Modelling, structure and development of domain-specific professional knowledge of Latin teachers

In this paper, the content knowledge and pedagogical content knowledge of teachers of Latin as a foreign language are modelled and examined using a convenience sample (N = 216) with newly validated test instruments. Bivariate correlations show significant relationships between domain-specific professional knowledge and indicators of school or academic success, but no relationships with professional experience. In a confirmatory factor analysis, the two categories of knowledge can be separated according to theory. Their correlation is lower among in-service teachers than pre-service teachers, as multigroup analyses suggest. Furthermore, in-service teachers have more content knowledge and pedagogical content knowledge than pre-service teachers

Fostering mathematical modelling competency of South African engineering students: which influence does the teaching design have?

This paper reports on empirical results about the influence of two different teaching designs on the development of tertiary students’ modelling competency and attitudes towards modelling. A total of 144 first year engineering students were exposed to a diagnostic entrance test, a modelling unit consisting of five lessons with ten tasks, enframed by a pre- and a post-test, and at the end a questionnaire on attitudes towards mathematical modelling. Similar to the German DISUM study, in the modelling unit, one group of participants followed an independence-oriented teaching style, aiming at a balance between students’ independent work and teacher’s guidance, while two other groups were taught according to a more traditional teacher-guided style. Linear mixed regression models were used to compare pre- and post-test results. The results show that all groups had significant learning progress, although there is much room for further improvement, and that the group taught according to the independence-oriented design had the biggest competency growth. In addition, this group exhibited more positive attitudes than the other groups in five of six attitudinal aspects

Unidad de Modelización Matemática para estudiantes de primer año de Ingeniería

[EN] This paper is practice-oriented and reports on a mathematical modelling unit specifically developed for first-year engineering students in a South African context. The main idea with the unit was to foster students’ mathematical modelling competency development. This idea supports an essential goal of mathematics teaching, that is to enable students to solve real - world problems by means of mathematics. The unit consists of five lessons and several tasks, carefully planned to consider students’ mathematical pre-knowledge, the demands of the first-year mathematics (calculus) curriculum and the intended competency development. The unit was linked to the mathematical topic of functions and taught for different groups of students according to two different teaching designs, similar to the designs used in the German DISUM project. 144 first year engineering students from the extended curriculum programme of a large public university were divided in three groups and exposed to the unit. An empirical evaluation of the intervention (with a pre-post-test design) showed a significant competency growth for all groups, with substantial differences, dependent on the teaching design. Some strengths and shortcomings of the unit will be identified and implications for future practice will be discussed.[ES] Este artículo está orientado a la práctica e informa sobre una unidad de modelización matemática desarrollada específicamente para estudiantes de primer año de ingeniería en un contexto sudafricano. La idea principal de la unidad era fomentar el desarrollo de la competencia de modelización matemática de los estudiantes. Esta idea apoya un objetivo esencial de la enseñanza de las matemáticas, que es permitir a los estudiantes resolver problemas del mundo real por medio de las matemáticas. La unidad consta de cinco lecciones y varias tareas, cuidadosamente planificadas para tener en cuenta los conocimientos matemáticos previos de los alumnos, las exigencias del plan de estudios de matemáticas de primer curso (cálculo) y el desarrollo de competencias previsto. La unidad se vinculó al tema matemático de las funciones y se impartió a distintos grupos de estudiantes según dos diseños didácticos diferentes, similares a los utilizados en el proyecto alemán DISUM. Se dividieron en tres grupos 144 estudiantes de primer año de ingeniería del programa curricular ampliado de una gran universidad pública y se les expuso la unidad. Una evaluación empírica de la intervención (con un diseño pre-post-test) mostró un crecimiento significativo de las competencias en todos los grupos, con diferencias sustanciales, dependiendo del diseño didáctico. Se identificarán algunos puntos fuertes y deficiencias de la unidad y se discutirán las implicaciones para la práctica futura.This work is based on the research partially supported by the National Research Foundation (NRF) of South Africa, Unique Grant No. 121969.Durandt, R.; Blum, W.; Lindl, A. (2022). A Mathematical Modelling Unit for First-Year Engineering Students. Modelling in Science Education and Learning. 15(1):77-92. https://doi.org/10.4995/msel.2022.16646OJS7792151Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in Teach¬ing and Learning of Mathematical Modelling (ICTMA 14) (pp. 15-30). Dordrecht: Springer. https://doi.org/10.1007/978-94-007-0910-2_3Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S.J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education - Intellectual and Attitudinal Challenges (pp. 73-96). New York: Springer. https://doi.org/10.1007/978-3-319-12688-3_9Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics (pp. 222-231). Chichester: Horwood. https://doi.org/10.1533/9780857099419.5.221Blum, W., & Schukajlow, S. (2018). Selbständiges Lernen mit Modellierungsaufgaben - Untersuchung von Lern¬umgebungen zum Modellieren im Projekt DISUM. In S. Schukajlow, & W. Blum (Eds.), Evaluierte Lernumgebungen zum Modellieren (pp. 51-72). Wiesbaden: Springer Spektrum. https://doi.org/10.1007/978-3-658-20325-2_4Brown, J. S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18, 32-42. https://doi.org/10.3102/0013189X018001032De Villiers, L., & Wessels, D. (2020). Concurrent development of engineering technician and mathematical modelling competencies. In G. Stillman, G. Kaiser, & C.E. Lampen (Eds.), Mathematical Modelling Education and Sense-making (pp. 209-219). Cham: Springer. https://doi.org/10.1007/978-3-030-37673-4_19Du Plessis, L., & Gerber, D. (2012). Academic preparedness of students: An exploratory study. The journal for transdisciplinary research in Southern Africa, 8, 81-94. https://doi.org/10.4102/td.v8i1.7Durandt, R. (2018). A strategy for the integration of mathematical modelling into the formal education of mathematics student teachers. Doctoral dissertation, University of Johannesburg.Durandt, R., Blum, W., & Lindl, A. (2021). How does the teaching design influence engineering students' learning of mathematical modelling? An empirical study in a South African context. In F. Leung, G. A. Stillman, G. Kaiser, & K. L. Wong (Eds.), Mathematical modelling education in East and West. International perspectives on the teaching and learning of mathematical modelling (pp. 539-549). Cham: Springer. https://doi.org/10.1007/978-3-030-66996-6_45Haines, C., Crouch, R., & Davies, J. (2001). Understanding students' modelling skills. In J. Matos, W. Blum, K. Houston, & S. Carreira (Eds.), Modelling and Mathematics Education, ICTMA 9: Applications in Science and Technology (pp. 366-380). Chichester: Horwood. https://doi.org/10.1533/9780857099655.5.366Herget, W., & Torres-Skoumal, M. (2007). Picture (im)perfect mathematics! In W. Blum, P.L. Galbraith, H.-W. Henn, & M. Niss (Eds.). Modelling and Applications in Mathematics Education (pp. 379-386). New York: Springer. https://doi.org/10.1007/978-0-387-29822-1_41Hilbert, S., Stadler, M., Lindl, A., Naumann, F., & Bühner, M. (2019). Analyzing longitudinal intervention studies with linear mixed models. Testing, Psychometrics, Methodology in Applied Psychology, 26, 101-119.Kaiser, G. (2017). The teaching and learning of mathematical modeling. In J. Cai (Ed.), Compendium for Research in Mathematics Education (pp. 267-291). Reston: NCTM.Schau, C. (2003). Students' attitudes: The 'other' important outcomes in statistics education. In H. Pan, Q. Chen, E. Stern, & D.A. Silbersweig (Eds.), Proceedings of the Joint Statistical Meeting, (pp. 3673-3683), San Francisco, CA: American Statistical Association.Schau, C., Stevens, J., Dauphinee, T. L., & Del Vecchio, A. (1995). The development and validation of the Survey of Attitudes toward Statistics. Educational and Psychological Measurement, 55, 868-875. https://doi.org/10.1177/0013164495055005022Schukajlow, S., Kolter, J., & Blum, W. (2015). Scaffolding mathematical modelling with a solution plan. ZDM: The International Journal on Mathematics Education, 47(7), 1241-1254. https://doi.org/10.1007/s11858-015-0707-2Stender, P., & Kaiser, G. (2016). Fostering modeling competencies for complex situations. In C. Hirsch, & A.R. McDuffie (Eds.), Mathematical Modeling and Modeling Mathematics (pp. 107-115). Reston: NCTM.Stewart, J. (2016). Essential calculus. London: Brooks/Cole Cengage Learning.Stewart, J., Redlin, L., & Watson, S. (2012). Precalculus: Mathematics for calculus. London: Brooks/Cole Cengage Learning.Stillman, G. (2019). State of the art on modelling in mathematics education: Lines of inquiry. In G. Stillman, & J. Brown (Eds.), Lines of Inquiry of Mathematical Modelling Research in Education (pp. 1-19). Cham: Springer. https://doi.org/10.1007/978-3-030-14931-4_1Niss, M., & Blum, W. (2020). The Teaching and Learning of Mathematical Modelling. London: Routledge. https://doi.org/10.4324/9781315189314Plath, J., & Leiß, D. (2018). The impact of linguistic complexity on the solution of math¬ematical modelling tasks. ZDM: The International Journal on Mathematics Education, 50(1+2), 159-171. https://doi.org/10.1007/s11858-017-0897-xPollak, H. (1979). The interaction between mathematics and other school subjects. In: UNESCO (Ed.), New Trends in Mathematics Teaching IV (pp. 232-248). Paris: UNESCO.Reddy, V., Winnaar, L., Juan, A., Arends, F., Harvey, J., Hannan, S., Namome, C., Sekhejane, P., & Zulu, N. (2020). TIMSS 2019: Highlights of South African grade 9 results in mathematics and science. Achievement and achievement gaps. Pretoria: Department of Basic Education.Vorhölter, K., Krüger, A., & Wendt, L. (2019). Metacognition in mathematical modeling: An overview. In S. A. Chamberlin, & B. Sriraman (Eds.), Affect in Mathematical Modeling (pp. 29-51). Cham: Springer. https://doi.org/10.1007/978-3-030-04432-9_

Statistical Methods in Transdisciplinary Educational Research

A central task of educational research is to examine common issues of teaching and learning in all subjects taught at school. At the same time, the focus is on identifying and investigating unique subject-specific aspects on the one hand and transdisciplinary, generalizable effects on the other. This poses various methodological challenges for educational researchers, including in particular the aggregation and evaluation of already published study effects, hierarchical data structures, measurement errors, and comprehensive data sets with a large number of potentially relevant variables. In order to adequately deal with these challenges, this paper presents the core concepts of four methodological approaches that are suitable for the analysis of transdisciplinary research questions: meta-analysis, multilevel models, latent multilevel structural equation models, and machine learning methods. Each of these approaches is briefly illustrated with an example inspired by the interdisciplinary research project FALKE (subject-specific teacher competencies in explaining). The data and analysis code used are available online at https://osf.io/5sn9j. Finally, the described methods are compared, and some application hints are given