Abstract:

In everyday life, new concepts are often built by combining existing concepts and by using classification of instances, objects, events, etc. Cognitive psychologists have paid particular attention to concepts that identify kinds of things, i.e. to those that classify or categorize objects. The ability to categorize objects by identifying their significant characteristics is a critical ability in the processes of learning and solving complex logical tasks. Boolean algebra is a powerful theoretical basis for understanding relations between components of a learner’s mental model (Feldman, 2000; Goodwin et al., 2010). The authors of both of the above works claim that people are able to construct complex concepts by establishing Boolean relations between characteristics of given objects.
In our work, we study the relation between the cognitive complexity of certain logical tasks given to a group of children, and the complexity of Boolean functions corresponding to these tasks. We observe the way the children solve a number of specific logic problems. We use the so-called Set game (www.setgame.com) to define the logic problems. According to the plan of our study, a certain subset of cards from the Set game is presented to the children. Each card comprises a number of characteristics such as a number of contours, their color, shape, and filling. The experiment we conduct aims to study how the regularity of the cards' characteristics can be recognized by children and, consequently, how it supports children in solving logic problems. We construct a number of tasks for this purpose. According to one of these tasks, after observing an initial set of cards, the children are asked to guess which card from a given subset is the most suitable to accomplish the initial set. For each card of the subset, the children were required to response “Yes,” “No,” or “NA” (they were told to respond “NA” when the card is unspecified). After responding, the children were told what the correct answer was according to the target concept, but they were never given any explicit instruction/explanation on the target concept.
We have developed an approach for estimating a children's way of solving the problem of accomplishing sequences of cards. The approach is based on estimation of the cognitive complexity of logical problems of the above type. For this purpose, every possible answer is measured by using a newly developed so-called “function of regularity”. The function estimates the level of logical reasonableness of the corresponding answer.
Results of the study comprise both a set of the children’s answers and a set of values of the function of regularity. Comparison between the above two sets of data serves the basis to analyze correlation between the children’s success in problem solving and the complexity of a certain logic task. Our paper provides results of the analysis. The research indicates that children recognize the regularity of some certain characteristics more successfully than the regularity of others. This result is of a great importance for developing children's logic thinking.

Keywords:

Concept learning, Boolean logic, cognitive complexity, set game.