Virtually all mathematics is based on pattern and structure. A mathematical "pattern" is any predictable regularity, usually involving numbers or space. In every pattern, the various elements are organised in some regular fashion. The way a pattern is organised is called its "structure," which may be numerical or spatial. In…

Learning in educational settings emphasizes declarative and procedural knowledge. Studies of expertise, however, point to other crucial components of learning, especially improvements produced by experience in the extraction of information: perceptual learning (PL). We suggest that such improvements characterize both simple sensory and complex…

The National Board for Professional Teaching Standards (NBPTS) proposition 3 states "teachers are responsible for managing and monitoring student learning." They know how "...to organize instruction to meet instructional goals." This article provides 14 organizational patterns for use in organizing instruction in any of the content areas. The 14…

This reprinted "Mathematics Teacher" article gives a brief history of the mathematics of Escher's art. (Contains 9 plates.)

Interpersonal dynamics within friendships were observed in a sample of 120 (60 male, 60 female) ethnically diverse 16- and 17-year-old adolescents characterized as persistently antisocial, adolescent-onset, and normative. Dyadic mutuality and deviant talk were coded from videotaped friendship interactions. Persistently antisocial adolescents…

Human infants possess powerful learning mechanisms used for the acquisition of language. To what extent are these mechanisms domain specific? One well-known infant language learning mechanism is the ability to detect and generalize rule-like similarity patterns, such as ABA or ABB [Marcus, G. F., Vijayan, S., Rao, S. B., & Vishton, P. M. (1999).…

This article introduces "expertise-based training" (XBT) as an instructional design theory that draws on the theories, findings, and methods of expertise research in order to create instructional strategies that can hasten the development of advanced learners into experts. The central tenants of XBT are: 1) Key cognitive sub-skills that…

Ensuring quality teaching in every classroom across an entire system of schools--that's what a district leader's job is all about. A district leader's challenges are unique so "The Learning System" was created with that in mind. This issue contains: (1) Imagine the Possibilities: 2020 Forecast Explores 6 Change Forces that Will Shape the…

An outline of frameworks for conceptualising and analysing news media roles in the representation of teachers, is followed by a discussion of quantitative and qualitative approaches to the study of news coverage. An argument is made for the benefit of using corpus linguistic tools within the overall conceptual focus on lexical and syntactical…

The Third International Conference on Data Mining (EDM 2010) was held in Pittsburgh, PA, USA. It follows the second conference at the University of Cordoba, Spain, on July 1-3, 2009 and the first edition of the conference held in Montreal in 2008, and a series of workshops within the AAAI, AIED, EC-TEL, ICALT, ITS, and UM conferences. EDM 2011…

This study investigated an innovative approach of program evaluation through analyses of student learning logs, demographic data, and end-of-course evaluation surveys in an online K-12 supplemental program. The results support the development of a program evaluation model for decision making on teaching and learning at the K-12 level. A case study…

The purpose of this study is to analyze changing patterns of governance in Korean higher education through the window of the NPM, so as to compare policy developments in Korea to wider international trends. Building upon Braun & Merrien (1999)'s earlier analytical framework on university governance, the study focuses on the following…

Visual intelligence is a key element in the thought processes of the most capable and creative among individuals, and this intelligence is closely related to analogical thinking, a learner's ability to make connections between prior knowledge and newly presented information. This article describes an approach to teaching scientific inquiry at…

The age of networked research and networked data analysis is upon us. "Wired Magazine" proclaims on the cover of their July 2008 issue: "The End of Science. The quest for knowledge used to begin with grand theories. Now it begins with massive amounts of data. Welcome to the Petabyte Age." Computing technology is sufficiently complex at this point…

This study illustrates how a diagnostic testing model can be used to make detailed comparisons between student populations participating in international assessments. The performance of Turkish students on the TIMSS-R mathematics test was reanalyzed with a diagnostic testing model called the Rule Space Model. First, mathematical and cognitive…