This study investigated the effectiveness of an instructional program (schema-based instruction, SBI) designed to teach 7th graders how to comprehend and solve proportion problems involving ratios/rates, scale drawings, and percents.
Program Schemas With Equality.
In the second part of the paper, we discuss the decision problems of program schemas with equality.
We discuss the class of program schemas augmented with equality tests, that is, tests of equality between terms.
It turns out that the class of program schemas with equality is more powerful than the "maximal" classes of schemas suggested by other investigators.
Program schemas should capture not only structured program design principles, but also domain knowledge, both of which are of crucial importance for hierarchical program synthesis.
We suggest, however, limited equality tests which can be added to certain subclasses of program schemas while preserving their decidability property.
The method uses a 0 1 programming schema, having feasible solutions corresponding to prime implicants.
The latter is based on adding a suitable minimization function to the basic 0 1 programming schema so that finding optimal solutions corresponds one-to-one to generating prime implicants of the original theory.
The former amounts to solving the basic 0 1 programming schema first, to obtain an implicant ψ′ (not necessarily a prime one), and then generating a prime implicant implied by ψ′.
Topics in this volume include: exploiting subprograms in genetic programming, schema frequencies in GP, Accessible AI, GP for Big Data, lexicase selection, symbolic regression techniques, co-evolution of GP and LCS, and applying ecological principles to GP.
