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Using Fathom® statistical education software in high school to examine students' acceptance of virtual simulation and use of simulation to model sample size when sampling from large and infinite populations

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Bill, AF (2012) Using Fathom® statistical education software in high school to examine students' acceptance of virtual simulation and use of simulation to model sample size when sampling from large and infinite populations. PhD thesis, University of Tasmania.

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Abstract

Statistical literacy is regarded as essential for good citizenship, employment, and
practical day-to-day living. The ubiquitous nature of data and computers in
contemporary society has increased both the need for statistical literacy and the means
of developing statistical literacy.
This study investigated students’ acceptance of Fathom® virtual simulation and resampling
as a legitimate mathematics tool, the teaching and learning of the explicit
determination of sample size when sampling from large populations, and students’
development of use of Fathom statistics education software.
The study was conducted as a three-week long classroom unit of work taught in two
Year 9 classes and a detailed study of twelve students in Tasmania, Australia.
Pedagogical best practice principles derived from statistics education research guided
the study. These included engagement with the big ideas of statistics, active learning
and data sets students can understand and value, statistical enquiry that cultivates
statistical habits of mind, the use of technology tools that allows students to explore
data and concepts, mathematical experiences of substance, provision of a
developmental pathway for students to study statistics at more senior years, and
authentic assessment.
Fathom was developed for senior high school and tertiary study, and its use in
Australian high schools is relatively novel. Students’ unfamiliarity with the software
presented at least two challenges: developing acceptance of Fathom’s virtual resampling
probability simulator as a legitimate mathematical tool and acquiring basic
fluency in the software’s use such that the software was not a constraint on learning.
Students’ acceptance of the probability simulator was cultivated purposefully through a
process of formal statistical enquiry where students examined the fairness of the
Fathom virtual die. Students’ development of use of Fathom re-sampling was examined
from the three aspects of key terminology, graphical data representations, and their
relationship with Fathom. The principles of instrumental genesis guided the
introduction to, and the examination of, students’ use of Fathom.
Sample size is presently ignored in the high school curriculum, and students may
complete formal school education with unsophisticated notions of sample size, possibly
first acquired in upper primary school. The sample size model e=+/Vn, which
relates the sample size n, to the margin of error e, of the accuracy of measurement, was
used in this study. A foremost consideration was that the model was potentially
accessible and that students could apply their understanding in a real-life context. Large
populations were studied because formal mathematical treatment is relatively simple.
Students’ work samples were assessed using the SOLO taxonomy, and situated
abstraction was used to observe students’ development of understanding of selected
mathematical concepts.
The study concluded that a process of statistical enquiry may be used both to promote
acceptance of virtual simulation and to foster the development of statistical “habits of
mind.” The sample size model e=+/Vn has application in Year 9 principally to
mathematise traditional Law of Large Numbers activities, where the computing power
of virtual simulation allows exploration of very large sample sizes. The introduction of
re-sampling and the sample size model in Year 9 provides the foundation for the
consideration of contextual tasks in more senior school years. The study suggests that
Fathom is suitable for Year 9 students, but recommends further research in the use of
re-sampling to exploit fully the software’s potential.

Item Type: Thesis (PhD)
Keywords: Fathom®, sample size, simulation, re-sampling, statistics, high school, beliefs
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Date Deposited: 22 Jan 2013 02:44
Last Modified: 11 Mar 2016 05:52
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