The results of the TIMSS 2011 research for Slovenia and the results of the annual National Assessment of Knowledge examinations in the nine-year primary education programme show the lowest mathematics achievement of pupils in Pomurje region. The results of the National Assessment of Knowledge examinations highlight two important facts. Firstly, that the results are strongly correlated with socio-economic factors of families and secondly, that the achievements in mathematics of children with special educational needs, significantly fall behind their peers. Slovenian primary school teachers have observed that pupils have a lot of problems with learning arithmetic, which means learning basic arithmetic operations, fractions, equations and expressions with variables. Pupils with learning disabilities in arithmetic (hereinafter referred to as LDA) often have arithmetic procedural problems, underdeveloped cognitive skills, weakly developed conceptual knowledge, poor memory, visual-spatial intelligence problems, poorly developed language skills, less well developed fine motor skills and attention-deficit disorders. Procedural knowledge is built throughout the years of education by automation of arithmetic facts and procedures, with exercise and mechanical drill or by direct learning strategies. Many pupils with LDA have problems with the automation of basic arithmetic operations, which are intensified in the last three-year period of elementary school, when they have to cope with complex arithmetic operations such as calculating with fractions and other rational numbers, as well as solving equations.
The main purpose of working with pupils with LDA is to develop such methods and approaches that would compensate their learning difficulties if not completely eliminate them. This is also emphasized by the updated Maths curriculum, which states that the teaching methods and approaches of learning mathematics for pupils with special educational needs should be adapted accordingly. Teachers should use a different teaching approach and a different access to the technology as for the rest of the pupils. In the classroom we can help pupils with LDA by using the strategies of good teaching practice, the direct teaching approach of mathematics and cooperative (collaborative) learning forms of teaching and learning. This encourages pupils to involve in active learning, verbalization of problem solving, use of teaching aids and metacognition. Domestic and foreign authors recommend the implementation of the additional professional assistance for children with special needs within the class, using strategies of cooperative learning and teaching, as these pupils with LDA gain in the learning field, becoming more confident, while they develop social skills and strengthen relationships with their peers.
The central aim of the research was to design, implement and analyse a training to improve the arithmetic procedural knowledge for a group of pupils with LDA, which was based on the implementation of the additional professional assistance, on the strategy of team teaching of the Maths teacher and the additional professional assistant, as well as on peer collaborative learning. The Maths teacher was teaching according to the methods of good teaching practices and together with the additional professional assistant, at least 20 lessons of team teaching in the 7th, 8th and 9th class were carried out, in which pupils with LDA were involved as well. The additional professional assistant carried out 20 or more individual assistance lessons, as well as assistance in pairs for each pupil with LDA, while these pupils were still involved in organized peer collaborative learning in the range of 10 lessons.
The research is an example of a multiple case study with clinical teaching strategy. The sample included 8 pupils with LDA from the 7th, 8th and 9th grade and 39 peers without LDA from the same classes. In the research, a variety of measurement instruments were used to investigate arithmetic skills and the acquired learning objectives of arithmetic in accordance with the curriculum. Numerical results of the tests were presented in a tabular form including a comparison of results of both groups, pupils with LDA and pupils without LDA. The results were analysed using descriptive statistics or by testing the differences between the achievements of pupils with LDA and peers without LDA by t-test for independent samples, respectively. The achievements of pupils with LDA on set objectives of the curriculum were qualitatively interpreted. Furthermore, the implementation of additional professional assistance, team teaching, cooperation with parents and collaborative peer learning was evaluated.
It is evident from the results of the initial diagnostic assessment that the group of pupils with LDA showed from the beginning of their education process difficulties of a weak representation of numbers and a poor working and semantic memory, which has hindered the normal retrieval of facts and processes. Additionally, visual-spatial deficits and poorly developed conceptual knowledge was present, which was reflected in a feeble understanding of the concepts and procedures. Comparing the results before and after training, demonstrated that pupils with LDA had in both cases worse arithmetic skills and less well automated arithmetical facts and procedures. They were slower and less flexible using arithmetical facts and procedures, and they were statistically less precise and they used the appropriate strategies for solving the arithmetic word problems less frequently. Representation of numbers, solving equations and arithmetic operations are the fields of arithmetic procedural knowledge, where the most evident differences between the groups before training were observed. Both groups of pupils have improved their results in the field of automation and flexible use of arithmetic facts and procedures; in average, the group with LDA has achieved higher progress than the other group. In the testing of arithmetic word problems only the pupils with LDA achieved a minimum progress. Five of eight pupils with LDA assimilated 70% or more minimum standards of knowledge after the training. Two pupils failed to assimilate the minimum standards entirely. Pupils with LDA mostly had difficulties with assimilating the objectives of the editing fractions, of arithmetic operations with rational numbers (the biggest setbacks were in arithmetic operations of division) and solving text tasks with rational numbers and equations.
The results of the analysis of the implementation of additional professional assistance, team teaching and peer collaborative learning showed that pupils with LDA appreciated the assistance and the support of the training. The results also showed that the teachers in the collaborative lessons often chose an alternative teaching style or a pair teaching style, while an actual team teaching style had been used rarely. Another conclusion was that the team teaching methods have many benefits for pupils and teachers as well.
The present study is a model of treatment of children with LDA exploiting the resources available in the system, as foreseen by the model "respond to treatment". With the strategies of good teaching practices of the Maths teacher in the classroom, intensive systematic treatment in the additional professional assistance lessons, team teaching of the Maths teacher and additional professional assistant and with other teaching lessons (such as remedial classes and individual and group support) and peer collaborative learning, pupils improve procedural knowledge in arithmetic. At the same time, pupils with LDA learn about independence, organization, they strengthen emotional stability, raise self-esteem and improve their position in society.
We believe that the described training is also suitable for pupils who have beside specific deficits in arithmetic also other specific learning disabilities, as is dyslexia and disorders of attention and concentration (the phenomenon of co-morbidity), and for pupils with LDA who come from families with lower socio-economic status and lower educational levels of parents.
The results of this research have a great practical value for the pedagogical practice in the field of special and rehabilitation pedagogy and mathematics. Conducted comprehensive treatment of pupils with LDA in the third period of elementary school is a model of intensive training by the cooperation between the special and rehabilitation educators and teachers of mathematics, while it included peers.
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