Purpose. This exploratory case study investigated the problem-solving strategies used by secondary mathematics teachers to solve and teach word problems conducive to proportional solutions. / Method. In individual interviews 20 randomly selected teachers described their thinking as they (1) solved four problems, two depicting direct relationships and two inverse; (2) explained how they would teach two of the problems; and (3) solved four similar problems after being asked to use proportional approaches. Responses were categorized using an eight-category classification scheme. Three categories are proportional--proportion formula (a/b = c/d form), proportion strategy (correct strategies which research indicates secondary students prefer to the formula) and proportion attempt (an incorrect use of proportion). The remaining categories are no answer, intuitive, additive (a focus on difference rather than ratio which is a common error of secondary students), algebraic (a correct equation other than the proportion formula), and Other. / Findings. On the first task, 74% of the responses were correct. Performance was almost perfect on the direct items; only half the responses to the inverse items were correct. There was no significant change in performance when teachers attempted to use proportional strategies. Middle school teachers were less successful than high school teachers, chiefly due to difficulties with the inverse items. When simply asked to solve the problems, the teachers used a variety of strategies which tended to vary with the problem; algebra accounted for one-fourth of the solutions and proportional approaches for one-half. The proportion formula was used far more often than other proportional strategies. The additive strategy was not used. When asked to use proportional approaches, the teachers increased their use of the proportion formula. The majority indicated that they would use the same strategies to solve and teach the selected items. Few teachers used informal proportional strategies to solve or teach these problems. The most unique and ingenious solutions tended to be devised on the inverse items for which many teachers had no ready solutions. / Source: Dissertation Abstracts International, Volume: 44-06, Section: A, page: 1715. / Thesis (Ph.D.)--The Florida State University, 1983.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_75102 |
| Contributors | FISHER, LINDA CANTRELL., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 258 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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