Classification and Analysis of Pre-Service Teachers’ Errors in Solving Fermi Problems

Carlos Segura,Irene Ferrando

doi:10.3390/educsci11080451

Abstract

Fermi problems are useful for introducing modelling in primary school classrooms, although teachers’ difficulties in problem solving may hinder their successful implementation. These difficulties are associated with the modelling process, but also with the estimation and measurement skills required by Fermi problems. In this work, a specific categorization of errors for Fermi problems was established, and it allowed us to analyse the errors of N = 224 pre-service primary school teachers. The results showed that prospective teachers make a large number of errors when solving this type of task, especially conceptual ones, which are associated with the process of simplifying/structuring the real situation and the mathematization process. They also showed that there is a significant relationship between the characteristics of the problem context and the error categories. Knowing the types of errors that prospective teachers make and designing task sequences that make them emerge so that prospective teachers learn from them could be an effective way to improve initial teacher education in modelling and estimation problem solving.

Highlights

Modelling tasks pose a problem related to a real-world situation that requires formulating, interpreting, and solving a mathematical model, the answer to which must be validated both mathematically and in its own context [1]
We studied errors in the productions of N = 224 pre-service primary school teachers when they were confronted with a sequence of Fermi problems
We focused on one type of modelling problem, with the aim of classifying and analysing the future teachers’ types of errors, considering both the errors inherent in the modelling process and the errors in the process of estimating measurements and quantities

Summary

Introduction

Modelling tasks pose a problem related to a real-world situation that requires formulating, interpreting, and solving a mathematical model, the answer to which must be validated both mathematically and in its own context [1]. Fermi problems are accessible modelling tasks that allow students to connect their mathematical knowledge with real-world phenomena [3,4]. In a Fermi problem, by its realistic nature, the statement presents a situation where little concrete information is known, requiring students to make assumptions and estimations in order to obtain a solution to the initial question [5]. It is important to know how future teachers solve tasks that allow modelling to be introduced in primary school in order to improve their initial training and promote their effective practice in the classroom [6,7]. The introduction of mathematical modelling activities in primary school classrooms is a challenge for teachers

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