Facilitating Middle Secondary Modelling Competencies

Lines of Inquiry in Mathematical Modelling Research in Education, 2019

Teachers play an important role in determining how students work on modelling activities. In the current study, practising and prospective teachers engaged with modelling activities to develop their ability to identify students' modelling process. The study sought to answer the research question as to how the teachers' participation in modelling affects their interpretation of students' modelling activity. Data included two sets of participants' reports on their observations of a video-recorded modelling activity carried out by a group of five sixth-grade students, pre and post participation in four modelling activities. The findings indicate that prior to engaging with modelling activities, most participants described the students' modelling as linear, noting only the final mathematical model and mathematical results. After participating in the activities, most of the practising teachers' reports and a third of the prospective teachers's reports identified cyclical processes in the modelling.

Journal of pedagogical research, 2023

Educators have long emphasized the importance of relating mathematics to everyday life situations. During the primary school years, mathematical modeling activities play an important role in this regard. Through a mathematical modeling activity prepared in accordance with the length and area measurement learning outcomes in the primary school 4th-grade mathematics curriculum, the purpose of this study was to determine students' mathematical modeling competencies. The study adopted a qualitative approach using a teaching experiment model. The study involved three students selected from 33 in a state primary school through criterion sampling. Farmer Uncle Hüseyin model eliciting activity (MEA) was given to the focus group to work on, and the whole process was videotaped. Each video recording was transcribed in detail. Transcriptions, student handouts, and researcher field notes were analyzed using the mathematical modeling competencies cycle developed by Blum and Kaiser and adapted by Maaß (2006). Modeling competencies of students were found to be at different levels. Based on the study, the students' warm-up activities, the context of the MEA, and their previous modeling experiences all contributed to the students' representation of different levels of modeling competency. Due to the frequent use of multiple-choice questions in their classrooms, students also had difficulty interpreting qualitative data and understanding the mathematical task they were given.

2006

Three current interpretations of the term 'mathematical modelling' as it is used in mathematics education are described. The modelling cycle appropriate to one of these interpretations forms the basis for research into blockages that emerge in the solution process for problems with real world connections. The development of a framework documenting key elements that enable (or disable) progress during transitions between phases in the modelling process is described, and a selection of elements illustrated. Associated implications for learning and teaching are discussed.

2019

Mathematical modelling has recently taken the spotlight in mathematics education as a means to prepare students for the challenges they face in the modern world, and there have been numerous proposals on the modelling cycles describing students' approaches to solve modelling tasks. Within these proposed modelling cycles, researchers emphasize the importance of building a real model to describe the real situation and the application of extra-mathematical knowledge to highlight the relationship between reality and mathematics. However, the concept of extramathematical knowledge and the process to establish a real model have only been described in broad strokes and these descriptions lack details. This thesis aims to add to the descriptions of extra-mathematical knowledge and the process to develop a real model based on empirical data by closely examining students' mathematical Modelling behaviors. To achieve these goals, I administered two rudimentary mathematics complex tasks, a special type of tasks that present a complex situation but allow the audience to apply their well-worn tools in mathematics to establish a solution, to two groups of junior secondary school students. These tasks allow me to tip the balance of between reality and mathematics in mathematical modelling in order to focus on students' modelling behaviors. With regard to the process leading to a real model, my analysis indicates that students hold different intentions in building a real model and these intentions affect the strategies they use and therefore their modelling process and the quality of their solutions deeply. In the analysis of these strategies, I also apply flow theory to understand these intentions. As for extra-mathematical knowledge, my analysis demonstrates that extra-mathematical knowledge is a multi-faceted, complex construct composed of various competencies, that contains different characteristics and can deeply affect students' engagement with the tasks.

Perspectives in Education, 2020

This article reports on third-year mathematics students' competency and sub-competency development through providing intentional support in the learning of mathematical modelling. Students often experience modelling as difficult, and obstructions in the modelling process can lead to a dead end. Literature reports confirm that the modelling task is central in the modelling experience and a carefully planned task, aligned with a suitable activity sheet, can be used as a scaffold in learning mathematical modelling. Hence, this inquiry was conducted to provide a scaffold, as strategic support, for students' mathematical modelling competency development in the early stages of a modelling cycle. Guided by the framework of the Zone of Proximal Development, key elements suggested by the metaphor scaffolding are considered in the learning experience. Based on an analysis of activity sheets collected through group work, an example of a realistic and an unrealistic solution is presented, and students' development of mathematical modelling competencies is argued. Finally, suggestions for intentional support in the modelling process are discussed.

2000

Scientia in educatione, 2018

Modelling is considered an important approach that requires prospective teachers to be qualified both in modelling competencies and in pedagogical knowledge. In order to investigate the development of these competencies, we examined 49 prospective mathematics teachers studying in a course that included a sequence of modelling activities. During the course, groups of 5–6 participants engaged in these modelling activities as learners. The data include two sets of reports by the prospective teachers on their observations of a recorded modelling activity carried out by a group of five 6th grade students. The first set of reports was collected before the prospective teachers worked on any modelling activities, while the second set was collected after they had engaged in the modelling activities. The findings indicate that, prior to working on modelling activities, most of the prospective teachers described the students’ modelling activity as a linear process and focused on the final math...

New ICMI Study Series, 2007

The paper deals with the gap between the relevance of applications and modelling in didactical discussions and its minor importance in everyday mathematics teaching. Results of our own empirical studies that describe mathematical beliefs of teachers and students as being central obstacles are presented. Further, the studies demonstrate the possibility to change these beliefs as well as ways to promote modelling competencies.

Trends in Teaching and Learning of Mathematical Modelling, 2011

In the Netherlands, modelling is a compulsory topic for all pre-university science-stream students. Nevertheless, these students have difficulties in building a mathematical model. Our research aims at identifying the occurrence and removal of blockages when students create mathematical models. By means of a pilot study, we looked for an appropriate framework to identify students' obstacles and opportunities during this process. The results show that the initially chosen framework, which describes modelling as a cyclic process, ...

2013

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