Table 4
Third Post-Assessment: Identifying Names and Characteristics of Platonic Solids
Name of Platonic Solid |
Net Diagram |
Faces |
Vertices |
Edges |
Correct Responses |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
8 |
2 |
3 |
1 |
0 |
3 |
8 |
3 |
12 |
6 |
5 |
2 |
2 |
4 |
85 |
92 |
95 |
95 |
82 |
5 |
After 23-minute sessions in the lab, more than 90% of the students in this block were able to draw the net diagrams, recognize the shapes and number of the faces of the platonic solids, and determine the number of vertices. More than 80% of the students were able to name the platonic solids and to apply Euler's formula to determine the number of edges for each of the platonic solids. Teachers reported that the use of math and science applets increased their pedagogical and content specific skills. They also observed that applets strengthened students' visual literacy skills while revealing students' misconceptions and learning difficulties.
Comments on Targeted Areas
Seventh Grade Project-Platonic
Initially, students identified the names of the five platonic solids, the shapes of their faces, and the number of faces found in each. Students visited Math World where they rotated images and looked at net diagrams. The Platonic Solids and Platonic Duals were helpful in cultivating students' understanding of platonic solids, whereas Nets and Unfolding Polyhedra helped them understand net diagrams, and Euler's formula helped them recognize the mathematical relationship among the edges, faces, and vertices.
Students' active construction of knowledge increased as they engaged in the interactive process of identifying and manipulating edges and vertices. Platonic Duals assisted students in understanding Euler's formula 
as indicated in the following table:
Table 5
Euler's Formula
As students explored the concept of platonic duals, they discovered that Euler's formula enabled them to calculate edges and vertices when the number of faces is known. For example, the number of edges for hexahedra and octahedra are 12. (For the hexahedron: 6 faces + 8 vertices = 12 edges + 2; conversely, for the octahedron, 8 faces + 6 vertices = 12 edges + 2.)
Sixth Grade Projects-Factoring
and Relationships among Decimals, Fractions, and Percents
Applets at Utah State provided
excellent assistance for teaching factoring,
comparing
fractions, and relationships
among decimals, fractions and percent. Our sixth-grade math teachers
commented on the ease and speed with which students learned these concepts
using the applets. In an independent standardized evaluation taken in
spring 2006, 81% of our sixth graders mastered factorization.
Eighth Grade Projects-Three-D
Visualization
Teachers liked the 3-D visualization applets: 2-D,
3-D,
and house-building.
Students rotated 3-D applets to determine what 2-D representations of
the figure would look like from the right, left, top, and bottom. Color-coding
of student responses helped teachers know how students were progressing.
Immediate feedback enabled students to correct their responses and provided
for deeper engagement. The MathsNet transformation
site helped students learn about dilations, translations, and rotations.
Teachers supplied their students with additional instructional scaffolding
supported by transformation
applets.
Extensions Many teachers who were using applets in 2005 have begun writing their own curriculum and linking to several websites that contain applets. Several of the non-math teachers requested support from the technology coordinator to imbed applets within their curriculum. Use of science applets was especially effective in teaching plate tectonics: ring of fire, plate movement, ridges and zones, timeline, collisions, rocky relationships, and spreading. Science teachers also used web quests, which contained links to animations to teach about rocks and minerals. Teachers who worked collaboratively to develop these units were able to share their experiences and lessons with other science teachers in the district. We also observed a 100% increase in the use of the virtual science labs on CD-ROMs.
Summary
The two goals of our professional development model using applets were to increase student performance and to increase teacher confidence with technology. As illustrated above, we saw short-term gains as demonstrated by the pre and post assessments. We also saw long-term gains in some areas as indicated by state standardized testing. Additionally, we found that teachers' self-efficacy for classroom usage of the computer labs increased during the 2005-2006 school year as indicated by the state's self-assessment of technology proficiency administered in February 2005 and April 2006. Computer activities for students ranged from drill and skill to Internet research and the production of multimedia products.
Comparison of data from 2005 and 2006 teacher self-efficacy surveys indicted teachers were moving beyond the awareness level, the lowest level, and were currently scoring at levels three and four, the target level. During the 2004-2005 school year, 20% of teachers self-assessed their skills at the awareness level. With the 2005-2006 spring survey, no teachers assessed their skills at the awareness level. Additionally, the researchers have observed teachers being more outgoing in creating their own technology-integrated lessons resulting in more student-created multimedia projects.
Teachers responded enthusiastically to ongoing support received while integrating technology into their curriculum. This just-in-time support increased teachers' self-efficacy for technology integration and enhanced student learning. Integrating applets into the curriculum proved to be an efficient, effective way to promote student engagement, activate higher order thinking, and reduce student frustration. Teachers indicated that math applets helped their students visualize difficult concepts. In most cases, math teachers introduced the math concept of the day during classroom time. Then, non-math teachers, using applets during the mid-day sessions throughout the week, supported the classroom activities. Examination of pre-post surveys showed that students improved their understanding of math concepts after a 20-minute session of interactive engagement with the math applet. Follow-up surveys indicated that most students had retained and built upon their ability to understand the concepts that math applets targeted. Additionally, teachers reported that peer collaboration and the use of applets encouraged them to create and implement technology-rich lessons plans.
About the Authors
 |
Dr. Ali Mahdi
Ahmad, associate professor of math at New Mexico State
University-Doña Ana Branch Community College, has taught
at middle school, high school, community college, and at the university
levels. He has presented at several local and national conferences
and received honors for his excellence. Awards include the Donald
Roush award from New Mexico State University and National Institute
of Staff Development excellence award.
Email: aahmad@nmsu.edu
Send correspondence
to:
Ali Mahdi Ahmad, Ph. D
Associate Professor
Department of Mathematics/Physical Sciences
General Studies Division
New Mexico State University-Doñna Ana Branch College
(505) 527-7687 |
 |
Jan Farnam,
a doctoral candidate at the University of Texas at El Paso, is
the technology coordinator at a middle school in El Paso where
she is actively involved in action research in science, math,
and technology. She is a fellow with the Teacher Leaders in Research
Based Science Education Program, funded by the National Science
Foundation's Directorate for Education and Human Resources.
Email: jfarnam@sisd.net
|
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