Currently I am reading and re-reading Making Thinking Visible by Ron Ritchhart, Mark Church and Karin Morrison. I picked up this book because there was a lot of talk this past year about making thinking visible and I wanted to learn more about it. This is going to be one of many posts concerning what I’ve learned from this book. I’m finding that the ideas in the book are drawing together a lot of things I’ve been thinking about and trying to accomplish with my students.

*Routines for Digging Deeper Into Ideas* (Chapter 6)

The post details one-third of the ‘Thinking Routines’ outlined in the book. 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. What Makes You Say That? **(Reasoning with evidence): A question that teachers can weave into discussions to push students to give evidence for their assertions. ‘Fosters a disposition toward evidential reasoning – correctness of an answer doesn’t lie in a lone outside authority, but in evidence that supports it; empowers the learning community to examine the reasons and evidence’

*This strategy could easily work its way into almost every math discussion and make a big shift in seeing/understanding what/how students are thinking!*

**2. Step Inside** (Perspective Taking): Stepping into a position and talking or writing from that perspective to gain a deeper understanding of it

*This could be a way to explore functions and/or function transformations (Pre-Calculus, Algebra 2). Give a group of students a particular function and each member steps inside the function from a different representation (table, graph, verbal, algebraic). The group could share and ‘get to know’ their function from each perspective, then each group shares with the class.*

*Geometry – A way for students to explore parallel and perpendicular lines (or maybe a slope activity) through the graphs, tables and equations. They could possibly narrate their perspective in first person (Each time I climb up 3 units, I step right one unit. When I look up I see another line above me. Each time I climb up 3, so does that line. I’m never going to catch it!)*

**3. Claim-Support-Question** (Identifying generalizations and theories, reasoning with evidence, making counterarguments): Can be used with text or as a basic structure for mathematical and scientific thinking. Frames the enterprise of mathematics as being about speculation, generalization, analysis, and proof

*Math Idea from text – introduce a math problem with a vari**ety of entry points and strategies; give individual work time; discussion of their findings, ideas and generalizations; documents claims; more work time with a focus on evidence to support or refute initial claims*

*a specific math classroom example on p. 195-197

**4) Circle of Viewpoints** (Perspective Taking): Identification of perspectives around an issue or problem

*Math applications are a stretch…the concept is based on seeing something from different perspectives, so it could work as an introduction in Geometry viewing 3-D figures from different sides.*

**5) Sentence-Phrase-Word: **(Summarizing and distilling): Text-based protocol aimed at eliciting what a reader found important or worthwhile; used with discussion to look at themes and implications.

*Math applications N/A; **Professional Development Idea – a protocol for discussing readings with other adults; share in rounds with a chance to comment after each person shares; document to help find themes*

**6) Red light, Yellow light** (Monitoring, identifying of bias, raising questions) – Used to identify possible errors in reasoning, over-reaching by authors, or areas that need to be questioned. This is used to spot occasions to be skeptical, ask questions and for application. (Note – highlight text or identify with Y or R., then document responses)

Math applications N/A

Potential Professional Development Uses from text

*a. Facilitating PD ‘when teachers share their classroom efforts, student work, or reflections around professional reading…to move conversations beyond merely agreeing or disagreeing…creates a sense of safety to navigate difficult ideas.’*

*b. Discussing of action plans and proposals – conveys that there are natural points of dispute that need working through*

**7) Tug-of-War **(Perspective taking, reasoning, identifying complexities) – Identifying and building both sides of an argument or tension/dilemma; to suspend taking a side and think carefully about the multiple pulls or reasons in support of both sides

*M**ath applications N/A; **Possibly use for an advisory lesson*

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I’ve actually used RLYL with math. We did it with Shel Silverstien’s poem “one inch tall.” Student read it and then think which statements seem way off mathematically (RL) and which might be slightly off, not quite right (YL). We then discuss those. Could be used the same way with a proof, an article with statistics. Students could also use it while reading a math text: what makes you slow down, you have to reread it to get it (YL), which things stop you in your tracks (RL).

I just looked up “One Inch Tall” – what a great poem! I love the idea of using Red Light Yellow Light (RLYL) with proofs! That would be a great way to gauge their understanding of the different parts of the proof. Since SO many students struggle with proofs, I’m sure there would be a lot of RL and YL to start, which would help the students see that they are not alone in the struggle. I rarely have students read from our textbook, but I think you have a great point that this strategy could help us work through that difficult text. Thanks for the ideas!

Well done! I am a big fan of “Making Thinking Visible” and really like your exploration of the work within the Maths classroom.

Thanks Paul! Although I’ve been doing this type of thing in my classroom, I’m relatively new to the formal term “Making Thinking Visible” and all the research to support it. Since I’ve picked up the book I’ve been fascinating to think about thinking in this way! And I’m enjoying the process of considering how I can do this better in a math class. I would love to hear about how you have used it.

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