This article extends initial ideas on what hope is, why it matters to democracy, and how to teach it in schools, which were first presented by Sarah M. Stitzlein in her book "Learning How to Hope: Reviving Democracy through Our Schools and Civil Society" (Oxford University Press, 2020). It accounts for recent obstacles to hope,…

This paper demonstrates that a teachable agent (TA) can play a dual role in an online learning environment (OLE) for learning by teaching--the teachable agent working as a synthetic peer for students to learn by teaching and as an interactive tool for cognitive task analysis when authoring an OLE for learning by teaching. We have developed an OLE…

Research focusing on the integration of computational thinking (CT) into science, technology, engineering, and mathematics (STEM) education started to emerge. We conducted a semi-systematic literature review on 55 empirical studies on this topic. Our findings include: (a) the majority of the studies adopted domain-general definitions of CT and a…

Tentativeness is often framed as a deficit, synonymous with timidity or a lack of confidence. In this article, I situate the notion of tentativeness in an enactivist framework and describe its role as both a strategy and affordance in a spatial visualization exercise. Drawing on insights from mathematics education and ecological psychology, I…

The development of technology and science has progressed very rapidly. Students are required to master various kinds of abilities, one of which is problem-solving ability. Problem-solving ability need to be developed in the learning process. The learning model that can facilitate students in practicing problem-solving ability is the Reading,…

Place value is one of the 'big ideas' in number and plays a critical role in helping students develop their number sense, problem solving and computation skills. Yet, the elegant simplicity of our place value system belies the abstract nature of the construct. This paper presents data from 606 Year 3-6 students (ages 8-12) from two metropolitan…

The aim of this paper is to present a teaching proposal for the theoretical part relating to the first- and second-order linear difference equations with constant coefficients suitable for the first-year students at various types of universities. In contradistinction to the methods often applied (memorization of algorithms without a proper…

Mathematical reasoning, which plays a critical role in students' capacity to make sense of mathematics, is now emphasised more strongly in various curricula internationally. However, reasoning is sometimes difficult for teachers to recognise, let alone teach. This case study considers video of one teacher's implementation of a problem-solving…

Mathematical modeling and applications are an important part of curriculum and considered to be important for students' current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the…

Background: To create design solutions experienced engineering designers engage in expert iterative practice. Researchers find that students struggle to learn this critical engineering design practice, particularly when tackling real-world engineering design problems. Purpose/Hypothesis: To improve our ability to teach iteration, this study…

This paper illustrates the design-based learning (DBL) approach to promoting the deep learning of students and improving the quality of teaching in engineering design education. We performed three aspects of research with students in a typical educational activity. The first study investigated students' deep learning before and after the DBL…

The problem-based learning model via cloud technology (PBL model via cloud technology) is a research tool fabricated with the concepts of problem-based learning management, in which students are stimulated and enabled to foresee the problems that will arise. Also, in this learning style, teachers will define the problem situations and encourage…

Examining the still underexplored elements in educational theorist Paulo Freire's work, this essay begins from his claim that problem-posing pedagogy works as a "kind of psychoanalysis." Situating Freire between the critical philosophical and psychoanalytic traditions, Alex Armonda offers a new reading of the problem-posing dialectic,…

In this study, we examined one experienced mathematician's class practices, with particular attention to cognitive model described in genetic decomposition. Our findings indicate that students only had limited opportunities to be familiar with the first three steps in genetic decomposition, which may potentially lead students to answer limit tasks…

Are you frustrated when students focus on "getting the right answer" without understanding why the physics works that way, or even why their own brains came to that conclusion? If so, this might be less about the student and more about the pedagogy--you might be stuck on the "One True Path," a way of thinking "that assumes…