1. Inicio
  2. Atrás
Título: An analysis of the processes used in solving algebraic equations and determining their equivalence in the early stages of learning /
Autores: Kieran, Carolyn.
Fecha: 1987
Publicador: McGill University - MCGILL
Fuente:
Tipo: Electronic Thesis or Dissertation
Tema: Algebra -- Study and teaching -- Research.
Problem solving in children -- Case studies.
Descripción: This dissertation reports the results of a three-phase study on the learning of algebra. The first phase involved interviews with ten seventh graders (12 and 13 years of age) to uncover some of their pre-algebraic notions on equations and equation solving. Six of these novice subjects were kept on for the second phase: a two-month teaching experiment on equation solving which emphasized the symmetric procedure of performing the same operation on both sides. The pretest and two posttest interviews of the second phase included both equation-solving and equivalent-equations tasks. The third phase involved interviews with nine more-experienced algebra students from grades eight to eleven, to investigate their equation-solving procedures, errors, and methods of determining the equivalence of equation-pairs. Their approaches were compared with those of the novices on the same tasks.
The study uncovered two distinct paths followed in the learning of equation solving: one by those already predisposed toward inversing; the other by those with a predisposition toward using surface operations. The latter group was more receptive to the procedure taught during the teaching experiment. A relationship was found to exist between subjects' view of the literal term in equations and their preferred equation-solving method. Novices with an inversing preference applied learned principles to equivalence tasks, but not to equation solving. More-expert subjects relied on inversing for both.
Theoretical implications of these findings concern: the processes used in the early stages of learning a new domain, the modeling of the procedures used to determine equivalence, the relationship between errors and structural knowledge, and the representation of word problems by equations. Finally, the characterization of an arithmetic approach and an algebraic approach to the learning of equation solving is used to suggest a basis for a theory of algebra learning.
Idioma: en