with methods students brainstorming about specific features of a “successful” top. Most groups
listed criteria such as: 1) spins at least five seconds, 2) spins perpendicular to the floor, 3) spins
on a point, and 4) has a funnel or cone shape.
Working in groups of three and four, students were then asked to create their top. With a
variety of materials and tools available, students created, tested, revised, and collected data with
their tops. After initial explorations each group formulated a conjecture or question to test or
answer.
Figure 1 – Pre-service teachers test their conjecture that a successful top must have
sides of equal length.
Some mathematical questions explored by the pre-service teachers involved the geometry of
the top (see Figure 1), the ratios of axis length below the top’s body to the axis length above,
varying dowel rod lengths while holding the top’s diameter constant (see Table 1), and the
location and distribution of weight (such as weight along rim or weight centrally located, see
Figure 2).
Table 1 – Pre-service teachers explore the effect of axis length on spin time of top and
investigate how the spin time is affected by the ratio of dowel length below top to dowel
length above top.
Diameter of plate – 18.4 cm; Total length of axis – 8.7 cm.
Amount below
plate
Amount above
plate
Ratio of
amounts
Spin time
1.2 cm
7.1 cm
0.17
25.00 sec
1.7 cm
6.4 cm
0.27
19.12 sec
2.3 cm
5.9 cm
0.39
14.20 sec
Diameter of plate – 18.4 cm; Total length of axis – 18.6 cm.
Amount below
plate
Amount above
plate
Ratio of
amounts
Spin time
2.7 cm
15.9 cm
0.17
8.80 sec
3.9 cm
14.6 cm
0.27
2.80 sec
5.2 cm
13.4 cm
0.39
2.50 sec
After pre-service teachers proposed their question or conjecture, they planned how they
would collect and analyze their data. All groups were required to generate a representation of
their data collection. As shown in Figures 1 and 2 and in Table 1, students chose to represent
their data through sketches and narration, tabular format, and with a bar graph.
Convention