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.

Organizing lessons for heterogeneous learning groups is a challenge for student teachers and novice teachers. To observe and improve classroom management during student teaching, we have developed an assessment tool. The aim of this study is to evaluate and improve the instrument “Scale for Classroom Management in Inclusive Schools (InClass)” with data from 480 student teachers in internships at elementary or special schools in Germany and Austria. The instrument consists of the three dimensions Adaptive Teaching Scale (ATS), Relationship Scale (RS), Behavior Management Scale (BMS). Confirmatory factor analyses revealed good reliable values (CFI = 0.97, TLI = 0.96, RMSEA = 0.06, SRMR = 0.04) for the three-factor InClass model and could confirm the theoretically developed scales. The latent correlations were between r = 0.74 and r = 0.63. Teachers in elementary schools also showed latent correlations between the three dimensions and their assessment of the implementation of inclusive education in the school ranging from r = 0.51 to r = 0.84. In order to meet the individual needs of all students, with and without special educational needs (SEN), novice teachers in particular should be supported in dealing with heterogeneous learning groups and in using effective classroom management. Instruments such as InClass help student teachers evaluate and reflect on instruction and therefore have an important contribution to teacher education.

Der Umgang mit Größen wird vom ersten Schuljahr über die Sekundarstufe bis zur Berufsschule angelehnt an die Zahlenräume aufgebaut und stetig erweitert. Ziel ist, dass die Schüler*innen über Größenvorstellungen zu lebenswelt- und berufsrelevanten Größen wie Gewichte, Längenmaße, Flächenmaße, Volumen- und Hohlmaße, Geldwerte und Zeitspannen verfügen. Als wichtige Kompetenzen werden der Größenvergleich, das Messen und Schätzen von alltagswichtigen Standardeinheiten sowie die Darstellung von Größenangaben in unterschiedlichen Schreibweisen (Umwandeln) erlernt. Für einen guten adaptiven Unterricht und zur Differenzierung werden Screenings und Lernverlaufstests benötigt, die diese Kompetenzen reliabel messen können. (DIPF/Orig.)