The effectiveness of van Hiele-based instruction

2005 ◽  
Author(s):  
Kin-wai Liu
Keyword(s):  
Van Hiele ◽  
Based Instruction

scholarly journals Mapping pre-service teachers’ faulty reasoning in geometric translations to the design of Van Hiele phase-based instruction

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Nokwanda P. Mbusi ◽  
Kakoma Luneta
Keyword(s):  
Teacher Knowledge ◽  
Geometric Transformations ◽  
Effective Learning ◽  
Van Hiele ◽  
Test Items ◽  
Diagrammatic Representation ◽  
Bachelor Of Education ◽  
Transformation Geometry ◽  
Based Instruction ◽  
Instructional Programme

Background: Pre-service teachers (PSTs) training does not equip students with adequate skills and knowledge of geometry to enable them to teach this section of mathematics competently. Inadequate teacher knowledge of transformation geometry, in particular, requires intervention that targets PSTs’ faulty reasoning displayed in errors they make.Aim: The aim of this study was to explore the use of Bachelor of Education (BEd) students’ faulty reasoning in geometric translations, in designing a Van Hiele phase-based instructional programme that could address such faulty reasoning.Setting: The setting for the study was a newly established rural university in South Africa.Methods: Tests on geometric translations were administered to BEd Foundation Phase students, followed up by interviews to explore errors made when responding to the test items. The errors were then mapped to the design of a Van Hiele phase-based instructional programme.Results: The results revealed that the students had several misconceptions with geometric translations. The misconceptions were delineated into the errors that the students displayed and these were classified under two themes. The first theme was incorrect properties of transformation and under this theme, the errors were coded as confusing translation with rotation, wrong translation method, incorrect interpretation of coordinates and confusing the x and y axis. The second theme was errors involving basic mathematics operations including wrong diagrammatic representation of coordinates and incorrect calculations.Conclusion: The study showed that if the students’ misconceptions and the resulting errors are mapped to specific instructional approaches, their faulty reasoning in geometric transformations is addressed and effective learning is enhanced.

Cognition of Fundamental Concepts in Geometry

1994 ◽  
Vol 10 (4) ◽  
pp. 349-371 ◽  
Author(s):  
Mian Muhammad Yusuf
Keyword(s):  
Classroom Teacher ◽  
Treatment Plan ◽  
Eighth Graders ◽  
Control Groups ◽  
Van Hiele ◽  
Logo Programming ◽  
Based Instruction ◽  
And Control ◽  
Experimental Group ◽  
Geometry Curriculum

The purposes of this study were: 1) to investigate the effects of Logo Based Instruction (LBI) for the cognition of the four fundamental concepts in geometry, and 2) to explore the possibility of integrating the Logo programming language in the geometry curriculum. The regular classroom teacher taught both the experimental and control groups following the treatment plan designed by the researcher. Interviews of sixteen seventh and eighth graders from each group were audio taped. The results showed that the students in the experimental group had a deeper conceptualization of fundamental concepts in geometry. An ANCOVA test applied to the scores of Interview Sheets, and the t-test applied to the gain in van Hiele levels, were significant in favor of the experimental group. These results are encouraging and support the integration of Logo in the geometry curriculum.

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