Mathematical skills of students with special educational needs in the area of learning (SEN-L) in pre-vocational programs in Germany

Context: Students with special educational needs in the area of learning (SEN-L) attend vocational trainings to be provided with qualifications for the labor market. Competences in arithmetic operations and comparing quantities such as weights and lengths are indispensable for obtaining a vocational qualification. Therefore, the study investigates whether students with SEN-L in Germany convert job-relevant quantities and master arithmetic operations accurately and with a certain speed before beginning vocational training. Methods: 152 students with SEN-L in pre-vocational training programs in southern Germany were examined using curriculum-related computer tests for formative assessment. Three skill-based tests were constructed as progress monitoring tests comparing weights and lengths and arithmetic operations including a speed component. Results: All newly developed tests meet the requirements of the Rasch model. Students' performance on the lengths test and the weights test correlates with a significant linear relationship (r = 0.64). Only weak correlations (r > 0.29 < 0.45) are found between the performance in the arithmetic operations and the weights and lengths tests. For items in the weights and lengths tests, participants show on average significantly higher probability of solving than in the arithmetic operations test. Furthermore, students with SEN-L show slow processing speed (median processing speed weights test 6.37 seconds, lengths test 6.26 seconds, arithmetic operations test 33.97 seconds on average per item). The students solve more items of the weights and lengths tests correctly than of the operation test (median for weights 25 items, for lengths 24 items, for arithmetic operations 7 items). Conclusion: The majority of the students with SEN-L were not able to solve the expected number of items correctly and show that the participants' accuracy in dealing with arithmetic operations and quantity comparison is low. It can be assumed that this might lead to difficulties in mastering mathematical items in the context of vocational training. This is the case, in particular, where a certain speed is required (fluency). Math instruction in pre-vocational programs needs a stronger focus on building up and expanding arithmetic operations and quantities and has to be complemented by monitoring the learning process of students with SEN-L.