ABSTRACT
Mathematics educators face the challenge of helping students to build on the natural intuition to bridge the gap between human intuition and mathematical theory. The natural frequency representation is adapted to cognitive processes in a way that makes the solution to evidential reasoning problems transparent. Mathematics educators are likely to be more successful if they engage their students in a cooperative pursuit of knowledge than if they act as adversaries pouncing on the students’ every perceived mistake. Modern mathematics education treats representations of mathematical entities as a fundamental aspect of didactics in the classroom. Special attention has been devoted to the issue of multiple representations of numerical entities and the advantages of switching between them as a means of achieving mathematical competencies for dealing with them. One reason Herbert Simon, along with many early artificial intelligence researchers, was far too optimistic the time frame during which critical milestones would be achieved, was the contrast between how computers, humans process information.
