TASK ANALYSIS IN CURRICULUM DESIGN: A HIERARCHICALLY SEQUENCED INTRODUCTORY MATHEMATICS CURRICULUM¹

Abstract

A method of systematic task analysis is applied to the problem of designing a sequence of learning objectives that will provide an optimal match for the child's natural sequence of acquisition of mathematical skills and concepts. The authors begin by proposing an operational definition of the number concept in the form of a set of behaviors which, taken together, permit the inference that the child has an abstract concept of "number". These are the "objectives" of the curriculum. Each behavior in the defining set is then subjected to an analysis that identifies hypothesized components of skilled performance and prerequisites for learning these components. On the basis of these analyses, specific sequences of learning objectives are proposed. The proposed sequences are hypothesized to be those that will best facilitate learning, by maximizing transfer from earlier to later objectives. Relevant literature on early learning and cognitive development is considered in conjunction with the analyses and the resulting sequences. The paper concludes with a discussion of the ways in which the curriculum can be implemented and studied in schools. Examples of data on individual children are presented, and the use of such data for improving the curriculum itself, as well as for examining the effects of other treatment variables, is considered.The curriculum presented in this paper is an intermediate result of a research program exploring application of detailed task-analysis procedures to the problem of designing sequences of learning objectives. The aim of this research program is to develop a systematic method of specifying and validating learning hierarchies so that instructional programs can be designed that provide an optimal match for a child's natural sequence of acquisition. It is assumed that curricula that closely parallel this sequence will facilitate learning under a wide variety of specific teaching methods.The basic rationale for the methods employed here has been presented in papers by Resnick (1967) and by Resnick and Wang (1969).Briefly, the strategy is to develop hierarchies of learning objectives such that mastery of objectives lower in the hierarchy (simpler tasks) 'Preparation of this paper was supported by a grant from the Ford Foundation. Reprints may be obtained from Lauren B. Resnick,

TEACHING PEDESTRIAN SKILLS TO RETARDED PERSONS: GENERALIZATION FROM THE CLASSROOM TO THE NATURAL ENVIRONMENT1

“…A task analysis similar to one done by Res-nick, Wang, 'and Kaplan (1973) Procedure Task sequence and response definitions. A component analysis of pedestrian behavior yielded five major skills.…”

Medidas Comportamentais de Eficácia: Contribuições na Avaliação do Ensino de Operações Aritméticas

“…Quando se conhece o objetivo terminal a ser alcançado, avaliar a eficácia fica muito mais fácil. Resnick et al (1973), por exemplo, desenvolveram um programa para o ensino de comportamentos matemáticos. Isso foi feito por meio da análise dos comportamentos que compõem (a) o conceito de número, (b) a contagem, (c) a comparação de conjuntos, (d) a seriação e a ordenação e (e) a soma e a subtração, e da indicação da sequência de ensino e da hierarquia de aprendizagem que pode ser adotada com base em uma análise de quais são os comportamentos mais básicos e mais complexos na aprendizagem desses conceitos.…”

“…133,Caçari I,Boa Vista,Roraima, Estudos apontam sistematicamente dificuldades no ensino do comportamento de resolver problemas de adição e subtração (Fossa & Sá, 2008;Magina, Santana, Cazorla, & Campos, 2010;Neef, Nelles, Iwata, & Page, 2003;Vasconcelos, 1998). Para um ensino eficaz, o professor precisa conhecer o repertório comportamental que define a solução de problemas, bem como o que determina a dificuldade do problema e as habilidades necessárias para resolvê-lo (Haydu, Pullin, Iégas, & Costa, 2010;Resnick, Wang, & Kaplan, 1973). A forma de apresentação do problema e as estruturas semântica e sintática, em especial a posição da incógnita, são algumas das variáveis que interferem na dificuldade do problema (Haydu, Costa, & Pullin, 2006;Henklain & Carmo, 2013a;Henklain & Carmo, 2013b).…”

A computer-oriented task analysis method for mathematics instruction

“…For example, consider their Objective l-2:E, to count out a subset of n objects from a set of movable objects, moving them out of the set as they are counted. The Resnick et al (1973, p.687, p.690) analysis of this objective has the child "store" the numeral (Box lla in their Figure 6 Like Resnick et al (1973) and Suppes (1973), the present article employs both cognitive and behavioral concepts in its task analysis. A temporal hierarchy is implied by the analysis of Table 2 above.…”

“…In a very extensive task analysis of introductory mathematics, Resnick, Wang, and Kaplan (1973) have developed hierarchies of high-level behavioral objectives. For example, consider their Objective l-2:E, to count out a subset of n objects from a set of movable objects, moving them out of the set as they are counted.…”