In Could John Stuart Mill Have Saved Our Schools?, Siegfried Engelmann and Douglas Carnine discuss the philosophical foundations of their acclaimed Direct Instruction programme (see Part 1). They write of their serendipitous rediscovery of Mill’s work and that they
came across Mill’s work and were shocked to discover that they had independently identified all the major patterns that Mill had articulated. Theory of Instruction  even had parallel principles to the methods in [Mill’s] A System of Logic [published in 1843].
— location 543 Kindle edition
What Engelmann and Carnine are attempting to do is no less than develop a scientifically reliable model of education. In their view, learners learn by constructing inferences based on the evidence or examples presented by the teacher. In other words, learners use the rules of reason and logic (consciously or unconsciously) to develop general principles from specific examples by inductive reasoning.
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