AN EVALUATION OF PROCEDURES FOR MEASURING BASIC MATHEMATICS COMPETENCE UNDER CONDITIONS WHERE DIAGNOSTIC/PRESCRIPTIVE INFORMATION IS PROVIDED AS A BASIS FOR CORRECTIVE TEACHING: STUDY II.
- UTAIRAT, SUWATTANA
- Physical Description:
- 212 pages
- Additional Creators:
- Pennsylvania State University
- This study is a follow-up of an investigation undertaken by Assaf (1979) in which he conducted an intensive analysis of a test that had been designed to measure essential mathematical competencies. Assaf reported that the test, referred to as ECT-1, had some basic weaknesses, and he made a number of recommendations for its improvement.
The ECT-1 subsequently was revised into a form referred to as ECT-2, and is divided into three parts. Part I is concerned with basic arithmetic, and it consists of 34 items covering five strands: basic number/numeration ideas, addition, subtraction, multiplication, and division. Part II is concerned with more advanced arithmetic, and it consists of 37 items covering three major strands: fractions, decimals, and ratio/proportion/percent. Each of these strands is further broken down into substrands. The fractions strand is comprised of FRA-I (basic concepts and terminology), FRA-II (additional and subtracting fractions), and FRA-III (multiplying and dividing fractions). The decimals strand is comprised of DEC-I (basic concepts and terminology) and DEC-II (computation with decimals). The ratio/proportion/percent strand is comprised of RA/PRO (ratio/proportion) and PCT (percent). Part III is unchanged from its original form and is concerned with informal geometry and functional literacy (applications) and consists of 27 items. The intent in constructing ECT-2 was to produce a test whose diagnostic/prescriptive qualities are better than those provided by ECT-1, particularly in part II of the test.
The foci of this study centered around two major questions: namely, the reliability of ECT-2 and also the relationships between the performances that students exhibit on the computational and the functional portions of the test. In order to study the reliability of the ECT-2, parts I and II of the test were administered in the fall term of 1978 to available students of the 8th and 10th grades of the Jersey Shore Area School System, Jersey Shore, Pennsylvania. The KR20 was computed and the confidence interval for all KR20 values was established. All the KR20 values were significant at the .001 level, except for the addition strand and the FRA-III substrand for grade 10. In terms of the data that were collected, the ECT-2 was judged as reliable. In order to examine the relationships between computational and functional performance, each applications test item was task analyzed so as to identify the computational competencies it entailed--the hypothesis being that if the computational prerequisites for a problem were not part of an individual's knowledge repertoire, he/she would not be able to solve the problem. An examination of the data indicated that only three out of 15 items were in disagreement with the statistical hypothesis in at least one of the two instances it was tested. Thus, the apparent absence of the competencies that are identified as prerequisites for solving a particular verbal problem is a good indicator of being unable to solve the problem.
Since the principal intent of constructing ECT-2 was to obtain an improved version of the original ECT in the sense of its prescriptive qualities, the revised hierarchies upon which it was based were examined separately for each grade level using Guttman scalogram analysis: (1) within each of the strands/substrands, (2) within the basic arithmetic subset, (3) within the advanced arithmetic subset, and (4) over the entire strands/substrands of the test. The results of this analysis revealed that the hierarchies for part I of the test are adequate, but that those for part II may still be in need of some additional adjustment.
- Other Subject(s):
- Dissertation Note:
- Ph.D. The Pennsylvania State University 1980.
- Source: Dissertation Abstracts International, Volume: 41-08, Section: A, page: 3407.
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