A Model for the Sun and a Close Star. The third item analyzed in detail examined the mental
models that students construct for the relative disposition of stars. Stars are very far from us
on the scale of the solar system. The closest star to our solar system is about 200,000 times farther
from it than the sun is from the earth. Or, to put it another way, if the sun were a grape the
earth would be a speck of dust 3 ft away and the closest star would be another grape 100 miles
from us. At this scale, even Pluto would be close to the sun, at a distance of 100 ft. Item 8 asks
just this question with five options for answers; two grapes would make a good scale model of
the sun and a close star, if separated by 1 ft, 1 yard, 100 yards, 1 mile, 100 miles. Since stars
and planets are almost indistinguishable in the night sky, students may not make a distinction
between their distances from us. Among 200 11- to 13-year-old Italian students interviewed,
there was no distinction between stars and planets (Loria et al., 1986).
The probability of answering this question correctly declined slightly from 22.0 to 0.0 and
then rose sharply, reaching a value of 0.5 at an ability of 0.9 (Figure 3). The “don’t know” option
dropped to a value of 0.5 at a u of 0.2. Examining the detail of the trace lines of the four
incorrect options shows a progression of preferences from 1 ft at ability 20.2, to 1 yard at ability
0.1, to 100 yards at ability 0.7, to 1 mile at ability level 0.8.
This result is quite surprising in that it was thought that the item was testing for knowledge
of a fact, a memorizable number. Yet, student choice of distractors followed a pattern that con
A Model for the Sun and a Close Star. The third item analyzed in detail examined the mental
models that students construct for the relative disposition of stars. Stars are very far from us
on the scale of the solar system. The closest star to our solar system is about 200,000 times farther
from it than the sun is from the earth. Or, to put it another way, if the sun were a grape the
earth would be a speck of dust 3 ft away and the closest star would be another grape 100 miles
from us. At this scale, even Pluto would be close to the sun, at a distance of 100 ft. Item 8 asks
just this question with five options for answers; two grapes would make a good scale model of
the sun and a close star, if separated by 1 ft, 1 yard, 100 yards, 1 mile, 100 miles. Since stars
and planets are almost indistinguishable in the night sky, students may not make a distinction
between their distances from us. Among 200 11- to 13-year-old Italian students interviewed,
there was no distinction between stars and planets (Loria et al., 1986).
The probability of answering this question correctly declined slightly from 22.0 to 0.0 and
then rose sharply, reaching a value of 0.5 at an ability of 0.9 (Figure 3). The “don’t know” option
dropped to a value of 0.5 at a u of 0.2. Examining the detail of the trace lines of the four
incorrect options shows a progression of preferences from 1 ft at ability 20.2, to 1 yard at ability
0.1, to 100 yards at ability 0.7, to 1 mile at ability level 0.8.
This result is quite surprising in that it was thought that the item was testing for knowledge
of a fact, a memorizable number. Yet, student choice of distractors followed a pattern that con
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