By examining the three textbooks, the researcher generalized ten sets of objects evident in the three textbooks. These ten objects are:
1: Abstract Graph 2: Circular Frustum 3: Cone 4: Cylinder 5: Pyramid Frustum 6: Platonic Solid 7: Prism
8: Pyramid
9: Real-World or Composite Solid 10: Sphere
The distribution of the counts of 3-D objects in each curriculum standard is captured in Table 5-4, and Table 5-5 illustrates the counts in each textbook. The total counts of 3-D objects are slightly larger than the total counts of units in both tables because some of the units include more than one 3-D object.
In the CS-US, real-world or composite solid is the most used object, which is due to the emphasis on mathematical modeling and the connection to the real world. Cylinder, sphere, cone, and pyramid are almost equally required with counts of 2, 1, and 1 respectively. In the CS-
NCTM, among the 4 standards, virtually no specific 3-D object type is mentioned, but there is a mention in mathematical modeling of connecting geometry to arts and architecture. CS-NCTM tends to give general requirements rather than denote the objects. CS-China states eight types of 3-D objects identified in this study, all except the circular frustum and Platonic solids. Clearly, CS-China acknowledged more varieties of 3-D objects than the other two standards, as CS-US only identified five types, and CS-NCTM recognized just one type.
The Discovering Textbook covers nine types of objects, among the total ten objects. Real-world or composite solid, prism, and pyramid are the most used objects, which generate 30, 18 and 11 references. The least used objects are abstract graph, pyramid frustum and platonic solid, which have one or two counts. The circular frustum doesn’t appear in the text at all. This text seems to use relatively diverse objects in the unit because the entire objects counts are slightly larger than the counts of units, and real-world and composite solids account for almost half of the units.
Table 5-4: Three-dimensional Objects across Three Curriculum Standards CS-US CS-China CS-NCTM 1: Abstract Graph 0 1 0 2: Circular Frustum 0 0 0 3: Cone 1 2 0 4: Cylinder 2 2 0 5: Pyramid Frustum 0 2 0 6: Platonic Solids 0 0 0 7: Prism 0 4 0 8: Pyramid 1 2 0 9: Real-world or Composite solid 6 3 1 10: Sphere 2 3 0 Total 12 19 1 Units in total 7 18 4
*Each unit can have one count at most of each sort of 3-D object. However, there might be multiple sorts of objects evident in one unit.
Table 5-5: Three-dimensional Objects across Three Texts USA Discovery textbook USA Pearson Textbook China People's Education Textbook 1: Abstract Graph 1 4 48 2: Circular Frustum 0 0 4 3: Cone 6 8 3 4: Cylinder 6 7 4 5 : Pyramid Frustum 1 0 1 6: Platonic Solids 2 0 0 7: Prism 18 31 28 8: Pyramid 11 10 7 9: Real-world or Composite solid 30 21 21 10: Sphere 7 5 4 Total 82 86 120 Units in total 72 89 104
*Each unit can have one count at most of each sort of 3-D object. However, there might be multiple sorts of objects evident in one unit.
The Pearson textbook covers seven objects out of the total ten objects. Prism, real-world or composite solid, and pyramid are the most used three objects, which account for 31, 21 and 10 references. The least used two objects are abstract graph and sphere, which have 4 and 5
references respectively. Three objects, which are the circular frustum, pyramid frustum, and platonic solids are not shown in the text at all.
In the People's Education textbook, among the total ten objects, nine objects appear in the content, all except platonic solids. It tends to use abstract graph, prism and real-world or
composite solids more frequently, which account for 48, 28, and 21 references. The least frequent objects are frustum and cone, which have 1 and three references respectively. This text tends to use relatively diverse objects in each unit similarly to the Discovering Textbook.
Prism and real-world or composite solid are the primary objects across the three texts, which number around 20-30 in each text. It shows that all texts underscore connection to the real world, and students’ own experiences. Although all texts mention cone, cylinder, pyramid, and sphere almost equally, they are less visible, around 5-6 counts in each document. The circular frustum is not mentioned at all in either US text. While in Chinese text, the pyramid frustum is integrated with prism and pyramid, to show the connection between the three, and similarly, the circular frustum is associated with cone and cylinder. The logic behind associating the three types is: prisms and cylinders are the most common objects, and the top bases and bottom bases are parallel and congruent; pyramids and cones are extreme cases of prisms and cylinders, whose top bases become points; while pyramid frustums and circular frustums are the partial leftovers of pyramids and cones when dissected by a cross-section parallel to the bottom base. The Discovering Textbook only mentions platonic solids as unique regular solids. Abstract graphs seldom appear in the US texts but are the most popular object in the Chinese text. This is mainly because China text stresses abstract thinking. The US texts tend to emphasize volume and surface areas of specific objects.
The author also compared the differences and commonalities among the three textbooks in a diagram, Figure 1-3 in Appendix D.