Mathematical Modelling with a Solution Plan: An Intervention Study About the Development of Grade 9 Students’ Modelling Competencies

Beckschulte, Catharina

doi:10.1007/978-3-030-37673-4_12

Cited by 9 publications

(7 citation statements)

References 14 publications

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“…Based on these results, intervention methods for further modelling activities with graph-theoretical problems can be developed as scaffolding measures (Stender & Kaiser, 2015). Due to its process character, the modelling perspective offers the possibility for controlling the solution processes at the metalevel by using metacognitive aids (Beckschulte, 2020;Stillman, 2011;Vorhölter, Krüger, et al, 2019). For example, in the intuitive approach described above, a metacognitive aid to search for the mathematical model could open the view in the direction of more abstract generalisations.…”

Section: Discussionmentioning

confidence: 99%

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: Discussionmentioning

confidence: 99%

Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

Greefrath

Siller

Vorhölter

et al. 2022

ZDM Mathematics Education

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“…Given the importance of modelling in mathematics classrooms, a large body of research exists which examines teacher methods for promoting modelling processes, including collaborative work (Mueller et al, 2014), four-or five-step solution plans (Beckschulte, 2020;Schukajlow et al, 2015), and metacognitive strategies (Vorhölter, 2019). However, these strategies do not consider the role of discussions among students, a context, where argumentation can be fruitfully encouraged.…”

Section: Discussionmentioning

confidence: 99%

“…These studies show differences in the impact of the solution plan depending on the stage of the modelling process, with results improving toward the end of the plan as a result of interpreting and evaluation (Schukajlow et al, 2015). More specifically, the five-step solution plan has a significant impact in the interpreting stage, but the rest of the stages of the mathematical modelling cycle exhibit no results, suggesting that more qualitative research on the use of the solution plan is needed (Beckschulte, 2020).…”

Section: / 15mentioning

confidence: 99%

“…Other authors have divided the fourth step into two parts (interpreting and evaluating), resulting in a fivestep plan (Beckschulte, 2020). These studies show differences in the impact of the solution plan depending on the stage of the modelling process, with results improving toward the end of the plan as a result of interpreting and evaluation (Schukajlow et al, 2015).…”

Section: / 15mentioning

confidence: 99%

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Argumentative orchestration in the mathematical modelling cycle in the classroom

Solar

Ortiz

Arriagada

et al. 2022

EURASIA J Math Sci Tech Ed

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Given the importance of modelling in mathematics classrooms, and despite the extensive body of research on teacher support for promoting the mathematical modelling cycle in the classroom, authors have overlooked how teacher support for argumentation can contribute to this cycle. This study is aimed at characterizing teacher support for argumentation in the mathematical modelling cycle in the classroom. We analyzed 10 class episodes taken from the cases of two teachers, Soledad and Ángeles. The episodes were analyzed considering teacher support for argumentative orchestration (communicative strategies and pattern recognition). In the two cases studied, we found that argumentative orchestration exhibited different types of overall presence and recurrence throughout the stages of the mathematical modelling cycle, with communicative strategies being more present across the board and more recurrent in the mathematical modelling cycle than pattern recognition strategies.

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“…Seperti yang terlihat di Gambar 1, peserta dapat mengikuti skenario pelatihan daring sekaligus dapat memperoleh materi pelatihan. Pola seperti ini, sesuai/mirip dengan pola intervensi pemberian solution plan bagi peserta didik (Beckschulte, 2020). Beberapa dokumentasi kegiatan luring dan daring yang telah dilaksanakan dapat dilihat pada Gambar 2 dan Gambar 3.…”

Section: Pelaksanaan Kegiatanunclassified

Training for high school teachers to develop learning modules based on mathematical modeling in Magetan, East Java

Abadi,

Savitri,

Artiono

et al. 2024

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Preparing teaching modules that lead to AKM requires skills in framing abstract mathematical material into a situation or problem context known to students. This is a new challenge for teachers. The process of arranging mathematical material into a context familiar to students is called mathematical modeling. However, in practice, teachers often overlook the importance of modeling skills in teaching. This activity aims to equip mathematics teachers with mathematical modeling skills to enhance their teaching, particularly in preparing students for AKM. The activity, attended by 25 MGMP Mathematics High School teachers in Magetan Regency, was conducted in a hybrid manner (offline and online). Based on the analysis of questionnaire data, it can be concluded that there is an improvement in teachers' understanding of the Independent Curriculum, mathematical modeling, and the application of mathematical modeling in preparing teaching modules for mathematics topics. Similarly, there is an increase in awareness of self-development as professional teachers.

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Mathematical Modelling with a Solution Plan: An Intervention Study About the Development of Grade 9 Students’ Modelling Competencies

Cited by 9 publications

References 14 publications

Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching

Argumentative orchestration in the mathematical modelling cycle in the classroom

Training for high school teachers to develop learning modules based on mathematical modeling in Magetan, East Java

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