Recent research suggests the benefits of supporting a progressive understanding of concepts of inference prior to the teaching of procedures and formal calculations through the study of informal statistical inference (ISI). To contribute to the growing knowledge about the early learning and teaching of statistics, particularly regarding the…

This study investigated whether an instructor's gestures can signal the underlying conceptual structure of a lesson and foster learning. In Experiment 1, 123 undergraduates watched a video comparing eastern and western steamboats in which the instructor produced structure gestures, surface gestures, structure and surface gestures, or neither…

An online authentic learning environment (OnALE) is proposed in this study to facilitate students' learning of inferential statistics in a real-life context. The efficacy of the OnALE, in comparison to the conventional approach relative to the students' performance, was explored. Respondents from the experimental group were purposively selected to…

This commentary provides an overview of abduction, also known as Inference to the Best Explanation, and argues that the term and relevant problem-solving methods should be adopted by chemistry educators. Abductive reasoning, especially within the context of science and medicine, continues to be an active area of exploration for philosophers and…

Researchers have hypothesized and, in some cases, shown that hypothetical learning trajectories (LT)s can be effective tools in teaching, but implementation, across individual teachers, varies. From the literature base, we have identified six ways researchers have hypothesized teachers might be able to use LTs in their work as teachers:…

In undergraduate mathematics, deductive reasoning plays important roles in teaching and learning various ideas, and is primarily characterized by the concept of logical implication. This comes up whenever conditional statements are applied, i.e., one checks if a statement's hypotheses are satisfied and then makes inferences. In calculus, students…

This study explored the role of word knowledge dimensions in second language (L2) word-meaning inference. College-level L2 learners (N = 121) participated in this study and completed a series of word knowledge tests including vocabulary size, word associates, morpheme-form knowledge, morpheme-meaning knowledge, morpheme discrimination, and…

Children develop and learn within dynamic contexts, yet the simplifying assumptions of common statistical methods often relegate such complexity to unexplained error. This chapter discusses ideas from the dynamic systems literature, which focuses on the interplay within and between components of complex systems, such as individuals and their…

We examine the challenges of teaching probability through the use of modelling. We argue how an integrated modelling approach might facilitate a coordinated understanding of distribution by marrying theoretical and data-oriented perspectives and present probability as more connected to the social lives of modern-day students. Research is, however,…

Thinking quality is one of the important parts of the core competencies of English courses at senior high schools in China, indicating the cognitive ability and level of thinking in logical, critical, and innovative aspects. This study attempts to integrate the development of cognitive skills into reading instruction, showing how to immerse…

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…

How do we teach and learn with our students about data literacy, at the same time as Biesta (2015) calls for an emphasis on 'subjectification' i.e. 'the coming into presence of unique individual beings'? (Good Education in an Age of Measurement: Ethics, Politics, Democracy. Routledge) Our response to these challenges and the datafication of higher…

Fredrich Froebel was a scientist, both in instinct and in training, and his life coincided with an important and dynamic period of scientific growth. I take this opportunity to delve both into some history and futurology to examine the heritage and legacy of his work. The usual of interpolation is of reading into data: where there exist some…

In second language teaching and learning, making errors is inevitable as language learning requires a lot of cognitive effort and concentration on the part of learners. Understanding the types and frequencies of student errors is, therefore, an important issue for ESL and EFL teachers to determine how students can be helped to improve their skills…