Informal Inferential Reasoning Using a Modelling Approach within a Computer-Based Simulation
The article investigates how 14- to 15- year-olds build informal conceptions of inferential statistics as they engage in a modelling process and build their own computer simulations with dynamic statistical software. This study proposes four primary phases of informal inferential reasoning for the students in the statistical modeling and simulation process. Findings show shifts in the conceptual structures across the four phases and point to the potential of all of these phases for fostering the development of students- robust knowledge of the logic of inference when using computer based simulations to model and investigate statistical questions.
[1] Aberson, C. L., Berger, D. E., Healy, M. R., & Romero, V. L. (2003).
Evaluation of an interactive tutorial for teaching hypothesis testing
concepts. Teaching of Psychology, 30, 76-79.
[2] Bakker, A., Kent, P., Derry, J., Noss, R., & Hoyles, C. (2008).
Statistical inference at work: Statistical process control as an example.
Statistics Education Research Journal, 7(2), 131-146.
http://www.stat.auckland.ac.nz/ iase/serj/SERJ7(2)_Bakker.pdf.
Accessed 10 January 2013.
[3] Batanero, C. (2005). Statistics education as a field for research and
practice. In Proceedings of the 10th international commission for
mathematical instruction. Copenhagen, Denmark: International
Commission for Mathematical Instruction.
[4] Batanero, C., Tauber, L. M., & S´anchez, V. (2004). Students’
reasoning about the normal distribution. In D. Ben-Zvi & J. Garfield
(Eds.), The challenge of developing statistical literacy, reasoning and
thinking (pp. 257–276). Dordrecht, The Netherlands: Kluwer Academic
Publishers.
[5] Belia, S., Fidler, F., Williams, J., & Cumming, G. (2005). Researchers
misunderstand intervals and standard errors bars. Psychological
Methods, 10, 389-396.
[6] Chance, B., delMas, R., & Garfield, J. (2004). Reasoning about
sampling distributions. In D. Ben-Zvi and J. Garfield (Eds.), The
Challenge of Developing Statistical Literacy, Reasoning, and Thinking
(pp. 295-323). Dordrecht, The Netherlands: Kluwer Academic
Publishers.
[7] Cobb, G. W. (2007). The introductory statistics course: a ptolemaic
curriculum? Technology innovations in statistics Education, 1 (1).
[8] Garfield, J., delMas, B., & Zieffler, A. (2012). Developing statistical
modelers and thinkers in an introductory, tertiary-level statistics course.
ZDM−The International Journal on Mathematics Education, 44(3),
883-898. doi:10.1007/s11858-012-0447-5
[9] Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical
reasoning: Connecting research and teaching practice. Berlin:
Springer.
[10] Kirk, R. E. (2001). Promoting good statistical practices: Some
suggestions. Educational and Psychological Measurement, 61 (2),
213−218.
[11] Konold, C., & Pollatsek, A. (2002). Data analysis as the search for
signals in noisy processes. Journal for Research in Mathematics
Education, 33(4), 259-289.
[12] Lipson, K. (2002). The role of computer based technology in developing
understanding of the concept of sampling distribution. In Proceedings
of the sixth international conference on teaching statistics. Voorburg,
The Netherlands: International Statistical Institute.
[13] Makar, K., & Rubin, A. (2009). A framework for thinking about
informal statistical inference. Statistics Education Research Journal,
8(1), 82-105. http://www.stat.auckland.ac.nz/ iase/
serj/SERJ8(1)_Makar_Rubin.pdf. Accessed 10 January 2013.
[14] Pfannkuch, M. (2005). Probability and statistical inference: How can
teachers enable learners to make the connection? In G. Jones (Ed.),
Exploring probability in school: Challenges for teaching and learning
(pp. 267-297). Dorcdrecht, The Netherlands: Kluwer Academic
Publishers.
[15] Prodromou, T. (2012). Developing a modeling approach to probability
using computer-based simulations. Proceedings of the 12th
International Congress on Mathematical Education, Topic Study Group
11, pp. 2394-2403. COEX, Seoul, Korea: ICME.
http://www.icme12.org /upload /UpFile2/TSG/0978.pdf. Accessed 10
January 2013.
[16] Robson, C. (1993). Real world research. Oxford, England: Blackwell.
[17] Saldanha, L., & Thompson, P. (2003). Conceptions of sample and their
relationship to statistical inference. Educational Studies in Mathematics,
51, 257-270.
[18] TinkerPlots: Dynamic data exploration (Version 2.0) [Computer
software]. Emeryville: CA: Key Curriculum Press.
[19] Watson, J. M., & Moritz, J. B. (2000). Development of understanding of
sampling for statistical literacy. Journal of Mathematical Behaviour, 19,
109-136.
[20] Wilensky, U. (1997). What is normal anyway? Therapy for
epistemological anxiety. Educational Studies in Mathematics, 33(2),
171–202.
[1] Aberson, C. L., Berger, D. E., Healy, M. R., & Romero, V. L. (2003).
Evaluation of an interactive tutorial for teaching hypothesis testing
concepts. Teaching of Psychology, 30, 76-79.
[2] Bakker, A., Kent, P., Derry, J., Noss, R., & Hoyles, C. (2008).
Statistical inference at work: Statistical process control as an example.
Statistics Education Research Journal, 7(2), 131-146.
http://www.stat.auckland.ac.nz/ iase/serj/SERJ7(2)_Bakker.pdf.
Accessed 10 January 2013.
[3] Batanero, C. (2005). Statistics education as a field for research and
practice. In Proceedings of the 10th international commission for
mathematical instruction. Copenhagen, Denmark: International
Commission for Mathematical Instruction.
[4] Batanero, C., Tauber, L. M., & S´anchez, V. (2004). Students’
reasoning about the normal distribution. In D. Ben-Zvi & J. Garfield
(Eds.), The challenge of developing statistical literacy, reasoning and
thinking (pp. 257–276). Dordrecht, The Netherlands: Kluwer Academic
Publishers.
[5] Belia, S., Fidler, F., Williams, J., & Cumming, G. (2005). Researchers
misunderstand intervals and standard errors bars. Psychological
Methods, 10, 389-396.
[6] Chance, B., delMas, R., & Garfield, J. (2004). Reasoning about
sampling distributions. In D. Ben-Zvi and J. Garfield (Eds.), The
Challenge of Developing Statistical Literacy, Reasoning, and Thinking
(pp. 295-323). Dordrecht, The Netherlands: Kluwer Academic
Publishers.
[7] Cobb, G. W. (2007). The introductory statistics course: a ptolemaic
curriculum? Technology innovations in statistics Education, 1 (1).
[8] Garfield, J., delMas, B., & Zieffler, A. (2012). Developing statistical
modelers and thinkers in an introductory, tertiary-level statistics course.
ZDM−The International Journal on Mathematics Education, 44(3),
883-898. doi:10.1007/s11858-012-0447-5
[9] Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical
reasoning: Connecting research and teaching practice. Berlin:
Springer.
[10] Kirk, R. E. (2001). Promoting good statistical practices: Some
suggestions. Educational and Psychological Measurement, 61 (2),
213−218.
[11] Konold, C., & Pollatsek, A. (2002). Data analysis as the search for
signals in noisy processes. Journal for Research in Mathematics
Education, 33(4), 259-289.
[12] Lipson, K. (2002). The role of computer based technology in developing
understanding of the concept of sampling distribution. In Proceedings
of the sixth international conference on teaching statistics. Voorburg,
The Netherlands: International Statistical Institute.
[13] Makar, K., & Rubin, A. (2009). A framework for thinking about
informal statistical inference. Statistics Education Research Journal,
8(1), 82-105. http://www.stat.auckland.ac.nz/ iase/
serj/SERJ8(1)_Makar_Rubin.pdf. Accessed 10 January 2013.
[14] Pfannkuch, M. (2005). Probability and statistical inference: How can
teachers enable learners to make the connection? In G. Jones (Ed.),
Exploring probability in school: Challenges for teaching and learning
(pp. 267-297). Dorcdrecht, The Netherlands: Kluwer Academic
Publishers.
[15] Prodromou, T. (2012). Developing a modeling approach to probability
using computer-based simulations. Proceedings of the 12th
International Congress on Mathematical Education, Topic Study Group
11, pp. 2394-2403. COEX, Seoul, Korea: ICME.
http://www.icme12.org /upload /UpFile2/TSG/0978.pdf. Accessed 10
January 2013.
[16] Robson, C. (1993). Real world research. Oxford, England: Blackwell.
[17] Saldanha, L., & Thompson, P. (2003). Conceptions of sample and their
relationship to statistical inference. Educational Studies in Mathematics,
51, 257-270.
[18] TinkerPlots: Dynamic data exploration (Version 2.0) [Computer
software]. Emeryville: CA: Key Curriculum Press.
[19] Watson, J. M., & Moritz, J. B. (2000). Development of understanding of
sampling for statistical literacy. Journal of Mathematical Behaviour, 19,
109-136.
[20] Wilensky, U. (1997). What is normal anyway? Therapy for
epistemological anxiety. Educational Studies in Mathematics, 33(2),
171–202.
@article{"International Journal of Business, Human and Social Sciences:50729", author = "Theodosia Prodromou", title = "Informal Inferential Reasoning Using a Modelling Approach within a Computer-Based Simulation", abstract = "The article investigates how 14- to 15- year-olds build informal conceptions of inferential statistics as they engage in a modelling process and build their own computer simulations with dynamic statistical software. This study proposes four primary phases of informal inferential reasoning for the students in the statistical modeling and simulation process. Findings show shifts in the conceptual structures across the four phases and point to the potential of all of these phases for fostering the development of students- robust knowledge of the logic of inference when using computer based simulations to model and investigate statistical questions.
", keywords = "Inferential reasoning, learning, modelling, statistical inference, simulation.", volume = "7", number = "6", pages = "1396-6", }
