Figure 2. Interactive
spinner from BrainAbility.
Research suggests that 21st-century
students tend to be visual learners. Visual literacy (VL) is “the critical
ability which will enable [people] to use visual images accurately and
behave appropriately” (Christopherson, 1997, p. 69). VL is becoming
an integral part of student learning for the digital generation. Healy
(1998) asserts, “It is likely that visual literacy will increasingly
infiltrate other disciplines...[but, visual literacy] skill[s] must
be taught and linked to important learning” (p. 301). By working collaboratively
with teachers to select math applets that are connected directly to
the curriculum's scope and sequence, our professional development activities
promote visual learning skills that are timely, relevant, and effective.
Context of Our Professional Development
This study involved a middle school, serving primarily low social economic and minority students, which achieved double-digit gains in its scores on the state's standardized math test. In order to maintain achievement gains, the staff developer, math curriculum leader, technology coordinator, and representatives from the math department implemented a campus-wide plan to increase math instruction and enlist the support of other non-math teachers. First, using disaggregated student data, district benchmarks, and the state curriculum framework as its guide markers, the committee generated scope and sequence and tied it to a calendar that delineated the amount of time afforded to each sub-objective.
Raising scores and maintaining gains in math scores would become a whole campus effort, with math teachers offering tutoring before and after school and non-math teachers implementing a 30-minute, mid-day session. Non-math teachers supported and facilitated the campus plan for increasing math proficiency. Math teachers developed lessons which non-math teachers could implement during these 30-minute, mid-day sessions. By enlisting non-math teachers, math teachers could reach four times as many students.
Math Teachers Develop and Revise Plans
The technology coordinator/staff-developer showed math teachers how they could use search engines to locate interactive applets to enhance instruction. A rubric for rating the applets helped in the selection process and revealed the wide-ranging quality and appropriateness between applets. Three sites provided the majority of applets that our math teachers needed for their projects: 1) the National Library of Virtual Manipulatives website (http://nlvm.usu.edu/en/nav/vlibrary.html); 2) the Shodor Interactivate website (http://www.shodor.org/interactivate/); and 3) the MathsNet website (http://www.mathsnet.net/geometry).
From Selection to Implementation
Successful training sessions involved hands-on activities, continuous training, modeling and mentoring, and the availability of follow-up training (Roblyer, 2000). Our math teachers and the technology coordinator collaboratively constructed web pages with links to task-related applets. They also created a calendar for each grade level, which depicted the math concept of the day and a link to the applet that would support the strategy. Next, math teachers shared implementation plans with the non-math teachers. The math teachers, curriculum coach, and technologists provided ongoing peer assistance for non-math teachers. Mentors described applets, explained their targeted use, and demonstrated the integration process as they coached their fellow teachers. The technologists provided just-in-time support as non-math and math teachers brought their students to the computer labs during the mid-day sessions. Non-math teachers supervised students' use of the math applets during the mid-day math sessions.
Sample Data for One Block
During 180 minutes of traditional
instruction over a period of one week, one of the math teachers used
overhead acetates, models, manipulatives, and dittos to assist students
in learning about platonic solids. Five days later, students were administered
a 5-question assessment in which they were asked to name the platonic
solids, draw the shapes, and describe their attributes (edges, faces,
vertices). This test served as a pre-test for the lab phase of the study.
Results on the pre-test indicated that 87% of the students were unable
to name more than two of the shapes, 97% were unable to draw more than
three of the shapes, and 50% correctly identified the number of faces
in three or more of the solids. Less than 10% could identify the number
of vertices and no students were able to identify the number of edges
in all of the platonic solids. Thirteen students were absent on one
or more days or failed to complete the tests, therefore data was computed
using data from the remaining 100 students. Students received instructions
during the first five minutes, spent 20 minutes on the computer manipulating
applets, and completed their session with a 5-minute post-assessment.
Table 1
Pre-Assessment : Identifying Names and Characteristics of Platonic Solids
Name of Platonic solid |
Net Diagram |
Faces |
Vertices |
Edges |
Correct Responses |
5 |
5 |
10 |
30 |
90 |
0 |
60 |
8 |
50 |
40 |
5 |
1 |
20 |
20 |
30 |
22 |
5 |
2 |
14 |
60 |
7 |
6 |
0 |
3 |
1 |
3 |
2 |
2 |
0 |
4 |
0 |
0 |
1 |
0 |
0 |
5 |
The first post-test indicated improvement in two areas: the shapes and faces of platonic solids. During the session, students discovered that using the shift key and clicking on the vertices and edges colorizes the lines and points, facilitating counting accuracy. Students spent the majority of their time exploring the tetrahedron, hexahedron, and octahedron.
Table 2
First Post-Assessment: Identifying Names and Characteristics of Platonic Solids
Name of Platonic Solid |
Net Diagram |
Faces |
Vertices |
Edges |
Correct Responses |
0 |
2 |
0 |
10 |
22 |
0 |
10 |
0 |
2 |
40 |
16 |
1 |
50 |
30 |
11 |
28 |
38 |
2 |
27 |
60 |
22 |
6 |
20 |
3 |
8 |
8 |
34 |
12 |
2 |
4 |
5 |
0 |
21 |
4 |
2 |
5 |
The first post assessment indicated that the students continued to have difficulty with the names and shapes of the dodecahedron and the icosahedrons. Two days later, we administered a second 20-minute session, this time asking students to focus on net-diagrams, names of the figures, and number of faces and vertices. Students wrote the names of the solids on paper as they worked with the animations at Platonic Solids. Students explored net diagrams at Nets, Unfolding Polyhedra.
Table 3
Second Post-Assessment: Identifying Names and Characteristics of Platonic Solids
Name of Platonic Solid |
Net Diagram |
Faces |
Vertices |
Edges |
Correct Responses |
0 |
0 |
0 |
10 |
22 |
0 |
10 |
0 |
0 |
20 |
10 |
1 |
10 |
2 |
2 |
48 |
36 |
2 |
68 |
1 |
12 |
6 |
24 |
3 |
7 |
81 |
15 |
12 |
4 |
4 |
5 |
16 |
71 |
4 |
4 |
5 |
The second post assessment showed that students more closely associated the faces and names with the net diagrams for each platonic solid. Although we encouraged students to verbalize the name of the solid as they counted the faces, edges, and vertices, post assessment clearly indicated more work was needed in this area. However, we began to see an emerging understanding of the relationships between faces and vertices as students worked with the animations.
During the third session with the online platonic solids, students were encouraged to look at relationships among the edges, faces, and vertices as they explored the platonic duals using Euler's formula and the applet Platonic Duals.
