The results of the analysis are sho

The results of the analysis are shown in Table 2 above. In the discussion following, the
research questions will be addressed in turn. Excerpts are used to elucidate some distinctions
between students' responses.
Overall, students found difficulty in visualising three-dimensional objects with an accurate
awareness of their mathematical properties. Table2 shows that for Task 1 most children could
visualise a three-dimensional object, but could not describe the three-dimensional aspects of it.
Results from Task 2 showed that a number of students were unable to match their
visualisation ofa cereal box shape to any similar shape in the real world (33% in Year 1, 30%
in Year 3 and 18% in Year 5). Some oftlie responses givenby students were related to a twodimensional
rather than a three-dimensional image eg "a door", "a piece of paper".
Results for Task 3 indicate that most students were unable to give the visualised box
shape its correct mathematical name and even those students who did name the shape
correctly in Task 3, sometimes misnamed it in later tasks," It seems that, considerable
confusion existed at all grades about the correct meaning of the terms side, face, corner, edge,
rectangle, and square as well as rectangular prism.
Task 6 revealed that most student::; had difficulty selecting the cardboard shapes that
would make up into a cereal box shape. Table 2 shows that only 36% of Year 5 and 30% of
Year 3 students completed the task accurately. The large number of students (a total of 91 %
for Year 1, 50% for Year 3 and 27% for Year 5), who choose either four shapes only or any
other incorrect combination of shapes (i.e., not six shapes) reinforces results of Task 1 where
students were unable to describe the number of faces of the cereal·box shape. Although Task 6
was completed after the students had handled a cereal box in Task 5, it required a good deal of
visualisation ability to imagine the cardboard shapes, which were laid flat on the table, built up
and stuck together as a single three-dimensional shape. It appears that the visualisation ability
necessary to complete this task had not yet developed for the majority of students.
Task 7, in which students were asked to examine five possible nets of a cereal box shape
and identify the correct nets, was poorly answered by all students. This task required more
developed visualisation ability than for Task 6 as the students had to imagine all the faces
folded up without the opportunity to handle the individual faces.
2. In their visualisations, do students focus on critical or non-critical aspects of threedimensionalobjects?
Are these aspects mathematical properties?
The results showed that non-mathematical aspects featured strongly in students'
responses across grade levels. Overall, a majority of students used a combination of nonmathematical
and mathematical properties. Table 2. shows that for Task 1, 17% of Year 1
students described the shape using non-mathematical properties only. These students talked
about the colour, the illustrations and the texture of the cereal box shape, but did not use
mathematical terms such as faces, vertices or edges. For example: Mark (Year 1): "It has
pictures on it, it's fat and sort of hard and it's got red and white writing on it".
247 MERGA23 - July 2000
A further 83% of Year 1 students, 80% of Year 3 and 73% of Year 5 students described
the shape using a combination of non-mathematical and mathematical properties. However,
20% of Year 3 and 27% of Year 5 were able to describe the shape using mathematical terms
only, even though at times the mathematical descriptions were not always correct. For
example: Toa (Year 5): "It's a rectangle and it's got 6 faces and 4 sides."
Similar results appear for Task 5, when the students were asked to describe the shape of a
cereal box they were given to hold. Again most students used a combination of nonmathematical
and mathematical properties in their descriptions (83% in Year 1,90% in Year 3,
and 82% in Year 5). The attention to non-mathematical properties in Tasks 1 and 5 continued
despite the researcher's prompt, "Is there anything else you can tell me about the shape of the
box" (with emphasis on the word shape). Similarly in Task 8, despite the removal of stimuli,
students continued to mention the colour, design and texture of the shape as well as some
mathematical properties. For example: Amber (Year 1): "It's brown and it feels rough and it
has sticky tape on it and it has four corners and it's a square".
Responses to Tasks 1, 5, and 8 which described the shape using mathematical terms only
were low (0% Year 1, 20% Year 3 and 27% Year 5 respectively). In their visualisation for
Task 1, most Year 1 students (92%) were unable to name correctly any mathematical
properties of the shape. With the box held in their hands, 75% of these Year 1 students were
still unable to name correctly any mathematical properties of the s