Grey (Ed.), Proceedings of the First International Conference on Teaching
Statistics (pp. 766-783). London: Statistics Teaching Trust.
Hammerman, J., & Rubin, A. (2003). Reasoning in the Presence of Variability. In C. Lee
(Ed), Reasoning about Variability: A Collection of Current Research Studies [On
CD]. Dordrecht, the Netherlands: Kluwer Academic Publisher.
Konold, C., & Miller, C. D. (2005). TinkerPlots: Dynamic Data Explorations . Emeryville, CA:
Key Curriculum Press.
Makar, K., & Ben-Zvi, D. (2011). The role of context in developing reasoning about informal
statistical inference. Mathematical Thinking and Learning , 13 , 1-4.
Makar, K., & Confrey, J. (2007). Moving the context of modeling to the forefront. In W.
Blum, P. Galbraith, H-W. Henn, & M. Niss (Eds.), Modelling and applications in
mathematics education. New York: Springer.
Makar, K., Fielding-Wells, J., & Allmond, S. (2011, July). Is this game 1 or game 2? Primary
children’s reasoning about samples in an inquiry classroom. Paper presented at
the Seventh International Forum for Research on Statistical Reasoning, Thinking,
& Literacy. Texel, The Netherlands.
Makar, K., & Rubin, A. (2007, August). Beyond the bar graph: Teaching informal statistical
inference in primary school. Paper presented at the Fifth International Research
Forum on Statistical Reasoning, Thinking, and Literacy (SRTL-5). Warwick, UK.
Meletiou-Mavrotheris, M. (2003). Technological Tools in the Introductory Statistics
Classroom: Effects on Student Understanding of Inferential Statistics. International
Journal of Computers for Mathematical Learning , 8(3), 265-297.
Meletiou-Mavrotheris, M., and Paparistodemou, E. (2015). Developing Young Learners’
Reasoning about Samples and Sampling in the Context of Informal Inferences.
Educational Studies in Mathematics, 88(3), 385-404.
National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standards
for School Mathematics . Reston, VA: Author.
Paparistodemou, E., Noss, R., & Pratt, D. (2008). ‘ The Interplay between Fairness and
Randomness’ International Journal of Computers for Mathematical Learning, 13,
-110.
Paparistodemou, E., & Meletiou-Mavrotheris, M. (2008). Enhancing Reasoning about
Statistical Inference In 8 Year-Old Students. Statistics Education Research Journal,
(2), 83-106.
Paparistodemou, E. & Meletiou-Mavrotheris, M. (2010). Engaging Young Children in
Informal Statistical Inference. In C. Reading (Ed.), Data and Context in Statistics
Education: Towards an Evidence-based Society. Proceedings of the Eighth
International Conference on Teaching Statistics (ICOTS8, July, 2010), Ljubljana,
Slovenia. Voorburg, The Netherlands: International Statistical Institute.
Pratt, D. (2000). Making Sense of the Total of two Dice. Journal of Research in Mathematics
Education, 31, 602-625.
Pratt, D., Johnston-Wilder, P., Ainley, J., & Mason, J.(2008). Local and Global Thinking in
Statistical Inference. Statistics Education Research Journal, 7(2), 107-129.
Pfannkuch, M. (2006). Informal inferential reasoning. In A. Rossman & B. Chance
(Eds.), Working Cooperatively in Statistics Education: Proceedings of the Seventh International Conference of Teaching Statistics, [CDROM]. Salvador, Brazil Voorburg, The Netherlands: International Statistical Institute.
Rubin, A., Hammerman, J., & Konold, C. (2006). Exploring informal inference with
interactive visualization software. In A. Rossman & B. Chance (Eds.), Working
Cooperatively in Statistics Education. Proceedings of the Seventh International
Conference on Teaching Statistics, [CDROM]. Salvador, Brazil. Voorburg, The
Netherlands: International Statistical Institute.
Shaughnessy J. M., Ciancetta M., Best K., & Canada D. (2004, April). Students’ attention
to variability when comparing distributions. Paper presented at the 82nd Annual
Meeting of the National Council of Teachers of Mathematics. Philadelphia, PA.
Sorto, M. A. (2006). Identifying Content Knowledge for Teaching Statistics. In A. Rossman
and B. Chance (Eds.), Proceedings of the Seventh International Conference on
Teaching Statistics. Salvador, Brazil. Voorburg, The Netherlands: International
Statistical Institute.
Stohl, H. & Tarr, J. E. (2002). Using Multi-Representational Computer Tools to Make Sense
of Inference. In D. Mewborn (Ed.), Proceedings of the Twenty-fourth Annual Meeting
of the North American Chapter of the International Group for the Psychology of
Mathematics Education. Athens, GA: PME-NA.
Στυλιανού, Δ., & Μελετίου-Μαυροθέρη, Μ. (2003). Δυναμικά Λογισμικά: Νέες Προοπτικές
για τη Χρήση Τεχνολογίας στη Διδασκαλία των Μαθηματικών. Σύγχρονη Εκπαίδευ -
ση , 132, 27-37.
Watson, J. (2007, August). Facilitating beginning inference with TinkerPlots for novice
grade 7 students. Paper presented at the Fifth International Research Forum on
Statistical Reasoning, Thinking, and Literacy (SRTL-5). Warwick, UK.
Watson, J.M., & Moritz, J.B. (2000). Developing concepts of sampling. Journal for
Research in Mathematics Education, 31, 44-70.
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry (with
discussion). International Statistical Review, 67(3), 223-265.
Zieffl er, A., delMas, R., Garfi eld, J., & Gould, R. (2007, August). Studying the development of
college students’ informal reasoning about statistical inference. Paper presented
at the Fifth International Research Forum on Statistical Reasoning, Thinking, andLiteracy (SRTL-5). Warwick, UK.
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