A second theme begins to intertwine literature from many interdisciplinary fields, revealing a profound and deeply rooted pedagogical underpinning, accessible to art and design researchers and educators to aid with their move toward future transformation. Next, a sequential, implicit logic is revealed in linking the literature of the originators’ old intentions for the course, reflections by their students, and directions taken by later colleagues (particularly design scientists and the theorists addressing the current paradigm combining aspects of art, design, mathematics and science education), revealing some limitless, possible new dimensions.The first focus of this article points to the foundations course as a common denominator for the assimilation of complex new material through aesthetic play, paving the way for new cultural forms. The version of Foundations introduced to America by Josef Albers, although hardly changed, is shown to have continued, timeless relevance. Research concerning the basic course known as Foundations of Art and Design strengthens the pedagogical approach for K‐16 art and design education. 13 The rules of transformation operate on the equations, not on the situation the equations represent. As the transformation rules are being applied, in many cases the intermediate states of solution do not make much sense in terms of the original problem (note the bold cells in Figure 2). In even a relatively simple 'toy' problem, such as the one shown in Figure 2, we can see how an algebraic solution represents a situation as a set of equations within a notation system and then applies transformnation rules to the equations to produce a solution. A prodigious advance in the development of mathematics was the creation of another, more general and therefore more powerful set of algorithms for representing and manipulating quantitative relationships: namely, the development of algebra and the rules for manipulating algebraic symbols to solve equations, transform character strings into one or another canonical form, and so on (Bochner, 1966). The base-ten placeholder system of numerals and the algorithms build upon it have been a critical factor in the development of our culture (Swetz, 1987). Terminology from our most current algorithms like 'carry the one' or 'borrow from the next column' reflect the extent to which we think of the processes of arithmetic as a set of rules for manipulating numerals. The process of addition (or subtraction, multiplication, etc.) can be represented by a set of rules for manipulating strings of numerical symbols (digits). Algorithms for addition and subtraction of numerals have existed for thousands of years. The symbols of the number system are also one of the first instances of a system of notation with rules of transformation. In the case of integers, from a cultural, if not a psychological perspective, a specific symbol (or combination of symbols) represents a specific number and no other. of numbers, particularly of whole numbers. Illustration from USA Today of a graph that uses lines in both pictorial and notational modes.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |