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.

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4 thoughts on “Can we teach math without numbers?

  1. Here’s a few things I used to do when teaching statistics:
    1: the Mean – Keep chopping bits of the taller kids and sticking them onto the shorter kids until they are all the same height (shades of Procrustes and his bed)
    2: the Median – stand them in a row according to height. The middle one has the median height.
    3: the Standard deviation – There is a direct match between standard deviation and radius of gyration in mechanics. Requires imagination – Take a long enough stick of wood and put a scale on it. At each data value fix a brick on the stick. Suspend the stick and bricks at the mean point of the data and whizz it round. Move all the bricks to the same distance from the mean point ( half on one side, half on the other). If it requires the same effort to whizz it round you have found the radius of gyration AND the standard deviation of the data values. (this sure doesn’t tell you how to find that point, but that doesn’t matter yet)
    ( I couldn’t find anything in the CCSS on applied math/mechanics)
    4. Correlation – I never got to work on this one !!!!!!!

    1. I am going to have to think about the gyration idea. It may tie into the thought that multiplying by i is the same as counterclockwise turns around the circle!

      I used the height / median idea with success. I realized they had no clue what average really was, they just performed the algorithm. I took squares and stacked them in uneven piles, had the kids separate them evenly into the same number of piles, and we discussed what averaging really did. This helped tremendously with calculating standard deviation, and they had to wrap their heads around taking the average of a bunch of distances! The fun has begun!

      1. The mean without numbers: needs a bit of imagination or a very lightweight stick (ruler). Scale the stick according to the values in the set of data, and fix a weight (a quarter may do) at the scale value, for each piece of data. The stick will balance at the mean value of the data – NO calculations. They can do this graphically with blobs at the data points but it’s not as good.
        Regarding standard deviation, you need actual data from two related situations, plot the data as blob(dots) on two different equal scaled lines and ask about differences. Show two of these with similar range, or similar interquartile range, but wildly different standard deviations…..

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