This study focuses on the role of multiple solution tasks (MST) incorporating multiple learning tools and representation systems (MTRS) in encouraging each student to develop multiple perspectives on the learning concepts under study and creativity of thought. Specifically, two types of MST were used, namely tasks that allowed and demanded…

In the current reform of mathematics classrooms teachers are charged with the role of facilitating collaborative groups during problem-solving activity. The challenge is for teachers to engage students in making mathematical meaning during collaborative group discussions. In this paper we draw on the concept of adaptive expertise to report on…

This article discusses an activity designed to encourage writing to learn in mathematics. There were three stages of data collection. An assessment, requiring basic algebra only, was completed by 118 undergraduates from statistics and calculus courses. Students were given summaries of all participant responses, along with the correct answers.…

The aim of this study was to examine prospective mathematics teachers' proof processes for algebraic concepts. The study was conducted with 10 prospective teachers who were studying at the department of secondary mathematics teaching and who volunteered to participate in the study. The data were obtained via task-based clinical interviews…

In this postmodern era, artists have gone far beyond traditional and technical skills. In her own teaching practices, the author looks to implement practice of a twenty-first-century art educator that inspire students to develop creative and innovative thought processes while relating to the world around them. In this article, she encourages…

We compared the performance of 3- and 5-year-old children with that of chimpanzees in two tasks requiring collaboration via complementary roles. In both tasks, children and chimpanzees were able to coordinate two complementary roles with peers and solve the problem cooperatively. This is the first experimental demonstration of the coordination of…

This study analyzed a stratified random sample of 1,707 senior students at 60 four-year universities in South Korea to explore the gender-specific pathways to Korean students' development of generic skills--analytical thinking and problem-solving skills. Multiple regression analyses were performed to investigate the involvement factors…

The blue-eyed islanders puzzle is an old and challenging logic puzzle. This is a narrative of an experience introducing a variation of this puzzle on the first day of classes in a liberal arts mathematics course for non-majors. I describe an exercise that was used to facilitate the class's understanding of the puzzle.

There are, it seems, few instances when "unintended consequences" are regarded as having a positive and beneficial effect. Here a well-used activity takes on a "life of its own" as a result of the enthusiasm of the learners. The outcome provides insights for all those involved, including the "teacher". Maybe it is…

As a team of teacher educators at a university in the United States, we engage in participatory action research to reflect on how reflective tools which we design engage teacher candidates (TCs) in their reflecting on teaching. In this paper, we describe how we invite TCs to write in-class reflections, respond to self-assessment probes, and…

Teaching design to middle and high school students can be challenging. One of the first procedures in teaching design is to help students gather information that will be useful in the design phase. An early stage of engineering design as described by Lewis (2005), calls for the designer to establish the state of the art of the problem. During this…

The goals of this study were: 1) to study the situation, problems and needs for a learning model to enhance the social skills of sixth grade students; 2) to develop a learning model that would address those needs; 3) to study the effectiveness of that learning model; 4) to compare performance on pretests and posttests of social skills; and 5) to…

As the National Middle School Association wrote, "No other age level is of more enduring importance because the determinants of one's behavior as an adult, self concept, learning interests and skills, and values largely are formed in this period of life." During this influential time in the lives of gifted adolescents, it is important to…

A Virtual Resource Center (VRC) has been brought into use since 2008 as an integral part of a task-based language teaching and learning program for Business English courses at Nantes University, France. The objective of the center is to enable students to work autonomously and individually on their language problems so as to improve their language…

The field of EDM has focused more on modeling student knowledge than on investigating what sequences of different activity types achieve good learning outcomes. In this paper we consider three activity types, targeting sense-making, induction and refinement, and fluency building. We investigate what mix of the three types might be most effective…