Inconsistency of students’ mental object of numbers with irrational numbers
Behnaz Savizi1* , Ahmad Shahvarani Semnani2 , Mohammad Hasan Bijan zadeh3
1*PhD student in mathematics education, Department of mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2Assistant professor in mathematics education, Department of mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
3Professor in mathematics (algebra and mathematics education), Department of mathematics, Payame Noor University, Tehran, Iran *corresponding author; Bsavizifirstname.lastname@example.org,
Abstract :This study focuses on the Iranian students’ notions on irrational numbers. Since there was not a clear view on student’s notions to lead our future investigations, the general question “what is an irrational number?” was asked from 30 students in second year of high school in Tehran/Iran. Three categories were extracted from the answers: representation, operation and inclusion. In the second phase, through a questioner of 8 questions answered by 50 students in the same grade, their professed knowledge and performance on quadratic irrational numbers was determined. After analyzing the gathered data, in order to have more validity on our considerations, two more questions on quadratic irrationals was asked from the 30 students of the same group. Finally, ten students’ were interviewed. The results showed that in addition to students’ deficiencies in formal knowledge, in three aspects, students’ mental object of a number in general is not consistent with their conceptions of irrational numbers: closure in representation, the relationship of the number and its correspondent point on the real number line and the basic function of a number.
[Behnaz Savizi, Ahmad Shahvarani Semnani, Mohammad Hasan Bijan zadeh. Inconsistency of students’ mental object of numbers with irrational numbers. Life Sci J 2013;10(1):762-771]. (ISSN: 1097-8135).http://www.lifesciencesite.com. 120
Keywords: Irrational numbers, mental object, misconception, closure in representation, process