The logos of many atomic energy regulatory bodies present a paradox in that the depictions of atomic structure that they portray tend to be 'wrong' in relation to the rules that govern pictorial representations of atomic structure that we teach. These logos present chemistry educators with excellent classroom resources to enhance critical thinking…

It is expected that children increasingly learn to identify errors throughout their schooling process and even before it. As a further step, however, some scholars have suggested how a culture of error should be implemented in the classroom for the student to be able not only to locate errors but also, and above all, to learn from them. Yet the…

Cognitive flexibility refers to various processes which enable behaviors to be modified on the basis of a change in the contingencies between stimuli or responses and their associated outcomes. Reversal learning is a form of cognitive flexibility which measures the ability to adjust responding based on a switch in the stimulus--outcome…

As educators, we've all probably experienced presenting in new places and/or audiences, and having some sort of mishap. Therefore, as part of their professional preparation, we should prepare our students with realistic presentation practice, mishaps and all! Within this paper, I will outline a pedagogical tool that randomizes potential…

Mistakes can be a source of frustration for teachers and students in mathematics classrooms because they reveal potential misunderstandings or a lack of learning. However, increasing evidence shows that making mistakes creates productive pathways for learning new ideas and building new concepts (Boaler 2016; Borasi 1996). Learning through…

This is a study of my dramatized narrative based on a true story of what took place in a mathematics class in an international school setting. My narrative includes the exploration of a mathematical "mistake" and the discovery of newly emergent problems. The drama, commentary, and reflections provide a close examination of the conduct…

The article describes how one fifth-grade teacher helped her students to exercise their Rights of the Learner (e.g., to be confused; to claim a mistake; to speak, listen, and be heard; and to write, do, and represent what makes sense) as they learned to graph and interpret non-linear data.

Research has shown that word problem difficulty is influenced by various linguistic, numerical and general variables, but results in this area are inconsistent. This paper focuses on the question of how the order of numerical data, the context, the position of the unknown transformation, and the length of the statement in an additive word problem,…

Coding is a process of assigning meaning to a given piece of evidence. Evidence may be found in a variety of data types, including documents, research interviews, posts from social media, conversations from learning platforms, or any source of data that may provide insights for the questions under qualitative study. In this study, we focus on text…

The goal of this article is to assist individualized education program (IEP) team personnel to not make errors in the placement of students. To do so the authors: (1) describe what a placement decision is and who makes the decision; (2) review the placement requirements of the Individuals With Disabilities Education Act (IDEA, 2006); (3) examine…

The articles presented in this Special Issue provide evidence for many statistically significant relationships among error scores obtained from the Kaufman Test of Educational Achievement, Third Edition (KTEA)-3 between various groups of students with and without disabilities. The data reinforce the importance of examiners looking beyond the…

Evaluating Learners' Response in an e-Learning environment has been the topic of current research in areas of Human Computer Interaction, e-Learning, Education Technology and even Natural Language Processing. The current paper presents a twofold strategy to evaluate single word response of a learner in an e-Learning environment. The response of…

It is widely accepted dogma that consequential decisions are better made with multiple measures, because using but a single one is thought more likely to be laden with biases and errors that can be better controlled with a wider source of evidence for making judgments. Unfortunately, advocates of using multiple measures too rarely provide detailed…

This paper provides a set of five indicators of CAS use, which provide a means to analyse a student's written solution to determine whether they used CAS for solving a given problem. These indicators provide a way for researchers and teachers to determine CAS use without requiring classroom observation or the explicit recording of extra…

This article endeavours to define how the application of incorrect or wrong solutions to mathematical equations or problems can be used to help stimulate students to perform a critical analysis of the mathematics being applied or the context of the equations used. The context of the application is discussed together with the specific learning…