Page 114 - Contributed Paper Session (CPS) - Volume 2

CPS1447 Russasmita S.P. et al.
lesson, teachers made a point to never instruct the students to calculate the
arithmetical mean, but to ask questions like “what is the typical height of the
students in the classroom?”. To save time, the students measured their heights
prior to the lessons and submitted the data to the teachers.
In the first lesson, the students worked in groups, forming a total of seven
groups in the classroom. They were presented by a box containing pieces of
paper, on which the height and sex of each student is written. The students
had to take an instructed numbers of papers from the box, which is different
for each group and ranged from 8 to 12. They presented it as dot plot, with
red dots represent girls and blue represent boys. Each group then summarize
their dot plot, which is referred as ‘group plot’ from this point onward. To
emphasise that the data they collected is a part of a whole, the students were
asked to predict what the class dot plot would look like and explain why. After
working in groups, the students constructed the class dot plot together. Each
student got a sticky notes; red for girls and blue for boys, and stuck it on a
provided blank poster paper in front of the classroom. From this point onward,
this chart will be referred to as ‘class plot’.
The conjecture of the students’ reaction was that the students will
summarize the dot plot visually without employing arithmetic mean. In
predicting the class chart, we predicted that the students will use the
characteristic of the group plot (for example extreme points or modal values)
and build the class chart around it. In the second lesson, every group was
provided with one copy of the class plot and one copy of each of the group
plot – seven in total. The students summarized the sample, compared it to the
class chart, and determined which group plot can represent the plot of the
whole class the best. The students then took the group plot that is the least
representative and predict what would happen if more data points are added
into the group plot, before physically taking more pieces of paper from the
population box and add it to the group plot.
We conjectured that the students will stick to visual analysis when
comparing the group dot plots, for example the shape of the plot or the modal
values, or to characterize the group plot based on the height difference
between boys and girls. The different samples that exhibit varying degree of
similarity to the class chart will help to expose the students to the idea of
sampling variability. Since each group plot has different data size, we
predicted that the students will notice that dot plots with larger data size will
resemble the class chart more, which will be their reason when asked to predict
what happens when more data points added to the group dot plot.
Physically drawing sample from population and predicting class plot based
on the information provided in the group plot are designed to give the
students concrete imagery of sample being a part of population. On the other
hand, comparing different samples taken from the same population is

103 | I S I W S C 2 0 1 9