Traditionally, geometry at school starts on a formal level, largely ignoring prerequisite
skills needed for formal spatial reasoning. Ignoring that geometry has a sequential and
hierarchical nature causes ineffective teaching and learning.
The Van Hiele theory postulates learner progression through levels of geometry
thinking, from a Gestalt-like visual level through increasing sophisticated levels of
description, analysis, abstraction, and proof. Progression from one level to the next
does not depend on biolog~caml aturation or development only, but also on appropriate
teachingllearning experiences. A higher thinking level is achieved through the
application of a series of learning phases, consisting of suitable learning activities. The
teacher plays an important facilitating role during this process.
In accordance with the social cognitive learning perspective on self-regulated learning,
geometry learners must direct their thoughts and actions while completing activities in
order for effective learning to take place. Learners can be described as being selfregulated
to the degree that they are metacognitively, motivationally, and behaviorally
active in their own learning. The social cognitive theory assumes that students enter
learning activities to acquire knowledge, learning how to solve' problems and
completing learning activities. Self-regulated learners are aware of strategic relations
between self-regulatory processes and learning outcomes and feel self-efficacious
about using strategies. Self-regulation is similar to metacognitive awareness, which
includes task and personal knowledge. Self-regulated learning requires that learners
understand task demands, their personal qualities, and strategies for completing a task. A Van Hiele-based geometry learning and teaching program was designed (with a
problem solving context in mind) and implemented in four Grade 7 classes (133
learners) at two schools. The study investigated factors and conditions influencing the
effective learning and teaching of spatial concepts, processes and skills in different
contexts.
Results suggest that the implementation of a Van Hiele based geometry learning and
teaching program in a problem solving context had a positive effect on the learners'
concentration, when working on academic tasks, and level of geometric thought. The
higher levels of geometric thought included higher categories of thought within these
levels. Learners who completed the program reasoned on a higher level, ,gave more
complete answers, demonstrated less confusion, and generally exhibited higher order
thinking skills than their counterparts who did not take part in the program. The only
prerequisite' is that the teacher should consistently teach from a learner-centered
approach as the program will deliver little or no advantages if the program is presented
in a teacher-centered content-based context. / Thesis (M.Ed.)--Potchefstroom University for Christian Higher Education, 2000.
| Identifer | oai:union.ndltd.org:NWUBOLOKA1/oai:dspace.nwu.ac.za:10394/48 |
| Date | January 2000 |
| Creators | Van der Sandt, Suriza |
| Publisher | Potchefstroom University for Christian Higher Education |
| Source Sets | North-West University |
| Detected Language | English |
| Type | Thesis |
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