Conceptual and procedural knowledge training of fractions in pupils with mild intellectual disability

Pupils with a mild intellectual disability experience a larger setback in cognitive development as their peers, which is why they need additional support for learning abstract math lessons. Fractions are of vital importance because pupils will encounter them in their everyday lives as well as in their professional careers. For children attending schools with special needs programme, it is very important that lessons as abstract as fractions are planned systematically and that each step of the lesson verbalised. It is also important to gradually include different visual aids and to regularly check pupils’ comprehension. The difficulty of the topic is annually confirmed with the results of a national assessment for pupils attending special needs programme. The aim of this master’s thesis is to discover if we can improve conceptual and procedural knowledge of fractions with the help of different strategies and learning aids in ninth-grade pupils with a mild intellectual disability who are attending a primary school with a special needs programme. In this thesis, we present a 15-hour training lesson, the aim of which is to deepen the pupils’ knowledge and motivation for learning fractions with the help of different representations and real-life examples and show them the importance of the topic in everyday life. Before the training, we checked the pupils’ knowledge with a test for identifying the automatization of arithmetic facts, which also included objective questions for checking fractions mastery. We used the acquired data to prepare and plan the training, which we performed in remedial class. While we were planning our training, we focused on the most common mistakes in understanding fractions, based on the findings of different researchers, since the same mistakes were also present with our group of ninth-graders. Pupils had the most problems with understanding nominal ratios between fractions and with determining fractions of equal values (conceptual knowledge), because they were generalizing the characteristics of integer numbers and applying them to rational numbers. To explain and understand the relation between fractions, we used the number line as the main representation aid. It proved effective for understanding the relation between the numerator and the denominator, the size ratios, arranging fractions in order and for finding equivalent fractions. In calculating with fractions (procedural knowledge), pupils were mistakenly generalizing the rules of calculating with integer numbers for fractions. At the same time, they were held back because of a bad automated declarative knowledge of arithmetic. The comparison of initial and final results showed that pupils deepened their conceptual and procedural knowledge of fractions with this training, which included different representations, activities, strategies and everyday examples. The fractions training included a systematic approach of predispositions as well as a conceptual and procedural knowledge of learning to add and subtract fractions. With this training programme, pupils had additional preparation for the national assessment and at the same time, they also deepened their knowledge of fractions for use in everyday situations. Every didactic material, aid, activity and strategy that we used will be available to special and rehabilitation teachers for devising appropriate approaches for explaining and teaching fractions