An analysis of geometry learning in a problem solving context from a social cognitive perspective

Abstract

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.