Basics of qualitative research: Grounded theory procedures and techniques

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

According to W. Edwards Deming, American companies require nothing less than a transformation of management style and of governmental relations with industry. In Out of the Crisis, originally published in 1982, Deming offers a theory of management based on his famous 14 Points for Management. Management's failure to plan for the future, he claims, brings about loss of market, which brings about loss of jobs. Management must be judged not only by the quarterly dividend, but by innovative plans to stay in business, protect investment, ensure future dividends, and provide more jobs through improved product and service. In simple, direct language, he explains the principles of management transformation and how to apply them.

Out of the Crisis

This article reports the authors' efforts to develop a practice-based theory of content knowledge for teaching built on Shulman's (1986) notion of pedagogical content knowledge. As the concept of p...

https://harringtonmath.com/wp-content/uploads/2013/11/Content-knowledge-for-teachers.pdf

Content Knowledge for Teaching: What Makes It Special?

The culture of education

Foreword.- 1. Visions of the Mathematical.- 2. Laying the Foundations.- 3. Tools and Technologies.- 4. Ratio World.- 5. Webs and Situated Abstractions.- 6. Beyond the Individual Learner.- 7. Cultures and Change.- 8. A Window on Teachers.- 9. A Window on Schools.- 10. Re-visioning Mathematical Meanings.- References.

Windows on Mathematical Meanings: Learning Cultures and Computers

Windows on Mathematical Meanings

In this review, we distinguish two categories of digital technologies, programmable microworlds and expressive tools, chosen to highlight the different ways in which software shapes and is shaped by its incorporation into mathematical teaching and learning environments. The review indicates that software tools do indeed shape learning, but often do so in unpredicted ways. Furthermore, apart from its unsurprising dependence on tasks and activity structures, research suggests that learning is highly sensitive to small changes in technologies, and that the design of tools and learning have tended to co-evolve. The chapter identifies a common research trajectory for the study of any particular software in relation to mathematical education as well as drawing attention to two emergent issues: the openness of tools, and the reconceptualisation of mathematical teaching and learning.

What can digital technologies take from and bring to research in mathematics education

In this paper, we explore the relationship between learners' actions, visualisations and the means by which these are articulated. We describe a microworld, Mathsticks, designed to help students construct mathematical meanings by forging links between the rhythms of their actions and the visual and corresponding symbolic representations they developed. Through a case study of two students interacting with Mathsticks, we illustrate a view of mathematics learning which places at its core the medium of expression, and the building of connections between different mathematisations rather than ascending to hierarchies of decontextualisation.

The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic

We investigate how expert nurses undertake the calculation of drug dosages on the ward. This calculation is error-critical in nursing practice and maps onto the concepts of ratio and proportion. Using episodes of actual drug administration gleaned from ethnographic study, we provide evidence that experienced nurses use a range of correct proportional-reasoning strategies based on the invariant of drug concentration to calculate dosage on the ward instead of the single taught method they describe outside of the practice. These strategies are tied to individual drugs, specific quantities and volumes of drugs, the way drugs are packaged, and the organization of clinical work. The centrality of mathematics to school curricula has been justified partly in terms of its importance for the world of work, and many researchers have attempted to articulate the relationships between school-taught mathematics and the mathematics found in occupational and everyday lives. We believe that the study of mathematics in work provides a particularly fruitful setting for illuminating fundamental issues concerning the construction of mathematical meanings more generally. In essence, it offers an opportunity to focus attention on the ways in which professional discourses shape mathematical meanings and, reciprocally, on how the use of mathematics-however defined-structures the discourse of work. One might hope that such insight will afford leverage on didactical strategies within and beyond workbased settings. Until the middle of the 1980s, research in this field was undertaken largely within a framework in which the researchers assumed that mathematics was unproblematically visible in workplace settings and that it consisted mainly of calculation (see, for example, Fitzgerald, 1981). Later, researchers, for example Wolf (1984) and Harris (1991), adopted methodologies that were considerably more sensitive to the complexity of the practice/mathematics relationship. Yet all using such approaches encountered a fundamental obstacle: Most employees did not describe their activities in mathematical terms, and they often declared that they used very little mathematics in their work. The fundamental difficulty, it seems, is that the math

Richard Noss

Papers

Windows on Mathematical Meanings: Learning Cultures and Computers

Windows on Mathematical Meanings

What can digital technologies take from and bring to research in mathematics education

The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic

Proportional Reasoning in Nursing Practice