COMPUTE-A-COLOR® MATH … AN INTEGRATED FOUNDATION
This is a recent e-mail exchange between the originator Ann Preus, and Dr. Lyelle Palmer, Ph.D., retired Winona State professor. Dr. Palmer's permission is granted.
EARLY UNDERSTANDING AND INSIGHTFUL GROWTH
Palmer: “ Integrated is a descriptor that captures the essence of the Compute-A-Color early math curriculum. Integrated curriculum means that one material serves to link and teach two or more concepts. Compute-A-Color math materials are designed for early childhood learning, to make basic foundational numeracy fun and easy to understand.
These materials use a spare color-code much as is universally found in business and industry. A meaningful color-code is an efficient and effective form of labeling for instant communication. In the same manner, Compute-A-Color number relationships are swiftly recognized by the brain – simply match the color of prime numbers to their multiples (composites.)”
Preus: “Color response becomes an easy ‘match-maker'. This concept of color coded to number is applied to three dimensional numerals (1-10) that are graduated in thickness – unique only to the Compute-A-Color math system. As beginners feel and discover which numerals are thinner and which are thicker; they can create a ‘stairway' of these numerals – and see an elegant pattern of color emerge. Their fingers have formed it!
They see, touch, trace and name these numerals using the familiar tools of color and thickness. Number relationships become real as students see and group numerals in matching colors. Children thereby integrate the foundational concept of primes, (the ‘building blocks of mathematics') to their composites, (i.e. multiples.)
Children can stack any combination of numerals side by side to feel matching thickness and ‘prove' or ‘disprove' what = what.”
See and Feel Thickness
Here is the “Key”
EARLY INTEGRATION BUILDS HIGHER SKILLS
Palmer: “Conceptual understanding at an early age leads to higher progress in skill levels.
Effective: Materials are attractive and engaging. Young children grasp the underlying principles and apply them. Mastery of foundational concepts results.
Economical: Mastery is quick and complete. Materials are affordable and teachers learn to use them with reasonable reading, viewing and training.
Efficient: Integration means that children can learn several concepts which are combined in relationship to a single material, activity and lesson. Compute-A-Color is less time consuming and more concrete in developing basic related concepts.”
Preus: “This math system is appropriate for a broad range of age, skill levels and circumstances. The concept of color-coded to number serves as visual language for non-English speaking students – and offers global learning opportunities.”
THE CAC MATH SYSTEM EMBEDS AND INTEGRATES MULTIPLE CONCEPTS
Palmer: “Children see, feel, play and understand multiple concepts using these materials. New material is introduced and combined with concepts already learned.
Numeral recognition: The numerals are large and quickly perceived through visual recognition and also finger/hand tracing. Children can easily see and feel the graduated thickness of the 1-10 series and recognize a color pattern.
Seriation: Whereas typical childhood curriculum isolates seriation to specific separate occasions, Compute-A-Color provides a direct application and everyday usage. Other kinds of curriculum teach seriation through arranging blocks or stringing beads in a color series.
Set recognition in three dimensions: The quantitative value of number concepts is the major comprehensive aspect in numeracy. The beginner can recognize and match colors, stack and compare the thickness of any set of numerals, and count the dots on each. Quantitative skills and comprehension grow via these qualitative multiple challenges.
Color consistency: The sparing four-color code is used consistently throughout the materials to assure clarity in these foundational concepts.
Factor recognition: The color-code indicates the seriation and factor relationship to other numbers. Children can integrate their early three-dimension concrete experiences of number facts and concepts to more abstract understanding using a two-dimension ‘Squares Board' and a ‘Multiplier/Finder Board' for factor and space recognition.”
Preus: “This use of a diminishing stimulus (that is, three dimensions to two dimensions) is a recognized advantage for learning. Because it is a child's natural inclination to think of growth as upward movement, boards and grids place unit 1 at the bottom and 100 at the top. Perceptual activity changes from being ‘captured' by a color stimulus to develop as ‘conceptual thought' and visual search. That is a coveted goal in learning – exploring conceptually for discovery.”
Preus: “ The Compute-A-Color math system uses color, mass and length both individually and through interaction as TOOLS for understanding number patterns and relationships; as SUPPORTS for logic and memory; and as a BRIDGE to integrate facts and concepts from concrete to abstract understanding.” (© 1982)
Palmer: “Materials with this degree of integration are uncommon in early childhood education. It is useful from basic skill levels and beyond. Mastering number skills using these concrete materials extends to higher abstract understanding using the same color code as a bridge.”
© Ann Preus, Lyelle Palmer 2006
EAST MEETS WEST
The Compute-A-Color math system incorporates Eastern and Western theories of number. Over the centuries, mathematicians have argued whether number should be regarded as having aspects that are quantitative (i.e., Western black/white linear) or qualitative (i.e., Eastern color, symbolism, and emotional aspects.) So how does the Compute-A-Color math system fit into this East/West division? The design activates both left and right brain hemispheres as these qualitative and quantitative aspects are joined. This intends to capture the nature of number more fully, to provide a holistic understanding of math facts and concepts.
Color as concept can usefully compare and differentiate ‘this' from ‘that'-- but this is only the beginning in Compute-A-Color math. For example, color-coded primes can be grouped with their composites to visualize ‘class inclusion'. Next, a patterned linear representation of color-coded primes and composites reveals their ‘relationships of order.' By exploring and integrating color-coded concepts of ‘class inclusion' and ‘relationships of order', Piaget's ‘number synthesis' is uniquely assimilated using a simple four-color code. This phenomena of color transcends age, language and social class as totally as any sensory representation.
Color response has unlimited conceptual depth. Ulric Neisser quotes research that suggests “…visual search must develop from a state in which the gaze is controlled by the nature of the stimulus and its intrinsic features to one in which it is “an instrument of thought.” Along the same ‘vein' he adds that “attention changes from being captured to being exploratory.” (Neisser, Ulric. “Cognition and Reality”. San Fransisco: W. H. Freeman and Company, 1976.)
Color as concept is a good illustration of this kind of perceptual activity, if color is used not only to identify attributes but is used as conceptual thought. This affirms a statement in “Language and Intelligence”, (Huttenlocher, 1976, p. 266) that stated ”Symbol schemes used in active memory generally, like those in problem solving, need not involve the symbols of natural language.”
Consider how coded color can seep into memory and thought – as languid or arresting ‘emotional' color, color as meaning, and color as synthesis. Conceptual knowledge which employs color does not need the burden of language, nor does it need translation; however, color as concept can follow the same cognitive structure in relation to knowledge. (Preus, 1978.)
A CONCEPT OF COLOR
The fundamental reason for the evolution of color sense is alike for all vertebrates – survival. Comparisons of vertebrates' color responses have often been made. One of these is an essay by British Grant Allen, a contemporary of Charles Darwin in 1879, “The Colour-Sense – It's Origin and Development”. For the general groundwork of his theory Allen first acknowledges the works of Darwin and Herbert Spencer.
This was in opposition to Hugo Magnus, who believed the color-sense of man was a late acquisition; also, A. R. Wallace who disagreed with Darwin's theory of sexual selection, Nevertheless, Allen set forth his theory: “The taste for bright colors has been derived by man from his frugivorous ancestors, who acquired it by exercise of their sense of vision upon bright-colored food-stuffs; that the same taste was shared by all flower-feeding or fruit-eating animals; and that it was manifested in the sexual selection of brilliant mates, as well as in other secondary modes, such as the various human arts.” Grant Allen, The Colour-Sense, (London:Trubner and Co., Ludgate Hill, 1879” p vi. )
Color is one of the first stimuli to which babies can differentiate. Human response to color is immediate. Our eyes' color receptors (foveal cones) have a one to one direct nerve connection to the brain. Thus, each foveal cone can send a direct signal uncomplicated by other nerve impulses. It seems that employing strongest functions (e.g. color) for survival is as appropriate for humans as for lower vertebrates.