The Use of Mathematical Modeling As a Tool for Learning Mathematics

2019

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.

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.

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.

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.

Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and learning mathematics in terms of definitions of models and modeling, the theoretical backgrounds of modeling, and the nature of questions used in teaching modeling. This study focuses on two issues. The first section attempts to develop a unified perspective about mathematical modeling. The second section analyzes and discusses two approaches to the use of modeling in mathematics education, namely modeling as a means of teaching mathematics and modeling as an aim of teaching mathematics.

2019

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.

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.

This article presents a review of literature exploring five different perspectives on mathematical modeling in mathematics education. Because there is not a single agreed-on definition of what mathematical modeling is or how it should be done, a focused and extensive review of mathematical modeling is essential. The five broad classifications discussed in this article include realistic modeling, educational modeling, models and modeling perspective, socio-critical modeling, and epistemological modeling. For each perspective, we present (a) the goals of mathematical modeling, (b) the definition of a mathematical model, (c) the mathematical modeling cycle, (d) the design of the modeling task, and (e) key researchers and research foci. In this article, we aim to present the different perspectives of mathematical modeling in an organized way so as to (1) demonstrate the rich and diverse background of mathematical modeling and (2) clarify theoretical foundations of seminal works in mathematical modeling.

1995

ZDM, 2006

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,