Construction and validation of a test to measure problem solving skills of students in college algebra

Date of Publication

1988

Document Type

Master's Thesis

Degree Name

Master of Science in Teaching Major in Mathematics

Subject Categories

Educational Assessment, Evaluation, and Research | Science and Mathematics Education

College

Br. Andrew Gonzalez FSC College of Education

Department/Unit

Science Education

Thesis Adviser

Melecio Deauna

Defense Panel Chair

Severino B. Diesto

Defense Panel Member

Herminia D. Torres
Leonor L. Aquino

Abstract/Summary

The primary concern of this study is to construct and validate a test to measure problem solving skills in college algebra. Specifically, it attempts to answer the following questions: 1. What is the concurrent validity of the test? 2. What is the reliability of the test? 3. How appropriate is the test with regard to difficulty level for the freshmen science students of College Algebra? 4. What are the statistics of the norm group which includes the mean, standard deviation, standard score and corresponding percentile equivalents of the test scores? Procedure: Freshmen science students (BS Biology, BS Chemistry, BS Mathematics, BS Physics) who were enrolled in College Algebra during the first semester of school year 1987-1988 comprised the subjects of the study. The tryout test consisting of 200 questions distributed into four equivalent forms, was administered to 213 students of Philippine Normal College and De La Salle University. After item analysis, forty five good items were retained. The final form of the test was given to 256 students, from which 128 were randomly chosen by simple random sampling. Students from Adamson University and St. Scholastica's College constituted the validation sample who took the final problem solving test. The test scores and NCEE mathematics percentile scores of the students in the norm group provided the data used in the statistical analysis of the problem. Treatment of data: Item analysis was done in both the field test and final form of the test. In analyzing each item, the index of difficulty and index of discrimination were determined.

To estimate the reliability of the test, the Kuder-Richardson formula 20 was utilized. To determine the concurrent validity of the test, the Pearson r formula was used. To test the significance of both coefficient of validity and coefficient of reliability, the t-test was applied. The mean and standard deviation were the basic statistics used to express raw scores in terms of z-scores and the corresponding percentile equivalent was obtained from a table of areas in the standard normal distribution. Findings: 1. The concurrent validity coefficient of the test was found to be 0.45 2. The reliability coefficient of test results was 0.62 3. The indices of difficulty ranged from 0.11 to 0.82. Thirty or 66.67 percent of the total number of items are of moderate difficulty whose indices ranged from 0.30 to 0.70. One or 2.22 percent has a difficulty index greater than 0.70. Fourteen or 31.11 percent have difficulty indices lower than 0.30 4. The mean and standard deviation of the test scores were computed at 15.82 and 4.90, respectively. An actual score of 16 is equivalent to a percentile score of 51.60. Conclusions: 1. The problem solving test which was developed to measure the problem solving skills of freshmen in College Algebra is valid and reliable. 2. The general difficulty of the test encountered by the respondents of the problem solving test was reflected on the relatively low scores obtained by majority of the students. 3. The use of percentile equivalent facilitates the interpretability of test results, especially for people who have insufficient statistical background. 4. The test is practical since it provides a good measuring instrument in a desirable time limit of one hour. Recommendations: 1. It is suggested that the test be given to first year students taking College Algebra before or after the teaching of problem solving. 2. It is recommended that similar construction and validation studies be made on other mathematics areas such as arithmetic, geometry, statistics, and College Algebra achievement.

Abstract Format

html

Language

English

Format

Print

Accession Number

TG01592

Shelf Location

Archives, The Learning Commons, 12F Henry Sy Sr. Hall

Physical Description

89 leaves ; 28 cm.

Keywords

Algebra--Examinations--Design and construction; Algebra--Examinations--Validity; Examinations--Design and construction; Examinations--Validity

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