(Page 5 of 7) - Children's Evolving Understanding of Polyhedra in the Classroom authored by Ambrose, Rebecca. and Kenehan, Garrett.

otherwise attended to those features of the polyhedra. Students tended not to appropriate this
way of analyzing polyhedra perhaps because these attributes were not salient to them.

Individual children varied in the extent to which their responses changed. The median change

of number of property codes from pre- to post- was 3 and the median change in the number of
visual codes was 0. Table 1 contains pre/post- data for four children who represent the diversity
of change observed in individuals. The child who changed the least on the written assessment,
Janet, continued to write about the appearance of polyhedra. For example in responding to the
prompt to describe the elongated square pyramid on the pre-assessment, she wrote, “It looks like
a house, shark and very weird.” Her response to the post-assessment was similar. She wrote, “It
looks like a house, bird’s beak and pour spout.” Both of these responses were coded as

FAMILIAR ASSOCIATION

, a visual code, because the child associated the figure with an everyday

item (a house). While Janet demonstrated the ability to be more analytic in her descriptions, as
will be demonstrated below, a visual approach dominated her thinking. The child whose change
was identical to the median change for the class, Fang, initially wrote about the difference
between a cube and an antiprism as, “they are different because they don’t look the same,” which
was coded as

SAME

, a visual code, because he based his comparison on a visual inspection

without mentioning specific attributes of the polyhedra. In the post-assessment Fang wrote, “they
are different because it don’t have a lot of squares,” which was coded as

TYPE OF 2D SHAPE

because he noticed that the square pyramid had fewer squares than the cube. Fang, like many of
his classmates, tended to focus on the 2D shapes that polyhedra were made of and typically
wrote about that in his descriptions. The child, whose change was among the most dramatic in
the class, Yessenia, initially described the elongated square pyramid as “it looks like a house.” At
the end of the study she wrote, “It has a pyramid on the top and a cube on the bottom and it top
of the cube is open up (sic).” She went from a

FAMILIAR ASSOCIATION

to a more analytic

response where she considered

DECOMPOSE

(ing) the shape into its component parts. She also

noted that when the two parts were put together the top of the cube had to be taken off. Peter, the
student with the most codes on the post-assessment, began the study describing the elongated
pyramid as “it is shaped like a house, lots of squares and lots of triangles, like a cube.” This was
coded as

FAMILIAR ASSOCIATION

(shaped like a house),

TYPE OF 2D SHAPE

(lots of squares and

lots of triangles), and

CORRECT ASSOCIATION

(like a cube). Even at the beginning of the study

Peter was attending to several features in his description. At the end of the study he wrote, “It has
4 triangles, 5 squares, a base, an apex, can spin, 9 faces.” This was coded as

NUMBER OF

SHAPES

(4 triangles, 5 squares),

BASE, APEX, SYMMETRY

(can spin), and

NUMBER OF FACES

showing that Peter considered a variety of attributes as he looked at polyhedra and all were
related to properties rather than visual images. The children’s results showed that they used some
properties in their analysis, most of which were related to type of shapes, while they continued to
refer to visual properties. Some children adopted a more analytic approach than others.

Classwork
After four class sessions, which included building and describing polyhedra, the class

engaged in a sorting and building session to promote understanding of pyramids. To begin the
activity the children were shown a large triangular pyramid and a large square pyramid and
asked what they had in common. After the group established that these pyramids had “mostly”
triangles, and pointy tops (we provided them with the term apex), each child was given a
polyhedron and asked to determine if it was a pyramid or not. In progressing through the sorting
activity, two ideas came up – all of the triangles around the sides of the pyramid had to come all
the way down to the base and a pyramid was all triangles except possibly for the base which