A Novel Modelling Process in Chemistry: Merging Biological and Mathematical Perspectives to Develop Modelling Competences

Models are essential in science and therefore in scientific literacy. Therefore, pupils need to attain competency in the appropriate use of models. This so-called model–methodical competence distinguishes between model competence (the conceptual part) and modelling competence (the procedural part), wherefrom a definition follows a general overview of the concept of models in this article. Based on this, modelling processes enable the promotion of the modelling competence. In this context, two established approaches mainly applied in other disciplines (biology and mathematics) and a survey among chemistry teachers and employees of chemistry education departments (N = 98) form the starting point for developing a chemistry modelling process. The article concludes with a description of the developed modelling process, which by its design, provides an opportunity to develop students’ modelling competence.

Test Instrument

Key didactic aspects of mathematical modelling (see Sects. 1.1, 1.2 and 1.3), in particular the possibilities of characterising and acquiring modelling competence (see Sects. 1.1.3 and 1.4), were explained in previous sections.

Keefektifan pembelajaran matematika realistik ditinjau dari kemampuan pemodelan matematika dan prestasi belajar

Tujuan penelitian ini adalah untuk menguji perbedaan keefektifan antara pembelajaran mate­matika realistik dan pembelajaran ekspositori ditinjau dari kemampuan pemodelan matematika dan prestasi belajar siswa SMP. Penelitian ini adalah penelitian quasi-experiment menggunakan pretest-posttest nonequivalent control group design. Populasi dalam penelitian ini adalah siswa kelas VIII SMP Negeri 15 Yogyakarta yang terdiri atas 10 kelas dan dipilih secara acak dua kelas yaitu siswa kelas VIII C (kelas eksperimen, n = 33) dan siswa kelas VIII F (kelas kontrol, n = 33) sebagai sampel penelitian. Instrumen yang digunakan dalam penelitian ini adalah tes uraian untuk mengukur kemampuan pemodelan matematika dan tes pilihan ganda untuk mengukur prestasi belajar siswa. Uji statistik menggunakan analisis multivariat Hotelling’s Trace pada taraf signifikansi 5% dilakukan untuk menguji hipotesis penelitian. Hasil penelitian menunjukkan bah­wa pembelajaran matematika realistik lebih baik dari pembelajaran ekspositori ditinjau dari kemampuan pemodelan matematika dan prestasi belajar siswa.Effectivity of realistic mathematics education viewed from mathematics modelling competence and learning achievementAbstractThe purpose of this study was to examine the difference in effectiveness between realistic mathematics education and expository learning viewed from mathematical modelling compe­tence and achievement of junior high school students. This study was quasi-experiment research with the pretest-posttest nonequivalent control group design. This study's population was the 8th-grade students of SMP Negeri 15 (junior high school) in Yogyakarta, Indonesia, consisting of ten classes. The sample in this study was the students of class VIII C (experiment group, n = 33) and VIII F (control group, n = 33) selected randomly. In this study, the instruments used were essay questions to measure mathematics modelling competence and multiple-choice questions to measure learning achievement. Statistical test using the Manova with the Hotelling's Trace test at a significance level of 5% was conducted to examine the hypothesis. The results showed that realistic mathematics education was better than expository learning viewed from students' ma­thematics modelling competence and learning achievement.

Mathematical modelling competence. Selected current research approaches

Current research areas in the field of mathematical modelling are identified on the basis of specific research and development projects. Modelling cycles are an important theoretical basis for this. The measurement of students modelling competencies as well as that of competencies for teaching mathematical modelling with the help of written tests are important components. The investigation of different mathematical modelling tools, such as the use of technology in larger control group studies, and the evaluation of lecture series in teacher education, are current lines of research in the field of modelling in mathematics education. Overall, selected studies from Germany are used as examples to provide insight into the current research landscape.

Dialogue and Artificial Intelligence

The article focuses on a few central issues of dialogic competence-in-performance which are still beyond the reach of models of Artificial Intelligence (AI). Learning machines have made an amazing step forward but still face barriers which cannot be crossed yet. Linguistics is still described at the level of Chomsky’s view of language competence. Modelling competence-in-performance requires a holistic model, such as the Mixed Game Model (Weigand 2010), which is capable of addressing the challenge of the ‘architecture of complexity’ (Simon 1962). The complex cannot be ‘the ontology of the world’ (Russell and Norwig 2016). There is no autonomous ontology, no hierarchy of concepts; it is always human beings who perceive the world. ‘Anything’, in the end, depends on the human brain.