Konzeption und Evaluation eines Kinematik/Dynamik-Lehrgangs zur ...

262 9 Abstract
tion is totally different. In this case, the problems are merely solved by an average of 12 % of students
at the beginning of 11 th grade (n = 373), whereas an average of 71 % give answers as if velocity
had been asked for (chapter 6.4.2.3). After traditional instruction, 47 % of the students on average
answer correctly (n = 188), and 37 % answer as if velocity has been asked for. In case of motions
to the left, an average of 7 % answer as if acceleration were the change of the magnitude of
velocity (“+” = speeding up, “-” = slowing down). Items with motions to the right are solved correctly
more often than items with motions to the left. Within one direction of motion, items with
motions at constant velocity are answered correctly most frequently, followed by items with speeding
up motions, whereas items with slowing down motions yielded the worst results (chapter
6.4.2.3).
A problem regarding the acceleration when tossing a coin vertically up into the air, for which the
algebraic sign for the acceleration with a given coordinate system had to be indicated, produced
similar results. After instruction, only 7 % of the students (n = 188) give the correct answer for all
three phases (upwards, up, downwards), another 10 % at least for the upward phase and the downward
phase (chapter 6.4.3.1). 36 % of the students give an answer regarding the change of the magnitude
of velocity; the task of drawing an arrow for the direction is a problem for many of these
students. 41 % give an answer pertinent to velocity instead of acceleration (chapter 6.4.3.1).
Thus it can be said that in the cases of both types of problems regarding acceleration (graphs and
coin toss) approx. 40 % of the students give answers pertinent to velocity, and approx. 50 % showed
a certain degree of understanding of acceleration, but often only regarding to the change of the mag-
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nitude of velocity a = ∆ v / ∆t
.
Finally problems were set according to which the acceleration had to be given as an arrow only,
with no coordinates system being defined, so that the students could not give “+” for speeding up
and “-” for slowing down. After mechanics instruction, approximately 90 % of the students provide
a correct solution for motions along a straight line (n = 217), whereas only an average of 9 % give
the correct solution for motions along a curved path (at constant speed, speeding up, and slowing
down) (chapter 6.4.1.1). In contrast, an average of 59 % give an arrow representing more or less the
tangential acceleration (possibly curved arrow), whereas it can be assumed that often the conception
of “speeding up/slowing down” was illustrated with arrows.
All in all, the conclusion can be drawn that in traditional instruction, only few students achieve a
physically adequate understanding of acceleration, enabling them to solve problems on acceleration
consequently correctly, also in case of change of direction or two-dimensional cases.
In contrast to the US, in Germany only few classes and a large number of university students have
done the established FCI test on the physical concept of force up to now, whereas this test has been
done for the first time by a larger number of students within the framework of this test (first version
of the test). At the beginning of 11 th grade, the students solve 28 % of the 29 qualitative items correctly,
and 41 % after mechanics instruction (n = 258), which makes up a normalized gain (= ratio
of average gain to maximum possible average gain) of only 18 % (chapter 6.5.1.2). There are especially
low normalized gains with the subscales “Newton’s Second Law” and “superposition”. Here