Page 113 - Contributed Paper Session (CPS) - Volume 2

CPS1447 Russasmita S.P. et al.
that are compatible with Indonesian context and the supporting hypothetical
learning trajectory. The research question that directs this paper is how can we
support novice students to develop reasoning about sample variability and
sample representativeness?

2. Methodology
The study reported in this paper is a part of a larger design research aimed
to support the students in developing informal inferential reasoning. A set of
activities and accompanying hypothetical learning trajectory (HLT) are
developed based on literature review, before being implemented to a small
group of students as pilot research. The design was then refined based on the
findings from pilot research, before entering the first cycle of design research
which is an implementation to a larger group of students.
The main data collected in this study is video recording. The video
recording was transcribed to acquire the students’ actual learning trajectory
(ALT). The transcript of video recording and the students’ working were
analysed using matrix proposed by Dierdorp (2011). HLT and ALT are
compared to find background data to support or reject HLT. The result of
analysis contributes to the refinement of the lesson design and the HLT.
Due to space constraint, this paper will leave out the pilot study and report
the result from the first cycle only. The participants of this study were thirty
7th grade students in a public school in Indonesia. The students are novice in
a way that they have limited statistical background, comprising only collecting
and representing data which they previously learned in 6th grade. The cycle
consisted of two meetings spanning two weeks and taught by the
mathematics teacher who normally teaches the students.

3. Result
The preparation and design phase of design research resulted in design of
activities and the accompanying HLT. The activities consist of two lessons, each
built around a big idea that is the main topic of the activity. The big idea aimed
for the first lesson is a part of data can represent the whole data, while the big
idea for the second lesson is all samples taken from a population provides
different information and the larger the samples, the more likely it represent
the population.
Both lessons are set in real-life context, which is investigating whether or
not the length of scout staff is compatible to the height of the student in their
class. Due to the varying heights of the students in the classroom, it is
necessary for them to determine one number that is the typical height of
everyone in the classroom to be compared to the length of the scout staff. The
urgency in the context engages and motivate the students as well as give them
to playground to apply statistics in solving real life problems. During the

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