Developing insight into teachers' didactical practice in geometric proof problem solving
Developing insight into teachers' didactical practice in geometric proof problem solving
Research is needed towards developing understanding of the complexity of students’ cognitive structure and the significance of teachers’ instruction in the learning and teaching of geometry.
This study investigates how school teachers in China approach the teaching of proof in geometry. In particular, this study focuses on two aims: To explore and elucidate the complexity of individual teacher’s didactical practice towards the development of students’ thinking for writing proofs in geometry; to understand in what way the van Hiele model is a useful research tool to help analyse and interpret classroom teaching and learning of geometrical proof problem solving.
This study concentrates on three teachers’ regular classes at Grade 8 in two common lower secondary schools in Shanghai (students’ age, 13-14 years old). The van Hiele model is applied to analyzing data in this study. The data analysis consists of case study and statistical analysis of the three teachers’ lessons which were on the topic of the quadrilateral family (parallelogram, rectangle, rhombus and square) for approximately 13 hours over a three week long school curriculum. Interview data regarding teachers’ didactical views and small-scale survey data of Grade 8 students’ learning results on formal proof writing was also collected.
Findings of the study indicate that students’ geometric thinking in solving geometrical proof problems appears to be more complex than that ascribed by the van Hieles. On the one hand, across a set of proof problems, the visual, analytic and deductive thinking may concurrently grow up together; on the other hand, however, they may limit each other’s development. Thus, this study proposes a dynamic view of the van Hiele levels of geometric thinking.
University of Southampton
Ding, Liping
e04dabec-984e-4644-b838-16fba10454d2
2007
Ding, Liping
e04dabec-984e-4644-b838-16fba10454d2
Ding, Liping
(2007)
Developing insight into teachers' didactical practice in geometric proof problem solving.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
Research is needed towards developing understanding of the complexity of students’ cognitive structure and the significance of teachers’ instruction in the learning and teaching of geometry.
This study investigates how school teachers in China approach the teaching of proof in geometry. In particular, this study focuses on two aims: To explore and elucidate the complexity of individual teacher’s didactical practice towards the development of students’ thinking for writing proofs in geometry; to understand in what way the van Hiele model is a useful research tool to help analyse and interpret classroom teaching and learning of geometrical proof problem solving.
This study concentrates on three teachers’ regular classes at Grade 8 in two common lower secondary schools in Shanghai (students’ age, 13-14 years old). The van Hiele model is applied to analyzing data in this study. The data analysis consists of case study and statistical analysis of the three teachers’ lessons which were on the topic of the quadrilateral family (parallelogram, rectangle, rhombus and square) for approximately 13 hours over a three week long school curriculum. Interview data regarding teachers’ didactical views and small-scale survey data of Grade 8 students’ learning results on formal proof writing was also collected.
Findings of the study indicate that students’ geometric thinking in solving geometrical proof problems appears to be more complex than that ascribed by the van Hieles. On the one hand, across a set of proof problems, the visual, analytic and deductive thinking may concurrently grow up together; on the other hand, however, they may limit each other’s development. Thus, this study proposes a dynamic view of the van Hiele levels of geometric thinking.
Text
1184030.pdf
- Version of Record
More information
Published date: 2007
Identifiers
Local EPrints ID: 466480
URI: http://eprints.soton.ac.uk/id/eprint/466480
PURE UUID: 9f1ffd3b-59d8-4f23-84ce-33a06489a4f5
Catalogue record
Date deposited: 05 Jul 2022 05:18
Last modified: 16 Mar 2024 20:43
Export record
Contributors
Author:
Liping Ding
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics