ideas about measurement in terms of point and set paradigms

14 A. BUFFLER ET AL.
Table 4.
Students’ use of paradigms for data collection/processing and
data set comparison after instruction.
Paradigms used in data collection/processing
Consistent
Consistent
point Mixed set Not
paradigm paradigms paradigm codeable Total
Paradigms Mixed 9 25 13 2 49
used in paradigms (13%) (37%) (18%) (2%) (70%)
data set Consistent set 0 3 15 0 18
comparison paradigm (0%) (4%) (21%) (0%) (26%)
Not 0 1 2 0 3
codeable (0%) (1%) (3%) (0%) (4%)
Total 9 29 30 2 70
(13%) (42%) (43%) (3%) (100%)
The Different Mean Same Uncertainty (DMSU) probe.
Two other groups of students compare their results for d obtained by releasing the ball at h = 400
mm. Their means and standard deviation of the means for their releases were:
Group A: d = 434 5mm
Group B: d = 442 5mm
A: Our result agrees with yours.
B: No, your result does not agree with ours.
Responses to the DMSU probe were associated with the point paradigm if the
comparison between the two results was made either using only the mean values,
or only the numerical value of the standard deviations, as illustrated by:
The means are different so the results are different.
The uncertainties are the same so the results are the same.
(DMSU response)
(DMSU response)
Sometimes a comparison was made using both the mean and the numerical value
of the standard deviation:
Although the uncertainty is the same the results are the different because the means
are different.
(DMSU response)
On the other hand, a student’s response was identified with the set paradigm if the
student attempted to reach a decision according to the degree to which the intervals
of the two measurements overlap, for example:
The two measurements agree with each other since the intervals defined by their
standard deviations overlap with each other.
(DMSU response)
The responses to the DMSU probe could therefore involve an action which is in
keeping with the set paradigm but the reasons given may or may not have followed
from that paradigm. Table 5 shows the classification of students on the basis of all
the probes discussed thus far, together with the results of the DMSU probe.
Although more than half the students (57%) carried out a set paradigm action,