Thinking Routines – Introducing and Exploring Ideas (part 3)

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

5) 3-2-1 Bridge (Activating prior knowledge, questioning, distilling, and connection making through metaphors) – Works well when students have prior knowledge but instruction will move it in a new direction; can be done over extended time during the course of a unit


I love the added components to the traditional 3-2-1 prompt! I think the key to using this effectively at the beginning and end of instruction is to be sure the students have some prior knowledge for the initial 3-2-1 and that the lesson has enough new information for a different set of responses. One way that I’ll use this thinking routine is to give (and collect) the initial 3-2-1 prompt as an exit ticket that the day before a lesson. This could act as a quick pre-assessment that I could use then use to adjust the next day’s lesson. I love the bridge component! What a great way for students to make connections to the new content and identify what they’ve learned. 

6) Compass Points (Decision making and planning, uncovering personal reactions) – Solicits the group’s ideas and reactions to a proposal, plan, or possible decision

Visible6I teach 10th graders, the year when they take the state math test, so this activity could be an opportunity for the students to express their Needs and Worries about the test. I think this could help them realize that they are all anxious about the test and allow them to self-assess (and in turn inform me) of the skills they already know they need to improve. I wonder if they would have anything to add to Excitement…maybe this could be where they come up with the benefits of learning these skills and not referring to the test itself. In regards to the test, I’m not sure if I would have anything positive to add here, but maybe they could help me think of what’s exciting about the MCAS. I will delete ‘stance’ and just focus on the Steps or Suggestions phase as a tool that allows their responses to direct the strategies I implement as we prepare throughout the year. I’m planning on doing this in September to give me a sense of this group’s learning preferences. At first I thought this activity would be a stretch, but now that I’ve written it out, I kind of like it! I think there is the potential of building a culture of naming the reasons why something may worry us (a.k.a. math!), looking at this from other perspectives, then being proactive and planning how we are going to proceed.

Another suggested for the use of Compass Points is for the introduction of a potential or new program to faculty. At our school, each department collectively chooses a goal in the fall. As with any consensus, not everyone can “win”. I’m thinking of using Compass Points after choosing the goal to look at it from a number of perspectives. By detailing Excitement, it will remind us of the reasons for choosing this goal and it will be good to refer back when we are frustrated with it in February. =) The Needs and Worries will give insight into the professional development that teachers need to reach this goal. The Steps/Suggestions may help us to split up the work involved in the steps or to create groups of teachers with similar plans.

Although not math related, I also teach an advisory class every other week. I think this could be a great routine to use in that class. We are given general themes or topics to work with, and I bet this will work great with one of them.


7) The Explanation Game – (Observing details and building explanations) – Variation of STW that focuses on identifying parts and explaining them in order to build up an understanding of the whole from its parts and their purposes

Visible7If you think back to the See-Think-Wonder routine, the students were presented with a new or ambiguous figure/photo/diagram. Yet in the Explanation Game, the students are looking at a figure/photo/diagram that they may recognize, but are not sure how or why it is the way it is. “…students may examine the features of a mathematics diagram to determine what those features do or what purposes they serve.” I think this routine could be a great tool when working through real-world data. I anticipate using this as my Pre-Calculus students work with real-world piecewise graphs. The first component of the routine, Name It, is for students (in pairs) to name all the different parts they are observing (e.g. ‘increasing linear function’, ‘horizontal line, ‘decreasing linear function’). This could even be extended to finding the equation to accompany the part that they ‘named’. The second component, Explain It, is where the students would then work to apply the real-world situation to what they see on the graph (e.g. ‘the income increased at a consistent rate for 3 years’, ‘for 5 years the income remained the same’, ‘the income decreased at a consistent rate for 2 years’). Students often struggle with applying the situation to the graphic representation. I think the exercise of naming each distinct part first would make this transition less overwhelming for students. Plus, by working in pairs they would have the opportunity to talk it out with their partner, which always helps! I think the last components, Give reasons and Generate alternatives, often are passed over in math classes. I think this is the part that would make a “real-world situation” actually feel real to students. I often have students interpret a graph, but rarely ask them why these things may be happening. When I create my own graphic representation of data (in the real-world, if you will), I do want to see the trends, but I also want to figure out why those trends may be occurring. Just thinking about these last two components makes me feel like I’ve been robbing my students a fun part of data analysis. I’m definitely going to take the time to work this thinking routine into my practice this year!

**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 third 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 thought on “Thinking Routines – Introducing and Exploring Ideas (part 3)

  1. Pingback: A Homework Philosophy | Making Math Visible

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