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Washington Parent Magazine

Pictures of The-cognitive sensory connection for Mathematics
Nanci and Kimberly Bell Tuley
http://www.lindamoodbell.com/

Why does not everyone think with the numbers? Why do some children learn math with ease, handle money and time concepts with ease, retain information from year to year, and think with numbers effortlessly? What cognitive processes do some have that others do not?

Mathematics is a cognitive process thinking that requires the dual coding of images and language. The images are essential to the process of thinking with numbers. Albert Einstein, whose theories of relativity helped explain our universe, using images as the basis for mental processing and problem-solving. Perhaps best sums up the importance of images when he said, "If I can not see me, I can not understand."

For people who "get" math, the language of numbers becomes images. Use language and images that allows them to calculate internal and verify the math, but "see" your logic.

Imaging is the basis for thinking with numbers and the concept of their functions and their logic. The Greek philosopher Plato said, "And you also know that despite that [mathematicians] make use of the visible forms and reason about them, not thinking about them, but the ideals that seem ... they really are looking for to see things themselves, can only be seen with the eye of the mind? "

The relationship of the images to the ability to think is one of the theories quintessential human cognition. Allan Paivio, author of the dual coding theory (DCT) and a cognitive psychologist, said: "Cognition is proportional to the extent that mental representations (images) and language are integrated. "Investigation of the 1970s and the 1990s has validated the Dr. Paivio work as a viable model of human cognition and practice and theoretical application to the understanding of language (Bell, 1991). Dr. Paivio considers that, to think and understand, humans must be able to generate both images and the appropriate language to describe these images.

The Mathematics is the essence of cognition. It is thought (dual coding) with numbers, images and language, reading / writing is thinking with the letters images and language. Both processes, often mirror images of each other, require the integration of language and images to understand the fundamentals and apply them. Double coding in math, like reading, involves two aspects of the images: the symbol, the number of images (parts / details) and concept images (all / Gestalt).

Numeral Images

Display of numbers is one of the processes necessary for the basic cognitive understanding of mathematics. For example, the image that the number "2" for the concept of two. When we see that the number "3" represents the concept we know that three of something: three pennies, three apples, three horses, three points. If someone gives us two pennies for the numeral three, we a discrepancy between the image of our number three and reality (concept) of three. The first imagery is needed for math is the symbolic (or number) images representing the reality of a concept of number.

What numeral images look like? Here's an example. Cecil was very good at math. He could not think with numbers, get answers in his head, and mentally check for discrepancies in mathematical finance or life situations easily. He explained this capacity, "I see the numbers and their relationships. Certain numbers are in certain colors, and line number in my head will address specific. "Not only could see Cecil figures and concepts, the two types of images, but also had an unusual talent for images in color. Numbers assigned to specific colors!

"What color is the number 14?" Was asked.
His eyes went, and in all seriousness, said, "Blue Light." Similarly, the number 3 was reddish pink and the number 88 "a sort of purple." Asked again months later, Cecil assigned the same colors for the same numbers. chronological relationships appear in our mind on a number line, the days of the week months of the year. Image is the way our sensory systems "to make the abstract real. It is a means to experience mathematics.

Concept Imagery

While the numbers of image is important for mathematical calculation, another aspect of the images is of equal importance: the images concept. Understanding the problem solving mathematics and computing require another form of images - the ability to process the gestalt (the whole). A Sometimes children or adults can display numbers, the parties, but can not bring the parts to a whole, as sometimes you can display the individual words but can not bring those words as a whole to form concepts. mathematical skill involves the ability to get the gestalt, see the big picture, to understand the process underlying mathematical logic.

Concept imagery is the ability of the image of the Gestalt (whole), "Bell (1991). Concept image is fundamental to the process involved in oral language comprehension and written language expression, critical reasoning and mathematics. Sensory information is that connects us with the language and thought.

The ability to create mental representations of mathematical concepts is directly related to success on the mathematical reasoning and computation. However, because some children do not have this capability of imaging, often mistaken for not trying, unable to retain information, or have dyscalculia (the inability to perform arithmetic).

Manipulators It may not be enough

second grade class covered a review of Joanie recognize numbers, add, subtract, multiply and even some. They worked lot with concrete manipulatives and Joanie was doing well at the end of the year. But his third-grade teacher complained that Joanie did not know anything about the numbers.
Concrete experiences manipulation have been used for many years in teaching math (Stern, 1971). However, as Joanie, many children and adults have often had success with manipulatives, but failure in the computing world (NCTM, 1989; Moore, 1990; Papert, 1993). They have what has often been described as "implementation problems."

Joanie second grade class had spent much time with manipulatives. Some of the children to move to third grade continued to "think with numbers." His experience with manipulatives became part of your deposit of mental images. Like a bank deposit these images can be built at will. However, not all children create mental images as they work with concrete manipulation. For these children, the process of converting the specific experience of the images must be aware stimulated.

The Cloud Nine ® Math
Concrete the images to computers

Arnheim (1966) wrote: "The thought has to do with objects and events in the world we know ... When objects are not physically present, are represented indirectly by what we remember and know about them ... Experiences deposit images. "

Numbers can be experienced and the relationships between them can realize through the use of manipulatives. What seems abstract may be experienced and photographed specific. Mathematical roots are in the realm of the concrete, and images is the link to mathematical treatment, retention and application.

To develop the concept and images numeral, the On Cloud Nine ® math program (developed by the authors) integrates and consciously applies imagery to the process cognitive computing and conceptualizing math and mathematical principles. As individuals become familiar with cement handlers who disagree and proceeded to transfer the experience of conscious image. They image the concrete and attach the language to their images. The integration of images and language is then applied to computers. Individuals develop sensory processing, cognitive understanding and using the logic of mathematics.

The program moves through three basic steps to develop mathematical reasoning and calculation using: 1) manipulatives to experience the reality of mathematics, 2) images and language to achieve such a reality in the sensory system, and 3) the calculation of applied mathematics problem-solving. The Cloud Nine ® manipulatives serve two purposes: 1) to specify the numbers and mathematical concepts, and 2) to serve as the basis for the establishment of images.

When asked to add the numbers 3 + 2, children who are turning to the packaging of images can see three apples and two oranges to show five pieces of fruit. Others may use an image of a number line and place your finger in the 3 mental starting point. The "+" indicates to move forward and "2" indicates how many places. They know the answer because it can "see" in the eye of his mind. These children may look up, and that access to images (blur).
Children who do not seem to have a vault of images can say things like "I do not remember that one." Need instruction concrete explicit images and application of those images to the computer.

How image as a process of conscious work? Instruction On Cloud Nine ® math program begins with the numbers in the images of isolation-clause. A student is asked to see the number written, and is then removed. The student must demonstrate the "number" based the figure to show how many cubes represent that number. The student sees, says and writes the number in the air. The goal is for the student, when he sees the figures immediately to create an image of the formation of that number and value behind it.

The process experience continues with the line number, first as a concrete handling, and then as a mental image flexible. "Show me where you see the number 15? "" What is the number one step up from that? "" Are you close to 3 at 15 or far far away? "" What number is closer to the 15 - 10 or 5? Students "develop a line of numbers that carry with them in their vault of images. These students can access their vault of images at will. Aware of images and the ability to create images simultaneously and verbalize these dual image coding-are continued as the children are taught addition, subtraction, word problems, multiplication, division and more advanced math.

The Cloud Nine ® integrates math and consciously applies imagery to the cognitive process of computing and conceptualizing math and principles mathematicians. Children of the concrete image and put the language to their images. The integration of images and language is then applied to all aspects of calculation mathematician.

All children can develop sensory processing, cognitive understanding and using the logic of mathematics. In all aspects of mathematics, children can have access to what becomes a bank vault innate images to the memory and computation.

Nanci Bell, owner and director of Lindamood-Bell Learning Processes, is the author of two books on the images as the basis for language processing. Kimberly Tuley, the director of operations Lindamood-Bell is a trainer and consultant in the implementation and refinement of the Lindamood-Bell ® programs.

Bibliography
Aristotle. (1972). Aristotle on memory. Providence, Rhode Island: Brown University Press.
Arnheim, R. (1966). Image and thought. In G. Kepes (Ed.). Signal, image, symbol. New York: George Braziller, Inc.
Bell, Nanci. (1991). Display and Speak for the understanding of language and thought. Paso Robles: NBI Publications.
Moore, David S. (1990). On the shoulders of giants: New approaches to calculation. Steen, L. (Ed.). Washington, DC: National Academy Press.
Papert, Seymour. (1993). Children's Machine: Rethinking school in the Information Age. New York: Basic Books.
Paivio, Allan. (1981). Mental representations: A dual coding approach. New York: Oxford University Press.

Stern, Catherine and Stern, Margaret B. (1971). Children Discover Arithmetic. New York: Harper & Row, Publishers, Inc.

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About the Author

Why can’t everyone think with numbers? Why do some children learn math readily, handle money and time concepts with ease, retain information from year to year, and think with numbers effortlessly? What cognitive processes do some have that others do not?

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