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CPS1447 Russasmita S.P. et al.
During the ‘growing sample’ activity, the teacher made a mistake of not
asking the prediction from the students and instead directly instructed the
students to add more data points to the plot.
While the students were able to notice the change in the group plot right
away and described that it is getting ‘higher’, they were unable to connect the
change that they see to the characteristics of the class chart. Only after
prompting by the teacher, for example the difference in typical values before
and after adding more data points, that the students could see that the larger
the plots, the more they resemble the class plot.

4. Discussion and Conclusion
The question that leads the study is how can we support novice students
to develop reasoning about sample variability and sample representativeness?
Several activities conducted in this study reveals what work and what do not
work in regard to the question posed above, which will be explained as follows.
The predicting activity revealed interesting way of the students thinking
about sample and population. The fact that they did not consider sample
characteristics a possibility for population parameter show that the notion of
part of data can represent the whole does not come naturally to the students.
Therefore, the traditional approach of introducing sample and population
simply through the terminological definition is proven to be insufficient.
In predicting the class plot, the students were more concerned in
spreading out the dots and filling in empty spaces to make the plot look more
‘even’. Even after summarizing the sample and discussing the characteristics,
including the variation, the students did not transfer this finding to the
predicted class plot. This is one of the common misconception people have
about statistics, which is believing that there is no variability in the real world
(Shaughnessy, Garfield and Greer, 1996).
The second meeting showed that the students can acknowledge and
describe the variation in different samples taken from a population. At the
same time, they can identify that some samples are better at representing the
population than the others.
The fragment from the second meeting showed that the students opted
for an interesting way to describe the dot plots, i.e. to use shape. This can be
interpreted as a budding understanding of data as an aggregate (a whole that
has characteristics that are not visible in individual cases), which is a common
challenge with young students who tend to see data as a series of individual
cases (Ben-zvi, Bakker and Makar, 2015).
However, reasoning involving shape can possess dangerous turnabout.
Even though it enables the students to see data as an aggregate, they seem
to view the dot plot as a geometric figure. P1’s remark about the size of the
graph did not refer to the number of data points in the set, like the formal

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