Modelling and Simulation with the Help of Digital Tools

Greefrath, Gilbert; Siller, Hans-Stefan

doi:10.1007/978-3-319-62968-1_44

Cited by 23 publications

(9 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…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. They studied the phases of the modelling cycle in which digital tools were used, and the activities that were carried out using these tools, during modelling activities.…”

Section: Connecting Educational Aspectsmentioning

confidence: 96%

Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

Greefrath

Siller

Vorhölter

et al. 2022

ZDM Mathematics Education

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Connecting Educational Aspectsmentioning

confidence: 96%

Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

Greefrath

Siller

Vorhölter

et al. 2022

ZDM Mathematics Education

Self Cite

View full text Add to dashboard Cite

show abstract

“…Referring to the scaffolding concept in mathematical modelling (Stender & Kaiser, 2015), the hints feature takes the role here. With the latest technological developments, digital tools can be used as an aid in learning mathematical modelling (Greefrath & Siller, 2017;Siller, 2011;Greefrath & Siller, 2018a;Greefrath et al, 2011;Greefrath & Siller, 2018b). Along with the condition, in this project, hints provided in the form of a 3D virtual display resembles the real object being targeted.…”

Section: Figure 3 Examples Of Hints Displayed By Appmentioning

confidence: 99%

Learning Mathematical Modelling With Augmented Reality Mobile Math Trails Program: How Can It Work?

Cahyono¹,

Sukestiyarno²,

Asikin³

et al. 2020

J. Math. Educ.

View full text Add to dashboard Cite

The aim of this study is to investigate how an augmented reality mobile math trails program can provide opportunities for students to engage in meaningful mathematical modelling activities. An explorative research design was conducted involving two mathematics teachers and 30 eight grades in Semarang, Indonesia. An Augmented Reality Mobile Math Trails App was created, and several math trail tasks were designed, then students run the activity. Data were gathered by means of participatory observation, interviews, questionnaires, tests, and worksheets. Data analysis began with the organisation, annotation, description of the data and statistic tests. The findings indicate that an educational program was successfully designed, which offered students a meaningful mathematical experience. A mobile app was also developed to support this program. The mobile app with augmented reality features is helpful for students as a tool that bridges the gap between realworld situations and mathematical concepts in problem-solving following the mathematical modelling cycle. The program thus contributes to a higher ability in mathematical modelling. The study identified a link between instrumented techniques in programs and mathematical modelling, as built during the instrumentation process. Further studies are essential for project development and implementation in other cities with different situations and aspects of study. AbstrakTujuan dari penelitian ini adalah untuk menyelidiki bagaimana program Augmented Reality Mobile Math Trails dapat memberikan kesempatan bagi siswa untuk terlibat dalam kegiatan pemodelan matematika yang bermakna. Sebuah penelitian dengan desain penelitian eksploratif dilakukan dengan melibatkan dua guru matematika dan 30 siswa SMP di Kota Semarang, Indonesia. Sebuah aplikasi Augmented Reality Mobile Math Trails telah diciptakan, beberapa tugas math trails telah didesain, kemudian siswa menjalankan kegiatan. Data dikumpulkan melalui observasi partisipatif, wawancara, pemberian angket, tes, dan lembar kerja. Analisis data dimulai dengan pengorganisasian, anotasi, deskripsi data, dan uji statistik. Temuan menunjukkan bahwa program pendidikan ini berhasil dirancang untuk menawarkan pengalaman matematika yang bermakna kepada siswa. Aplikasi perangkat seluler juga dikembangkan untuk mendukung program ini. Aplikasi ini dilengkapi dengan fitur augmented reality yang bermanfaat bagi siswa sebagai alat yang menjembatani kesenjangan antara situasi dunia nyata dan konsep matematika dalam pemecahan masalah mengikuti siklus pemodelan matematika. Dengan demikian, program ini berkontribusi positif pada kemampuan siswa dalam pemodelan matematika. Studi ini mengidentifikasi hubungan antara teknik instrumen dalam program dan pemodelan matematika, yang dibangun selama proses instrumentasi. Studi lebih lanjut sangat penting untuk pengembangan dan implementasi proyek di kota-kota lain dengan berbagai situasi dan aspek studi.

show abstract

“…The affordances here are local behaviour predict-ability and global behaviour predict-ability with recursion being a key mathematical idea that could be introduced and understood as student modellers explore the way such systems evolve. Greefrath and Siller (2017) recommend "the uses of simulations that naturally link modelling with the use of digital tools" (p. 537). See also Frejd and Ärlebäck (2017) who used simulation to investigate a pandemic.…”

Section: Affordances Of Technology-rich Teaching and Learning Environmentioning

confidence: 99%

Conclusions and Future Lines of Inquiry in Mathematical Modelling Research in Education

Brown

Ikeda

2019

Lines of Inquiry in Mathematical Modelling Research in Education

View full text Add to dashboard Cite

This final chapter overviews the 12 contributions to the monograph, organising this along the lines of inquiry suggested by Stillman. Contributors share understanding of mathematical modelling as solving real-world problems. The value and purposes of implementing modelling varies, in part due to local curricula. Theoretical underpinnings of the research include prescriptive modelling, modelling cycles, and modelling competencies. The challenges of engaging in modelling see empirical foci on modellers, teachers, and tasks whilst acknowledging interactions between these. Other important areas of the field, where researchers need to focus in the future include research with experienced student modellers, research on experienced teachers of modelling, and successful mathematisation by modellers. Keywords Modelling tasks • Teachers of modelling • Prescriptive modelling • Affordances 13.1 Mathematical Modelling: What Lines of Inquiry? Defining the bounds of research reported in this monograph is important. This includes the shared understanding by authors as to what mathematical modelling is. Modelling occurs when teachers, students, mathematicians, and others attempt to describe some aspect of the real-world in mathematical terms in order to understand something better or take or recommend actions (e.g. Blum 2015; Blum et al. 2007).

show abstract

Modelling and Simulation with the Help of Digital Tools

Cited by 23 publications

References 7 publications

Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

Learning Mathematical Modelling With Augmented Reality Mobile Math Trails Program: How Can It Work?

Conclusions and Future Lines of Inquiry in Mathematical Modelling Research in Education

Contact Info

Product

Resources

About