The Childcare Act 2006 provides the underpinning legislation for a single quality framework for supporting children's learning development and care from birth to five. This is encompassed in the early years foundation stage (EYFS). EYFS has been designed to deliver improved outcomes for all children, by providing a flexible, play-based framework,…

The aim of this paper is to present a simple way of establishing the general solution of the linear, second-order differential equation without using complex numbers.

Contractions play a considerable role in the theory of fractals. However, it is not easy to find contractions which are not similitudes. In this study, it is shown by counter examples that an affine transformation of the plane carrying a given triangle onto another triangle may not be a contraction even if it contracts edges, heights or medians.…

This is a comprehensive study of the many facets of an entirely online organic chemistry course. Online homework with structure-drawing capabilities was found to be more effective than written homework. Online lecture was found to be just as effective as in-person lecture, and students prefer an online lecture format with shorter Webcasts. Online…

\The purpose of this study was to investigate population invariance of the true-score linking functions with respect to the ability subgroups (i.e., average-achieving students, low-achieving students, and students with learning disabilities). The mean/mean linking functions for five alternate forms of a curriculum-based math problem solving…

Within his classroom, the author is often confronted by students who fail to see, or accept, the relevance of mathematics both to their lives and the world around them. One topic which is regularly perceived as being disconnected from people's daily lives is that of circle theorems, especially among less motivated students. In this article, the…

Prior research has shown that tutored problem solving with intelligent software tutors is an effective instructional method, and that worked examples are an effective complement to this kind of tutored problem solving. The work on the expertise reversal effect suggests that it is desirable to tailor the fading of worked examples to individual…

There is widespread agreement within the scientific and education communities that undergraduate biology curricula fall short in providing students with the quantitative and interdisciplinary problem-solving skills they need to obtain a deep understanding of biological phenomena and be prepared fully to contribute to future scientific inquiry.…

The purpose of this study was to systematically replicate and extend previous studies of the TOUCHMATH program, a multi-sensory mathematics program (Bullock, Pierce, & McClellan, 1989). Three middle school students with moderate and multiple disabilities (e.g., autism and moderate intellectual disabilities) participated. Students were taught how…

Robotic toys present unique opportunities for teachers of young children to integrate mathematics learning with engaging problem-solving tasks. This article describes a series of tasks using Bee-bots and Pro-bots, developed as part a larger project examining young children's use of robotic toys as tools in developing mathematical and metacognitive…

The purpose of the study was to examine how teachers enhance their knowledge of rational numbers focused on modeling problem tasks using multiple representations. The professional development summer institute and the follow-up Lesson Study (Lewis, 2002) throughout the academic year focused on engaging teachers in rational numbers and proportional…

Math is often taught poorly emphasizing rote, procedural methods rather than creativity and problem solving. Alberta Education developed a new mathematics curriculum to transform mathematics teaching to inquiry driven methods. This revised curriculum provides a new vision for mathematics and creates opportunities and requirements for professional…

This paper presents case studies of two teachers at Crescent Girl's School (an all-girls high school in Singapore) who implemented strategies learned through a teacher professional development program called 21st Century Learning Design (21CLD). Policymakers often state requirements for teachers to focus on 21st century (21C) competencies without…

Because of the complex interaction between economic class and learning, improving mathematics education for all while narrowing achievement gaps is no simple task. As a young teacher, the author conducted action research to determine how low-SES and high-SES 7th graders responded to a problem-centered mathematics curriculum. To her dismay, she…

Can a rich problem-solving task challenge a diverse range of students? How would students across various grade levels, from elementary school to secondary school, respond to the same task? These were the questions five different teachers in different schools wanted to explore in their respective classes, ranging from first grade through ninth…