Research Project OModA-E (since 2025)

Funding Organisation

Abstract

Open problems that can be solved by using different solution methods are an important part of the school curriculum in mathematics and science. One important type of open problem is related to the real world. Open real-world problems can be solved by constructing mathematical models and are known as open modelling problems. Prior research analyzed open problems that did not include all information that is essential for solving the problems. In this type of open problem, the initial state is open. In this grant application, we are going to analyze problems with open goal state. While solving the problems with an open goal state, different factors (e.g., temporal, and financial) can be considered to answer the question. In the project we will investigate the effects (1) of instruction that is focused on important barriers in solving problems with open goal state and (2) how the teaching of problems with open goal state affects students' cognitive and motivational learning outcomes. We will carry out an experimental study to investigate the impact of instructions in a) how to identify solution-related factors in the goal state, b) how to set up a mathematical model, and c) how to interpret and validate mathematical results on students' solutions. Further, we will contrast two treatment programs in a quasi-experimental study and analyze the effects on interest and performance. In the first teaching program, students will solve modelling problems with an open goal state, and in the second teaching program, they will solve real-world problems with a closed goal state. The main aim of this application is to investigate students' cognitive barriers while they solve modelling problems with an open goal state and to analyze the effects of interventions (instruction and teaching program) for problems with open goals state on students' performance. Further, we will analyze, how interventions in solving modelling problems with an open goal state will affect students' cognitive and motivational development. This research will contribute to the overarching aim of getting new insights about dealing with open problems in instructional settings that are oriented toward self-regulation.

Research Project OModA (2020-2024)

Abstract

One characteristic feature of open modelling problems is that numerical information that is essential for solving the problems is missing. Solving open modelling problems in classes should prepare students to apply their mathematical knowledge in their current and future lives. On the basis of research on mathematical modelling, on open problems, and on self-regulated teaching methods, we aim to investigate (1) the effects of instruction that is focused on important barriers in solving modelling problems and (2) how the teaching of open modelling problems affects students' cognitive and motivational learning outcomes. We will carry out an experimental study to investigate how learning how to identify missing numerical information and how to set this information affects students' performance. Further, we will contrast two treatment programs in a quasi-experimental study: In the first teaching program, students will solve open modelling problems, and in the second teaching program, they will solve closed real-world problems. The current project is grounded in cognitive and motivational theories of learning and should give new insights into the importance of open modelling problems for students' cognitive and motivational development in instructional settings that are oriented toward self-regulation. Further aim of the present project is to investigate which variables influence the quality of teaching with respect to modelling problems. This project focuses on the investigation of modelling problems with open initial state, whereas in the following project, we are going to investigate modelling problems with open goal state.

Publications

Journal Articles (peer-reviewed)

Wiehe, K., Schukajlow, S., Krawitz, J., & Rakoczy, K. (2025). Openness in mathematical modelling: Do experiences of competence and autonomy mediate the effects of an intervention on modelling problems on task values and cost? ZDM - Mathematics Education. https://doi.org/10.1007/s11858-025-01670-7

Schukajlow, S., Krawitz, J., Kanefke, J., Blum, W., & Rakoczy, K. (2023). Open modelling problems: Cognitive barriers and instructional prompts. Educational Studies in Mathematics, 114(3), 417-438. https://doi.org/10.1007/s10649-023-10265-6

Book Chapters and Conference Proceedings (peer-reviewed)

Schukajlow, S., Krawitz, J., Wiehe, K., & Rakoczy, K. (2024). Effects of teaching students to solve open modelling problems on utility, intrinsic, and attaiment values. In T. Evans, O. Marmur, J. Hunter, G. Leach, & J. Jhagroo (Eds.), Proceedings of the 47th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 81-88). PME

Wiehe, K., Schukajlow, S., Krawitz, J., & Rakoczy, K. (2024). The OModA project: Designing a teaching method to help students dealing with openness in modelling problems. In H.-S. Siller, G. Kaiser, & V. Geiger (Eds.), Researching Mathematical Modelling Education in Disruptive Times. (pp. 377-386). Springer. https://doi.org/10.1007/978-3-031-53322-8_30

Krawitz, J., Schukajlow, S., Wiehe, K., & Rakoczy, K. (2023). Experiences of competence and autonomy during a teaching intervention on mathematical modelling. In P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, & E. Kónya (Eds.), Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13) (pp. 1458-1465). Alfréd Rényi Institute of Mathematics and ERME.

Kanefke, J., & Schukajlow, S. (2022). Students' processing of modelling problems with missing data. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.), Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). Free University of Bozen-Bolzano and ERME.

Krawitz, J., Schukajlow, S., Kanefke, J., & Rakoczy, K. (2022). Making realistic assumption in mathematical modelling. In C. Fernandez, S. Llinares, A. Gutierrez, & N. Planas (Eds.), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 59-66). PME

Schukajlow, S., Krawitz, J., Kanefke, J., & Rakoczy, K. (2022). Interest and performance in solving open modelling problems and closed real-world problems. In C. Fernandez, S. Llinares, A. Gutierrez, & N. Planas (Eds.), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 403-410). PME

Teacher Journals

Krawitz, J., & Schukajlow, S. (2022). Eine Aufgabe viele Lösungen: Natürlich differenzieren mit Modellierungsaufgaben [One task many solutions: natural differentation with modelling problems]. mathematik lehren, 233, 28-32

Conference Proceedings (not peer-reviewed)

Schukajlow, S., Krawitz, J., Kanefke, J., & Rakoczy, K. (2023). Effekte einer Instruktion zu offenen Aufgaben: "Wenn ich wüsste, was hier fehlt, dann könnte ich sie lösen". In IDMI-Primar Goethe-Universitäst Frankfurt (Ed.), Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik (pp. 337-340). WTM. https://doi.org/10.37626/GA9783959872089.0

Wiehe, K., Krawitz, J., Schukajlow, S., & Rakoczy, K. (2023). Lösen offener Aufgaben fördern - Konzeption einer Unterrichtsstudie im Projekt OModA. In IDMI-Primar Goethe-Universitäst Frankfurt (Ed.), Beiträge zum Mathematikunterricht 2022. 56. Jahrestagung der Gesellschaft für Didaktik der Mathematik (pp. 231-234). WTM. https://doi.org/10.37626/GA9783959872089.0