Develop a range of instructional and assessment methods and test preparation methods. Instruction Linda Gojakformer NCTM President, noted that "Over the last three decades a variety of instructional strategies have been introduced with a goal of increasing student achievement in mathematics.
Nanci Bell and Kimberly Tuley Mathematics is cognitive process-thinking-that requires the dual coding of imagery and language. Imagery is fundamental to the process of thinking with numbers. Albert Einstein, whose theories of relativity helped explain our universe, used imagery as the base for his mental processing and problem solving.
Imaging is the basis for thinking with numbers and conceptualizing their functions and their logic.
Paivio believes that in order to think and understand, humans must be able to simultaneously generate imagery and corresponding language to describe that imagery. Mathematics is the essence of cognition. Both processes, often mirror images of each other, require the integration of language and imagery to understand the fundamentals and then apply them.
Dual coding in math, just as in reading, requires two aspects of imagery: Numeral imagery Visualizing numerals is one of the basic cognitive processes necessary for understanding math. If someone gives us two pennies for the numeral three, we have a discrepancy between our numeral-image for three and the reality concept of three.
The first imagery needed for math is the symbolic or numeral imagery that represents the reality of a number concept. What does numeral imagery look like?
Cecil was very good in math. He could think with numbers, arrive at answers in his head, and mentally check for mathematical discrepancies in finance or life situations easily. Certain numbers are in certain colors, and the number-line in my head goes specific directions.
He assigned colors to specific numbers! Chronological relationships appear in our minds on a number line, the days of the week, the months in the year.
It is a means to experience math. Concept imagery While imaging numerals is important to mathematical computation, another aspect of imagery is equally important: Understanding, problem solving and computing in mathematics require another form of imagery--the ability to process the gestalt the whole.
Sometimes children or adults can visualize the numerals, the parts, but cannot bring those parts to a whole, just as they can sometimes visualize individual words but cannot bring those words to a whole to form concepts.
Mathematical skill requires the ability to get the gestalt, see the big picture, in order to understand the process underlying mathematical logic. Concept imagery is basic to the process involved in oral and written language comprehension, language expression, critical reasoning and math. It is the sensory information that connects us to language and thought.
The ability to create mental representations for mathematical concepts is directly related to success in mathematical reasoning and computation.
However, because some children do not have this imaging ability, they are often mislabeled as not trying, unable to retain information, or having dyscalculia the inability to perform arithmetic operations.
They worked a lot with concrete manipulatives and Joanie was doing well at the end of the year. Concrete experiences-manipulatives-have been used for many years in teaching math Stern, However, like Joanie, many children and adults have often experienced success with manipulatives, but failure in the world of computation NCTM, ; Moore, ; Papert, Like a bank deposit, these images could be drawn upon at will.
However, not all children create mental imagery as they work with concrete manipulative. For these children, the process of turning the concrete experience into imagery must be consciously stimulated.
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