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29 MARCH 2013

Mathematics is the foundation of activities such as knitting, stitching, measuring and cutting that are crucial to crafting and fabrication

The exhibition "Beauty is the First Test" runs form 27 April – 30 June 2013 at The National Centre for Craft & Design, Navigation Wharf, Carre Street, Sleaford, Lincolnshire NG34, UK.

"The group show explores how mathematical concepts underpin craft techniques, aiming to 'demystify a subject that intimates both adults and children', according to the centre. The exhibition demonstrates how mathematics is the foundation of activities such as knitting, stitching, measuring and cutting that are crucial to crafting and fabrication. Showcasing works in disciplines including textiles and sculpture, the show will feature work from artists including Michael Brennand–Wood, Janice Gunner, Lucy McMullen and Ann Sutton.

Alongside the visual proof that maths can indeed be fun – and pretty – the exhibition also presents case studies of five makers, including Gail Baxter and Margo Selby, exploring how the development of their work was furthered by an understanding and appreciation of mathematics."

(Emily Gosling, 27 March 2013, Design Week)

Fig.1 Janette Matthews, "Optical Ellipse". Fig.2 Ann Sutton, "Four Ways from a Square", 2009.




2013algorithmic art • Ann Sutton • Beauty is the First Test (exhibition) • computational aestheticscraft techniquescraftingDesign Weekexhibition • fractal art • Gail Baxter • geometric abstractiongeometric formsgeometric shapes • Godfrey Hardy • group exhibitionharmony • Janette Matthews • Janice Gunner • knitting • Lesley Halliwell • Lucy McMullen • Margo Selby • mathematical abstractionmathematical conceptsmathematical patternmathematicsmaths • Michael Brennand-Wood • National Centre for Craft and Designpattern • Peter Randall-Page • sculpture • spirograph • Stella Harding • Suresh Dutt • textilesvisual abstractionweaving


Simon Perkins
21 JULY 2012

LaTeX: programmable desktop publishing

"LaTeX is a document preparation system for high–quality typesetting. It is most often used for medium–to–large technical or scientific documents but it can be used for almost any form of publishing.

LaTeX is not a word processor! Instead, LaTeX encourages authors not to worry too much about the appearance of their documents but to concentrate on getting the right content. ...

LaTeX is based on the idea that it is better to leave document design to document designers, and to let authors get on with writing documents. ...

LaTeX is based on Donald E. Knuth's TeX typesetting language or certain extensions. LaTeX was first developed in 1985 by Leslie Lamport, and is now being maintained and developed by the LaTeX3 Project."

(LaTeX3 Project)



desktop publishingDocBook • document layout • document preparation • document preparation system • documentsDTP • editing formulas • formula • free softwareGNUGNU General Public LicenseGNU Public License • high-level language • LaTeX (tool) • LaTeX documents • LaTeX Project Public License • LaTeX2e • LaTeX3 Project • Leslie Lamport • LPPL • mark-up • mathematical • mathematical equations • mathematical formula • mathematicsmathsPDF • programmable desktop publishing • publishing • scientific documents • SRI International • technical documents • TeX • TeX (application) • TeX formatting commands • TeX macros • typetypesettypesetting • typesetting programme • typesetting system • word processorXMLXML-based format


Simon Perkins
24 JANUARY 2011

Pearson moves into online tutoring

"This week the publishing company Pearson announced it had bought a majority stake in an Indian online tutoring company Tutorvista for just under £80m.

Sanchia Berg reports on the company that provides online tutoring and support, especially for high school students in the US and John Fallon of Pearson explains the thinking behind the new venture. "

(BBC Radio 4, 21 January 2011)


2011BBC Radio 4 • biology tutor • call centre • chemistry tutor • contexteducationeducation marketelearning • english tutor • high schoolICTIndiainstruction • John Fallon • knowledge-based economylearningmaths • maths tutor • mediated interactionNorth America • online tutoring • outsourcingPearsonpedagogyphysics tutor • Sanchia Berg • social interactionsolutionsupplemental learningteachingtechnologytechnology education • tutoring • TutorVista • UKusability


Simon Perkins
03 NOVEMBER 2010

High Tech High: building a high-tech work force

"High Tech High was originally conceived by a group of about 40 civic and high tech industry leaders in San Diego, assembled by the Economic Development Corporation and the Business Roundtable, who met regularly in 1996–98 to discuss the challenge of finding qualified individuals for the high–tech work force. In particular, members were concerned about the 'digital divide' that resulted in low numbers of women and ethnic minority groups entering the fields of maths, science, and engineering. Gary Jacobs, Director of Education Programs at Qualcomm, and Kay Davis, Director of the Business Roundtable, were key participants in these discussions.

In late 1998 the group voted to start a charter school and engaged Larry Rosenstock, then President of Price Charities in San Diego, as the founding principal. The founding group was clear about its intent: to create a school where students would be passionate about learning and would acquire the basic skills of work and citizenship. Rosenstock, a former carpentry teacher, lawyer, and high school principal who had recently directed the U.S. Department of Education's New Urban High School project, brought a vision and a sense of the design principles by which this mission might be accomplished (see Design Principles, below).

From January 1999 to the opening of the Gary & Jerri–Ann Jacobs High Tech High in September of 2000, Rosenstock and the founding group, led by Gary Jacobs, worked in tandem. Rosenstock located a site, prepared the charter application, hired staff, and oversaw the development of the program, while Jacobs and the business community took the lead in addressing issues of financing and facilities development."

(High Tech High Foundation)

Fig.1 Christopher Gerber/High Tech High



1996-98 • 2000business community • charter school • digital divideengineering • ethnic minority groups • Gary Jacobs • High Tech High • High Tech High Foundation • high-tech work force • horizontal relationships • innovation • Kay Davis • knowledge-based economyLarry Rosenstocklearningmaths • New Urban High School • participationpedagogypeer learningSan Diegosciencesocial practicesteachingtechnologywomenworkforceworld of work


Simon Perkins
15 NOVEMBER 2009

Learning algebra in a computer algebra environment : design research on the understanding of the concept of parameter

"Design research – also known as developmental research or development research – is a research methodology that aims at developing theories, instructional materials and an empirically grounded understanding of 'how the learning works' (Research Advisory Committee, 1996). The main objective of design research is understanding and not explaining (Bruner, 1996). This objective implies different norms of justification than would be the case in comparative empirical research. One important feature of design research is the adaptation of the learning trajectory throughout the research; based on previous experience, the instructional sequences and teaching experiment conditions are adjusted. Therefore, design research is particularly suitable in situations where a full theoretical framework is not yet available and where hypotheses are still to be developed. The methodology of design research is addressed in many recent publications (e.g. van den Akker, 1999; Brown, 1992; Edelson, 2002; Freudenthal, 1991; Gravemeijer, 1993, 1994, 1998; Gravemeijer & Cobb, 2001; Leijnse, 1995; Treffers, 1993). In spite of varying interpretations of the notion of design research, there is agreement on the identification of two key aspects: the cyclic character of design research and the central position of the design of instructional activities. We now address these two issues.

The cyclic character of design research

Design research has a cyclic character: a design research study consists of research cycles in which thought experiments and teaching experiments alternate. We distinguish macro–cycles that concern the global level of the teaching experiments, and micro–cycles that concern the level of subsequent lessons. Gravemeijer argued that the cycles lead to a cumulative effect of small steps, in which teaching experiments provide 'feed–forward' for the next thought experiments and teaching experiments (Gravemeijer, 1993, 1994).

A macro–cycle of design research consists of three phases: the preliminary design phase, the teaching experiment phase, and the phase of retrospective analysis. In the last–mentioned phase, the reflection captures the development of the insights of the researcher. Following Goffree (1986) and Schön (1983), Gravemeijer called this 'reflection–in–action' (Gravemeijer, 1993, 1994). As a result, new theories, new hypotheses and new instructional activities emerge, that form the feed–forward for the next research cycle that may have a different character, according to new insights and hypotheses. The process of the researcher's thinking should be reported, to ensure the trackability of this development for others (Freudenthal, 1991; Gravemeijer, 1994).

As far as the role of theory in design research is concerned, the term 'theory–guided bricolage' is used (Gravemeijer, 1994). The researcher is like a tinkerer, who tries to combine and integrate global and local theories, which may be issued from other domains, to develop a learning trajectory and a local instruction theory for a specific topic. This local instruction theory contributes to the development of the domain–specific instruction theory.

In our study, three full macro–cycles – indicated as G9–I, G9–II and G10–II – and one intermediate cycle were carried out. The first phase of preliminary design includes two related parts, the development of a hypothetical learning trajectory (HLT) and the design of instructional activities. This phase is followed by the teaching experiment and the retrospective analysis. Fig. 2.1 shows the three full research cycles. Cycle 1 started with a conceptual analysis that is described in Chapter 4. Each of the phases is elaborated on in Sections 2.3 – 2.6, whereas specific information on each of the cycles is presented in 2.7.

The role of design

A second characteristic of design research is the importance of the development of a learning trajectory that is made tangible in instructional activities (Gravemeijer, 1994). The design of instructional activities is more than a necessity for carrying out teaching experiments. The design process forces the researcher to make explicit choices, hypotheses and expectations that otherwise might have remained implicit. The development of the design also indicates how the emphasis within the theoretical development may shift and how the researcher's insights and hypotheses develop. We agree with Edelson, who argued that design of student texts is a meaningful part of the research methodology:

(...) design research explicitly exploits the design process as an opportunity to advance the researchers' understanding of teaching, learning, and educational systems. Design research may still incorporate the same types of outcome–based evaluation that characterize traditional theory testing, however, it recognizes design as an important approach to research in its own right. (Edelson, 2002, p.107)

This is particularly the case when the theoretical framework involved is under construction:

(...) it [the research] started with only a partial theory and has proceeded with the explicit goal of elaborating that theory before attempting any summary evaluation. The lessons that are emerging from this effort are being shaped by the concrete, practical work of design. (Edelson, 2002, p. 112)"

(Paulus Drijvers, Maria Hendrikus, 2003)

Fig.1 David Coghlan & Teresa Brannick (2001).



2003action researchalgebra • CAS • computer algebra • cyclicdesign-based research • development research • developmental research • how learning works • instructional materials • instructional sequences • learning trajectorymathematicsmathematics educationmathsmethodology • realistic mathematics education • reflection-in-actionresearchresearch methodologyresearch methods • retrospective analysis • technologytheoretical framework • theory-guided bricolage • tinkerer


Simon Perkins

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