Can we teach math without numbers?

The idea of math without numbers is, for me, a way of sharing concept before sharing algorithm. Math isn’t JUST answer getting. It is the rich process of discovery and delight in seeing the patterns. For example, Unit 1, statistics, the idea is learning how to interpret the data depending on the presentation. Generally kids are asked to calculate a bunch of numbers from the data, which they will do without any clue as to why these numbers are important.
I used box plots as an opportunity to teach “without numbers”. I took away the number line below the plot, and we examined the shape and form and usage – why use this shape? Why divide into four parts? Why whiskers? It helps students when they see beyond the number assigned by the data to the reason for assembling the data in what seems an arbitrary fashion (to them!). Range finding without understanding is subtraction to many, and just number-finding, if they have no context for why finding that number is so important.
I asked them what Standard Deviation is. Several students replied in unison, “it’s the answer.”
I haven’t thought thru the whole course yet, (Alg II) but I will try to be more faithful to blogging about what is working and what is not.

(Thanks to Susan, who pushed me to respond to a comment I made in reply to one of Justin Lanier’s) posts.