Marlo’s Networks of Expectations in the Classroom: A Tool for Heterogeneous Reasoning

Abstract

In this article we present some results obtained between 2016 and 2019 using Marlo’s expectations networks (M.E.N.) as a tool in the teaching of logic in a secondary school in Huelva, Spain. M.E.N is a Bayesian tree structure implemented with logical nodes in which the propositions can be encoded as true, false, probable or uncertain. These networks have been used with students be-tween the ages of 14 and 18 to solve problems of first-order logic and mathematical probability. The networks, which have been developed in parallel with the Marlo diagram, represent in an exhaustive and heterogeneous manner all combinations of variables that can take place in the universe of discourse. Students make inferences by interpreting, on the one hand, the spatial information offered by the coordinates of the variables within the system, and on the other hand, the labels of natural and formal languages. But in addition, the truth values of each of these nodes can be expressed by perfectly synchronized numerical and chromatic scales. From these heterogeneous forms of graphic representation, we have created digital infographics that can be used on laptops and mobile phones in the classroom. From daily practice with these tools, we verify that some students with mathematical learning disabilities can reason in a surprisingly fluid and rigorous manner using colors. It is also notable that some of the best mathematical students cannot reason using colors. In any case, all students (chromatic, based on numbers and mixed) benefit from the diagrams.