Page 118 - Contributed Paper Session (CPS) - Volume 2

CPS1447 Russasmita S.P. et al.
definition in statistics, but the colloquial meaning as in how much space the
plot takes on the paper. P1’s statement about height also reveals similar
situation. This finding need to be met with caution because according to the
findings of Wijaya, Robitzsch, Doorman, and Heuvel-Panhuizen (2014),
treating graph as a picture is one of the common errors in solving context-
based mathematics task.
Even though the students needed teacher’s prompting, the growing
sample activity while comparing it to the population is proven to be a simple
yet effective and engaging way for the students to learn about the effect of
sample size on representativeness. The students can experience by themselves
what happens as the sample grow larger and larger, which support stronger
understanding of effect of sample size.
To summarize, the activities designed and conducted in this study can
support novice students in developing reasoning about sample and
population. This activity is also low in cost and does not demand much in
facilities. We hope that the result of this study can revolutionize the way
sample and population being introduced in Indonesian mathematics
curriculum.
There is several suggestion that we offer for future researchers interested
in this topic or teachers interested to implement this lesson design in their
classroom. Regarding the first lesson, we suggest the teacher to prompt the
students to choose one number that best represent the whole class, especially
in situation where there are two modal values. We also did not further inquire
the students’ reasoning in predicting the class plot, which we strongly suggest
the future researchers to do. Inquiring the students’ reasoning about their
preference to ‘fill-in’ the plot might provide more insight on typical
misconception about sample and population that might occur with novice
students.
For the second lesson, we suggest the teachers to provide a list of question
that can help the students to identify the characteristics of each group plot
(i.e. sample statistics). It might prevent them to view the plot as picture.
Teachers should also emphasis in the end of the lesson about what sampling
variability is, or ask the students to do so. The list of question might also help
during the growing sample activity. Next step for future research that we think
will be interesting is to analyse the students’ utterance during classroom
activities or pre- and post-test according to the framework proposed by
Watson and Moritz (2000).

References
1. Arnold, P. et al. (2011) ‘Enhancing Students ’ In ferential Reasoning :
From Hands-On To “ Movies’, Journal of Statistics Education, 19(2), pp.
1–32.

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