Is the natural number 7 rational? Is it complex? We argue that the answers to these questions relate to the ways numbers are taught. Commonly, a new kind of numbers is presented as an expansion of a previously familiar kind of numbers, which results in a nested image of the relations between number sets. In this article, we introduce an…

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…

Understanding how physicists solve problems can guide the development of methods that help students learn and improve at solving complex problems. Leveraging the framework of cognitive task analysis, we conducted semistructured interviews with theoretical physicists (N=11) to gain insight into the cognitive processes and skills that they use in…

We examine the relationship between how teachers talk about teaching and their actual teaching practices. Analyses of their talk were based on extensive transcripts and writings and focused on metaphors and images invoked when discussing knowledge, learning, and teaching. Three distinct and coherent webs of association were identified, which we…

This research aimed to determine the metaphorical perceptions of class teachers and reveal whether these perceptions are affected by the teaching approaches they adopt. Because teachers' opinions were collected in written form, this study is a descriptive survey model study. The participants of the study consisted of 64 class teachers chosen…

Metaphors are well-known tools for teaching statistics to novices. However, educators might overlook metaphor theoretical developments that offer nuanced and testable perspectives on their pedagogical applications. This article introduces the notion of metaphor types--"correspondence" (CO) and "class inclusion" (CI)--as…

This study investigated the relationship between a metaphor-based approach to teaching English as a foreign language (EFL) and involvement of the brain's right hemisphere. Specifically, it examined learners' understanding of three levels of sureness associated with different expressions in English -- those that are "certain,"…

Research on incidental focus on form (FonF) has established associations among the nature of learner error, corrective feedback (CF), and effectiveness of CF measured through uptake. In this line of research, the analysis of learner error has been limited to errors with grammar, pronunciation, vocabulary, and spelling (nonformulaic). Consequently,…

Helping preservice teachers use hybrid language representations in science is important if they are to become scientifically literate and able to engage in the discourse for understanding scientifiyc issues. Using hybrid language representations based on the framework of computer-supported collaborative learning, the teacher educator applied the…

In this study, teachers explored their professional identities by reflecting on their teaching role(s) and contexts through elicitation of textual (written) metaphors and visual (drawn) metaphors of teaching. Participants created impromptu drawings emblematic of their conceptualized metaphor. Analysis of participants' written metaphors and…

Purpose: Cognitive Linguistics has repeatedly pointed out the major significance of metaphors. In particular, metaphors are highly effective in the context of political and economic discourse. We analyze the as yet ignored use of metaphors in standard economic textbooks as exemplified by Paul A. Samuelson and N. Gregory Mankiw. The following will…

According to general relativity (GR), we live in a four-dimensional curved universe. Since the human mind cannot visualize those four dimensions, a popular analogy compares the universe to a two-dimensional rubber sheet distorted by massive objects. This analogy is often used when teaching GR to upper secondary and undergraduate physics students.…

This article hypothesizes that one of the reasons for Chinese EFL learners' rigid use of nominalization and insufficient use of hedging in academic writing can be attributed to the unclear understanding of the relationship between these two expressions. The aim of the research is to first prove and then explain the possible co-occurrence of…

This article focuses on the relationships between social justice, environmental justice, and sustainability from the local to global levels. We envision social and environmental justice as involving not only human beings, but also the rights of all species to life and respect. We advocate an ecological justice approach based on the equality and…

This pilot study explores the effectiveness of a strategy for overcoming post-primary students' misconceptions within the topic of algebra. Although central to the study of mathematics, algebra can be an area of difficulty for many students. A misconception is typically classified as flawed understanding of a concept causing repeated errors, and…