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CPS1447 Russasmita S.P. et al.
why it is possible to only use a group of students to represent the whole or
the necessary considerations in determining its representativeness. As a
comparison, the statistics content of Common Core State Standards (National
Governors Association, 2010) specifically states “…begin informal work with
random sampling to generate data sets and learn about the importance of
representative samples for drawing inferences.” Mathematics curriculum of
Japan (Takahashi, Watanabe and Yoshida, 2008) lists “to understand the need
for and the meaning of sampling” as prerequisite for making inference from
sample.
It is concerning that mathematics curriculum of Indonesia do not see the
need to expand sample and sampling content beyond terminological
definition because this topic is prone to misconception. Research by Tversky
and Kahneman (1971) suggested that people tend to believe that a sample is
inherently representative to the population and be oblivious to the effect of
sample size. They also tend to think that representative sample is all about
being a certain large percentage of a population (Garfield, 2002) which is
deemed as one of the challenge in developing statistical reasoning.
Literature has attempted to address this problem by proposing two crucial
yet counterintuitive ideas: sampling representativeness and sampling
variability. Focusing on sampling representativeness too much leads the
students to believe that a sample provides all information about a population,
while focusing on sampling variability leads the students to believe that
sample is unreliable (Rubin, Bruce and Tenney, 1991). The balance between
the two ideas are needed for comprehensive understanding of sample and
sampling.
In response to this, research-based activities have emerged, designed
specifically to address the need for balance between sampling
representativeness and sampling variability. Sampling variability can be
introduced by taking repeated samples from a population and comparing
sample statistics (Garfield and Ben-zvi, 2008). Computer software have grown
in popularity, for example TinkerPlot in “growing sample” activities by Bakker
(2004) to introduce the effect of sample size and in activities by Brown and
delMas (2018) which is designed as informal introduction to Central Limit
Theorem. On the contrary, some research opt for hands-on activity to provide
more concrete experience, such as pieces of paper inside a bag called
“population bag” (Arnold et al., 2011) from which the students physically draw
the sample themselves to compare two groups of data. Hands-on activities
are also used prior to computer simulation, to make it easier for the students
to believe the result of the simulation (Garfield and Ben-zvi, 2008).
We feel like mathematics curriculum of Indonesia can learn something
from the extensive body of research in this area. Therefore, we propose a
sequence of activities designed for upper primary or lower secondary schools

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