Numerous classroom-based research projects have examined the important role social skills play in an elementary classroom (Browning, Davis, and Resta 2000; Burns 2003; Palmer and Wehmeyer 2003; Stone 2001). As Stone (2001, 18) suggested, "Teachers have an enormous influence on children's behavior by speaking directly and honestly to them,…

In a future that is likely to be increasingly dominated by new technology, it is important to consider what mathematics is and how it might be taught. This article discusses these and related issues in the context of both universities and schools.

We describe two classes of sequences that give rise to accessible problems for undergraduate research. These problems may be understood with virtually no prerequisites and are well suited for computer-aided investigation. The first sequence is a variation of one introduced by Stephen Wolfram in connection with his study of cellular automata. The…

This paper provides a pragmatic view of efficient use of graphics calculators. Efficiency is described in terms of quick and easy calculation, as debated and evidenced in a Year 12 calculus class. Students' methods of calculation are analysed in terms of the algebraic understanding and technical skills that underpinned them. Patterns in students'…

This third part continues the exploration of how we can overcome the limitations of the present knowledge system. In preparation, two aspects of current engineering theory and practice are examined because they are paradigmatic: the concept that engineering is essentially problem-solving, which goes against our understanding of human skill…

Problem-based learning (PBL) works with a series of problems that form the syllabus for a course or the basis of a curriculum. Learning occurs through the definition of the problem and its attempted resolution. PBL is challenging but offers much potential for geography with its interdisciplinary character. The challenge to geography lecturers is…

In this paper, characteristics of mathematics classrooms in the East Asian countries of Hong Kong and Japan are discussed based on an analysis of the data of the TIMSS 1999 Video Study. The data shows that although students in these East Asian countries did not talk a lot in the classroom, they were exposed to more instructional content. The…

Struggling learners and their parents often are exasperated by homework. They find it difficult, frustrating, and laborious, producing resistance, slipshod work, stress at home, and conflicts between struggling learners, parents, and school personnel. The author (1) identifies several causes of struggling learners' homework difficulties, (2)…

Gaining expertise in leadership requires time, commitment, an adequate knowledge base, and a working plan for learning and growth. Without a plan for learning, only tacit or "how-to" expertise is developed. Leaders often know how to solve the problems facing them, but fail to analyze and act on the underlying causes. This results in administrators…

Heartland Area Education Agency in Iowa illustrates how it has sustained a problem-solving service delivery system for 15 years and adapted to changing state and federal requirements while remaining consistent with its guiding principles that emphasize direct assessment, intervention, progress monitoring, and the evaluation of student results. The…

This article discusses three solutions to the "Tower of Hanoi" problem offered by students in a mathematics content course for prospective elementary school teachers. The course uses standards-based pedagogy and teaching via problem solving. Within this work, we consider the growth supported by collaboration at both the students' level…

This is the second of two papers that propose an expanded and enriched view of arithmetic problem solving by stressing the need to provide learning activities that include problems of varying structures. The first paper included a framework for the enhancement of text-based problems. This second paper proposes a scheme for the development of…

Over the past thirty years, Problem Solving Therapy (PST) has been shown to be an effective treatment for many different problems and patient populations (Nezu, 2004). Among its many clinical applications, PST interventions were developed for persons with intellectually disabilities (ID), where improving problem-solving skills led to adaptive…

Three key features of a proposed capstone mathematics course for the preparation of teachers at the secondary level are: 1) teacher candidates examine concepts from the curriculum at a deeper level in the context of rich problems; 2) they investigate common themes in the math curriculum, such as shape and change, then collaborate on and present…

In Fall 2004, Virginia Commonwealth University (VCU) piloted a modeling-based approach to college algebra. This paper describes the course and an assessment that was conducted to determine the effect of this approach on student achievement in comparison to a traditional approach to college algebra. The results show that compared with their…