**AMMA**

**Algebraic Approach Towards Shaping „Minus”**

**in School Mathematics**

Difficulties in understanding negative numbers and algebraic expressions involving operations on them are well known in the mathematics classroom practice and reported in research. The main motivation for this project is to find a way to overcome these difficulties.

A common practice for introducing negative numbers in schools is to use educational models based on the number line (e.g. traditional liquid thermometer as a model of number line, walking on number line, lift ride, debts and losses), where we are building the notion of a negative number on the assumption a negative number is less than zero. In the partner countries of the project, i.e. in Poland and Slovakia, there exists in practice almost exclusively this teaching models. The consequence of learning negative numbers only on the basis of this model can be a very common mistake and crucial misunderstanding that „-x < 0 ” so “-x” is not interpreted in algebraic terms – as an element opposite to x. This misinterpretation leads to profound difficulties in understanding and dealing with algebraic expressions.

The results of the project provide the algebraic interpretation of the sign „minus” as „the opposite to”, which is consistent with the interpretation of „minus” for „-x”, hence the name of the project: “Algebraic Approach Towards Shaping „Minus” in School Mathematics”.

We claim that the introduction of our proposed approach as an additional pedagogical model with the use of tokens in mathematics teaching should help to overcome the difficulties described above for a wide range of students, including those with special educational needs.

The aim of the project was therefore 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. The approach was designed to serve both as an introduction to negative numbers and algebraic expressions and to help students who had difficulty understanding concepts already introduced. It should be suitable for inclusive education for students with learning difficulties and for mathematically gifted young children.

The project concerns improvements of mathematics teaching for primary school students (4-8 grades), including high-ability students (grade 4) and low-ability students (grade 8).

Target groups include:

1. School students of primary school, grades 6-8,

2. Gifted and talented school students in STEAM subjects, especially mathematics, grades 4-5,

3. Underperforming school students in STEAM subjects, especially mathematics, grade 8-9,

4. Mathematics teachers supporting school students of grades 3-8,

5. Educational authorities interested in developing STEAME teaching and learning,

6. Researchers interested in mathematics education.

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 (see: Negative Numbers).

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 (see: Algebraic Expressions).