Algebraic Approach Towards Shaping "Minus" in School Mathematics
▶Summary
The aim of the project was to develop, introduce to schools and evaluate a method of teaching the concept of "minus" in school mathematics (negative numbers and their opposites) on the basis of an...
▶Objectives
The aim of the project was to develop, introduce to schools and evaluate a method of teaching the concept of "minus" in school mathematics (negative numbers and their opposites) on the basis of an educational game, implementing the constructivist approach to teaching with the use of activity-based methods and work with concrete materials - tokens, developed in the project. Our approach aimed to help students overcome common misconceptions such as "-x is less than zero". The approach has been designed to serve both as an introduction to negative numbers and algebraic expressions, and to help students who express difficulty in understanding concepts already introduced. It should be suitable for inclusive education for students with learning difficulties and for mathematically gifted young children.
▶Activities
The project carried out two main sets of activities to achieve its objectives. Firstly, to develop, introduce to schools and evaluate a method for teaching the concept of negative numbers and the operations of their addition and subtraction, based on an educational game with the use of tokens, and finally to develop the field-tested teacher's guide. Secondly, to develop, introduce to schools and evaluate a method for teaching the concept of opposite terms (algebraic expressions) and the operations of their addition and subtraction, based on an educational game with the use of tokens, and finally to develop the field-tested teacher's guide. The other activities defined in the project had a complementary role, such as designing and preparing the prototype sets of concrete models for teaching negative numbers and algebraic expressions.
▶Impact
Two main groups of concrete outputs have been developed. The first set of outputs are three language versions of the internationally field-tested series of lessons developed in the form of Teacher Guides for teaching negative numbers and their addition and subtraction, based on an educational game with the use of tokens in languages: English, Polish and Slovak. The second set of outputs are three language versions of the internationally field-tested series of lessons developed in the form of Teacher Guides for teaching algebraic expressions and their addition and subtraction, based on an educational game with the use of tokens in languages: English, Polish and Slovak. Both sets of teacher guides were developed as a result of theoretical - mathematical and pedagogical - research, subsequent discussion of the initial versions with teachers before implementation, then evaluation of the scenarios in practice in public and private schools with different numbers of pupils and at different levels (grades 4-8) in two Polish and two Slovak schools, and also taking into account the results of the evaluation and detailed comments formulated by a foreign expert.