Analogical reasoning is a core facet of higher cognition in humans. Creating analogies as we navigate the environment helps us learn. Analogies involve reframing novel encounters using knowledge of familiar, relationally similar contexts stored in memory. When an analogy links a novel encounter with a familiar context, it can aid in problem…

To improve understanding of identities and inverses, and to provide a stronger foundation for future mathematics, Sandra Miles designed a two-part lesson that makes the relationship between identities and inverses explicit. This article illustrates Miles' teaching of the first part of the lesson, focused on addition and subtraction, and then gives…

A common motivation for adding control variables to statistical models is to reduce the potential for spurious findings when analyzing non-experimental data and to thereby allow for more reliable causal inferences. However, as I show here, unless "all" potential confounding factors are included in an analysis (which is unlikely to be…

Foreign language teaching is not to teach grammar and vocabulary of the target language and to gain basic language skills only. Foreign language teaching is teaching of the language's culture at the same time. Because of language and community develop and shape together, learning, understanding and speaking a foreign language literally requires…

This article focuses on the connections between the cognitive dimension of human meaning-making and creativity, using a metaphor from the artistic process of additive sculpture as a framework. The author weaves together various theoretical perspectives about cognition and creativity and shares the promise of recognizing the nexus of these notions…

We describe, discuss and illustrate a metaphoric parallel between the history of the most famous Spanish liqueur, "Anis del Mono" ("Anis" of the Monkey), and the evolution of living organisms in the light of Darwinian theory and other biological hypotheses published subsequent to Charles Darwin's "Origin of Species." Also, we report the use of a…

How are we to understand the power of certain literary metaphors? The author argues that the apprehension of good metaphors is importantly similar to the apprehension of fruitful mathematical analogies: both involve a structural realignment of vision. The author then explores consequences of this claim, drawing conceptually significant parallels…

This article describes aspects of classroom discourse, illustrated through vignettes, that reveal the complex relationship between the forms in which mathematical objects exist and their ostensive representations. We illustrate various aspects of the process through which students come to consider the reality of mathematical objects that are…

The notion of researcher as craftsman is not new. This article takes the analogy further, exploring the similarities between the research student's journey and the artisan's transition from apprentice to journeyman to member of the guild, in the light of the author's own PhD experience. Having completed her apprenticeship with the MSc, she…

This paper reports on five students' explorations of structural relationships between problem situations that they worked on over several years as participants in a long-term study. In particular, we describe the case of students who recognized isomorphisms between and among two problem situations and who used particular features of the problems…

This article explores the art form of dance as a metaphor for the teaching of theology. Employing the work of Maria Harris, the author contends that there are seven elements of dance than can serve as metaphors for teachers of theology: preparation, rhythm, movement, expectancy, response, embodiment, and performance. Each dance element is…