THE IMPORTANCE OF PROBLEM HETEROGENEITY TO PROGRAMMED LEARNING
Authors: Traub Ross E. 
Published: August 2014

A review of the programmed learning literature demonstrates the need for a conceptual framework to guide the programming of tasks. One such framework is the analysis of a complex task into a hierarchy of subtasks, all sequentially dependent and logically necessary for performance of the complex task. Programming then involves providing experience with the subtasks, the object being to develop the separate skills needed to solve the complex task itself.

In the present experiment, a complex task was analyzed into subtasks and then programmed. The main variable studied was the degree of similarity of problems given for practice on the subtasks. Problems were either heterogeneous or homogeneous. The expectation was that subjects who worked heterogeneous problems would perform the complex task better than subjects who worked homogeneous problems.

The task used in this study was graphical addition of positive and negative integers. Additions were to be performed on “the number line.” This is a line, frequently used in teaching elementary mathematics, on which positive and negative numbers are located. Addition on the number line is drawing an arrow of a specified length from the location of a specified integer in a positive or negative direction. If correctly drawn, the stopping point of the arrow locates the sum of the numbers being added.

The program of this complex task was written in four parts for administration on four successive days to 294 sixth grade children. On day one, all subjects learned the subtask of locating positive integers on the number line and the subtask of drawing arrows to represent positive integers. On day two, similar training was given for negative integers.

On day three, subjects learned the subtask of drawing arrows of specified lengths and directions from specified integer locations on the number line. This subtask involved most of the elements of the complex task but it was presented in a more highly structured and supporting context of explicit instructions. The subjects were divided into three groups (using scores on an arithmetic achievement test to ensure that each group covered the same range of arithmetic ability). The heterogeneous‐problems‐group worked 20 problems of the day three subtask that were solved on different number line segments. The starting locations and lengths of arrows were varied as well. The homogeneous‐problems‐group worked 20 problems that were solved on the same number line segment and the starting locations and lengths of arrows were varied minimally. The control group worked problems not directly related to the subtask of day three. The 20 control‐group problems merely gave extra practice on the subtask of drawing arrows to represent integers. Finally, on day four, subjects learned the complex addition task and worked 26 addition problems.

The effect of intellectual aptitudes on the problem variable was also studied. Prior to the administration of the learning program, 18 ability tests were given to all subjects. Another 18 achievement scores were obtained from school records. These were to be related to the analysis of scores on the complex task.

The major finding of the study was that the heterogeneous‐problems‐group performed significantly better on the addition task than either the homogeneous‐problems‐group or the control group. A reason for this finding was suggested by an analysis of the error responses made by the groups. The heterogeneous‐problems‐group made fewer stereotyped errors than the other groups. Such a finding suggests that heterogeneous problems do not readily permit the stereotyping of error responses. The effect of the different practice problems was also found to be independent of the intellectual aptitudes of the subjects.