Among the schooling pupils, there are between 5 % and 9 % of such pupils who have significant and persistent difficulties in acquiring mathematical knowledge and skills. A group of pupils with significant learning difficulties is heterogeneous and the common characteristic of these pupils is that they have significant problems in the acquisition of mathematical knowledge and skills. The early detection of pupils with significant learning difficulties in Mathematics is vital, because early and effective treatment can diminish or prevent the onset of the negative consequences of learning difficulties.
According to research, pupils with significant difficulties in Mathematics often have in common that they do not have such a developed number and quantity sense as their peers. A less developed number and quantity sense is supposed to be a predictor of the emergence of learning difficulties in Mathematics. A number and quantity sense is a construct, for which there is no single definition in the literature, but it is a fundamental precondition for the successful acquisition of mathematical knowledge. Authors recognize three types of notions of number and quantity sense: an inner, basic and useful number and quantity sense. In our master's degree thesis, we considered the concept of a fundamental number and quantity sense in which the number and quantity sense is perceived as fluency in quantity estimation, the ability to recognize meaningless results, the flexibility in mental calculation, and the ability to represent different representations of numbers and the use of the most appropriate representation. Research shows that the effects of a weakly developed number and quantity sense have a significant impact on lifelong learning in Mathematics. For a successful development of a number and quantity sense, early recognition of pupils with an insufficiently developed number and quantity sense is crucial, and then an immediate and appropriate treatment of pupils.
The goal of our master's degree thesis was to design and use the test of the number and quantity sense in the 3rd grade, which would be available to specialists and rehabilitation pedagogues and other professionals to help them evaluate the development of the number and quantity sense in pupils. A test of the number and quantity sense was carried out with 50 pupils of the 3rd grade, who were perceived by professional staff at school that they had significant learning difficulties in Mathematics. The pupils came from 19 schools of the central region of Slovenia. The sample consisted of 3 subgroups: pupils who are directed into a programme with customized implementation and further professional assistance (N = 21), pupils without a program of customized implementation and further professional assistance (N = 22) and pupils in the process of obtaining a programme of customized implementation and further professional assistance (N = 7). The experiment was also conducted with a control group of pupils of the 3rd grade (N = 9) who do not have significant learning difficulties in Mathematics. At the same time, we distributed the questionnaires to the teachers of the pupils and asked them to indicate on the three-tier assessment scale the extent to which in their opinion the pupil has mastered certain mathematical knowledge. The questionnaire settings for teachers tally with the test tasks, but we did not include all the experiment tasks in the teachers’ questionnaire. We tested the reliability of the test and the questionnaire with Cronbach's alpha coefficient.
The results confirmed that pupils with significant learning difficulties achieved statistically significantly less points than pupils from the control group in the test of the development of the number and quantity sense of 3rd grade. We have established that the highest predictive value for achieving points in the test of the development of the number and quantity sense for the 3rd grade have the task of determining the predecessor and successor, the mathematical textual task, the task of understanding the concept of place values, setting the sum of money, numbering, counting, arranging numbers to quantity, managing quantity and decomposition.
The results also showed that there is no statistically significant difference between the pupils’ results in the number and quantity sense of the 3rd grade and gender. A statistically significant connection also exists between the pupils’ results in the test and the average grade in Mathematics and between the teacher’s assessment of the success of solving the tasks and demonstrated pupil’s performance in the corresponding tasks in the test. We have found that there is no statistically significant difference in the pupils’ results in the test with respect to subgroups of pupils with significant learning difficulties.
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