Development and validation of an achievement test in college Algebra for Philippine Christian University freshmen / Lira B. Bayona. 6

Thesis (Ph.D.) -- Pamantasan ng Lungsod ng Maynila, 1993.;A dissertation presented to the faculty of the Graduate Programs in Arts, Sciences, Education and Nursing in partial fulfillment for the degree Doctor of Education. 56

5

ABSTRACT: STATEMENT OF THE PROBLEM: The study was motivated by the need to develop a valid instrument for measuring achievement in first year Algebra. Thus, the purpose of the study was to develop and validate an achievement test in College Algebra for Philippine Christian University. This study attempted to answer the following questions: 1.

What items could be written to comprise the College Algebra achievement test? 2.

What evidences are established for the reliability of the College Algebra achievement test? 3.

What evidences are established for the validity of the College Algebra achievement test? 4.

How does achievement in College Algebra among Urban and Rural PCU freshmen compare? NULL HYPOTHESIS: Ho: Au= Ar There is no significant difference in the achievement in College Algebra among urban and rural PCU freshmen. PROCEDURE: To ensure that a valid achievement test is constructed, the researcher identified clearly what she was testing for and how she plans to use the results. For this reason, the researcher divided the process of test constructions into three phases: PHASE I-ITEM DEVELOPMENT: Before the achievement test was constructed, the researcher examined the syllabi in College Algebra for the last three years and noted common objectives stated and content included in it. A table of specification was developed from this. Test items from the item bank and items solicited from teachers currently teaching College Algebra were included in the test. For further improvement of the test items, the test was shown to her co-teachers and the department head who are considered authorities in mathematics. These evaluators have at least five years of very satisfactory teaching performance, are masters degree holders and have taught College Algebra for at least three consecutive years. To ensure that items follow principles of writing test items, the researcher presented it to experts it has been checked against the criteria for writing a good test. PHASE II-ESTABLISHING EMPIRICAL EVIDENCES For further improvement of the test items, pilot testing was done to a group 120 students comprising 15% of the freshmen population taking College Algebra. To gather empirical evidences, the researcher performed item analysis particularly two procedures determine item difficulty and discriminating indices. The discriminating index was determined by comparing the performances of two groups called the criterion group or the high and low performing groups. Item difficulty and item discriminating indices were computed so as to identify which items were to be included. PHASE III-ESTABLISHING RELIABILITY AND VALIDITY EVIDENCES For a test to be valid it must of necessity be reliable, hence the establishment of the coefficient of reliability and eventually validity, is a vital component of this phase. The coefficients of reliability were established through the use of coefficient of internal consistency and coefficient of stability. The establishments of reliability were established through the use of coefficient of internal consistency and coefficient of stability. The establishment of the evidences of validity namely content validity, construct validity, and criterion validity concluded this phase. TREATMENT OF DATA Percentage was used to present the profile of the PCU students taking College Algebra. To establish empirical evidences on item procedure and improvement, item-analysis procedure involving item difficulty indices and item discriminating power were used. The coefficient of internal consistency was established using the Kuder-Richardson formula while coefficient of stability, construct validity and criterion validity used the Pearson Product Moment Formula. To compare the achievement of College Algebra of urban and rural PCU freshmen the population means were computed and the t-test formula was applied at .05 level of significance. FINDINGS: 1.

Results show that items 35, 95, 98 and 100 manifest a difficulty index of .17 for the first two items, .13 and .19 respectively. 1.a Items which were correctly answered by respondents were those related to knowledge, followed by items to test understanding while item intended to measure skills applying the four fundamental operations come next. Students scored poorly on items related to Linear and Quadratics functions, particularly those related to higher level cognitive tasks or analysis. 2.

On test reliability, the coefficient of internal consistency has an r-value of .75 interpreted as marked to substantial, while the coefficient of stability established by the pre-test-post test method shows an r-value of .66 indicating further, that there is substantial or marked reliability. 3.

On content validity evidence, the accomplished content objectives namely knowledge, understanding, skills on the four fundamental operations, and analysis are below the 50% level achievement if the averages are taken. Except for concept number one, Algebra of Real Numbers which has achievement level of 58.6% the rest of the concept or content area has not reached the 50% level with analysis skills as the lowest. 4.

While four out of 100 items were rejected, these may be corrected by replacing them with more acceptable test items to measure up to the desired acceptable level of difficulty and discriminating indices. 2.

The number of rejected items do not significantly alter the degrees of acceptability of the entire achievement test. 3.

The test items included in the achievement test has satisfactorily measured the parameters of entry and achieved behavior skills and competencies as contained in the concept objectives. 4.

The constructed achievement test in College Algebra has shown substantial reliability and validity evidences. 5.

Based on the test scores it could be concluded that given similar experiences and exposed that given similar experiences and exposed to the same concepts culture gaps in terms of achievement could be bridged. This has been manifested by the mean scores of the constructed achievement test in College Algebra from both campuses. This validated achievement test serves as a contribution to the area of instrumentation. RECOMMENDATIONS: 1.

The constructed achievement test in College Algebra is recommended for use as an evaluation tool for diagnostic purposes to determine the levels of achievement or behavior entry of PCU freshmen in College Algebra. 2.

The same test could be used as a common evaluation tool in College Algebra for both the Taft and Dasmariñas campuses for purposes of determining students achievement within the semester. This is to make sure that final grades are based on a sound and valid measuring instrument to facilitate proper grading standards. 3.

Further validation and finally standardization of the test is highly recommended so that massive use of the instrument would be possible. 4.

Items 35, 95, 98 and 100 must be modified to ensure an acceptable difficulty index and high discriminating power. 5.

Analytic skill should be developed among students in general, through more student oriented activity such as group problem solving and the like. 6.

An in-service training for teachers on test construction and evaluation must be conducted regularly. 7.