The chapter presents research into the impact of logic patterns, based on logical reasoning, focusing on order and sequence in series, on achievements in mathematics using an application-game which was developed neither specifically for the purpose of the current research nor to address Attention Deficit Hyperactivity Disorder (ADD). Both experimental and control groups were used for checking the central hypothesis on subjects of the same age – first and fourth graders at a similar learning level. The experimenters were Bachelor's Degree (BA) students majoring in special education. The method employed an application-game providing virtual simulation in real time offering the unique opportunity to observe and manipulate normally inaccessible objects, variables and processes. The focus was on qualitative research comparing subjects' achievements in mathematics in pre- and post-intervention. The findings showed that using logic patterns through the application games had an impact on the subjects' mathematical skills, especially verbal problem-solving. Their mathematical achievements increased quickly to the surprise of the experimenters who reported improvement in subjects' logic, mathematical and concentration skills, sometimes even the total stoppage of involuntary tics among those who received the intervention program as opposed to a lack of improvement or even a significant regression among the controls. Moreover, the motivation of both experimenters and subjects was enhanced, and their self-confidence improved. All the findings led to the conclusion that using application-games, although not developed for improving mathematics, can serve as a bridge between using logic patterns and improving or increasing mathematical achievements involving especially verbal problem-solving based on order, sequence and probability, among others.
TopBackground
Existing research sheds light on the connections between logic, mathematics and computers (Horne, 2014; Klippel, Hardisty & Rui, 2011). Logic, from the Greek logos, is both the word which expresses the inward thought, oration in Latin, and the thought itself, ratio, reason, in Latin (Liddell & Scott, 1983). Logic is the language of order (Feibleman, 1979). Klippel, Hardisty and Rui, (2011) show the relationship between logic and mathematics as innate order, i.e., classification schemes, principles of ordering, types of order; and deductive pictoralizations, such as graphs and matrices and deductive logic.
The experiments described in this chapter are the implementation of formal logic as it relates to inductive logic. The experimenters are first taught the formal logic behind the experiments and only then do they implement the inductive logic and test its results. They then study how inductive and formal logic are mutually reinforced.
The Development of Elementary Logic
Courses in introductory logic generally reflect the analysis of the connection between distinctive psychological processes and their function in organizing and guiding the cognitive development of children (Piaget, 1964). However, these courses contain only the mechanical manipulation of symbols reflecting their highly subjective mapping to structures on which thoughts are presumably strung. The development is a spontaneous process related to learning by transmission experience of equivalent situations. Yet, what normally is taught fails to account for the four stages of the child’s development, according to Piaget’s theory: sensory-motor, pre-operational, concrete operations and formal operations. The operational structures can be learned only using more simple and basic structures, and
… only if there is a natural relationship and development of structures. The learning of these structures is held to follow the same basic laws as does their natural development, i.e., learning is subordinate to development. Piaget concludes that the basic relation involved in the development and learning is assimilation and not association. In the third stage the first operations appear … but those are concrete because they operate on objects and not yet on verbally expressed hypotheses. For example, there are the operations of classification, ordering, the construction of the idea of number, spatial and temporal operations, and all the fundamental operations of elementary logic of classes and relations, of elementary mathematics, of elementary geometry and even of elementary physics (Piaget, 1964, pp.19-20).
The subjects of the experiment described below belong to this third stage of development. They have not yet reached the level of formal or hypothetic-deductive operations characteristic of stage four. Here, one may research Piaget and others to find that logical operators, themselves, signify a level of intellectual complexity, some being apprehended earlier than others; cf, Piaget J., 1971; Piaget J., 1958; Piaget J.& Inhelder B., 1973; Patarnello S. & Carnevali P., 1989; Martland D., 1989, and Taylor B.W., 1987.