How do you do your mental math?
Do you have a picture of manipulatives or objects in your mind?
Do you have a 'chalkboard' to write or draw needed pictures in your mind?
Or do you just 'do the math' without a picture of any kind?
Several recent discussions, with friends working on math education, brought to mind the variety of methods people use for mental math.
My oldest (Dude) finds numbers very logical and simple. He does some number crunching and has his answer very quickly. While we still explained math in terms of real or concrete objects. We shot through pictorial and on to abstract very quickly. I am fairly certain he just uses the math, no picturing in the mind.
My daughter (Princess) finds the connection between numbers and physical objects a bit difficult. She used manipulatives to add and subtract far longer than either brother. She still to this day wants pictures and objects to understand her math. Complex multiplication and division require descriptive words like 'grapes to share' or 'bags of apples'. I don't know if she will ever give up imagining pictures (and sometimes drawing them) for her own math.
Are there other ways to visualize mental math? How many different paths to the same '4 + 4 = 8' can there be?
I don't remember ever visualizing things when adding 4 + 4 but I do remember picturing it on a black board. Did that mainly for things like 345 time 568 so I could remember what was there when it came time to add.
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