Proposição e avaliação de uma sequência hierárquica para o comportamento de contagem - Guimarães, Thais Albernaz M. C. (2015)
The objectives of this research were to identify and describe component behaviors and prerequisites involved in the mathematical behavior of counting, propose a hierarchical sequence for the acquisition of counting behavior and evaluate the suitability of the proposed hierarchical sequence. Hence, two studies were proposed. Study (1) is a research throughout the existing literature to identify and describe components behavior and prerequisites of counting. Three components of counting were identified regularly, namely: one-one correspondence, intraverbal of the number sequence and cardinality. As a result of Study (1) a hierarchical sequence, following the proposition Resnick, Wang, and Kaplan (1973), was developed. For each of the three components, prerequisites behaviors were established. In Study (2), we sought to evaluate the adequacy of the hierarchical sequence proposed in Study (1). Participants were 13 children with an average age of 4 ½ years of age. The process included teaching and testing steps related to the hierarchical sequence of counting behavior, as well as pre and post test involving supposedly more complex behavior such as sets comparison and arithmetic. The adequacy test of the hierarchical sequence was conducted in four distinct stages: 1) initial test; 2) test after teaching component A; 3) test after teaching component B; and 4) test after teaching component C. The method used was escale analysis in which performance of each participant was recorded in terms of approval (+) or failure (-) in the test for each component and prerequisite. The sequence was considered improper for instances where a supposedly more complex behavior was carried out according to the criteria but not its prerequisites. The results showed that the sequence was adequate for most participants in the proposed components and prerequisites. More specifically, this research showed that in the initial application of the hierarchical sequence, component A (one-one correspondence) was the one that most participants results differed. Prerequisites that seemed inadequate in regard to its ordination were A.1.1 (remove objects one by one in random order while assigning a number name to each of the items), C.3.1 (answer the question how many objects there are in a group after adding items in front of the childs) and C.2.1 (producing sets with fingers). For other prerequisites, the results were as expected. The data showed that after teaching, performance of most participants improved in the hierarchical sequence tests. Finally, the results of arithmetic test showed that 8 of 11 participants increased the number of correct answers on questions about sets comparison and all the 11 participants showed increased number of correct answers relating to problem situations, indicating a possible effect of teaching prerequisite counting behaviors upon more complex mathematical behavior. Research limitations on this topic and its importance to practice are discussed