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

Yw, Chang; Krawitz, Janina; Schukajlow, Stanislaw; Yang, Kai Lin

doi:10.1007/s11858-019-01090-4

Cited by 16 publications

(15 citation statements)

References 29 publications

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“…Nevertheless, it seems reasonable to assume that students' modeling routes are related to their national contexts because current styles of mathematics education can be seen as the result of a historical process where different learning opportunities are prepared in relation to predominant teaching styles. Since these learning opportunities highlight different aspects, for example technical competences or mathematical accuracy, it is probable that provably influential factors for modeling, such as self-efficacy (Krawitz & Schukajlow, 2018) or conceptual knowledge (Chang, Krawitz, Schukajlow, et al, 2019), differ between students from different countries. This mediating relationship should be analysed in further studies.…”

Section: Methodological Discussionmentioning

confidence: 99%

Mathematical modeling in Germany and France: a comparison of students’ modeling processes

Hankeln

2020

Educ Stud Math

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The study presented in this article takes a closer look at how French and German highschool students deal with a mathematical modeling problem, what blockages they encounter and how differences in the modeling processes between students from both nations can be explained by differences between the teaching and learning of mathematical modeling in France and Germany. To better understand these differences, firstly, a brief overview is provided on the historical development of mathematics education in both countries, with a focus on mathematical modeling, followed by a qualitative empirical study in both France and Germany. Two main differences can be identified: students' handling of the real-world situation and their striving for accuracy. Possible reasons for these differences are discussed in relation to national teaching traditions. 1 The distinction between mathematics and the rest of the world, sometimes also called the "real world", dates back to Pollak's work in 1977, where he distinguished different kinds of applications.

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Section: Methodological Discussionmentioning

confidence: 99%

Mathematical modeling in Germany and France: a comparison of students’ modeling processes

Hankeln

2020

Educ Stud Math

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“…The present sample involved 495 ninth graders, including 201 German students from nine classes from high-track schools (German gymnasium; 50% female, mean age = 14.96 years) and 294 Taiwanese students from 12 classes in which all performance levels were taught (52% female, mean age = 14.89 years). Prior studies (e.g., Chang et al, 2020;OECD, 2019) have demonstrated that Taiwanese students have much higher intramathematical competence than German students. In order to balance these differences and improve the comparability of the groups regarding this important background variable, we collected data from German high-track schools and regular Taiwanese schools.…”

Section: Sample and Proceduresmentioning

confidence: 96%

“…The few comparative studies that have analyzed students' achievement in modelling have pointed out that Western students are more experienced in solving modelling problems. Chang et al (2020) showed that German students had higher modelling competence than Taiwanese students when the students from the two countries were on the same level of intramathematical competence. This difference was particularly remarkable for students with a low level of intramathematical competence.…”

Section: Educational Environments In Germany and Taiwanmentioning

confidence: 98%

“…Students seem to lack meta-knowledge about modelling, particular the knowledge that solving modelling problems often requires learners to make assumptions (Krawitz et al, 2018), and it was found to be a particular strength of students educated in Germany compared with students educated in other countries. This is presumably because German students have more experience working with modelling problems (Chang et al, 2020;Hankeln, 2020).…”

Section: Educational Environment As a Moderator Of The Effects Of Reading Comprehensionmentioning

confidence: 99%

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The role of reading comprehension in mathematical modelling: improving the construction of a real-world model and interest in Germany and Taiwan

Krawitz

Yang

et al. 2021

Educ Stud Math

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To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving modelling problems, and fostering reading comprehension might lead to better modelling competence. Further, ease of comprehension and involvement have been found to increase interest in the learning material, and thus, improving reading comprehension might also increase interest in modelling. The aims of this study were to (a) determine whether providing students with reading comprehension prompts would improve the modelling sub-competencies needed to construct a model of the real-world situation and their interest in modelling and (b) analyze the hypothesized effects in two different educational environments (Germany and Taiwan). We conducted an experimental study of 495 ninth graders (201 German and 294 Taiwanese students). The results unexpectedly revealed that providing reading comprehension prompts did not affect the construction of a real-world model. Further, providing reading comprehension prompts improved students’ situational interest. The effects of providing reading comprehension prompts on the construction of a real-world model were similar in Germany and Taiwan. Students’ interest in modelling improved more in Germany. An in-depth quantitative analysis of students’ responses to reading prompts, their solutions, and their interest in the experimental group confirmed the positive relation between reading comprehension and modelling and indicated that the reading comprehension prompts were not sufficient for improving reading comprehension. Implications for future research are discussed.

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“…Undoubtedly, the differences mentioned above will shape different social and cultural conditions and further provide different opportunities for PSTs to learn how to teach mathematical modeling. To the best of our knowledge, only a few recent studies have compared students' knowledge of mathematical modeling from different cultures (e.g., Chang et al, 2020;Hankeln, 2020). However, an investigation of the impact of pre-service teacher preparation on teachers' professional mathematical modeling competences is necessary to understand the variation in teaching quality and to facilitate the effective development of such professional competences.…”

Section: Introductionmentioning

confidence: 99%

Pre-service mathematics teachers’ professional modeling competencies: a comparative study between Germany, Mainland China, and Hong Kong

2021

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Although mathematical modeling plays an important role in many curricula worldwide, significant discrepancies persist in the importance of mathematical modeling in ordinary mathematics classrooms and teacher education. This paper compares pre-service mathematics teachers’ professional mathematical modeling competencies in three different regions—Germany, Mainland China, and Hong Kong—where educational and cultural traditions differ, including the role of mathematical modeling. In total, 232 pre-service mathematics teachers from the three regions completed a modeling task covering mathematics content knowledge (MCK) of modeling and mathematical pedagogical content knowledge (MPCK) of modeling. The results show that pre-service teachers from Germany demonstrated the strongest MCK and MPCK of mathematical modeling; by contrast, pre-service mathematics teachers from Mainland China and Hong Kong demonstrated relatively weaker MCK and MPCK of mathematical modeling. MCK and MPCK of mathematical modeling were also found to be unevenly developed at different competence levels for the three regions. These differences may be attributed to the history of mathematical modeling in mathematics curricula, teacher education, and teaching culture in these three regions.

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

Cited by 16 publications

References 29 publications

Mathematical modeling in Germany and France: a comparison of students’ modeling processes

Mathematical modeling in Germany and France: a comparison of students’ modeling processes

The role of reading comprehension in mathematical modelling: improving the construction of a real-world model and interest in Germany and Taiwan

Pre-service mathematics teachers’ professional modeling competencies: a comparative study between Germany, Mainland China, and Hong Kong

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