See, Think, Wonder in Math.

I'm finishing off a class on flipped learning and as part of one assignment, I had to create a lesson.  As part of the lesson, I included having students look at a set of graphs, mappings, tables, and coordinates as an introduction to the topic.  They will explain what they see, what they think, and what they wonder as they look at them and then they will record their thoughts in Google Slides.

As I wrote the lesson, I realized it is easy to include the What do I see, What do I think, and What do I wonder in the math lesson.  It is perfect as a way of sparking previous knowledge, mathematical thought, and curiosity.  The picture does not have to be of a math equation, it might be something like the picture above that is filled with arcs.  Lots and lots of arcs used as part of the sculpture.  When I get ready to do slopes, etc I'll post pictures of mountains, or perhaps a picture of the Stockmarket.  Then when it is time to do three dimensional shapes, I can use pictures of buildings like the tower of Pisa, to introduce the topic.

This particular routine encourages careful observations while taking time to think about their interpretations of the picture.  As stated earlier, this routine can be used to introduce a topic or to provide a connection during the unit between real life and the math being studied.  It can also be used toward the end of a unit to make students think about extending the topic or starting the transference of knowledge.

This works best when putting the I see.... I think.... I wonder.... together as one unit and it is important to have them include reasons for their  thinking because one of the math standards is to communicate their thinking.  If you use this routine with visible patterns, start with asking "What do you see?" which has them describing what they see such as shapes, patterns, etc.  Next ask "What do you think?" which could have them thinking about the next step in the pattern, or what math is associated with what they see.  It takes them to the next step in the process of thinking.  The "What do you wonder?" asks them to take things a step further so they might figure out a way to predict the pattern after 10, 20 or 100, or maybe they'll wonder about the mathematics behind something.

Another use of see, think, and wonder is with graphs published in newspapers.  It might be a graph of  the latest pickup truck, the price of the average thanksgiving dinner, or other public graph found in an advertisement.  This activity has students explain what they see, what they think is going on, and what does it make them wonder so they get a better grasp on the idea that sometimes graphs can be misleading.

In addition, this can be used when beginning a new unit.  To do this, have students look through the new material while asking them what they see, what they think they will learn in the unit, and what questions they have about the unit.  If you place a templet online using Google Slides, students can record their thoughts for each question so you can go in later and read their responses. Furthermore, as the teacher, you can go into Desmos and create your own See, Think, and Wonder activities complete with places for students to record their thinking.

It is important to have students discuss their thinking because thinking leads to understanding.  In addition, this activity helps students improve their mathematical communication and increases their critical thinking skills.  Let me know what you think, I'd love to hear.  Have a great day.