As a theory of skill acquisition, the instance theory of automatization posits that, after a period of training, algorithm-based performance is replaced by retrieval-based performance. This theory has been tested using alphabet-arithmetic verification tasks (e.g., is A + 4 = E?), in which the equations are necessarily solved by counting at the…

A discussion of the history of error analysis in mathematics education research provides an overview of research published in German and Anglo-American publications since the early 1900s. (MP)

Theories--based on concretizing, assimilation, and structuring--of the use of metaphors in learning are assessed. Each is shown to predict different patterns of inferences and errors in problem solving. An experiment with 43 undergraduates involving college lectures indicated that structuring may provide the most important function of metaphors in…

This article discusses the importance of understanding the language learning process for more effective teaching. Language learning is seen as no different from other cognitive processes, and is considered a creative activity. Variables that determine the nature of language learning are discussed. (CLK)

Deals with the provisional grammar known as Learner's Language that foreign language learners develop in the learning process. Data derived from observing Learner's Language have two major implications for foreign language teaching: the reordering of learning sequences, and the need for providing a full communicative context throughout the…

Preliminary results from a longitudinal study of English-speaking children and adults learning Dutch in natural situations suggest that 12- to 15-year-olds learned faster than either older or younger subjects during their first 6 months in Holland. All age differences had disappeared in a group of advanced subjects (English-speakers who had been…

This study was designed to follow up earlier work on mapping instruction. The two main goals were to: (1) test the effectiveness of mapping instruction as a general cure for "buggy" subtraction algorithms, and (2) explore two alternative explanations of how this new form of instruction works. It was hypothesized that mapping cures bugs…

In a test administered to Spanish-speaking students of English as a second language at the elementary and intermediate levels, the results indicated the subjects' reliance on the strategies of overgeneralization and transfer was qualitatively different. Implications of the results are discussed. (Author/RM)

The results of a number of experiments with the memorizing of several different subject-matters are presented in such a way that the relationship between number of opportunities for error (word elements faded) and number of errors actually made can be observed for individuals and groups. The particular selection of word elements to be taught by…