Teaching mathematical modelling through project work

Blomhøj, Morten; Kjeldsen, Tinne Hoff

doi:10.1007/bf02655887

Cited by 93 publications

(46 citation statements)

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“…Although various researchers suggest that school and university mathematics curricula should place more emphasis on modeling tasks in order to develop students' modeling skills and to solve real-life problems (e.g., Berry, 2002;Lesh & Doerr, 2003;Niss, Blum, Galbraith, 2007;Verschaffel, Greer, & De Corte, 2002), teachers' lack of knowledge and inexperience regarding mathematical modeling and its pedagogy are the main shortcomings when modeling tasks are integrated into the classroom (Antonius, et al, 2007;Biembengut & Faria, 2011;Blomhøj & Kjeldsen, 2006;Çiltaş & Işık, 2013). In modeling activities, although students themselves experience being an active participant in the modeling process, when students tackle a point in the modeling process they could not pursue, the teacher should identify their difficulties and ask them to justify their conjecture or other approaches to the solution (Galbraith, 2012).…”

Section: Contribution Of This Paper To the Literaturementioning

confidence: 99%

“…In the process of solving modeling problems, students develop both their communication skills and gain insight into the function and power of mathematics in order to understand and formulate problems from different subject areas (English & Sriraman, 2010;Lesh & Doerr, 2003;Lesh & Zawojewski, 2007). Therefore, they improve their competency to solve real-life problems, in addition to developing their understanding of mathematical concepts (Blomhøj & Kjeldsen;English & Sriraman, 2010;Lesh & Doerr, 2003;Lesh & Zawojewski, 2007).…”

Section: Introductionmentioning

confidence: 99%

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Understanding Prospective Teachers’ Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

Zeytun

Çetinkaya

Erbaş

2016

EURASIA J MATH SCI T

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This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future classroom practices. The participants of this study were six prospective teachers selected among the nineteen who enrolled in the course. Data was collected through five modeling tasks. The results showed that the prospective teachers went through five main stages during the modeling process: understanding the task, devising a solution plan, working out the plan, interpreting and verifying the model, and presenting the model. The nature of prospective teachers' modeling processes was rather result-oriented, consisting of a single cycle as they did not seek an improved solution by revising and refining their models.

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Section: Contribution Of This Paper To the Literaturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Understanding Prospective Teachers’ Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

Zeytun

Çetinkaya

Erbaş

2016

EURASIA J MATH SCI T

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“…Other differences are that the arrows goes back and forth in Blomhøj and Højgaard Jensen's (2007) description of the modelling cycle but not in Blum and Leiβ's (2007) description, also the three ellipses in the centre of Figure 3 do not appear in Blum and Leiβ (2007). These ellipses are supposed to show that the epistemological base for the subprocesses is theory, experience or data (Blomhøj & Hoff Kjeldsen, 2006). The action/insight part in Figure 3, or action/realization (Blomhøj & Højgaard Jensen, 2003), is described as new insight gained from the investigated phenomena, which may put into action if it is supported and validated by the empirical data given.…”

Section: Modelling Cycles and Modelling Competencymentioning

confidence: 94%

“…However, the role of mathematical modelling in school mathematics differs significantly between different countries, as set out in national curriculum frameworks. In some countries it has been strengthened during the last decades, as for example in Swedish upper secondary mathematics (Ärlebäck, 2009), in Denmark and in Germany (Blomhøj & Hoff Kjeldsen, 2006;Schmidt, 2012). In some other countries it has a more weak position, such as for example in Norway (Utdanningsdirektoratet, 2013).…”

Section: Knowledge To Be Taughtmentioning

confidence: 99%

Modes of Mathematical Modelling : An analysis of how modelling is used and interpreted in and out of school settings

Frejd¹

2014

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“…to a mathematical model". Modelling applications must be integrated into daily mathematics lessons (Maaβ, 2006) because the development of students' modelling competencies can be ensured through these applications (Blomhøj & Kjeldsen, 2006). Important roles fall within not only the researchers in the field but also the mathematics teachers to ensure the integration in question.…”

Section: Introductionmentioning

confidence: 99%

Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

Yılmaz

Dede

2016

IJEMST

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Article History Received: 26 August 2015Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified variables. In this study, preservice elementary mathematics teachers' mathematization competencies are tried to be elicit by investigating their solution approaches while solving a modelling problem. It was seen the participants started to solve the problem by using only verbal explanations and then their expressions became more mathematical throughout the process. The participants, who made validations frequently in the process, displayed more comprehensive mathematization competencies by correcting their assumptions, mathematical models and solution. Accepted: 07 December 2015 KeywordsMathematical modelling Mathematization Competency Pre-service elementary mathematics teacher IntroductionMathematical modelling is defined as the process of expressing a real life problem situation mathematically and explaining this situation through the use of mathematical models (Blum & Niss, 1991). It is possible to define the real life situation mentioned in this definition as the whole world apart from mathematics in general (Pollak, 1979). In another definition which emphasizes the relationship between the real world and mathematical world, Heyman (2003) defines mathematical modelling as a simple way of applicability of mathematics, the relationship of mathematics with the real world, and revelation of this relationship, and it is stated that a mathematical model has to be constructed when mathematics is necessary to be benefitted from so as to explain real life problems, define and solve them (as cited in Peter Koop, 2004). In the modelling problems requiring mathematical models to be constructed, students mathematize real life situations and reach meaningful solutions depending on their experiences (Lesh & Doerr, 2003). In this context, in today's world in which only school success is not sufficient, students' performing mathematical modelling gains importance so that they will grow up as successful individuals in life and will be enabled to cope with the problems that they can encounter in real life.Because having knowledge on modelling process becomes important for students to engage in mathematical modelling, it seems to be important to discuss what modelling process means. Modelling process is defined as a cyclic process in which a real model is obtained through configuration of real life problems, in which mathematical model is constructed through mathematization of the real model, in which the mathematical model is solved and in which the obtained solution is interpreted and validated in the frame of real life (Borromeo Ferri, 2006; Maaβ, 2006). Many modelling processes and cycles are encountered in the literature depending on how...

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Teaching mathematical modelling through project work

Cited by 93 publications

References 4 publications

Understanding Prospective Teachers’ Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

Understanding Prospective Teachers’ Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

Modes of Mathematical Modelling : An analysis of how modelling is used and interpreted in and out of school settings

Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

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