A metrics and mapping framework is proposed to account for how heuristics, domain-specific reasoning, and intuitive statistical induction processes are integrated to generate estimates. Results of 4 experiments involving 188 undergraduates illustrate framework usefulness and suggest when people use heuristics and when they emphasize…

In this paper, we elaborate the "seeds of algebraic thinking" perspective, drawing upon Knowledge in Pieces as a heuristic epistemological framework. We argue that students' pre-instructional experiences in early childhood lay the foundation for algebraic thinking and are a largely untapped resource in developing students' algebraic…

The purpose of this study was to reconstruct writers' reasoning process as reflected in their written texts. The codes resulting from the text analysis were related to cognitive operations, ranging from simple to more sophisticated ones. The sequence of the cognitive operations as the text unfolded represents the writer's cognitive pathway at the…

Dual-process theories have become increasingly influential in the psychology of reasoning. Though the distinction they introduced between intuitive and reflective thinking should have strong developmental implications, the developmental approach has rarely been used to refine or test these theories. In this article, I review several contemporary…

Teaching in a manner consistent with reform recommendations is a challenging and often overwhelming task. Part of this challenge involves using students' thinking and understanding as a basis for the development of mathematical ideas (cf. NCTM, 2000). The purpose of this article is to address this challenge by developing the notion of "pedagogical…

This study seeks to establish which scientific reasoning skills are primarily domain-general and which appear to be domain-specific. The subjects, 12 university undergraduates, each participated in self-directed experimentation with three different content domains. The experimentation contexts were computer-based laboratories in d.c. circuits…

Gigerenzer (2000) and Anderson (1990) analyzed reasoning by asking: what are the reasoner's goals? This emphasizes the adaptiveness of behavior rather than whether a belief is normative. Belief in the ''hot hand'' in basketball suggests that players experiencing streaks should be given more shots, but this has been seen as a fallacy due to…

Examines tasks from the heuristics and biases literature in light of the understanding/acceptance principle of P. Slovic and A. Tversky (1974). Shows how the variation and instability of responses can be analyzed to yield inferences about why descriptive and normative models of human reasoning and decision making sometimes do not coincide.…