Students solve addition and subtraction exercises with missing factors as part of their earliest arithmetic lessons in primary school. These are understood to be basic mathematical skills, which are an essential foundation for further primary school studies. These skills are simultaneously important in an individual's everyday life and also considered one of the harder topics in mathematics. In order to successfully calculate the missing factors, students must first master and then use a number of previously acquired arithmetical and algebraical concepts. The results of different mathematics assessment tests, i.e. Slovenian national standardised testing and the Trends in International Mathematics and Science Study (TIMSS), also confirm that students have difficulty with algebra. Arithmetic tasks involving a missing factor are especially challenging for students with specific learning difficulties in mathematics, which is why problems with solving these tasks are often considered indicative of specific learning difficulties.
The aim of this master's thesis was to examine the problem of solving addition and subtraction exercises with missing factors from a theoretical standpoint and in connection with specific learning difficulties in mathematics. The primary goal of the empirical research was first to assess the developed sense for numbers, the degree of automation of arithmetic facts and procedures and the procedural and conceptual skills for solving addition and subtraction exercises with missing factors of the students taking part in the practice sessions and then to develop, carry out, and evaluate a practice programme for developing the conceptual and procedural skills necessary for solving addition and subtraction exercises with missing factors. The research sample included four students from Year 3 of primary school with specific learning difficulties in mathematics, who were included in Stage 3 of a 5-stage model for helping students with learning difficulties. The practice programme included various exercises for associating, breaking apart, and becoming familiar with the relationship between factors involved in addition and subtraction, learning about the relationship between addition and subtraction, and calculating missing factors using concrete pictorial and abstract examples. Following the completion of the practice programme, we also assessed the ability to solve addition and subtraction exercises with missing factors of those classmates not included in the programme, which allowed us to compare their results with the progress made by the study participants. Comparing the results of the first and second assessment of solving addition and subtraction exercises with missing factors with the results achieved by non-participating classmates during the final test showed that all the students included in the practice programme made progress in solving addition and subtraction exercises with missing factors, coming close to and almost equalling the average achieved by their classmates.
The theoretical bases, the practice programme outline, and the results of the empirical research can help teachers, staff offering remedial programmes and additional help, as well as specialised and rehabilitation teachers, when working with students with specific learning difficulties associated with solving addition and subtraction exercises with missing factors.
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