Saturday, October 16, 2010

Creating Meaning

I saw two similar manipulatives for creating meaning from symbolic manipulation.  The non technology manipulative uses integer chips which are manipulated as positive and negative 1’s to add and subtract positive and negative numbers.  The technology analogue to the chips is the virtual use of integer chips on an interactive white board.
I struggled to understand the balancing of an equation through the use of the virtual chips on the interactive white board. I think that is because I learned to balance equations in a pure purely procedural way.  Clearly I have some meaning attached to my knowledge of mathematical balancing procedures but this meaning leans heavily toward a symbolic meaning.  The chips, both real and technological, are creating a different meaning.  This meaning is a bit visual and easily translated into something real; the chips can be put in your pocket while the symbolic representation cannot.  I think there must be more manipulatives that offer other non symbolic ways to build meaning for different learners.
The translation between the manipulative and the symbolic can be rough for some learners.  One boy was struggling to apply balancing to the equation -24 = 8y. He really wanted to divide the 8y by 24.  The teacher kept bringing it back to positive and negative chips in boxes but I was not sure that way of considering it was helping him. I just wanted to tell him: “You want to get the y by itself on one side of the equal sign.”  I am conflicted: is that the “easy way out” for both the teacher and the learner?  Does the more difficult reference to chips really build meaning or is it possible it just creates confusion?

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