To better understand the role that ways of reasoning play in students' success on integer addition and subtraction problems, we examined the relationship between students' flexible use of ways of reasoning and their performance on integers open number sentences. Within groups of students in 3 participant groups--39 2nd and 4th graders who had…

This research shows that people can unconsciously initiate and follow arithmetic rules (e.g., addition). Participants were asked to detect whether a symbol was a digit. This symbol was preceded by 2 digits and a subliminal instruction: "add" or a control instruction. Participants were faster at identifying a symbol as a number when the…

This paper presents the results of a study that aimed at increasing students' problem-solving skills. Polya's (1985) heuristic for problem solving was used and students were required to articulate their thought processes through the use of a structured diary. The diary prompted students to answer questions designed to engage them in the phases of…

Characterizing the modes of reasoning typically applied by students to solve different types of chemistry problems is of central importance for the design of instructional strategies that can better support their learning of specific content. Thus, the central goal of this study was to identify dominant modes of reasoning expressed by college…

This article seeks to substantiate the need for the prognostic assessment of the degree to which school students are prepared to master new types of activity, which underlie their design of an individual learning route at an appropriate senior stage of learning. The authors discuss the concept of project competence as an integral characteristic of…

The Maker Movement is a community of hobbyists, tinkerers, engineers, hackers, and artists who creatively design and build projects for both playful and useful ends. There is growing interest among educators in bringing making into K-12 education to enhance opportunities to engage in the practices of engineering, specifically, and STEM more…

This paper discusses an alternative approach for developing problem solving experiences for students. The major argument is that students can develop their creativity by engaging in collaborative problem solving activities in which they apply a variety of mathematical methods creatively to solve problems. The argument is supported by: considering…

In this reflective essay, Eric Booth utilizes his Habits of Mind for Creative Engagement to offer two suggestions for intensifying the impact of arts learning in schools. Booth's first suggestion redefines what artistic engagement really means and where it can contribute to creative learning. His second suggestion advocates for the use of…

In this paper we present the results of an eye-tracking study on collaborative problem-solving dyads. Dyads remotely collaborated to learn from contrasting cases involving basic concepts about how the human brain processes visual information. In one condition, dyads saw the eye gazes of their partner on the screen; in a control group, they did not…

In this article, Garcia and Davis describe problem analysis as the process of examining a given mathematics exercise to find ways in which the problem can be modified and extended to create a richer learning opportunity for students. Students are often reluctant to attempt what they perceive to be higher-order thinking problems, but problem…

Most teachers agree that if a student understands a particular mathematical topic well, he/she will probably be able to do problems correctly. The converse, however, frequently fails: students who do problems correctly sometimes do not actually have robust understandings of the topic in question. In this paper we explore this phenomenon in the…

The work described here represents an effort to understand and influence visual attention while solving physics problems containing a diagram. Our visual system is guided by two types of processes--top-down and bottom-up. The top-down processes are internal and determined by ones prior knowledge and goals. The bottom-up processes are external and…

This paper reports a classroom-based study involving investigation activities in a university numerical analysis course. The study aims to analyse students' mathematical processes and to understand how these activities provide opportunities for problem posing. The investigations were intended to stimulate students in asking questions, to trigger…

The traditional approach to teach problem solving usually consists in showing students the solutions of some example-problems and then in asking students to practice individually on solving a certain number of related problems. This approach does not ensure that students learn to solve problems and above all to think about the solution process in…

Individual differences in working memory capacity (WMC) increase the ability and tendency to devote greater attentional control to a task--improving performance on a wide range of skills. In addition, recent research on enclothed cognition demonstrates that the situational influence of wearing a white lab coat increases controlled attention, due…