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The Learning Conference 2003

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Presentation Details

 

Teaching Periodic Decimals in Tertiary Education

Michael Kourkoulos.


Periodic decimals (pd) constitute a fundamental representation of rational numbers. Additionally, their study leads to the understanding of basic characteristics of the decimal system and to a more profound comprehension of the operation of division. Furthermore, the a-priori analysis of the properties of the pd indicates that this area is adequate for learning activities, in which students may work by combining the use of inductive and deductive methods. This claim is supported by the historical development of Number Theory.
However, only a very limited part of the Mathematics curriculum in elementary and secondary education is devoted to this area. Often, this is also true for the pre-service undergraduate studies of (elementary and secondary) schoolteachers of Mathematics in Mathematics and Education Departments.
In the first part of this work, we present results of an empirical study of the knowledge, which (elementary and secondary) schoolteachers of Mathematics and students of Departments of Education in Greece have on pd. Our results point out that the properties of pd are largely unknown both to the teachers and to the students who have been asked. For example, 96% of 207 students of Departments of Education don’t know that in all non-terminating divisions, the quotient is a pd.
In the second part of this work, we give an outline of a teaching approach concerning pd, which has been applied in the Department of Education of the University of Crete. In the context of this teaching approach, students become able to discover the basic properties of pd and to prove many of them, by combining the use of inductive and deductive methods. Apart from a significant improvement of the students’ knowledge concerning the pd and the decimal system, we have also observed an important improvement of their understanding of inductive methods and of the fruitfulness to combine such methods with deductive methods, in order to study problems in Arithmetic and elementary Number Theory.

Presenters

Michael Kourkoulos  (Greece)
Maitre de Conference en Didactique des Mathematiques
Departement of Education
University of Crete

Kourkoulos Michael is Doctor in Didactic of Mathematics of the University Louis Pasteur of Strasbourg. He teaches Mathematics and Didactic of Mathematics in the Department of Education of the University of Crete.

Keywords
  • Arithmetic
  • Decimal System
  • Operation of division
  • Teachers Education
  • Preservice teachers
  • Problem Solving
  • Guided research work



(Virtual Presentation, English)