MAD+. Introducing Misconceptions in the Temporal Analysis of the Mathematical Modelling Process of a Fermi Problem

Marta Pla-Castells,Gisela Chaparro,Carmen Melchor

doi:10.3390/educsci11110747

Abstract

This work describes how the combination of the mistakes committed by a group of pre-service teachers when solving a Fermi problem, with the representation of the temporal analysis of their resolutions, can offer more in-depth information about their conceptual misconceptions regarding mathematical and modelling concepts. The combined representation allows knowing when mistakes occur and provides a powerful tool for instructors to adapt the teaching–learning processes of mathematics at all levels of education. Our study is based on a recent categorisation of students’ mistakes, together with the creation of a new representation tool, called MAD+, that can combine all this information. The macroscopic view provided by the MAD+ diagrams gives insight into the context in which the mistakes take place and makes the analysis of the resolution of a Fermi problem more efficient.

Highlights

Introduction and Theoretical FrameworkIn recent years there has been an increasing interest in the introduction of real context and modelling activities in training at all educational levels [1]
We address the analysis of the performance of each group separately by means of the Modelling Activity Diagrams (MAD)+ diagrams
As we have seen in the previous section, MAD+ diagrams can provide a deep insight into the processes of solving Fermi problems

Summary

Introduction

Introduction and Theoretical FrameworkIn recent years there has been an increasing interest in the introduction of real context and modelling activities in training at all educational levels [1]. The inclusion of real-world problems in mathematics education has proven to be an effective tool in the education of future citizens [2]. Behind this consensus there are many discussions on how to integrate mathematical modelling into mathematics teaching and learning processes. Rita Borromeo, in her book Learning how to teach mathematical modeling in school and teacher education [9] shows how important it is for future primary school teachers to learn how to teach mathematical modelling This process involves the acquisition of modelling skills and their associated teaching skills. Those teachers who have conceptual and procedural mathematical errors will see their ability to apply modelling in their future classes diminished

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Conclusion