EDUCAÇÃO MATEMÁTICA E CÁLCULO MENTAL: UMA ANÁLISE DE INVARIANTES OPERATÓRIOS A PARTIR DA TEORIA DOS CAMPOS CONCEITUAIS DE GÉRARD VERGNAUD
Ciências
Sociedade
Cálculo mental
Invariantes operatórios
Cotidiano
Teoria dos campos conceituais
CNPQ::CIENCIAS HUMANAS::EDUCACAO
Abstract
The study proposes to identify operatory invariants used in mathematical problem-solving
requiring mental computation. The theoretical approach adopted was based on Gérard
Vergnaud s theory of conceptual fields, especially the notions of conceptual field, concepts,
situations, schemas and operatory invariants. Research procedures aimed at: analysing
operatory invariants - namely concepts-in-action and theorems-in-action at a microgenetic
level; characterizing the uses of mathematical strategies in everyday activities; identifying
speech and actions/gestures which indicate the use of mathematical knowledge. The study
took place in a large school in Juiz de Fora, Minas Gerais, where three pairs of 11 years-old
pupils, enrolled in the 4th year of primary schooling, were interviewed and carried out a group
activity. All data was recorded in videotapes and analysed according to a microgenetic
approach, which allowed for detailed analysis of relevant episodes involving mental
computation. The problems presented to the pupils required money-based calculations
involved in public transport, such as taking a bus, paying for the fare and getting change.
Findings concerning pupils use of strategies show that: two strategies used by the pupils,
composition and decomposition, require sound knowledge of the decimal system; on many
occasions, it is noticeable that strategies are used in combination, which present personal
variations; most of the strategies used rely on school-based knowledge, such as the decimal
number system and the basic properties of arithmetic operations, although the actual
procedures developed by the pupils were far from the typical problem-solving taught in
school. Analysis of operatory invariants shows similarities and differences in the strategies
used by pupils in school and out-of-school situations. The study offers contributions for
primary school maths teaching: first, through the identification of operatory invariants used in
different problem-solving situations; second, by way of primary school teachers increased
knowledge of problem-solving strategies, leading to further understanding of everyday uses of
mathematics.
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Document type
TeseFormat
application/pdf
Subject(s)
EducaçãoCiências
Sociedade
Cálculo mental
Invariantes operatórios
Cotidiano
Teoria dos campos conceituais
CNPQ::CIENCIAS HUMANAS::EDUCACAO