In this paper we analyse some peculiar students’ mistakes in a task selected from the Italian National Mathematics Standardized Tests. In particular we show different types of errors identified in the solutions of grade 6 students who faced an item that involved the management of the number line. We use both the statistical results of the national sample and the qualitative analysis of answers in a smaller sample of 181 students. Our study draws on previous research on difficulties that students face placing rational numbers on the number line. We use an intertwinement of different theoretical lenses to explain the possible causes of failure. We show how some students’ answers can be interpreted as results of different misconceptions. The identified mistakes are related both to the management of the rational numbers representations (i.e. decimal representation and fraction) and to the manipulation of the graduate scale of the number line.

Students’ difficulties dealing with number line: a qualitative analysis of a question from national standardized assessment”, Quaderni di Ricerca in Didattica (Mathematics) / A. Lemmo, L. Branchetti, F. Ferretti, A. Maffia, F. Martignone. - In: QUADERNI DI RICERCA IN DIDATTICA. - ISSN 1592-4424. - 25:Supplement 2(2015), pp. 143-150. ((Intervento presentato al 67. convegno CIEAEM : 20 - 24 Luglio tenutosi a Aosta nel 2015.

Students’ difficulties dealing with number line: a qualitative analysis of a question from national standardized assessment”, Quaderni di Ricerca in Didattica (Mathematics)

L. Branchetti
Secondo
;
2015

Abstract

In this paper we analyse some peculiar students’ mistakes in a task selected from the Italian National Mathematics Standardized Tests. In particular we show different types of errors identified in the solutions of grade 6 students who faced an item that involved the management of the number line. We use both the statistical results of the national sample and the qualitative analysis of answers in a smaller sample of 181 students. Our study draws on previous research on difficulties that students face placing rational numbers on the number line. We use an intertwinement of different theoretical lenses to explain the possible causes of failure. We show how some students’ answers can be interpreted as results of different misconceptions. The identified mistakes are related both to the management of the rational numbers representations (i.e. decimal representation and fraction) and to the manipulation of the graduate scale of the number line.
Dans cet article, nous analysons certains particulières erreurs des élèves dans une tâche sélectionnée à partir des tests standardisés national italien en mathématique. En particulier, nous montrons différents types d'erreurs relevées dans les solutions des élèves de 6e année qui ont repondu à une question qui a impliqué la gestion de la ligne graduée. Nous utilisons à la fois les résultats statistiques de l'échantillon national et l'analyse qualitative des réponses dans un plus petit échantillon de 181 étudiants. Notre étude se fonde sur des recherches antérieures sur les difficultés que les étudiants ont à placer des nombres rationnels sur la ligne graduée. Nous utilisons un combinaison des différentes lentilles théoriques pour expliquer les causes possibles de l'échec. Nous montrons comment les réponses de certains élèves peuvent être interprétés comme des résultats de différentes misconception. Les erreurs identifiées sont liés à la gestion des représentations des numéros rationnels (i.e. représentation décimale et fraction) et à la manipulation de la ligne graduée
Settore MAT/04 - Matematiche Complementari
Commission Internationale pour l’Étude et l’Amélioration de l’Enseignement des Mathématiques (CIEAEM)
International Commission for the Study and Improvement of Mathematics Education
Departimento di Matematica e Informatica, Università di Palermo
Gruppo di Ricerca sull'Insegnamento/Apprendimento delle Matematiche (G.R.I.M.)
http://math.unipa.it/~grim/quaderno25_suppl_2.htm
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/854314
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