This study compared two different approaches to the teaching of elementary probability to 196 community college students. These two approaches were identified as the single concept approach and the multi-formula approach. In the single concept approach the students solved probability problems by relying solely upon the definition of 'probability'. Students in the multi-formula approach solved probability problems by the traditional approach of using several formulas. / The multi-formula group and the single concept group were compared on achievement, retention, and transfer. An analysis of variance was used to analyze the achievement scores. The single concept group scored significantly higher (p-value = 0.0001). An analysis of covariance was used to analyze the retention scores. The single concept group scored significantly higher (p-value = 0.025). An analysis of variance was performed on the transfer items. Again, the single concept group scored significantly higher than the multi-formula group on the transfer items both on achievement and retention. The p-value was equal to 0.0001 for both analyses. / A depth of understanding may account for these results. Whereas the multi-formula group divided their time and effort among several concepts associated with their formulas, the single concept group concentrated their efforts and attention on the single definitional concept. One might conjecture that students versed in a single concept would outperform those spreading the same amount of time over many concepts (formulas). / In addition to investigating the learning of probability, this study relates to two types of understanding identified by Richard Skemp. Instrumental understanding is identified with the multi-formula group and Relational understanding with the single concept group. The results of this study suggest that the single concept approach may be better for learning other mathematical concepts. For example, the idea of perimeter as the distance around a figure contrasted with a collection of formulas for finding the perimeters of various figures. Another example is the definitional meaning of integral exponents contrasted with a variety of formulas addressing operations with exponents. / In view of the success with the single concept approach used in this study, additional research would tell if similar success may be realized with other mathematical topics. / Source: Dissertation Abstracts International, Volume: 51-12, Section: A, page: 4052. / Major Professor: Herbert Wills, III. / Thesis (Ph.D.)--The Florida State University, 1990.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_78361 |
| Contributors | Swiersz, Thomas Joseph., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 203 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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