Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

Based on Piaget's theory of logico-mathematical knowledge, 126 students in grades 2-5 were asked 6 questions about elapsed time. The main reason found for difficulty with elapsed time is children's inability to coordinate hierarchical units (hours and minutes). The educational implications drawn are that students must be encouraged to think about…

The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding…

Piaget (1971) made a distinction between intuitive (preoperational) time and operational (logico-mathematical) time. According to Piaget, operational time develops around 7-8 years of age and is characterized by children's ability to deduce, for example, that if A was born before B, A will always be older than B. When time is still intuitive,…

A content analysis of over 28,000 pages from 141 elementary school mathematics textbooks published between 1900 and 2000 shows that widely used mathematics textbooks have changed substantially. Textbooks from the early part of the century were typically narrow in content but presented substantial amounts of advanced arithmetic and also asked…

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.…

First and second graders (n=81) were randomly partitioned into experimental and control groups. The experimentals were given experiences in sorting and seriating objects. Significant treatment and grade effects (p.01) were found on a seriation test, but no significant relationships between classification and transitivity nor seriation and…

Seventy-five preservice elementary school teachers were given a Piagetian-related paper-and-pencil test involving the equilibrium of a beam balance. Results show a significant positive relationship between the developmental levels of the clearness, as measured by the test, and their performance on equation solving when different reversible…

To help the reader understand the scope and diversity of the Wisconsin R & D Center's research effort in mathematics, four perspectives are presented: (1) the Center's approach to research, development, and practice; (2) the origins of the current research effort; (3) a description of current research; and (4) a projection for future research. (JP)

Develops covariational reasoning and proposes a framework for describing mental actions when interpreting and representing dynamic function events. Investigates calculus students' ability to reason about covarying quantities in dynamic situations. Suggests that curriculum and instruction should emphasize moving students to a coordinated image of…

A study with 29 preschoolers showed that a statistically significant number of them successfully reassigned tags in counting (ordinality) but failed to predict that differently ordered counts would produce the same outcome (cardinality). Results indicated that children may not entirely understand implications of their counting actions. (Contains…

The investigation reported pursued the possibility of cross-cultural differences between American and Swiss children in terms of how they perceive and conceptualize spatial figures. There was statistical evidence that the preferences of American and Swiss children were different when compared as a whole or by sex and test version. (MK)

Described are the general problem-solving strategies and their nature and functions. The importance of integrating different types of general problem-solving strategies with content-specific teaching in mathematics classes is discussed. (KR)

The authors challenge some of the conclusions reached about Piaget by Brian Rotman in his book. (MK)

Presents a way of interpreting mathematics classrooms, by advancing the notion of sociomathematical norms, to account for how students develop mathematical beliefs and values and how they become intellectually autonomous in mathematics. Includes episodes from a second-grade classroom to clarify the processes by which sociomathematical norms are…