Design education exists to prepare students for design practice. Yet the goal state, design expertise, remains poorly defined. This paper presents a critical cross disciplinary literature synthesizing literature across design, engineering, expertise, creativity, and new evidence from a cognitive task analysis of expert designers to explore…

The trends of teaching mathematical thinking and the existence of two thinking skills (critical dan creative thinking) the required by 21st century skills have created needs for teachers to know their students' thinking processes. This study is intended to portray how mathematics teachers expect their students showing their thinking processes in…

The ability to learn in a self-regulated way is important for adolescents' academic achievements. Monitoring one's own learning is a prerequisite skill for successful self-regulated learning. However, accurate monitoring has been found to be difficult for adolescents, especially for learning problem-solving tasks such as can be found in math and…

In order to maintain the United States' global competitiveness and create new and innovative solutions to solve global challenges, more and diverse numbers of STEM graduates need to be attracted and retained in technical disciplines (Committee on Prospering in the Global Economy of the 21st Century: An Agenda for American Science and Technology,…

In an experiment, secondary students from Australia and Malaysia (n = 130) were randomly assigned to one of three approaches (equation, unitary, unitary-pictorial) to learn how to solve challenging percentage-change problems. In line with the differential types of cognitive load associated with the three approaches, the unitary-approach group…

Based on L. S. Vygotsky's sociocultural theory, previous scaffolding studies have examined some factors associated with adjustment of parental support during collaborative problem solving. However, a factor that remains unexplored in the literature is the potential relationship between parental empathy and parental support in collaborative problem…

Using data provided by an empirical exploratory study with mathematics undergraduates, this paper discusses some key variables in the interaction between affective and cognitive dimensions in the perplexity state in problem solving. These variables are as follows: heuristics, mathematical processes, appraisal processes [pleasantness, attentional…

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

Young children naturally engage in mathematics as they play and explore. Although many early childhood educators are aware that children are frequently interacting with mathematical ideas, a certain level of knowledge and awareness is required to identify and highlight the mathematics that children are engaging in and to create opportunities for…

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…

This paper uses multimodal discourse analysis to show that discursive form, in addition to words, gestures and sound dimensions of speech, is an important linguistic resource for expressing mathematical meaning. During a collaborative task, a student spoke an insight about an algebraic property five times over a few minutes, in slightly different…

The goal of this study is to determine the effectiveness of mind games played by secondary school sixth grade students as classroom activities in math and grammar courses on their perceived problem-solving skills and achievements. In the quantitative part of the study, the nonequivalent groups pre-test--post-test control group design from…

Recent evidence suggests that solving problems through insight can enhance long-term memory for the problem and its solution. Previous findings have shown that generation of the solution as well as experiencing a feeling of Aha! can have a beneficial relationship to later memory. These findings lead to the question of how learning in…

This article presents research into human mental spatial reasoning with orientation knowledge. In particular, we look at reasoning problems about cardinal directions that possess multiple valid solutions (i.e., are spatially underdetermined), at human preferences for some of these solutions, and at representational and procedural factors that lead…

This case study examined patterns in online communication using computer-mediated discourse analysis to better understand how teaching presence, social presence, and cognitive presence are manifested in an online learning environment. The findings indicate that study participants actively participated in the discussion. The instructor and…