Cognitive skill achievement of college freshmen using Piaget's logical operations in mathematics - Leongson, Jaime Acedillo (Animo Repository, 2001)
This descriptive empirical research attempts to investigate and assay the cognitive skill achievement of college freshmen using Piaget's seven logical operations in Mathematics, namely: Classification, Seriation, Compensation, Logical Multiplication, Ratio or Proportional Thinking, Probability Thinking and Correlational Thinking. Specifically, this study is designed to find out the sublevel of cognitive skills achievement possessed by the sample. The study is also geared to determine the reasoning patterns exhibited by the respondents for their answers on the Test of Logical Operations (TLO) in Mathematics, the major instrument through interviewing techniques. Reliability of the instrument was established through internal-consistency method and estimated through Kuder-Richardson Formula 20. Item analysis was also done to determine the difficulty level and discrimination index of each item of the instrument. Face, content and concurrent validity of the instrument were also established. Respondents were fifty-nine (59) college freshmen taking up Bachelor of Science in Education and associate course in Computer Technology. They were enrolled in College Algebra during the first semester of school year 2001-2002 at Bataan Polytechnic State College, Balanga Campus in Balanga City. Interviews were employed to randomly selected sixteen (16) students to determine their reasoning patterns. Scoring of the papers were guided by Schoenfeld Scoring Continuum while interviews were conducted with the use of the Interview Protocol and Raven's Reasoning Categories. Descriptive statistics particularly mean scores, frequency, percentages and ranks were utilized in describing the performance of students in the Test of Logical Operation in Mathematics. Likert's scale was also employed to further analyze the data. Majority of the student respondents who are expected to be at their formal operational stage were found to be at the concrete operational stage only. Generally, student respondents gave adequate reasons for their answers in the Test of Logical Operations in Mathematics on the following operations namely: Classification, Seriation, Logical Multiplication, Compensation, Probability Thinking and Correlational Thinking. Ambiguous reasons were exhibited on Ratio or Proportional Thinking. The researcher concluded that cognitive development as one of the many factors is considered important in learning mathematics, that the reasoning abilities are significantly related to cognitive skills achievement particularly in Mathematics and that as an individual goes with the four successive stages of cognitive development, expertise on logical operations develops progressively.