Reading strategies| Reading workshop| Reading across the curriculum| Reading in the content area
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- lindamoodbell
On Cloud Nine® Math
Concrete to Imagery to ComputationArnheim (1966) wrote, “Thinking is concerned with the objects and events of the world we know...When the objects are not physically present, they are represented indirectly by what we remember and know about them...Experiences deposit images.”
Numbers can be experienced and the relationships between them can be made concrete by using manipulatives. What appears abstract can be experienced and imaged to concreteness. Math’s roots are in the realm of the concrete, and imagery is the link to mathematical processing, retention, and application.
To develop concept and numeral imagery, the On Cloud Nine® math program (developed by the authors) integrates and consciously applies imagery to the cognitive process of computing and conceptualizing math and mathematical principles. As individuals become familiar with the concrete manipulatives, they are questioned and directed to consciously transfer the experienced to the imaged. They image the concrete and attach language to their imagery. The integration of imagery and language is then applied to computation. Individuals develop the sensory-cognitive processing to understand and use the logic of mathematics.
The program moves through three basic steps to develop mathematical reasoning and computation using: 1) manipulatives to experience the reality of math, 2) imagery and language to concretize that reality in the sensory system, and 3) computation to apply math to problem solving. On Cloud Nine® manipulatives serve two purposes: 1) to concretize numbers and mathematical concepts, and 2) to serve as a base for establishing imagery.
When asked to add the numbers 3 + 2, children who are drawing on their vault of images may see 3 apples and 2 more oranges to show 5 pieces of fruit. Others may draw on an image of a number line and place their mental finger on the 3 as a starting point. The “+” tells them to move forward and the “2” indicates how many places. They know the answer because they can “see it” in their mind’s eye. These children may look up as they access their images (defocusing).
Children who don’t seem to have a vault of images may say things like “I don’t remember that one.” They need explicit instruction in imaging the concrete and applying that imagery to the computation.How does imaging as a conscious process work? The On Cloud Nine® math program begins with numbers in isolation—numeral imagery. A student is asked to view the written numeral, and then it is taken away. The student must demonstrate the “number” underlying the numeral by showing how many cubes represent that number. The student sees, says, and writes the number in the air. The goal is for the student, when she sees the numeral, to immediately create an image of the formation of that number and the value behind it.
The process continues with experiencing the number line, first as a concrete manipulative, then as a flexible mental image. “Show me where you see the number 15?” “What’s the number one step up from that?” “Is the 3 close to the 15 or quite far away?” “What number is closer to the 15 – the 10 or the 5?” Students develop a number line they carry with them in their vault of images. These students can access their vault of images at will. Conscious imagery and the ability to simultaneously create images and verbalize these imaging—dual coding—are continued as children are taught addition, subtraction, word problems, multiplication, division and more advanced math.
On Cloud Nine® math integrates and consciously applies imagery to the cognitive process of computing and conceptualizing math and mathematical principles. Children image the concrete and attach language to their imagery. The integration of imagery and language is then applied to every aspect of mathematical computation.
All children can develop the sensory-cognitive processing to understand and use the logic of mathematics. In every aspect of math, children can have access to what becomes an innate bank vault of imagery for memory and computation.
More Information:
http://www.lindamoodbell.com/
http://inforequest.lblp.com/