Mathematical understanding and reasoning abilities related to cognitive stage of senior high school students

Abstract

The goal of this study is to analyse the relationships among students' mathematical understanding, reasoning abilities and their cognitive stage. The study is descriptive-analytic research involving 414 eleventh-grade students (17,43 years old) from seven senior high schools. The instruments of this study are tests on mathematical understanding and reasoning abilities, the Longeot Test and the Test of Logical Thinking (TOLT). The study revealed there were two kinds of attributes of the findings. First, based on the subject's age (17,43 years old) there were different findings on students' cognitive stages from the Piaget's theory, there were many students did not reach formal operational stage yet, namely 21 % students were still on the concrete stage, 34% of students were still in the transition stage, and only 45% were on a formal stage. Second, there were two kinds findings those were firm toward Piaget's theory, those were: a) the higher subject's school classes, the number of formal subjects; b) on students' mathematical understanding and reasoning abilities and mathematics formative and summative tests, formal students attained higher grades than transition students, and transition students attained higher grades than concrete students.