Notice, Wonder, Questions

Octoober 20, 2017

           I wanted to take a moment to write about interdisciplinary professional development. Whenever I have the opportunity to attend an interdisciplinary PD, I am hesitant because the mathematics is either nonexistent or extremely superficial. Today I went to a professional development put on by LACOE
and it was focused on integrating art and the new social studies standards. The presenter referenced the new common core standards, including ELA, history, art, and even science. The only content they didn’t seem to recognize was mathematics, which was not a surprise.

         What I didn’t anticipate was when we discussed pedagogy and different strategies for teaching art, I would recognize my own structures in mathematics. 

      For example, she talked about taking the time in silence to look at a painting and really appreciate what was happening. She called it notice, wonder, and think. It grabbed my attention immediately. Mathematics teachers constantly use the phrase "notice and wonder". In mathematics we ask students to look at a problem and notice anything they can. Then we have them take the time to wonder something else about the problem. Finally (referencing the 3 read protocol from San Francisco Unified) we have them create questions  they think might be asked about the scenario.

     This is the exact process we did with a painting called The Adoration of the Magi.

We were told to take several minutes in silence  to look at and appreciate the painting.

 From a mathematics teacher perspective, this was intimidating.

      However, the teacher gave us structure on how to look at the painting. She said to look left to right down to up and then from the center out. It was interesting because I’ve never thought about looking at art this way before and I noticed some interesting patterns with this guidance. It made me wonder what kind of insight I can give to my students about how to look at mathematics.

       After a while of allowing us to truly take in the painting and make our own decisions, we took the time to talk to someone near us (shoulder partners). We shared what we noticed, what we wondered, and we generated questions about the depicted scene.

      I have limited background knowledge in art history, but I noticed a lot more than I would have expected. Art is about representing stories through visual depictions. Mathematics is a way we represent scenarios and are able to use these representations to make decisions. It is also a way to structurally understand the world around us.

     I wonder how students could use this level of observation in a mathematics class. Equations, graphs, and tables model scenarios and therefore tell a story.                                            

For example,

we can look at data and  notice features and wonder about why it happens.

In this data, why would we include the outliers? They obviously are skewing the data. In the painting above, why does the wise man at the bottom have a porcelain cup? That doesn't seem like a valuable present.


Then we reveal more information. California has 55 electoral votes. We almost excluded ourselves!

In the art above, the teacher talked to us about the historical significance of the tea cup. It turns out that something simple as a white and blue porcelain tea cup in the center of an image is an example

of how the silk road had an impact on Western civilization. This was the wise man who brought gold to baby Jesus and he brought it in a very important, valuable symbol of the time. If you started with a porcelain cup in Japan or China and brought it along the silk road, every stop of the way would have a price increase on that item. By the time the cup reached the western world, only the extremely wealthy could afford it.

I had no idea!

 I almost didn't see the significance. Much like the California outlier above.

With little to no background knowledge and effective teacher facilitation enables me  to make these deep rooted connections.

Hello Inquiry Based Learning!

It looks the same no matter what we are looking at, and how the teacher guides us makes all the difference. What features will our students notice and not even wonder about because they don’t have the background knowledge to recognize its importance.

What can we do to bestow upon our students our passion and how can we help our students see the stories told from mathematics?  How can we help our students feel the same way I felt today?