Routines for Introducing and Exploring Ideas (chapter 4)
This is one of three posts that detail a third of the ‘Thinking Routines’ outlined in Making Thinking Visible by Ron Ritchhart, Mark Church and Karin Morrison. After each number is the title of the Thinking Routine followed by the ‘Key Thinking Moves’, then ‘Quick Notes and Descriptions’. All of this information is directly quoted from the book Table 3.1 Thinking Routine Matrix. Then are the details of the routine and questions to accompany it. Finally, in italics, is a brief brainstorm of how I thought I might use this in a math classroom and/or in math department meetings.
1) See-Think-Wonder (Describing, interpreting, and wondering) – Good with ambiguous or complex visual stimuli. This routine emphasizes the importance of observation as the basis for the thinking and interpretation step that follows the close looking. This routine was designed to draw on students’ close looking and intent observation as the foundation for greater insights, grounded interpretations, evidenced-based theory building, and broad-reaching curiosity.
I came across a very similar idea (that I LOVE) last October at the Baltimore NCTM conference. The protocol is called ‘I Notice, I Wonder’ out of Drexel University in Philadelphia. It’s based on math problems and built out of this same concept – teaching students to look closely, make observations and then allow their curiosity to drive the rest of the conversation. The ‘I Notice, I Wonder’ protocol became a regular part of my practice this year, and I saw a big difference in how my students approached and discussed problems (I will go into more detail about this in a future post).
There is a slight difference between these routines, as ‘See-Think-Wonder’ adds the ‘think’ component, which is described as an interpretation phase. Questions to lead this discussion include, “Based on what we are seeing and noticing, what does it makes us think? What kinds of interpretations can we form based on our observations? What else is going on here? What do you see that makes you say that?”
Based on what I learned from implementing this last year, I have a few suggestions for implementation: When introducing the problem, provide silent time for the students to look closely. I did have students record their observations, but first I insisted upon one minute with pencils-down, so they could just look. A big part of this process is the discussion that follows because the students build off of each other’s ideas. The quality and depth of their responses grows over time, so don’t be discouraged if it doesn’t go great the first time out. I always recorded their responses on chart paper to validate all the contributions and have a record of the conversation to refer to as we worked on the problem. During the discussion, try to be non-judgmental and record everything! There is not a right or wrong response with this activity, which allows all students the chance to contribute without worry. I used this routine in many different ways throughout the year. The key was to present an open-ended visual without given questions (sometimes I would use the visual representation from a multi-step problem and remove all the questions). Ideas: Graphs (anything real-world works great); different data representations; Dan Meyer’s Three Acts; Diagrams; Sequences represented by drawings; Tables, etc.
2) Zoom In (Describing, inferring, and interpreting) – Variation of STW using only portions of an image
I like that this routine lends itself to practicing elements of a growth mindset. As new portions of the visual are revealed, the students learn to be flexible with their hypotheses and re-work their ideas to encompass the new information as well.
This could be used as a means to introduce to piecewise functions. It could be implemented again when the students learn to write equations for piecewise functions. It could be used in a statistics unit with a carefully chosen data representation to look at what is occurring at different sections/areas of the data. With some creativity, it could possibly be applied to teaching proofs, complex geometric figures, composite figures, tessellations, and/or transformations.
The ‘Picture of Practice’ example in the book details Zoom In used in a math classroom. The teacher wanted students to realize that math is all around them and to see the big picture of math. She used M. C. Escher’s Day and Night image, which has a variety of rich elements to discuss. Great idea!