Learning Mathematics Through Mathematical Modelling

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.

HAL (Le Centre pour la Communication Scientifique Directe), 2022

Collaborative learning is a well-established approach to elicit reasoning. The ability to solve mathematical modelling problems depends much on the ability to reason, because mathematical modelling problems are usually presented to students through texts. Decisions have to be made at all stages of the mathematical modelling cycle, for instance on assumptions, simplifications and feasibility of the model. In this paper we present an observation instrument to study collaborative modelling. There are three core components: collaborative learning, mathematical modelling and the language that students use while working together.

Mathematical modeling of real world conditions should be part ofl mathematics classroom activities. In this paper I argue that when real world problems are taught at schools learners are not able to cope on their own, without the assistance of their educator. There is very little or no emphasis placed on this aspect of mathemtics at schools, although it is just beginning to make an appearance in our new Outcomes Based Curriculum. I also discuss an experiment conducted with Grade 10 learners (15 year old) and their responses to real world problems and the conditions that need to be considered. There is ample evidence that a lot of work on mathematical modeling of real world problems has been done elsewhere in the world, but not much has been done in South Africa. This experiment was fully conducted using Sketchpad as a mediating tool. This in itself was a difficult task because our learners have not been really exposed to dynamic geometry environments. 1. The Teaching Experiment This...

2000

On the basis of experiences and studies developed i n the last ten years, the contribution aims to discuss some different peculiarities between Coo perative Learning and Peer Tutoring models in Mathematics lesson. These models are specific interpretations of a way of conducting Mathematics lessons which requires the activity of students, their personal participation in the construction of knowledge. In

maia.ub.es

In these notes we present a recent experience developed with first course students of the Mathematics degree at the University of Barcelona. More precisely, the corresponding subject was "Introduction to differential calculus". This task consisted in designing an innovative use of the tutoring time of the faculty in which the students, divided in smaller subgroups, had the chance to explain in their own words the problems they had been working with in previous lessons.

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.

2003

Models and the modeling process are at the heart of mathematics. The paper discusses the importance of developing pupils’ modeling abilities and skills in the context of school mathematics and focuses in particular on the content, structure and the educational exploitation of a set of activities constructed to serve this purpose in a computational modeling environment.

2017

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.

Quaderni di Ricerca in Didattica