# Comparing German and Taiwanese secondary school students’ knowledge in solving mathematical modelling tasks requiring their assumptions

## Abstract

Mathematization is critical in providing students with challenges for solving modelling tasks. Inadequate assumptions in a modelling task lead to an inadequate situational model, and to an inadequate mathematical model for the problem situation. However, the role of assumptions in solving modelling problems has been investigated only rarely. In this study, we intentionally designed two types of assumptions in two modelling tasks, namely, one task that requires non-numerical assumptions only and another that requires both non-numerical and numerical assumptions. Moreover, conceptual knowledge and procedural knowledge are also two factors influencing students’ modelling performance. However, current studies comparing modelling performance between Western and non-Western students do not consider the differences in students’ knowledge. This gap in research intrigued us and prompted us to investigate whether Taiwanese students can still perform better than German students if students’ mathematical knowledge in solving modelling tasks is differentiated. The results of our study showed that the Taiwanese students had significantly higher mathematical knowledge than did the German students with regard to either conceptual knowledge or procedural knowledge. However, if students of both countries were on the same level of mathematical knowledge, the German students were found to have higher modelling performance compared to the Taiwanese students in solving the same modelling tasks, whether such tasks required non-numerical assumptions only, or both non-numerical and numerical assumptions. This study provides evidence that making assumptions is a strength of German students compared to Taiwanese students. Our findings imply that Western mathematics education may be more effective in improving students’ ability to solve holistic modelling problems.

## Keywords

Modelling tasks Making assumptions Mathematical knowledge## Notes

### Acknowledgements

This study was conducted in the framework of the TaiGer program. The meetings of the German and Taiwanese partners were funded by Deutsche Forschungsgemeinschaft (DFG, no. HE 4561/10-1) and Ministry of Science and Technology Taiwan (MOST, No. MOST 105-2911-I-003 -513), allocated to Aiso Heinze (IPN Kiel, Germany) and Kai-Lin Yang (NTNU Taipei, Taiwan) respectively. The authors thank the anonymous reviewers for their valuable comments and suggestions.

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