
02370472
j
2007e.00287
Souza Rosa Borba, Rute Elizabete de
Nunes, Terezinha
How meaning, invariant properties and symbolic representations influence the understanding of directed numbers. (Como significados, propriedades invariantes e representa\c c\~oes simb\'olicas influenciam a compreens\~ao do conceito de n\'umero inteiro relativo.)
Educ. Mat. Pesqui. 6, No. 1, 73100 (2004).
2004
Pontif\'{\i}cia Universidade Cat\'olica de S\~ao Paulo (PUCSP), S\~ao Paulo
PT
F42
C32
D22
directed numbers
attitudes
problem solving
conceptual fields
empirical investigations
primary education
http://revistas.pucsp.br/index.php/emp/article/view/4681
Summary: Based on Vergnaud this study investigated how problem solving is affected by the meanings involved, by invariant properties that were learned, and by systems of signs used to represent positive and negative numbers and the operations of addition and subtraction. In two experimental studies, with 60 children participating in each, it was observed that seven and eightyearolds already have some understanding of directed numbers and are able to perform some additions and subtractions with these numbers long before they are formally introduced to this concept at school  usually four to five years later. The form in which children were asked to solve the problems strongly affected their performance. Thus, in the teaching of mathematical concepts, such as directed numbers, the meanings, properties and symbolic representations should vary, so as to allow students' understanding to develop widely within a conceptual field.