Rumbaugh D. M., Warner H. & Glasersfeld E. von (1977) The Lana project: Origin and tactics. In: Rumbaugh D. M. (ed.) Language learning by a chimpanzee. Academic Press, New York: 87–90. Fulltext at http://cepa.info/1334

Four studies revealed that a 2½/2-year-old chimpanzee (Pan), after 6 months of computer-controlled language training, proficiently reads projected word-characters that constitute the beginnings of sentences and, in accordance with their meanings and serial order, either finishes the sentences for reward or rejects them.

Rumbaugh D., Glasersfeld E. von, Warner H., Pisani P., Gill T. V. & Bell C. L. (1973) A computer-controlled language training system for investigation of language skills in young apes. Behavioral Research Methods and Instrumentation 5(5): 382–390.

Smock C. D. & Glasersfeld E. von (1974) Epistemology and education: The implications of radical constructivism for knowledge acquisition. Report #14. Follow Through Publications, Athens GA.

Number is presented as a uniting operation that can have collections of sensory items as material and a unit of units as the result. One thesis of the paper is that children who have constructed this uniting operation have not necessarily constructed number sequences. Problem situations are suggested for such children that might encourage the internalization of counting and the concomitant construction of the iterable unit of one. Situations are then suggested in which the child can use the number sequence that is based on the iterable unit of one to construct other iterable units and their corresponding number sequences. A second thesis of the paper is that for children who are yet to construct the uniting operation, counting is a sensory-motor scheme that should be coordinated with spatial, finger, and auditory patterns. Problem situations are suggested for these coordinations. While a teacher cannot give a child the uniting operation, the suggested situations can encourage its construction by the child.

Steffe L. P. & Glasersfeld E. von (1988) On the construction of the counting scheme. In: Steffe L. P. & Cobb P. (eds.) Construction of arithmetical meaning and strategies. Springer, New York: 1–19. Fulltext at http://cepa.info/1399

In an earlier publication (Steffe, von Glasersfeld, Richards, & Cobb, 1983), we presented a model of the development of children’s counting schemes. This model specifies five distinct counting types, according to the most advanced type of unit items that the child counts at a given point in his or her development. The counting types indicate what children’s initial, informal numerical knowledge might be like, and reflect our contention that children see numerical situations in a variety of qualitatively different ways. These constructs constituted the initial theoretical basis of the teaching experiment and served as a catalyst for the first years work. Consequently, we provide an explanation of the counting types as we defined them in 1980.

Steffe L. P., Richards J. & Glasersfeld E. von (1979) Models for the child’s acquisition of counting, addition, and subtraction. In: Fuson K. C. & Geeslin W. E. (eds.) Explorations in the modeling of the learning of mathematics. Columbus, OH: ERIC, 22–44.

Tomasello M. & Glasersfeld E. von (1975) The concepts of appearance, disappearance, and reappearance: A developmental semantic analysis. Follow Through Report #17. Follow Through Publications, Athens GA.

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