This paper presents a series of basic computational problems that are mathematically and/or graphically appealing, and provides an idea of places one might go in trying to understand what is happening, integrating mathematics, computation, and graphics. The real point of this paper is to make a case, through those examples, for computation as an…

Background: The complexity and diversity of problems and concepts in different engineering subjects represent a great challenge for students. Traditional approaches to teaching statics are ineffective in helping some students overcome the learning barriers that underlie learning statics and developing problem-solving skills. Purpose: This article…

Even at the primary level, computational thinking (CT) can support young students to prepare for participating in futures that are immersed in data. In mathematics classrooms, there are few explanations of the ways CT can support students in formulating and solving complex problems. This paper presents an example of a primary classroom…

To expand students' preparation for civic life, many teachers regularly engage students in discussions related to contentious issues. These discussions, however, typically restrict the range of communicative styles allowed and prioritizes disagreements between fixed and competing choices. Keith C. Barton & Li-Ching recommend that educators…

This comprehensive book provides a theoretical understanding of how imagination contributes to effective leadership, as well as practical tools all educational leaders can employ to cultivate their imaginations and the imaginations of others in their communities. To support these goals, book chapters offer multiple perspectives on what imagination…

This study explores students' use of mathematical objects in each problem-solving phase based on an onto-semiotic perspective. The subjects of this research are students who solve problems in different ways but all with the correct result. The first student uses organizational data by applying the concept of permutations. In contrast, the second…

Including causal links in concept maps enables learners to meaningfully relate concepts to a larger context or problem in terms of how and where concepts apply within the chains of causal events that lead to a given goal or outcome. Given that higher quality maps are produced when students link and sequence events to flow temporally and…

Students have varying degrees of creativity and can develop their creative abilities in specific disciplines through various stimuli. Tracing the students' mathematical creativity is very important since creativity is not a gift for specific students; rather, all students have it. The participants of this study were 170 urban and rural middle…

This article considers the conception of transdisciplinarity as a knowledge distinct from disciplinary knowledge modes and especially drawing a distinction with interdisciplinarity. Such critical analysis assists in the recognition of the importance and value of transdisciplinarity within the ecology of knowledge in the complex systems of…

The application of decomposition strategies (i.e., associative or distributive strategies) in two-digit multiplication problem solving supports algebraic thinking skills essential for later complex mathematical skills like solving algebra problems. Use of such strategies is also associated with improved accuracy and speed in mathematical problem…

The close relationship between working memory and maths problem solving is generally accepted, but the specifics of how working memory and its subcomponents contribute to maths problem solving remain poorly understood. Tests of working memory, maths problem problem solving, calculation, and intelligence were administered to 246 university…

We contribute to the understanding of teacher noticing by focusing on what a teacher may notice in students' mathematical contributions in the context of problem-based lessons. Complementing approaches to research on noticing that focus on individual teachers' perceptual, cognitive, or situated skills, this conceptual article offers four…

Math modeling is a unique and powerful part of mathematics that is underutilized in contemporary classrooms. Teachers of all grade levels may utilize such modeling problems to better serve the students in their classrooms, with related analytical problem-solving activities that contribute to learners meeting the highest of learning standards. With…

Background: During school lessons participants can face challenging pedagogical problems such as when science and religion topics interact. Potential types of pedagogical problem and what participants can do in response are unclear. Research designs exploring pedagogical problem solving should investigate teachers' thinking processes and include…

Solving problems in organic chemistry often requires the consideration of reaction mechanisms. As such, much research has been devoted to the examination of how students consider mechanisms when solving various types of organic chemistry problems, such as predicting the products of a reaction or proposing a synthesis. This article provides a…