M.Gr.Voskoglou, The use of mathematical modeling as a
Michael Voskoglou
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Abstract
In this paper we discuss the use of mathematical modelling as a tool for learning mathematics in contrast with other views giving more emphasis to other factors (schemas, automation of rules et c). We sketch the "flow-diagram" of the modelling process in the classroom when the teacher gives such problems for solution to the students and we present methods to recognize the attainment levels of students at defined stages of the mathematical modelilng process and to measure the mathematical model building abilities of them.
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The Use of Mathematical Modeling As a Tool for Learning Mathematics
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Mathematical Modeling: An Important Tool for Mathematics Teaching
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The motivation behind this examination is to present the theoretical structure of Modeling Activities, which is believed to be a vital device for mathematics instruction. Modeling activities are defined as activities to figure out complex problems faced in real life situations that require the creation of a mathematical model as a product. In order to introduce the modeling activities within the scope of the study, the process of the developments of these activities is given in historical sequences and how they are defined by different educationists in the literature. Different steps of mathematical model formation, principles of mathematical model are illustrated. The importance of modeling activities in mathematics teaching, its different components and how they should be applied in courses are also included. IndexTerms Mathematical Modeling, Modeling Principles and Processes, Model Eliciting Activity, Mathematics Teaching.
A View of Mathematical Modeling in Mathematics Education
Journal of Mathematics Education at Teachers College, 2013
Consortium for Mathematics and Its Applications (COMAP) Mathematical Modeling is being introduced as a new product into the complex system of Mathematics Education. It has to fit with the existing parts and interfaces in this system. As one example, we will consider the effect of mathematical modeling on the transition from secondary to tertiary education. If mathematical modeling is of greater importance to the planners at one of these two levels of education than at the other, then stresses may result. As a second example, we propose to examine changes in teacher education necessitated by the introduction of mathematical modeling at the secondary level. Ideally, one might wish to prepare teachers to teach mathematical modeling by concentrating purely on modeling without the distraction of new mathematical ideas, but it is not clear that this can always be done. Finally, we plan to make some comments on the effect of mathematical modeling has on the relationship between mathematics education and mathematics itself. Each of these should gain from cooperation with the other.
The Implication of Mathematical Modeling in Teaching
Most teachers use lecture method frequently, giving the students little chances for more interaction, discovery approaches, team efforts, and experimentation in the classroom and relying on traditional mathematics textbooks which mostly provide single and straightforward solution problems at which students only apply a ready-made formula to reach a solution. This leads the students to believe the subject mathematics as a mere transmission of resolution techniques, being rather than a tool in another area of knowledge. On the contrary, students working on modeling activities focus on analyzing a problematic situation, setting and testing conjectures and model construction. This paper describes the main implications of modeling in the teaching of mathematics by designing and conducting in a short teaching intervention via model-eliciting activities. The data was collected through class observation, review of textbook, questionnaires, interviews, and students’ final reports detailing the processes used in developing the model for the model-eliciting activities. The analysis of the data revealed the following results: the participating students were able to work effectively with model-eliciting activities that enable them to discover the meaning of the mathematical concepts, few modeling tasks were incorporated in the textbook, students’ report showed that their prior experience gained from the first modeling activity helped them to develop a better model and interpret the solutions back to reality, and teachers and students believed that teaching and learning via model-eliciting activities could improve the teaching-learning of mathematics.
Mathematical Modelling Approach in Mathematics Education
Universal Journal of Educational Research, 2015
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using mathematics to explain and define the events in real life, to test ideas and to make estimations about real life events. Theoretical basis of the mathematical modelling approach, "model", "mathematical modelling" and "modeling activity" concepts are explained in this study and examples of these concepts are given. The importance of mathematical modeling, importance and the place of modeling topic in primary school, secondary school and high school (secondary education) mathematic programs based on social constructive approach, which were developed in 2005 and modified in 2013 by the Ministry of National Education (MNE) in Turkey, and how the modeling activities are included in the program are also presented in this study. It is considered that this study will contribute to the mathematical program development studies by MNE which are developed based on the constructive approach in Turkey.
The Role of the Situation Model in Mathematical Modelling—Task Analyses, Student Competencies, and Teacher Interventions Mathematics Subject Classification (2000) 97C30 · 97C70 · 97D40 · 97D70 · 97M10
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Modeling Students' Mathematical Modeling Competencies
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The study presented in this article takes a closer look at how French and German highschool students deal with a mathematical modeling problem, what blockages they encounter and how differences in the modeling processes between students from both nations can be explained by differences between the teaching and learning of mathematical modeling in France and Germany. To better understand these differences, firstly, a brief overview is provided on the historical development of mathematics education in both countries, with a focus on mathematical modeling, followed by a qualitative empirical study in both France and Germany. Two main differences can be identified: students' handling of the real-world situation and their striving for accuracy. Possible reasons for these differences are discussed in relation to national teaching traditions.
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This paper describes the development of mathematical modelling as an element in school mathematics curricula and assessments. After an account of what has been achieved over the last forty years, illustrated by the experiences of two mathematician-modellers who were involved,
An Investigation of Teachers’ Views on Applicability of Modeling in Mathematics Courses
Journal of Education and Training Studies
The purpose of this study has been to determine the views of elementary mathematics teachers on the applicability of modeling in mathematics courses. A case study was conducted with 17 elementary mathematics teachers working in various provinces in Turkey. An interview form consisting of open-ended questions was designed for the purpose of collecting data, which was obtained through semi-structured interviews. From the categories constituting the themes developed via the views of the teachers, four major conclusions and one minor conclusion were reached at the end of the study. Study results showed that the elementary mathematics teachers’ knowledge of the process and teaching performance had an impact on their views of the applicability of modeling.
Learning Mathematics Through Mathematical Modelling
2012
In a mathematics education course at the University of Gothenburg, students were asked to develop modelling tasks or modelling situations for each others. There are many reasons for encouraging the development of peer tutoring among students. When explaining something to a class mate, students must clarify their own thinking in order to give an explanation and must be prepared to have misconceptions confronted and corrected through discussion and listening. In general students learn much more if engaged in the teaching of a course. But will the receiving students learn what was intended or maybe something quite different? In this article I will discuss how this activity was carried out by two groups of students (one teacher group and one student group) and what they thought they learned from it. I will also discuss how the possibility to use technology enables learning of mathematics in a new way.
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Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches
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This paper aims at suggesting modelling tasks in teaching and learning of mathematics. It begins by providing the relevant literature of mathematical modelling and lays down how it is different from problem solving and word problems. It explores the importance and place of mathematical modelling in the curriculum and lays down related frameworks. It focuses on selected questions from the NCERT textbook of class 11 which have been modelled. Further, it analyses and mentions how these modelling tasks can be carried out by a facilitator in a classroom.
Investigations in Mathematics Learning Five different perspectives on mathematical modeling in mathematics education
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Many faces of mathematical modelling
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Mathematical modelling is a concept that covers a wide range of activities. Mathematical modelling can be understood both as formulation of an equation, a function, etc., describing a given situation and as a whole process of creating a model, starting from the real-world situation to the creation of a ready-to-use optimized tool. The work presents different approaches to mathematical modelling from the point of view of teaching mathematics. It presents the results of the research conducted on students (future teachers) regarding their theoretical knowledge and skills related to mathematical modelling.
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As a field of research, the teaching and learning of mathematical modelling and applications has been rapidly growing over the last decades, thanks to a significant involvement of researchers, presenting papers in specialized and broad-spectrum conferences in mathematics education. The number of theoretical perspectives has increased as well as the number of theoretical concepts developed. In fact, diversity and plurality are seen as distinctive features of this young field of research. This conference focuses on reviewing this theoretical expansion and, more particularly, on the work produced at the CERME conferences promoted by the European Society for Research in Mathematics Education. Then I will suggest the possibility of devising a common conceptual ground in the existing research that may play a key role in further conceptual advances and possible combinations of theoretical concepts: the development of the modeller thinking.
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Mathematical models and meanings by school and university students in a modelling task
Avances de Investigación en Educación Matemática
This study involves two classes from different educational levels, namely 9th grade and university. Students in both contexts were given a modelling task that required the development of a hand biometrics recognition system, during which they performed experimentation and simulation. As aims of the study, we look for distinctions and commonalities between the models developed in the two classes and seek to know how simulation and experimentation influence students’ production of meaning. The theoretical framework comprises the relationship between the modelling process and the prototyping process and adopts Peirce’s pragmatic perspective on meaning. The research is of a qualitative nature, assuming the characteristics of a case study. The results reveal many commonalities between the modelling in the two contexts. Moreover, experimentation and simulation were relevant elements for the production of meaning by the students, which is endorsed by a pragmatic perspective on meaning.
Mathematical modeling for teaching: An exploratory study
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We traced the impact of a designed unit of instruction on mathematical modeling on Prospective secondary teachers' knowledge about and efficacy towards teaching modeling. Analysis indicate that although teachers maintained modeling to be an important skill to be developed, absence of extensive experiences with mathematical modeling in the course of their own mathematical preparation hindered their ability to access pedagogical actions to be used in teaching.
Students’ mathematical modelling behaviors: Strategies and competencies
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.
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