The purpose of this study was to examine the relationship between the developmental levels of children on certain Piagetian conservation and concept tasks and the strategies the children were capable of using in finding answers to basic addition combinations. / Two major themes were examined in the literature search. How do children recall the basic addition facts? What is known about developmental levels of children and their relationship to performance in arithmetic? / Extensive individual interviews of 52 first graders and 60 second graders were conducted. Each child was tested developmentally on Number Identity, Number Equivalence, Class Inclusion, Meaning of Addition Identity, and Meaning of Addition Parts to Whole. On each test the child was classified as Lacked Vocabulary, Nonconserver, Transition Inconsistent, Transition No Explanation, or Conserver. The child was also shown six basic addition combinations and asked for both an answer and the strategy used to obtain the answer. / In a classroom setting the children were given a 25 item facts test. The 11 teachers of students participating in the study responded to a questionnaire dealing with methods of teaching the facts and the concept of addition. / Results of the study indicated that: (1) The developmental tests are Guttman scalable for both first and second grade in the order: Conservation of Number Identity, Conservation of Number Equivalence, Meaning of Addition Identity, Meaning of Addition Parts to Whole, and Class Inclusion. (2) Children use a great variety of methods (at least 18) for getting answers to the basic addition combinations, some of which probably have not been taught to them by their teachers. (3) There is a significant relationship between where a child is developmentally and the level of the strategy he or she uses in getting answers to the basic addition combinations. The higher a child's performance on the developmental scale, the more likely the child is to use higher level strategies with the addition facts. This trend is stronger in first grade than in second. (4) The linearity of the relationship between developmental levels and fact strategy levels is diminished in first grade by those students (about one third of the cases of conservers) who are developmentally advanced but who are using low level strategies. For second grade, one sixth of the students who are conservers on some of the tests are using low level strategies. (5) There is a second major departure from linerity. While almost two thirds of the cases classified as nonconservers are not using low level fact strategies, they also rarely use strategies higher than the intermediate methods of counting on. (6) When the students in the study are subdivided into four subgroups by school/grade, correlations remain significant for first grade except for tests (Class Inclusion and Number Identity) on which almost all the students are on one end of the developmental scale. For second grade, many of the comparisons lose significance due to the halving of the number of cases when the subgroups are considered, suggesting / that the correlation is not as strong as that in first grade. (7) In first grade there is a significant correlation between the class facts test scores and both the developmental levels and the strategy level of the facts. For second grade, administering the facts test with no time limit allowed so many students to get high scores that the significant correlations present for first grade have practically disappeared. (8) The teacher questionnaire revealed that some strategies for finding answers to the addition combinations which were taught by the teachers were not often used by the students. Other strategies not taught by the teachers were apparently invented by the students. / Recommendations for further study, implications of the research, and suggestion for teachers were made. / Source: Dissertation Abstracts International, Volume: 42-06, Section: A, page: 2548. / Thesis (Ph.D.)--The Florida State University, 1981.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_74522 |
| Contributors | THAELER, JOHN SCHROPP., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 152 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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