ideas about measurement in terms of point and set paradigms

FIRST YEAR PHYSICS STUDENTS’ IDEAS 15
Table 5.
Students’ use of paradigms for data collection, data processing
and data-set comparison after instruction
Paradigm used for DMSU
Point Set Not
paradigm paradigm codeable Total
Classification Consistent point 3 6 0 9
based on all paradigm (4%) (9%) (0%) (13%)
previous Mixed 11 17 1 29
probes paradigm (17%) (24%) (1%) (42%)
Consistent set 14 16 0 30
paradigm (20%) (23%) (0%) (43%)
Not 1 1 0 2
codeable (1%) (1%) (0%) (3%)
Total 29 40 1 70
(42%) (57%) (1%) (100%)
fewer than half of this group (23% of the sample) appear to be located firmly within
the set paradigm. Thus for the DMSU probe, three-quarters of the students either
resorted to a point paradigm action (42%) or appear to have used the correct set
paradigm action by rote or in an ad hoc way (33% = 57%723%71%). There
appears to be no relationship between ability of the students to apply the formalistic
rules of overlapping intervals and their underlying understanding of the
statistical nature of measurement. In other words, the present results suggest
that the ability of students to reason appropriately when the results are provided
in a formal way (i.e. as a mean and a standard deviation) does not imply that the
same students have developed a commensurate conceptual understanding of the
underlying principles.
Discussion
The results of the present study support the view that the procedural understanding
of the students during the phases of data collection, data processing (by
calculation or graph) and data set comparison (for quality or compatibility) can be
characterized in terms of point and set paradigms. These paradigms form a useful
basis for the interpretation of the decision-making processes and actions during
investigative activities in the laboratory and can therefore be used to inform
laboratory curriculum development.
Nearly all of the present students could be classified as subscribing to the point
paradigm prior to instruction. Even when an action associated with the set paradigm,
for example finding a mean, was used by the students, their responses to the
probes which dealt with the spread in sets of data (the SMDS and DMSS probes)
confirmed that their set reasoning was either undeveloped or nonexistent. After
their laboratory course, the vast majority of the students were able to represent a
set of measurements of a quantity by a mean. However, the fact that the mean of a
set of measurements has little significance without some indication of an interval of
uncertainty seems not to have been widely internalized (see tables 3 and 4). This
fact was evidenced by the response patterns in the probes (SMDS and DMSS and