In this third of a series of four articles, the author deconstructs the primary national strategy's approach to written multiplication. The approach to multiplication, as set out on pages 12 to 15 of the primary national strategy's "Guidance paper" "Calculation" (DfES, 2007), is divided into six stages: (1) mental…

Writing has special importance in anthropology. Writing fieldnotes is a central methodology for documenting and analyzing culture, and written personal reflections upon this process are viewed as providing insight into how knowledge is produced by a "situated" researcher. That said, there is little discussion in the discipline about the…

In 2007, the federal government appointed a group of education professionals, researchers, and stakeholders to study and advise on ways to "foster greater knowledge of an improved performance in mathematics among American students...with respect to the conduct, evaluation and effective use of the results of research relating to proven-effective…

This article presents two current research trends in e-learning that at first sight appear to compete. Competence-Based Knowledge Space Theory (CBKST) provides a knowledge representation framework which, since its invention by Doignon & Falmagne, has been successfully applied in various e-learning systems (for example, Adaptive Learning with…

Educators in professional degree programs are charged with multiple responsibilities in the classroom and in practice settings. We apply our professional knowledge in a variety of settings to serve our communities; we reflect on how to improve practice from our experiences in these settings; we observe our students engaging in learning experiences…

A problem given in the Australian Mathematics Competition for the Westpac Awards was stated as follows: With how many zeros does 2008! end? In this article, the author solves this problem, and provides further discussion on the related problems. These problems form a good model that helps students develop a logical thinking process toward problem…

Over the past decade, the analysis of what occurs when learners are involved in "work"-based learning (WBL) has, at best, been superficial and simplistic, i.e. it has been accepted that individuals learn by being in a knowledge-based work-based environment. It does not follow, however, that they will acquire the knowledge they are…

In this article, we describe features of learning goals that enable indexing knowledge for teacher education. Learning goals are the key enabler for building a knowledge base for teacher education; they define what counts as essential knowledge for prospective teachers. We argue that 2 characteristics of learning goals support knowledge-building…

We propose Lifelong Learning Organisers (LLOs) as tools to support the capturing, organisation and retrieval of personal learning experiences, resources and notes, over a range of learning topics, at different times and places. The paper discusses general requirements for the design of LLOs based on findings from a diary-based study of everyday…

It is argued that Humboldt's original definition of "scholarship" ("Wissenschaft"), as well as Humboldt's concept of the purpose of a university, continue to be relevant--with appropriate adaptations. They should be extended to include not only a unity between the practice of teaching and learning and research into teaching and…

In this paper I argue that there is a need to reconnect with the question of purpose in education, particularly in the light of a recent tendency to focus discussions about education almost exclusively on the measurement and comparison of educational outcomes. I first discuss why the question of purpose should always have a place in our…

The primary goal of the emerging field of Mind, Brain, and Education is to join biology, cognitive science, development, and education in order to create a sound grounding of education in research. The growing, worldwide movement needs to avoid the myths and distortions of popular conceptions of brain and genetics and build on the best integration…

Since the U.S.S.R. released Sputnik I into space in 1957, American science teachers have been focused on preparing scientifically literate students. New instructional approaches have emerged, with the 5E learning cycle being one of the more popular methods used. The 5E learning cycle gets its name from its five stages: Engage, Explore, Explain,…

Teachers try to help their students learn. But why do they make the particular teaching choices they do? What resources do they draw upon? What accounts for the success or failure of their efforts? In "How We Think", esteemed scholar and mathematician, Alan H. Schoenfeld, proposes a groundbreaking theory and model for how we think and act in the…

The advance of digital video technology in the past two decades facilitates empirical investigation of learning in real time. The focus of this paper is the combined use of real-time digital video and a networked linguistic corpus for exploring the ways in which these technologies enhance our capability to investigate the cognitive process of…