This study investigated four research questions concerning strategies students used in solving the multiplication and division combinations. / In 1943, Brownell identified several strategies students used to solve the multiplication combinations, such as counting and rote memory. Recent research has indicated that the strategies students use may be related to how they are taught. Teaching techniques advocated today are somewhat different from those used during the 1940's. Has this caused a change in the strategies students use? / If students use thinking strategies on the multiplication combinations, do they also use them on the division combinations? / Brownell claimed that students mastered the combinations by adopting more and more mature thinking strategies until they reached mastery, where strategy A is more mature than strategy B if it is more mathematically sophisticated, or is more time efficient or demonstrates a deeper understanding of the operation on the part of the student. Brownell claimed however that the maturity level of the strategies students use has no correlation with their achievement in those combinations. Brownell claimed students could become so efficient at using an immature strategy as to score well on a test. Recent findings seem to refute this claim. Can evidence be found to refute Brownell's claim? / Most elementary mathematics textbooks advocate teaching the division combinations by relating them to the multiplication combinations. In light of the recent findings concerning the relationship between teaching and student's strategy use, what is the nature of the interrelationship between students' achievement on the multiplication and division combinations, the strategies they use, and the maturity levels of those strategies? / Ninety-five fourth-graders from two elementary schools were given a division combination test, followed the next day by a test on the multiplication combinations. Both tests were given via a slide projector, at the rate of one combination every six seconds. Based on the results of these tests, a stratified random sample consisting of half the subjects from each school was selected for individual, tape-recorded interviews. The tapes were analyzed to identify what strategy each student used on each combination asked in the interview. A panel of judges was asked to rank the strategies identified by level of maturity. Using these rankings, multiplication and division maturity indices were computed for each subject. The maturity indices, test scores, and the distributions of the strategies were then analyzed to answer the research questions. / The results of the analyses indicate that these students use the same strategies to solve the multiplication and division combinations: (a) Habituation, (b) solution, (c) repeated addition, (d) skip counting, (e) rote memory, (f) recitation of tables, (g) single digit counting, and (h) guessing. Brownell and Carper's categories were too broad and masked some of these strategies. Positive relationships were discovered between strategy maturity and achievement in both multiplication and division. Positive relationships were also discovered between multiplication and division strategy maturity levels, between multiplication strategy maturity and division achievement, between multiplication achievement and division strategy maturity, and between multiplication and division achievement. / These results lead to the conclusion that students do use thinking strategies on both multiplication and division combinations, that there is a relationship between achievement and strategy maturity for both multiplication and division, and that perhaps the key to multiplication and division achievement is the level of multiplication strategy maturity a student has reached. / Source: Dissertation Abstracts International, Volume: 41-05, Section: A, page: 1989. / Thesis (Ph.D.)--The Florida State University, 1980.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_74184 |
| Contributors | ANDERSON, HALDON LEE., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 173 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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