Mathematische Modellierungskompetenz fördern durch Lösungsplan oder Dynamische Geometrie-Software? Empirische Ergebnisse aus dem LIMo-Projekt

Hankeln, Corinna; Greefrath, Gilbert

doi:10.1007/s13138-020-00178-9

Cited by 10 publications

(3 citation statements)

References 54 publications

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“…This is also the case in the context of mathematical modelling (e.g., Greefrath et al, 2018;Keune & Henning, 2003;Sinclair & Jackiw, 2010). In this regard, some empirical results have already been reported (Hankeln & Greefrath, 2021). For example, in a case study, Greefrath and Siller (2017) observed students working on a reality-based task with GeoGebra.…”

Section: Connecting Educational Aspectsmentioning

confidence: 88%

Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

Greefrath

Siller

Vorhölter

et al. 2022

ZDM Mathematics Education

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Discrete mathematics and mathematical modelling, along with the educational discourse surrounding these, have many connections. However, ways that the educational discourse on discrete mathematics can benefit from the inclusion of examples of mathematical modelling and the accompanying discussion are currently under-researched. In this paper, we elaborate on the educational potential of examples of mathematical modelling based on the usage of methods from discrete mathematics, with a focus on secondary education. We first describe vertex-edge graphs as possible topics of discrete mathematics that are accessible at school level within modelling lessons. Secondly, in the context of a case study, we describe modelling activities with students at the end of lower-secondary education, using a classical problem of discrete mathematics originating from the Königsberg bridge problem. The students’ solution processes for this optimisation problem based on graph theory are described. Their approaches are examined referring to the phases of the modelling cycle, using the method of qualitative content analysis. We studied in particular the extent to which students use concepts related to vertex-edge graphs in specific sub-phases of the modelling process. The analysis allows the required sub-competences of modelling to be identified and the connection of these competences with discrete mathematics to be worked out. On the basis of this analysis, educational opportunities of teaching discrete mathematics and mathematical modelling are assessed. Overall, we point out the possibilities and opportunities for using examples from the field of discrete mathematics to acquire modelling competences and to foster the linkage of mathematical modelling and discrete mathematics at school level.

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Section: Connecting Educational Aspectsmentioning

confidence: 88%

Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

Greefrath

Siller

Vorhölter

et al. 2022

ZDM Mathematics Education

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“…Research on modelling has provided initial indications that reading comprehension prompts might foster the construction of a real-world model and thereby enhance modelling competence. In the study conducted by Schukajlow et al (2015) and similarly also in the study by Hankeln and Greefrath (2020), students received a scaffolding instrument called a solution plan to guide their modelling processes. The solution plan consisted of prompts referring to the different phases of the modelling cycle, including prompts to trigger reading comprehension ("Read the text precisely!…”

Section: Reading Comprehension and Its Impact On Constructing A Real-world Model And On Interest In Modellingmentioning

confidence: 99%

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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“…Furthermore, some studies addressed on how students effectively learn mathematics in online learning environments and the factors affecting their motivation positively or negatively (Bringula et al, 2021;Santi et al, 2022;Rutherford, et al, 2022). Although online learning environments have become so widespread, it is observed that recent research on mathematical modeling is mostly focused on face-to-face education environments (Hankeln and Greefrath (2021); Hıdıroğlu et al, 2018;Molina-Toro et al, 2022). Focusing on technology-aided mathematical modeling processes in face-to-face education, Çevikbaş et al, 2023 examined the difficulties that students face due to the complex nature of digital technologies and technology disruptions whereas Klock and Siller (2020) emphasized the limitations that students face in using technology and drew attention to the deficiencies in this regard.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling in Online Learning Environments: Student Challenges

Altuntaş,

Ay,

Çetin

2024

Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi

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This research aims to examine the difficulties encountered by secondary school students in the mathematical modeling process applied synchronous in online learning environments (OLEs). The research was conducted on 11 8th grade students (8 girls, 3 boys) studying in a public secondary school in Türkiye, using the case study method, by recording audio and videos for 6 weeks. Participants worked collaboratively within a group to complete various problems using the Dynamic Mathematics Software (DMS) GeoGebra. The themes that students had difficulty with in the Online Mathematical Modeling (OMM) process were determined as technical difficulties, access to information and reliability, limited view, shared tasks, limited interaction, time management and time constraints. Using digital tools and instruments in the modeling process offers many advantages to students, however it can also create technical problems. Conspicuous difficulties encountered in the Mathematization and Working Mathematically process is noted, particularly in relation to the DMS. In addition, it was found that the difficulties encountered by students while obtaining information from different sources sometimes negatively affected their solution suggestions. Limitations about the students' interactions with their peers, teachers, and technology during the OMM process caused various difficulties in the stages of the modeling cycle. Future research should focus on developing methods to increase students' interaction and collaboration in OMM processes by overcoming technical difficulties.

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Mathematische Modellierungskompetenz fördern durch Lösungsplan oder Dynamische Geometrie-Software? Empirische Ergebnisse aus dem LIMo-Projekt

Cited by 10 publications

References 54 publications

Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

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

Mathematical Modeling in Online Learning Environments: Student Challenges

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