This paper aims to reveal the potential of inferentialism, an emerging philosophy in mathematics education, to extend contemporary constructivist research regarding conceptual development. Going against the traditional view of a notion as the name of a corresponding concept and a constructivist way of naming second-order models, we provide a new…

Although there is wide evidence on young children's category learning, questions concerning how cognitive mechanisms and social mediation work collaboratively in this process remain sparse. Here, we study the impact of pedagogy in young children's categorization of novel artifacts. A before-and-after micro-genetic study compared 58 3-year-old…

Learning trajectories are built upon progressions of mathematical understandings that are typical of the general population of students. As such, they are useful frameworks for exploring how understandings of diverse learners may be similar or different from their peers, which has implications for tailoring instruction. The purpose of this…

This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the predicate and inference structures among various proofs (in…

The transition from preformal and propaedeutic generalization-actions to a symbolically explicit use of the concept of variable has been a matter of significant attention in mathematics education, for example in the context of generalization processes on a preformal level and regarding the specific nature of algebraic concepts. This contribution…

This paper focuses on an inferential view on introducing new concepts in mathematics classrooms. A theoretical framework is presented which helps to analyse and reflect on the processes of teaching and learning mathematical concepts. The framework is based on the philosophies by Ludwig Wittgenstein and Robert Brandom. Wittgenstein's language-game…

Students' informal inferential reasoning (IIR) is often inconsistent with the normative logic underlying formal statistical methods such as Analysis of Variance (ANOVA), even after instruction. In two experiments reported here, student's IIR was assessed using an intuitive ANOVA task at the beginning and end of a statistics course. In both…

The study examined the knowledge of the functional relations between potential difference, magnitude of current, and resistance among seventh graders, ninth graders, 11th graders (in technical schools), and college students. It also tested the efficiency of a learning device named "functional learning" derived from cognitive psychology on the…

Investigated in 3 studies whether 2- to 4-year-olds make accurate causal inferences on the basis of patterns of variation and covariation. Found that all three age groups considered information from various patterns of variation and covariation in judgments regarding two objects and activation of a machine. Three- and 4-year-olds used the…

Previous research (e.g. "Cognition" 64 (1997) 73) suggests that the privileged level for inductive inference in a folk biological conceptual hierarchy does not correspond to the ''basic'' level (i.e. the level at which concepts are both informative and distinct). To further explore inductive inference within conceptual hierarchies, we examine…

A study investigated children's difficulty in learning color words and attempted to determine whether the difficulty was perceptual, conceptual, or linguistic. The subjects were 24 two-year-olds, half with knowledge of color words and half without, and a similar control group. The experimental subjects were given conceptual and comprehension tasks…

Scientific and everyday knowledge domains are compared so as to reveal the distinctive differences between their goals and the cognitive processes used to attain them. The main goals, working goals, learning difficulties, knowledge structure, concept specification, knowledge organization, role of school science, program-solving instruction, formal…

Presents a method for improving reading comprehension through direct instruction of inductive reasoning. Students gather clues to personality of characters as play progresses and from these arrive at an overall generalization concerning the complexities of the character. (SRT)

Describes study of undergraduates that investigated learners' preconceptions of the difficulty of interactive video, instructional television, and television. The effects of actively or covertly responding to practice questions on perceived mental effort, recall, and inferences are examined, and correlations between lesson time and inference or…