All model assumptions in the natural sciences are based on mathematical concepts, regularities or assumptions. For this reason, mathematical modelling is central to understanding the development and validation of models in the natural sciences. The ability to evaluate, change and apply models in the sense of gaining knowledge is understood as modelling competence. With the help of modelling cycles, the modelling process can be divided into individual steps. This enables an insight into the modelling process.

Blum & Leiß (2005) developed a framework for mathematical modelling. They distinguished between two main dimensions, "rest of the world" (which includes real-world problems, their structuring, mathematical description, and the interpretation and evaluation of mathematical results) and "mathematics". The translation between these dimensions is understood as mathematical modelling. Based on these dimensions, a seven-step modelling cycle was developed. Starting from a real situation/problem, the steps are to understand the situation (1), to simplify and structure it with a focus on the problem (2) followed by mathematisation (3), which results in the transition to the dimension of "mathematics". There, results are generated with mathematical methods (4) and translated back into the context and thus back into the dimension "rest of the world" with a focus on the problem (5). Now these results are validated in relation to the context (6) and an answer is given to the concrete problem (7).

Based on the cycle for mathematical modelling developed by Blum & Leiß (2005), various subject-specific modelling cycles were derived. Goldhausen & Di Fuccia (2014) derived a mathematical modelling cycle for the subject of chemistry. For this purpose, an additional dimension "chemistry" was added that is located between "rest of the world" and "mathematics". This is necessary because a real chemical situation (e.g. chemical experiment) must first be transferred into subject-specific models in order to be able to describe and interpret a situation.The steps of the mathematical modelling cycle were adapted to the specific requirements of a chemical contextualisation. In the first step, a problem/experiment is identified on a macroscopic level and a situation model is created (1). This is then translated into a chemical model (submicroscopic or symbolic level) ( Johnstone, 1991) (2). The chemical model is then mathematised (3), for which, according to Kimpel (2018), a deeper understanding of the model is necessary. With the developed mathematical model, mathematical results can be generated with the help of mathematical tools, similar to Blum & Leiß (2005) (4). These can then be translated back into the chemical model (5) and checked for their professional usefulness (6) so that they can finally be applied to the experiment/problem (7).

As diagnostic models, modelling cycles offer the possibility of gaining an insight into the complex cognitive processes of learners during modelling. In the field of mathematics didactics, modelling cycles have been used to develop a test instrument to measure mathematical modelling ability (Haines, Crouch & Davis., 2001; Brand, 2014; Hankeln, Adamek & Greefrath, 2019). In all cases, the steps of a modelling cycle were divided into empirically based categories. Items were constructed for these categories. Prior to testing, various models were postulated on the basis of empirical studies for the items. With the help of Rasch measurement, the data has been compared with the postulated models.

Since this type of test development has so far only been conducted for mathematical modelling in general, this study investigated if a questionnaire can be used to assess learners' mathematical modelling skills.

A test instrument for mathematical modelling was developed on the basis of the modelling cycle by Goldhausen & Di Fuccia (2014) and the methodological approach by Brand (2014). For this purpose, the cycle is divided into five sections (A1- A5). Four sections (A1, A2, A4, A5) each describe the change between the dimensions described in the model (rest of the world, chemistry and mathematics). For this categories, 12 items ( including question and assoociate answer format) from different chemical subject areas as well as different contexts from nature and technology were constructed. Category A3 focuses on answering mathematical questions and tasks from school mathematics of varying difficulty. Twelve areas were also developed for this, each containing three items of varying difficulty. In total, there were 36 items. Each of these categories focuses on a specific aspect of mathematical modelling ability. For example, category A1 includes questions that focus on understanding and constructing a problem or on structuring and simplifying problems or tasks. In addition, this category includes tasks in which relevant aspects of an issue have to be identified or suitable chemical models have to be selected. Category A2 revolves around mathematising the selected model. This means selecting suitable mathematical formulae, describing mathematical relationships or developing mathematical formulae. The third category (A3) is about working mathematically. Accordingly, mathematical concepts, working methods and solutions are applied here. In category four (A4), mathematical results have to be classified technically. For example, identifying the unit of a mathematical result, assigning mathematical results to variables or classifying mathematical results in the subject context. The last category (A5) of the cycle describes the interpretation of the result considering the initial situation. This means checking a result for its meaningfulness, checking whether the result fits the model used or also to generate answer sentences. All items in all categories have a closed answer format, with five answer options each. One correct answer, two 'plausible' answers based on misconceptions and two incorrect answers. All items were distributed across twelve test booklets each containing three (nine for A3) items per category. In order to obtain a linear scale, the coded data sets are evaluated using Rasch analyses (Boone, 2014). The person measures obtained for the individual categories served as the basis for a correlation analysis of the individual categories with the overall instrument.

The data for validating the test instrument was collected by questioning students. For this purpose, students in the STEM fields of chemistry, mathematics, physics, biology and mechanical engineering have been surveyed so far. The data collection will continue until the end of February 2023. N=296 students have participated in the study until now. On the basis of this data, a first analysis was made in order to be able to identify a first trend regarding the results. For this purpose, the interview data was coded with view to the distractors. With the help of the programme Winsteps (Lincare, 2000), the data was examined using a Rasch analysis. In a first step, the quality of the items used was analysed. So, it was to check how well the items fit. Mean-square fits outside the reasonable range were found for only three of the 90 items. In the individual categories, a misfit was calculated for a few further items (A1: none; A2: none; A3: 4 out of 36; A4: 1 out of 12; A5: 1 out of 12). Subsequently, the item reliabilities of the overall model and the individual categories were determined separately. These already showed values above 0.8 in almost all categories (A1-A5: 0.94; A1: 0.95; A2: 0.82; A3=0.87; A4=0.88; A5=0.82). In addition, the students' person abilities calculated using Rasch analysis were used for a correlation analysis. Significant and highly significant correlations between the individual dimensions were calculated pairwise. Examples include the correlation of category A3 with categories A1, A2, A4 and A5 [A1 (r=.325**, p<.001, n=159); A2 (r=.214**, p=.007, n=159); A4 (r=.288**, p<.001, n=140); A5 (r=.401**, p<.001, n=137)]. This indicates that the individual dimensions capture the overall construct of mathematical modelling well.

Blum, W., & Leiß, D. (2005). Modellieren im Unterricht mit der „Tanken “-Aufgabe. Mathematik lehren (128), p. 18-21, Karlsruhe. Boone, W. J., Staver, J. R., & Yale, M. S. (2013). Rasch analysis in the human sciences. Springer Science & Business Media. Brand, S. (2014). Erwerb von Modellierungskompetenzen: Empirischer Vergleich eines holistischen und eines atomistischen Ansatzes zur Förderung von Modellierungskompetenzen. Springer-Verlag. Goldhausen, I., Di Fuccia, D.-S., (2014) ‚Mathematical Models in Chemistry Lessons’, Proceedings of the International Science Education Conference (ISEC) 2014, 25-27 November 2014, National Institute of Education, Singapore Haines, C., Crouch, R., & Davis, J. (2001). Understanding students' modelling skills. In Modelling and mathematics education (pp. 366-380). Woodhead Publishing. Hankeln, C., Adamek, C., & Greefrath, G. (2019). Assessing sub-competencies of mathematical modelling—Development of a new test instrument. In Lines of inquiry in mathematical modelling research in education (pp. 143-160). Springer, Cham. Johnstone, A. H. (1991). Why is science difficult to learn? Things are seldom what they seem. Journal of computer assisted learning, 7(2):75-83. Kimpel, L. (2018). Aufgaben in der Allgemeinen Chemie: zum Zusammenspiel von chemischem Verständnis und Rechenfähigkeit (Vol. 249). Logos Verlag Berlin GmbH. Linacre, J. M., & Wright, B. D. (2000). Winsteps. URL: http://www. winsteps. com/index. htm [accessed 2013-06-27]