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Preservice Teachers Experiencing Mathematics through Moon Projects and Spinning Tops
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| | Unformatted Document Text:
Figure 1 displays a group’s conjecture that in order for a top to be “successful,” it must have
equal-length sides. This group found that this conjecture was untrue since right triangular and rectangular (geometric shapes with unequal sides) shaped tops were just as good at spinning as their counterparts with equal lengths.
Figure 2 – Pre-service teachers discover that their most successful top’s body was
located one inch from the floor and its weight was equally distributed along the top’s rim.
Table 1 illustrates two interesting features that emerged from another group’s data collection.
First, it appeared that the best spin time was obtained for the top with an axis length nearly equal to the radius of the top (a spinning plate). The second interesting relationship involved the ratio of the axis length below the spinning plate to the axis length above the spinning plate. The ratio that produced the best spin time was 0.17, which occurred when using both an axis length of 8.7 cm and an axis length of 18.6 cm. This group concluded that further data collection would be needed to test both of these new emerging mathematical relationships. Figure 2 displays a bar graph where this group discovered that their most successful top’s body was located one inch from the floor with weights (coins) evenly distributed along the top’s (a paper plate) rim.
Most students found the tops investigation accessible and interesting due to the fact that it
contextualized many mathematical concepts, such as ratios, limits, statistics, and geometrical relationships. Students also indicated that they would conduct mathematical inquiry with tops within their own classrooms. In fact, one pre-service teacher used the tops investigation during her student teaching assignment at an area middle school. She conducted the tops activity over a period of two days. The cooperating teacher within the classroom remarked that one seventh-grader reported working on the assignment at home, which was something that he had never done throughout the entire year in his mathematics class.
32.7 s
10.3 s
6.7 s
2.3 s
1.7 s
0.7 s
Inches (base from floor)
Outside weights
Inside weights
in
in
in
Seconds
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| | Authors: Wilhelm, Jennifer., Cooper, Sandi. and McMillan, Sally. |
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Figure 1 displays a group’s conjecture that in order for a top to be “successful,” it must have
equal-length sides. This group found that this conjecture was untrue since right triangular and
rectangular (geometric shapes with unequal sides) shaped tops were just as good at spinning as
their counterparts with equal lengths.
Figure 2 – Pre-service teachers discover that their most successful top’s body was
located one inch from the floor and its weight was equally distributed along the top’s rim.
Table 1 illustrates two interesting features that emerged from another group’s data collection.
First, it appeared that the best spin time was obtained for the top with an axis length nearly equal
to the radius of the top (a spinning plate). The second interesting relationship involved the ratio
of the axis length below the spinning plate to the axis length above the spinning plate. The ratio
that produced the best spin time was 0.17, which occurred when using both an axis length of 8.7
cm and an axis length of 18.6 cm. This group concluded that further data collection would be
needed to test both of these new emerging mathematical relationships. Figure 2 displays a bar
graph where this group discovered that their most successful top’s body was located one inch
from the floor with weights (coins) evenly distributed along the top’s (a paper plate) rim.
Most students found the tops investigation accessible and interesting due to the fact that it
contextualized many mathematical concepts, such as ratios, limits, statistics, and geometrical
relationships. Students also indicated that they would conduct mathematical inquiry with tops
within their own classrooms. In fact, one pre-service teacher used the tops investigation during
her student teaching assignment at an area middle school. She conducted the tops activity over a
period of two days. The cooperating teacher within the classroom remarked that one seventh-
grader reported working on the assignment at home, which was something that he had never
done throughout the entire year in his mathematics class.
32.7 s
10.3 s
6.7 s
2.3 s
1.7 s
0.7 s
Inches (base from floor)
Outside weights
Inside weights
in
in
in
Seconds
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