An investigation into the extent and nature of the understanding first year college of education students have of aspects of arithematic and elementary number theory - Oliphant, Vincent George (Rhodes University, Faculty of Education, Department of Education, 1996)
First Year College of Education students who have done and/or passed mathematics at matric level, often lack adequate understanding of basic mathematical concepts and principles. This is due to the fact that formal tests and examinations often fail to assess understanding at anything but a basic level. It is against this background that this study uses alternative and more direct means of assessing the level and nature of the understanding such students have of aspects of basic arithmetic and number theory. More specifically, the goals of the study are: 1. To determine the students' levels of understanding of the following number concepts: Rational numbers; Irrational numbers Real numbers and Imaginary numbers. 2. To determine whether the students understand the rules governing operations with negative numbers and with zero as principles rather than conventions. 3. To determine whether the students understand the rule governing the order of operations as a matter of convention rather than as a matter of principle. A survey of the literature concerning the nature of understanding as well as the nature of assessment is given. The students' understanding in the above areas was assessed by means of a written test followid by interviews. A sample of 50 students participated in the study while a sub-sample of 6 were interviewed. Some of the significant findings of the study were : 1. The students largely failed to draw clear distinctions between Real and Rational numbers as well as between Irrational and Imaginary numbers. 2. Very few of the students could explain the rationale behind the rules governing the. operations with negative numbers and zero. 3. Only half of the students had any knowledge of the rule governing the order of operations. Only one student demonstrated an understanding of the rule as a convention.
Keywords: Mathematics teachers -- Training of Mathematics -- Study and teaching