Brumbaugh, Douglas K.

The purpose of this study was the development of
a one trimester calculus course to meet the special
needs of management majors at Embry-Riddle Aeronautical
University. A traditional calculus course was previously
required of these students and the traditional course
provided subjects for the control group in a pretestposttest
quasi-experimental design.
The experimental course that was developed was
different from the traditional course that it was designed
to replace in several major respects. The slope
of a tangent line and the area under a curve as motivation
for the derivative and definite integral, respectively,
in the traditional course were replaced with examples
that seem more relevant to management students. The
concept of a limit is nearly eliminated from the experimental course. Intuitive arguments are used instead of
formal proofs as are given or cited in a traditional
course.
The achievement of an experimental group who took
the experimental course was compared with the achievement
of a control group who took the traditional calculus
course offered for management majors. Achievement was
measured by final examination scores and course grades.
When these measures of achievement were statistically
adjusted for initial differences in the control and
experimental groups, using prerequisite course grades,
the experimental group was significantly above (p < .01)
the control group.

This study uses Gagne's theory of learning hierarchies to analyze the learning tasks of a college remedial mathematics course into a sequence of subordinate tasks and designs a diagnostic test for the course based upon the model. Furthermore, a computer system that implements the diagnostic system based on the task analysis model of diagnosis is developed. The topics normally covered in college remedial mathematics courses are divided into ten major areas, and each topic is divided into a set of subordinate tasks. The subdivision is expressed through statements of performance objectives. A numbering which depicts the hierarchical structures of subtasks is used, and the test design conforms to this structure. Computer programs are written to allow the program user to enter the result of task analysis and the tests to be administered. The tests can be administered via a computer terminal identify the student's mathematical deficiencies. Test results and information from the task analysis can be used to produce a report of student deficiencies. It is hypothesized that such a detailed report of the student's deficiencies will enable the instructor to prescribe an individually tailored remedial course for the student. Each student's test performance is recorded, and a computer program is provided to perform item analysis and to compute test reliability coefficients for any group of students. The result of this study is a set of computer programs which implements the task analysis model of diagnosis for any subject where hierarchical relationships can be defined. This study also provides the testing instruments for separating college freshmen into remedial and non-remedial groups and for the diagnostic testing of the remedial group. It is concluded that the digital computer can be used to implement the task analysis model of diagnosis and that the software provided should be helpful to those who want to design and evaluate diagnostic tests.