Students need to decide, 'All right, well, does the height matter? Does the side of it matter? Does the color of the valve matter? What matters here?' - such an underrepresented question in math curriculum.
Dan MeyerThe physical five oranges goes up the ladder to the picture of the five oranges which goes up to the representation of the five oranges as a numeral. This points in the direction of a definition of abstraction: when we abstract we voluntarily ignore details of a context, so that we can accomplish a goal.
Dan Meyer