Thinking Routines – Introducing and Exploring Ideas (part 2)

Routines for Introducing and Exploring Ideas (chapter 4) continued…

3) Think-Puzzle-Explore (Activating prior knowledge, wondering, planning) Good at the beginning of a unit to direct personal or group inquiry and uncover current understandings as well as misconceptions


Similar to a KWL in structure, the key difference in Think-Puzzle-Explore is in how the questions are asked, which shifts the focus first to discovering students’ prior and partial knowledge (and misconceptions), then encouraging curiosity and planning. I’ve always found it hard to use a KWL in math class. Even when I was confident my students had prior knowledge about a topic, I found that they were reluctant to write things down in the ‘Know’ column, stating that they didn’t know if they were correct. The responses for what they ‘want’ to know lacked in depth and curiosity. Overwhelming the response was “I want to know how to solve it” or “how to get it right on a test.” I’m not great at going back to these types of activities at the end of a unit, so I never did follow through with the “Learned” column. I’m happy that the issues I have with a KWL chart are addressed with the Think-Puzzle-Explore routine. I think the shift to the phrase ‘Think’ will illuminate partial knowledge and misconceptions, which is really what I need to know when we start a new topic and is an essential tool in driving instruction. “… (‘Think’) gives permission to have a go, raise possible responses to the question, safe in the knowledge that you are not guaranteeing that you have the absolute facts but rather some thoughts about it.” I think the Puzzle section could be powerful as a whole class discussion providing a chance for students to build upon each other’s ideas. By recording a class list of ‘Puzzles’ on chart paper we could refer back to this list to check items off as they are discovered and add more ‘puzzles’ that arise as instruction continues throughout the unit.

4) Chalk Talk (Uncovering prior knowledge and ideas, questioning) – Open-ended discussion on paper; ensures all voices are heard, gives thinking time. A conversation conducted silently on paper. “It provides flexibility to move from one idea to another in a nonlinear way, to formulate questions as they arise, and to take the time needed to think through the collective information produced.”


With no names written on the posters, this routine gives students freedom to take risks and ask questions that they may not feel comfortable voicing in a verbal discussion. This routine gives every student equal contribution time and the chance for me to hear every ‘voice’, both of which are difficult to accomplish in other formats. The prompts can be single words and phrases, yet posing questions can take the conversation up a level. I used this activity once and didn’t love the result. I think the problem was that I stuck to phrases (e.g. Exponential Functions, Exponent Rules, etc), which seemed to stifle the conversation and they thought I was looking for a particular answer. I’m going to give this routine another try by posing questions instead. I find open-ended math questions hard to create, but I think it would result in a deeper conversation.

The authors suggest using Chalk Talk as a means to reflect on topics or learning moments – I love this idea! I envision using this activity before a cumulative test as a means to discover what the class remembers collectively about a variety of topics and to give them a chance to ask questions too. I anticipate misconceptions or gaps appearing in their work, that I could then use to structure the review activities that would follow. I also love the idea is to use this at the end of a term to reflect on what they learned. The authors provide sample questions to use for this purpose: “What have you been most surprised by in this unit of student? What is hard for you to master in this topic? Where would you most like to see improvement in yourself? What skills do you have around this topic that you could share with others? How do you know when you really understand something?” Nice!

I think this activity can be quite useful in a professional context as well. In a PD I attended last year, the instructor used this activity to pose questions about bullying and homophobic language. I found it to be very effective in giving every participant the opportunity to voice ideas in a safe environment. As a learner, I liked moving around the classroom, reading others responses and having the chance to respond or build off of these. I found it to be reflective and a chance to ‘hear’ many more voices than in a whole group discussion. An added benefit was that the follow-up discussion stayed on track, which I attribute to our collective focus on the chosen questions and realizing that a lot of people had meaningful ideas to share. Also, participants referred to ideas written the poster that struck them, which directed the conversation and fostered the idea of collective knowledge and experiences. I think this could be used in math focused PD, possibly to start the school year with questions focused on our department goals, the focus of the year, changes we are going to implement this year, etc.

**I would love to hear if you have used these routines OR if you have any ideas of what math topics for which they could work well.**

(Note: This is the second 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.)


One thought on “Thinking Routines – Introducing and Exploring Ideas (part 2)

  1. Pingback: A Homework Philosophy | Making Math Visible

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