"Process and Product"







The Arete of Line Designs


Michael Round

Center for autoSOCRATIC Excellence

13234 Long Street

Overland Park, Kansas  USA   66213


In the quest to make math "relevant and engaging", there has been a recent surge in "Line Designs" and "Curve Stitching".  The re-creation of many pictures and the use of computers has made for many design projects, but has it led to educational improvement?  How would we know if it had?  What is the nature of these designs that so fascinates both children and adults?  What is the goal of these designs?  Towards what end?  This workshop will explore the historical (including the George Boole connection), philosophical, and pedagogical nature of line designs, with a focus on good designs and what constitutes the proper context / good environment ensuring "joy in work" is realized, now and in the future.

Math curriculum frequently includes line design lesson plans, a careful structure on how to achieve a desired result, and a method to grade the results.  To ensure relevance to a topic, many line designs are crafted to mimic some picture, such as a face or a valentine.  Further “enhancements” include many java-enabled web sites affording ease of creation of these designs.  As this integration of line designs increases in math curriculum, it’s instructive to consider what it is about these designs we consider “good”.

Mary Everest Boole, wife of famed mathematician George Boole and known by many as the origin of this type of activity, said the following regarding this process: 

“The beauty of some of the designs is unquestionable; and there can be no second opinion about the value of the method, as training, from the point of view of geometry as well as from that of art.  What is not quite so obvious at first sight is its bearing on the training of the unconscious mind for science.  Without the slightest intellectual strain it puts the children through that normal sequence of orderly attention to classification and detail, interspersed with nodal points of synthesis, which may be called the very breathing-rhythm of the scientific discoverer. 


But to make this exercise of any use there must be no copying from diagrams; the value of it depends on the child evoking a curve, watching it growing, under his fingers, from mere obedience to a law … and beauty has resulted, not from understanding but from obedience … the act of evoking a curve ‘out of the everywhere into here’, by simple obedience to a rhythmic law, lodges an impression on the unconscious mind which will be ready to surge up in ten years’ time.” [1]


Clearly, what we as adults consider “good” qualities are necessary conditions for a good activity, but are they sufficient?  Ms. Boole addresses ‘orderly attention’ and ‘classification of detail’, leading to ‘beauty’ as the result, with a particular benefit the training of the mind for future excellence.  How is this process captured in a rubric concentrating on product?  To emphasize this point, Edith Somervell said the following about the “process versus product” dilemma: 

“Beautiful curves are produced by a process so simple and automatic that the most inartistic child can succeed in generating beauty by mere conscientious accuracy; and the habit of doing this tends to produce a keen feeling for line.  It has also been noticed in some cases, where clean, pure, and strong colour has been used, that a remarkable sensitiveness to colour relation has grown.”  “The results obtained by a child, of exquisite curved and flower forms on the ‘back’ of his card, by faithful obedience to a dull little rule in making straight stitches on the ‘front’, is of the nature a miracle.  It should, therefore, be hardly necessary to insist that the less said the better, when the little worker produces anything especially beautiful or unexpected.” [2]


What as adults can we do regarding the working environment to ensure a good process with beautiful results?  What types of designs are appropriate for children?  How do we translate “dull little rule” into practice?  And finally, if the method is so powerful we can see the impression years down the road, how can we ensure the children continue creating such designs outside the classroom?

This teacher workshop addresses many of these issues as the result of a number of after-school clubs I’ve conducted over the past couple of years, in addition to thoughts on current enhancements to the working environment, including the introduction of background percussion music, to highlight the rhythmic nature of the activities, and various materials demonstrating the dynamic quality of these patterns.


[1] Mary Everest Boole, Preparation of the Child for Sciences. University of Oxford. 1904

[2] Edith L. Somervell, A Rhythmic Approach to Mathematics. George Philip & Son, Ltd, London. 1906

[3] E.M. Standing, Maria Montessori: Her Life and Work. Penguin Books USA. 1984

[4] Mihaly Csikszentmihalyi, Flow: The Psychology of Optimal Experience. Harper & Row Publishers, New York. 1990

[5] Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance. William Morrow and Company, Inc.  1974

[6] W. Edwards Deming, The New Economics. MIT. 1993