# Mind the gap!

#### Faculty to integrate vocational learning opportunities for vocational training into mathematics instruction in a targeted manner

*Robert von Hering*

Mathematical skills play an important role in the transition from general schooling to vocational training. The requirements that school places on young people in the subject of mathematics are different from those that are placed on them in vocational training. These differences in understanding which mathematical competencies are desirable result in a difficult transition from school to vocational training. While a more knowledge-oriented concept of competence prevails in general education, vocational education focuses on the acquisition of operational competence. A study at the IPN investigated which perceived differences and similarities exist between general education and vocational mathematical requirements when working on parallel tasks.

Mathematical competencies are considered to play an important role in the successful transition from general education to initial vocational training. While requirements in mathematics classes at general schools focus on general mathematical competencies and are more oriented towards knowledge formation, vocational mathematical competencies are needed to cope with real professional requirements and are therefore more related to practical skills. Research has established the construct of vocation-related mathematical competencies as a mediating variable between the two views. The vocation-related mathematical competencies that young people are expected to acquire in school or in vocational training serve as a starting point for scientific studies on the transition from school to work. Based on this, we investigated to what extent such vocation-related mathematical competencies can be distinguished from general mathematical competencies. The occupational field of industrial clerks was selected as an example due to its proximity to the subject of mathematics.

### Mathematical competencies at the transition from general education to vocational training using the example of industrial clerks

Vocation-related mathematical competencies are intended to mediate between the general mathematical competencies in school and the practice-oriented mathematical competencies in vocational training. Therefore, mathematical competencies should be developed in authentic vocational application situations already in the context of general mathematics education. Whether this currently happens in general mathematics education, however, is questionable. Similarly, whether vocation-related mathematical competencies also differ from general mathematical competencies in practice or whether they are different manifestations of one and the same competency is also an open question.

This study focused on the training of industrial clerks. A popular and frequently chosen occupation, with mathematical requirements in many areas, for which the acquisition of competencies required for this occupation should already be established in general education settings with no difficulty.

### Do the differences between general education and vocation-related math skills show up in real-world situations?

Within the framework of an interview study with 42 prospective industrial clerks, the perceived differences and similarities of general education and vocation-related mathematical requirements were investigated when processing parallel tasks. Trainees were given three pairs of tasks to work on, whereby for each pair of tasks one task originating from the industrial clerk vocational context and one task with a non-commercial context had the same mathematical structure. While one task shows a typical (industrial) commercial vocational context, which is characterized by the use of commercial technical terms, the other task is a task from a non-vocational, i.e. general education context. Mathematical modeling skills are required for both tasks, and the mathematical solution to both tasks involves the repeated application of the percentage formula.

After completing the tasks, the trainees talked about the perceived differences and similarities of the parallel tasks as well as the underlying knowledge structures in stimulated recall interviews. This type of interview aims to provide deep insights into the inner view of the interviewee(s) and to relate to individual action practice. The interviews were subsequently examined using methods of qualitative content analysis. Most of the trainees stated that they had recognized the structure of the parallel tasks (mathematical-content equivalence with differences in context) during processing. Nevertheless, they were unable to solve the two tasks of a task pair equally well. Furthermore, according to their own statements, the trainees largely drew on knowledge and skills they had acquired during their vocational training (vocational school or company) when working on the industrial clerk mathematics tasks. They did not do this in the tasks with a non-commercial context. The theoretically assumed differences between general mathematical competencies and vocation-related mathematical competencies could therefore also be reflected in the individual processing of the prospective industrial clerks.

### Textbook analyses: To what extent are vocation-related mathematical competencies already applied in school?

Separate consideration of the two above-mentioned areas of competence therefore makes perfect sense. It also makes sense to initiate the acquisition of vocation-related mathematical competencies as part of general mathematics instruction to counteract problems at the transition to vocational training. To see to what extent this is already happening, it is worth looking at mathematics textbooks. These are used extensively in Germany and represent a good approximation of actual mathematics instruction, also in terms of the distribution of the content they contain. In a textbook analysis with 18 different textbooks of secondary level I (four textbook series, grades 6 to 10), a total of 20,000 learning opportunities (tasks, information texts, examples, mnemonics) were examined with regard to their relevance to industrial business. In a first step, all learning opportunities that are generally related to the commercial field were identified, before they were classified in a second step with regard to whether they are related to the profession. For example, a task in which various discount campaigns for buying T-shirts are to be compared from a private perspective has a low level of vocation-relatedness and thus does not serve as a learning opportunity for vocation-related mathematical competencies. A task devoted to maximizing profits in T-shirt sales from a commercial or industrial clerks perspective has a high degree of vocation-relatedness and thus the potential to promote vocation- related mathematical competencies.

The analysis showed that although about 6% of the learning opportunities are in a commercial context, 82% of them have a low vocational relevance. Overall, only about 1% of all learning opportunities have such a high degree of vocational relevance (in relation to commercial occupations) that they can function as learning opportunities for vocation-related mathematical competencies. Interestingly, the textbooks from grades 9 and 10, which are closer in time to the transition to vocational training than the other textbooks studied, had a significantly lower number of learning opportunities with a commercial focus. In an average book for grade 9, there are only four learning opportunities with at least a medium vocational relevance.

Thus, there is an opportunity for improvement in this area. Teachers should integrate vocational learning opportunities for commercial professions, but also for many other (training) professions, into mathematics lessons in a targeted manner. A collection of tasks from the PaNaMA project, in which mathematics is used in situations that are as authentic as possible, can provide assistance.

von Hering, R., Rietenberg, A., Heinze, A. & Lindmeier, A. (2021). Nutzen Auszubildende bei der Bearbeitung berufsfeldbezogener Mathematikaufgaben ihr Wissen aus der Schule? Eine qualitative Untersuchung mit angehenden Industriekaufleuten. *Journal für Mathematik-Didaktik, 42, *459–490. DOI: 10.1007/s13138-021-00181-8

von Hering, R., Zingelmann, H., Heinze, A. & Lindmeier, A. (2020). Lerngelegenheiten mit kaufmännischem Kontext im Mathematikunterricht der allgemeinbildenden Schule: Eine Schulbuch- und Aufgabenanalyse. *Zeitschrift für Erziehungswissenschaft, 23*(1), 193–213. DOI: 10.1007/s11618-019-00925-w

**Dr. Robert von Hering**

was until recently a research associate in the Department of Mathematics Education at the IPN. The results presented here are based on parts of his dissertation, which he wrote at the IPN. He is currently a research associate at the European University of Flensburg in the Department of Mathematics and its Didactics. Before coming to the IPN, he studied mathematics and German for teaching at grammar schools at the Christian-Albrechts-Universität zu Kiel.