Structural Learning Theory

Structural (Domain) Analysis

Structural analysis (SA) is a systematic method for constructing arbitrarily precise representations of what needs to be learned to master any given domain. To-be-learned competencies are represented in terms of cognitive constructs referred to as SLT rules. Each SLT rule consists of a procedural hierarchy operating on a data structure hierarchy. Both are represented formally in terms of abstract syntax trees (ASTs). Cognitively speaking, data ASTs represent increasingly automated encodings (directly perceived data) and corresponding (to-be-decoded) data generated therefrom. SLT rules may be thought of as hierarchies of equivalent programs, each with its own (hierarchical) data structure. In effect, SLT rules represent hierarchies of increasingly automated to-be-learned procedures operating on data at various levels of abstraction. Procedures higher in a hierarchy are simpler than those lower but operate on relatively complex data structures. Lower level procedures are more complex operating on simpler data.

Given a well-defined problem domain, the first step in SA is to specify SLT rules (cognitive constructs) that account for behavior in that domain. These SLT rules represent competences a subject matter expert (SME) believes should be learned for success—simultaneously at all levels of abstraction. SLT rules have no direct relationship to what may be in human brains. SA is a systematic method for identifying (cognitive) constructs that make it possible to explain, predict, and direct student behavior.

SA begins by selecting a prototypic set of problems in some domain. These prototypes represent what an SME believes adequately represents the range of behavior students are to perform. The first step is to assign a name to the top level operation along with its input and output parameters. Given the domain of solving linear equations, one top level operation might be solve (equation: ; solution); another might be solve (: equation;). The input-output parameter equation in the latter represents the equation before and after solution.

The next step is to create an SLT rule (hierarchy) sufficient for solving all problems judged similar to the prototype. As detailed in a U.S. patent (8,750,782) issued June 10, 2014, a small number of data and corresponding procedural refinement types are sufficient. Allowed data refinements are component, prototype, category, and dynamic. Corresponding procedure refinements are sequence, parallel, iteration (Repeat … Until, While … Do), selection (If … Then, Case), and interaction (callback). Furthermore, SMEs may construct any number of equivalent SLT rules (cf. borrowing and equal additions methods for column subtraction). The same top-down process is repeated for each prototype.

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