A study of the effect of selected mathematics instructional sequences on retention and transfer with logical reasoning controlled



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Based on the explanations given by newer points of view (Piaget, Bruner, Gagné, Lovell) on how individuals learn, this study was designed to help resolve or explain the apparent conflict between positions expressed by Bruner and Ausubel. Bruner hypothesizes three ways of knowing and contends that in general an optimal instructional sequence will traverse these ways of knowing. Ausubel contends that children over twelve do not need direct contact with concrete objects. This study provided empirical and descriptive data related to the following questions: (1) What is the effect of instructional sequence with logical reasoning controlled on (a) immediate retention and transfer, and delayed retention and transfer? (2) Which of several identified sequences is most optimal for teaching selected grade four students? (3) What is the difference in the effect of instructional sequence on immediate retention and transfer and delayed retention and transfer? Both immediate and delayed retention were measured by a test on the knowledge and comprehension levels according to Bloom. The test on transfer measured student's ability to solve advanced dependent subconcepts not taught during the experiment. The independent variable in the study was instructional sequence, and logical reasoning ability was controlled. The three types of instructional sequences were: CA: Concrete–Abstract; SA: Semi-concrete–Abstract and AA: Abstract–Abstract. Instruction using the CA, SA and AA sequences provided learning experiences that facilitated learner associations between objects manipulated and the mathematics symbols which represent these ideas, between visual embodiments and mathematics symbols which represent these ideas, and between symbols manipulated and mathematics ideas represented by these symbols, respectively. The students were administered the Roberge Conditional Reasoning Test – Form C, Assessing, to determine their logical reasoning ability. The subjects were fourth grade students in Ponderosa Elementary School in Spring, Texas. Immediate measures of retention and transfer were administered the day following the completion of the experimental treatment, delayed measures of retention and transfer were administered ten days after the conclusion of the treatment. The treatment period was one week. The 72 subjects were randomly assigned to one of the three instructional sequences. Subsequently, fifty percent of each treatment group was randomly selected to take the immediate retention and transfer tests; the remaining fifty percent took the delayed retention and transfer tests. Three hypotheses were tested utilizing a multivariate analysis of covariance. The FINNVER4 Program and the University of Houston computer facilities were used for all analyses. Each of the null hypotheses relative to difference in the testing groups, treatment and their interaction were accepted. Based on the treatment effect, the students in the delayed group mean retention and transfer scores did not differ significantly from those in the immediate group.



Mathematics--Study and teaching (Elementary)