STRUCTURAL LEARNING THEORY

The Structural Learning Theory (SLT) is a prescriptive theory conceived and developed by Joseph Scandura. This theory has been expansively applied to mathematics and its primary focal point as a theory is problem solving instruction (Scandura, 1977). According to Ikegulu (1996:6) the structural learning theory is an instructional theory that concerns itself to what occurs within the learner‟s brain during teaching (instruction) and the learning process. It is assumed that the learners organise their learning in the form of rules and they adjust and apply it to modify their existing knowledge. Educational psychologists Jean Piaget and William Perry who developed the cognitive approach also paid attention to what went on inside a learner‟s head hence they focussed on the mental processes involved.

In the SLT what is learned are rules of domain, range and procedure (Scandura, 1977). According to Scandura (1977) and Ikegulu (1996:10-11) domain is a set of inputs or internal cognitive structures that is relevant to a learning situation; range is outputs that the rules are expected to

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produce and procedure is the sequence of operations or the progression of unfolding events that is essential to generate the desired outputs.

SLT prescribes teaching the simplest solution path for a problem and then teaching more complex paths until the entire rule has been mastered (Ikegulu, 1996:8). When the higher order rules are facilitated then these rules generate new rules. This in turn makes it possible to solve complex problems by making it possible to learn new rules. This theory also suggests a strategy for teaching only the rules which the learner has not mastered. Content should be taught in the form of rules. This is a logical sequence by which the solution to the problem is derived. The lower order rules need to be taught, namely, teaching the basic concepts so that the learners are able to apply them when confronted with other problem situations. When applying the lower order rules, this brings about conceptual understanding to the problem. Through this, the higher order rules are derived which enables the learners to develop their background knowledge and solve mathematical problems in various forms (Ikegulu, 1996; Scandura, 1997). When the higher order rules are used, namely, rules that generate new rules, then problem solving may be facilitated whereby the learners are capable of solving problems that they have not confronted before (Ghazali, 2011; Scandura, 1977).

According to Scandura (1977) SLT is a methodology for identifying the rules to be learnt for a given topic and then breaking them down into components. SLT identifies the components for solving problems and this procedure is known as structural analysis. According to Ghazali (2011) and Scandura (1977) the major steps in structural analysis are to select a representative sample of problems; identify the rules for unravelling the rules for finding a solution to the problem. One needs to take into account the capabilities of the learners. The various operations involved in solving the problem must be taught according to the capabilities of the learners. The learners should therefore be taught procedural knowledge (step by step calculation procedures) that will enable them solve the problem; convert each solution rule into a higher order problem thereby eliminating lower order rules; identify a higher order solution rule for solving the new problems thus showing their understanding of the problems; assess and improve the rules by eliminating the redundant solution rules.

An importance aspect of this theory is the importance of learner‟s prior knowledge that will aid in creating new ideas (Scandura, 1977). According to Ikegulu (1996:19) having a well-structured knowledge connection allows for easier retrieval of prior knowledge and the facilitation of new knowledge.

SLT is a cognitively oriented model combining learning theories, instructional theories and instructional development theories (Ikegulu, 1996:7). As a cognitively model it is important to

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review the learner‟s previous level of understanding to establish their skills and knowledge for the lesson (Ikegulu, 1996:16-17). This will allow the teacher to present new material content in little steps using unambiguous language and positive examples. The teachers provide feedback when the answers are correct or reteaching occurs when conceptual understanding or answers are incorrect. The teachers spend more time on evaluating and teaching until the learners have an understanding and confidence in their techniques to solve the problems.

According to Ikegulu (1996:21-22) the SLT as an instructional theory support the learners creativeness and reduces or limits the learners rate of forgetting and recollection. This is attained through graphic organizers. This takes the form of diagrammatic expressions (using some sort of representation). The teacher provides the learner with a wide variety of diagrammatic representations and at the same time the learners are taught and encouraged to develop their own graphic representations to assist them problem solve. Together with this the learners should be provided with guided practice on solving problems on the chalkboard using examples. The learners should be engaged in discussing the steps to solving the problem (individually, group work or as a class). This practice is consistent with the cognitive model because it “paves the way for learners to construct their own mental model, adjust their existing schema, and reconstruct a “NEW” schemata” supported by the new knowledge obtained from the teacher (Ikegulu, 1996:25).