Provides an interpretation of the influence of constructivist thought on mathematics educators starting around 1960 and proceeding up to the present time, including Piaget's cognitive-development psychology, a preconstructivist revolution in research, beginnings of the constructivist revolution, and how this revolution served as a period of…

Discusses intersubjectivity and examines limitations of radical constructivism. Compares Piaget's positioning of the individual in relation to social life with that of Vygotsky in support of the claim that radical constructivism does not offer enough as an explanation of children's learning of mathematics. (Author/MKR)

We address the telling/not-telling dilemma in mathematics education. Telling is instructionally important, but has been downplayed because of (a) perceived inconsistencies between telling and constructivism, (b) increased awareness of the negative consequences of relying too heavily on telling, and (c) a focus on "non-telling" actions as…

Replies to Lerman, who presented Vygotsky as an irreconcilable opponent to Piaget's genetic epistemology and von Glasersfeld's radical constructivism. Argues that Lerman's stance does not reflect von Glasersfeld's opinion of Vygotsky's work, nor does it reflect Vygotsky's opinion of Piaget's work. Establishes compatibility between analytic units…

Piagetian theory describes mathematical development as the construction and organization of mental operations within psychological structures. Research on student learning has identified the vital roles of two particular operations--splitting and units coordination--play in students' development of advanced fractions knowledge. Whereas Steffe and…

Leslie Steffe, among the foremost mathematics education researchers in the world, has had a profound influence on three generations of researchers. In 2006, he received the first-ever Senior Scholar Award from the AERA Special Interest Group: Research in Mathematics for the excellence and seminal nature of his work. Steffe shares his thoughts…

Teaching experiments have generated several hypotheses concerning the construction of fraction schemes and operations and relationships among them. In particular, researchers have hypothesized that children's construction of splitting operations is crucial to their construction of more advanced fractions concepts (Steffe, 2002). The authors…

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional…

Quantitative and qualitative analyses of 37 first-graders' solutions to addition problems were conducted to re-examine inconsistencies in children's progress from counting-all to counting-on. The authors applied the constructivist's participatory-anticipatory stage distinction as a tool for fine-grained assessment. Among solutions given by…

The purpose of this study was to investigate children's construction of 10s out of the 1s they have already constructed. It was found that, for many younger children, a dime was something different from 10 pennies even though they could say with confidence that a dime was worth 10 cents. As the children grew older, their performance improved.…

In a small-scale, 8-month teaching experiment, the author aimed to establish and maintain "mathematical caring relations" (MCRs) (Hackenberg, 2005c) with 4 6th-grade students. From a teacher's perspective, establishing MCRs involves holding the work of orchestrating mathematical learning for students together with an orientation to…

This article reports on students' learning through conjecturing, by drawing on a semester-long teaching experiment with 6 sixth-grade students. It focuses on 1 of the students, Josh, who developed especially powerful ways of operating over the course of the teaching experiment. Through a fine-grained analysis of Josh's actions, this article…

The goal of this article is to examine students' mathematical development that occurs as a teacher works within each of 2 zones of learning: students' zones of proximal development (ZPD) and students' zones of potential construction (ZPC). ZPD, proposed by Vygotsky, is grounded in a social constructivist perspective on learning, whereas ZPC,…

Response to an earlier article in JRME in which the authors propose a constructivist alternative to the representational view of mind. Argues that the original article misinterprets the postepistemological perspective, confuses ontological and epistemological issues, and mistakes the pragmatic force of the constructivist argument. (45 references)…

Suggests that radical constructivists draw on a weak image of the role of social life. Argues that a thick notion of "social" leads to a complexity of sociocultural theories concerning the teaching and learning of mathematics, a perspective that is firmly located in the debates surrounding cultural theory over the last two decades.…