Certain aspects of theoretical frameworks in mathematics education can remain unexplained in the literature, hence unnoticed by the readers. It is thus interesting to participate in a dialogue where they can be discussed and compared in terms of the aims, objects studied, results and their relation to teaching. This study is focused on how APOS…

Researchers have studied the preparation of elementary teachers to teach mathematics to students from diverse racial, ethnic, and linguistic backgrounds by focusing either on teachers' learning about children's mathematical thinking (CMT) or, less frequently, about children's cultural funds of knowledge (CFoK) related to mathematics. Despite this…

Life is full of ambiguities, but as teachers we generally try to teach our students in a manner that sanitizes knowledge of all of its ambiguities. In doing so, we create an educational environment which forces students to learn in a rather meaningless fashion and this in turn leads to a lack of vitality and relevance within the academy. This need…

In this article, we obtain a genetic decomposition of students' progress in developing an understanding of the decimal 0.9 and its relation to 1. The genetic decomposition appears to be valid for a high percentage of the study participants and suggests the possibility of a new stage in APOS Theory that would be the first substantial change in…

This case study examines the salient features of two individuals' reasoning when confronted with a task concerning the cardinality and associated cardinal number of equinumerous infinite sets. The APOS Theory was used as a framework to interpret their efforts to resolve the "infinite balls paradox" and one of its variants. These cases…

In experiments on individual differences in learning, knowledge prerequisites and learning strategies have been shown to be important factors. The author questions whether learning optimization should rely on direct measures from outside the learner or should elucidate and strengthen the individual's capacity for learning decisions. He proposes to…

This report discusses research and theory that explore relationships between comprehension and knowledge acquisition. Studies are reported that indicate the lack of a one-to-one correspondence between initial comprehension activities and abilities to remember. It is noted that the value of comprehensive activities depends on how people must later…

A study was conducted to examine the process of the development of knowledge structures concerning events. Specifically, it investigated (1) the ways in which individuals build theories about events as they experience them; (2) the number of events an individual must experience, and how similar those events must be, before he or she begins to…

The knowledge-assembly theory is proposed to explain the acquisition, representation, and processing of knowledge. The theory assumes that both the representation and processing of knowledge change qualitatively as learning progresses. (Editor)

It is reasonable to assume that information such as the fact that "a beaver is larger than a mouse" is part of the average college student's generalized world knowledge. The present experiments examine the processes whereby new information is integrated with this type of generalized world knowledge. During the study phase of these…

Reports on a study in which college students wrote compositions that elicited their technical knowledge of three topics, then completed a questionnaire that assessed which of four information sources had contributed to their knowledge of the topics--formal education, mass media, social interaction, and direct experience. (FL)

Discusses previous articles in this journal issue and addresses issues concerning the acquisition of specific social knowledge. (FL)

In a study investigating the nature of questioning, a group of subjects with little relevant knowledge and a group with a great deal of relevant knowledge were asked to prepare a chocolate mousse. During the preparation, the subjects were allowed to ask any number of questions and each was answered immediately. Results showed that the number of…

Provides a critique of Paul Hirst's views on the forms of knowledge and outlines an original scheme for describing and understanding the forms that knowledge takes. (Author)