The use and understanding of mathematics is a crucial component of the physical sciences. Much work has been done in physics education research and science education more broadly to determine persistent difficulties with mathematics. This work has led to the development of numerous problem solving strategies aimed at helping learners approach…

The paper utilizes the fundamental components of social capital theory. It assesses a hypothesis that higher levels of social capital result in benefits for professional development of pedagogy in higher education institutions' faculty. A year-long study was conducted that offered faculty training in increasing critical thinking skills in…

The development of students' mathematical reasoning (MR) is a goal of several curricula and an essential element of the culture of the mathematics education research community. But what mathematical reasoning consists of is not always clear; it is generally assumed that everyone has a sense of what it is. Wanting to clarify the elements of MR,…

Suppose that there is an inexhaustible supply of $3 and $5 vouchers from the local supermarket. They may only be exchanged for items that cost an exact number of dollars made up from any combination of the vouchers. What is the highest amount not able to be obtained? This is an interesting problem in mathematical thinking and logic requiring only…

Purpose represents a unique opportunity for identifying and analyzing the complexity of human reasoning, considering that its constitution brings together cognitive, affective and social elements. In this article, we use the Theory of Organizing Models of Thinking (OMT), an epistemological and methodological approach based on developmental…

The move from respecting science to "scientism," i.e., the idealization of science and scientific method, is simple: We go from acknowledging the sciences as fruitful human activities to oversimplifying the ways they work, and accepting a fuzzy belief that "Science" and "Scientific Method," will give us a direct…

Our goal in this theoretical contribution is to connect research on knowledge revision and relational reasoning. To achieve this goal, first, we review the "knowledge revision components framework" (KReC) that provides an account of knowledge revision processes, specifically as they unfold during reading of texts. Second, we review a…

Students need lifelong skills to build their problem-solving capabilities for better understanding of the world and themselves. Working through design lessons allows them to directly apply thinking strategies and learning about facts, figures, and concepts while they are crafting meaningful ideas about the influence and social implications of…

The K-12 Science curriculum envisions the development of scientifically, technologically, and environmentally literate and productive members of society who are critical problem solvers, innovative and creative citizens, informed decision makers and effective communicators. To achieve these, higher order thinking skills must be developed among the…

This article develops some ideas concerning the "big picture" of how using computers might fundamentally change learning, with an emphasis on mathematics (and, more generally, STEM education). I develop the big-picture model of "computation as a new literacy" in some detail and with concrete examples of sixth grade students…

Our project seeks to draw attention to the rich mathematical thinking that is generated when students work on contextual mathematising tasks. We use a design-based research approach to create ways of reporting that raise the visibility of this rich mathematical thinking while retaining and respecting its complexity. These reports will be aimed for…

The development of critical thinking skills forms an important part of many higher education courses and has become increasingly visible in syllabi and assessment criteria. Yet, in spite of this, students often struggle to understand what it is and to demonstrate it in their work. This paper aims to explore how students understand the term…

The literature on insight problems--problems that supposedly can only be solved by rejection of an initial faulty problem representation and sudden comprehension of another, nonobvious representation (restructuring)--suggests that the size of initial representations affects the very process of problem solving. Large initial representations impose…

Reflecting on her efforts to improve her trainee's lesson conclusions, Paula Worth decided to brush up her own. A journey of self-evaluation led her to revisit the Cambridge Conclusions Project. Through its lens, she found her own lesson conclusions wanting. Worth examines the way in which the final episode of a history lesson needs to do a great…

Purpose: The purpose of this paper is to present computational algorithms as potential bearers of biases and also tools for reflection, and to advance strategies for engaging with them in education. Design/methodology/approach: Three example games (Dwarf Fortress, RimWorld, FreeCiv) are provided for introducing algorithms as meaningful and…