The Effects of an Integrated Learning Sequence on the Acquisition and Retention of Mathematics and Science Behaviors in Grade Five

Abstract

For many years, educators have used the relationship between mathematics and science in the teaching of both subjects. Science examples have been introduced into mathematics programs and often with the intention of facilitating the acquisition of mathematics behaviors. In other cases, mathematics behaviors assumed necessary for the acquisition of certain quantitative science behaviors are taught prior to the presentation of the quantitative science behaviors. There is some support for the notion that teaching the mathematics behaviors assumed necessary for the science behaviors facilitates the acquisition of the science behaviors. In this experiment, a comparison is made of the effectiveness of two l earning sequences in facilitating the acquisition and retention of certain mathematics and science behaviors. In one l earning sequence, the related mathematics and science behaviors are integrated; in the other sequence, they are not. It was hypothesized that the integrated sequence facilitates the acquisition and retention of the mathematics and science behaviors more than the non-integrated sequence. Three quantitative science behaviors were chosen as the final objectives of the learning sequence. By means of a task analysis procedure, twenty-two objectives were identified as prerequisite for the three terminal objectives. The twenty-five behaviors were then structured in a hierarchy. The three terminal objectives were placed at the top of the hierarchy. The subordinate behaviors were arranged below the terminal objectives in an order suggested by the analysis. This hierarchy was used as a guide in the construction of the two learning sequences. Each of the twelve lesson sequences was designed to promote the acquisition of the behaviors included in the hierarchy. A test was constructed which consisted of assessment items designed to test acquisition of each of the mathematics and science behaviors in the hierarchy. This test was administered on two occasions; once, on the day following completion of the learning sequence and, again, nine weeks later. Nine hundred students in thirty fifth-grade classes in the Baltimore County Public Schools completed all facets of the experiment. The classes were randomly assigned to one of the two sequences. An analysis of variance procedure was used on the class means to test the acquisition and retention of the mathematics and science behaviors. The following results were noted: The coefficient of stability for the criterion measure was 0.79; The coefficient of internal consistency was 0.81; The integrated sequence produced a significantly higher overall performance than the non-integrated sequence in acquisition of the mathematical behaviors although there were no significant differences in the effects of the sequence on the rate of forgetting; The two treatments had no differential effects on the overall performance or the rate of forgetting with regard to the science behaviors. It was concluded that the integrated learning sequence was generally superior to the non-integrated sequence in facilitating acquisition of the mathematical behaviors for the population defined in this study. It could not be established that the two sequences had differential effects on the rate of forgetting of the mathematics or science behaviors. The results and conclusions suggest that further consideration should be given to the use of integrated learning sequences as an instruction strategy.