Intelligent tutoring systems (ITSs) aim to deliver personalized learning support to each learner, aligning with the educational aspiration of many countries, including China. ITSs' personalized support is mainly achieved by providing individual prompts to learners when they encounter difficulties in problem-solving. The guiding principles and…

The main aim of this paper is to propose a critical view of the application of Toulmin's model of argument to mathematics education, focusing on aspects that have strong teaching implications. It is claimed that Toulmin's description of arguments in mathematics, in particular as regards the relations between form and meaning, is misleading and out…

It is crucial for engineers to anticipate the socio-ethical impacts of emerging technologies. Such acts of anticipation are thoroughly normative and should be cultivated in engineering ethics education. In this paper we ask: 'how do we anticipate the socio-ethical implications of emerging technologies responsibly?' And 'how can such responsible…

Because creativity is an essential 21st century skill that must be developed in gifted and talented student populations, it is important for gifted and talented programs to nurture mathematical creativity. To shed light on this topic, this article explores three questions: What is mathematical creativity? How can we develop students' mathematical…

Problem solving is widely regarded as a fundamental feature within the school mathematics curriculum. However, there is considerable disagreement over what exactly problem solving is, and if and how it can be taught. In this article, I define problems as non-routine tasks and propose the explicit teaching of domain-specific problem-solving tactics…

Because deficits in executive functions (EFs) characterize most neurodevelopmental disorders, it is appropriate to question the value of EFs for understanding learning disabilities. Two types of studies--those testing whether EFs moderate treatment effects and those testing the direction of effects between EFs and academic skills--are presented to…

Some readers thrive more than others because they are more actively involved in their learning. All students can become active participants in their learning through quality teacher prompting. In this article, teachers will learn how to promote emergent learners' active participation as they decode and comprehend, while problem-solving unknown…

In this work, we study several closely related problems involving chains, conveyor belts, and rockets, which are described and solved without the application of infinitesimal calculus, or even the concept of mathematical limit. On one hand, the novelty lies not in the problems themselves, but in the method used for their solution, which brings…

The tradition of studies involving the combinatorial approach to recurring numerical sequences has accumulated a few decades of tradition, and several problems continue to attract the interest of mathematicians in several countries. This work specifically discusses the Fibonacci, Pell, and Jacobsthal sequences, focusing on Mersenne sequences. The…

Modelling roles of mathematics in physics has proved to be a difficult task, with previous models of the interplay between the two disciplines mainly focusing on mathematical modelling and problem solving. However, to convey a realistic view of physics as a field of science to our students, we need to do more than train them to become fluent in…

This paper pushes beyond current debates over what is being called the science of reading to articulate a multidimensional complex conception of what is entailed in reading comprehension. Reading comprehension entails not only cognitive processes, but equally important is how issues of identity along multiple dimensions, perceptions of tasks and…

We explore the various Mathematica functions for performing Gaussian elimination, specifically when the linear system contains input parameters. On the one hand, we want the solution, perhaps heuristically found, to be in terms of the input parameters, and as general as possible. On the other hand, we must adhere to all necessary conditions and…

Years of failed attempts to engage my mathematics teacher students in exploration and co-creation led me to radically change my teaching approach. Inspired by literature that uses the jazz improv metaphor for teaching, I derived three tenets based on principles from jazz improv. First, I would bring no more than a single problem-solving task to…

The purpose of this article is to set out the design principles and architecture of a second language (L2) learning voice chatbot. Building on L2 acquisition theories and chatbot research, in this article, we report on a South Korean government-funded longitudinal project in which we designed and developed a chatbot called "Ellie".…

An augmented reality (AR) application and an activity worksheet have been developed to support students in visualizing the concepts involved when solving [superscript 1]H NMR problems. This instructional resource was designed to encourage conceptual problem-solving and prevent memorization by eliminating the use of chemical shift tables. It uses…