The main objective of this study was to investigate the hierarchical nature of the van Hiele levels in the learning of transformation geometry. Secondary school students in Singapore completed tasks using the concepts of reflection, rotation, translation and enlargement. In addition, the van Hiele levels of two current Singapore textbooks were analyzed for transformation geometry. / A level characterization for transformation geometry was written after interpreting related research reports. Test items were then developed, and critiqued by a nationally-based panel of mathematics educators. The items, revised for the first four levels were used in interviews with twenty secondary four students (ages 15-16) from a school. The audiotaped and videotaped interviews took two sessions of one and a half hours each. In the analysis, two persons independently assigned levels based on students' responses. These responses were analyzed for existence of level hierarchy using a Guttman Scalogram and for patterns of thinking. Textbooks were analyzed to identify levels for the content and the sequencing of the levels in the material. / Results indicated the levels form a possible hierarchy. The percentage of responses at each level of thinking was: 42.5%, Basic; 36.25%, Level 1; 6.25%, Level 2; 12.5%, Level 3. Analysis of responses revealed students: (1) had misconceptions with enlargement which is the least achieved concept; (2) perceived transformations in terms of motion before attending to the properties associated with the transformation; (3) lacked precise vocabulary to describe transformations; (4) had difficulties in relating a matrix to a transformational picture; (5) continually referenced teachers and text as reasons for their solutions; (6) did proofs using particular examples. The textbook analysis showed expository lessons with many worked examples and exercises characterized at Level 1 and Level 2 pertaining to coordinate and matrix system. Also there was an absence of hands-on activities and applications to real life situations with little opportunity for students to explore, reflect and conjecture. / The study has implications for teacher-educator in preparing the teachers to provide appropriate learning environments. The implication for the curriculum developer and textbook writer is in restructuring curricula. / Source: Dissertation Abstracts International, Volume: 50-03, Section: A, page: 0619. / Major Professor: Janice Louise Flake. / Thesis (Ph.D.)--The Florida State University, 1989.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_77973 |
| Contributors | Soon, Yee-Ping., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 200 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
Page generated in 0.002 seconds