Thinking Routines – Synthesizing and Organizing Ideas (part 2)

Routines for Synthesizing and Organizing Ideas (Chapter 5) continued… (part 1 here)

4) Headlines (Summarizing, capturing the heart) – Quick summaries of the big ideas or what stands out


I like this routine because it can be short and sweet or extended to a longer, collaborative activity. It originally was used as a way to wrap up PD meetings, allowing groups a succinct way to share without further discussion (good idea!). Individually or in pairs, give students time to create a headline that captures their new learning. Facilitating this work is important so the students create headlines that capture the learning and not just a title for an activity. For example, “Exponential Patterns: Predictable or Not” speaks to what was learned while “Investigation of Exponential Growth” describes the activity.

Then they share their headline and its meaning (their reasoning) with a small group. After the small groups share, post the headlines together and prompt students to find themes. It’s really important to emphasize that the goal is not a clever headline, but a forum to gain different perspectives on what was learned. One headline can’t capture everything, but collectively the big ideas will surface. In a whole class discussion the teacher can either ask students for the story behind their headline, or ask the class what another student’s story might be, then let the student that wrote the headline add anything that was missed.

A few examples/ideas that will work in a math class:

  • Students write the “words behind the headline” on the back of the paper to give the teacher clearer insight into the student’s thinking. This should be limited to a couple sentences to keep the activity relatively short.
  • Triads create a few headlines, then choose one to fine tune and add to the class headlines. While facilitating the teacher asks students to explain why they chose that one and not the other to reveal why they see that as most important.
  • Use after hands-on activities or labs to ensure they discovered the big idea.
  • Create a headline for a state test question to help reveal how they might solve the problem.


5) The 4C’s (Connection making, identifying key concept, raising questions, and considering implication) – A text-based routine that helps identify key points of complex text for discussion; demands a rich text or book. [Simplified vocabulary for the 4C’s – draw the connection they made, what they didn’t agree with, what was most important to them, when they had learned something new or important]

Visible12 Math doesn’t easily lend itself to complex texts, but I can think of a few times to use this. I’m going to show a data video and this routine could help us debrief. Also, in How Not to be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg I came across his response to the common question, “when will I ever use this?” I found it pretty inspiring. I’m going to have the students read it this year and I’ll use the 4C’s as a way to debrief this article.

 PD – Another suggestion is to use this as a means to lead discussions of professional readings.

6) The Micro Lab Protocol (Focusing attention, analyzing and reflecting) – Can be combined with other routines and used to prompt reflection and discussion


I’m really looking forward to using this routine!! This is a useful structure in directing discussions to ensure equal participation and that everyone will contribute. Students learn how to be better listeners and how to build on another’s ideas. Love it!

They provided several math examples for this routine =)

  • After an experiment or lab, this can be used as a summary. Give the students 5 minutes to review the lab, look at notes, and questions, then run the Micro Lab
  • Give groups of students a set of problems that are different but related (e.g., functions or transformations). They distribute the problems among themselves and they have 10 minutes to work on it. Then during the Micro Lab they explain what they did, why they did it that way and where they got stuck or confused. The silence can be used for note taking in this case.
  • Reflection prompts for Micro Lab: How are you becoming more accomplished as a mathematician? Where do you want to improve?

The teacher that used Micro Lab said that it led to collective problem solving and better math talk. The discussions that followed showed insight and students made connections between the problems in the set. This makes me even more excited to try it out!

 A couple of suggestions – The more time that is given to first reflect on paper to the questions, the better the discussions will be. Be strict with the time limits and silence. Debriefing about the silence is important. “The purpose of silence is to take in what was just said and to recent, getting ready to hear the next speaker a pair of fresh ears.” p.150

 PD idea – use Micro Lab to facilitate group reflection on a strategy. For example, “how is your classroom changing as a result of your work with these ideas?” 

7) I Used to Think…, Now I Think… (Reflecting and metacognition) – Used to help learners reflect on how their thinking has shifted and changed over time20140729-220448-79488708.jpg

This is a reflective routine that focuses attention on the thinking more than the activity. This routine can be used when they’ve had a chance to confront misconceptions or shift their thinking in fundamental ways. I bet this could be great with student portfolios to have the students refer to their past work and recognize growth. I’ve been focusing a lot on open response questions, trying to shift how my students think and feel about these problems. This could be a good way to reflect on how they used to approach these problems after I’ve taught them to use our open response protocol.

The authors suggest that when introducing this routine the students should share out as a whole group to model how to explain their thinking with guiding questions from the teacher. Once they get used to explaining their reasoning then this could be used as a think-pair-share.

 “…development of understanding is not just an accumulation of new information but often results in changes of thinking.” 

**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 two posts that detail one-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.)


Anchor Charts as a Review

In yesterday’s post, I described a review strategy I used this June. Part of the strategy was a think-pair-share activity, although I didn’t use that label at the time. While planning, I listed the main topics on the final exam and I came up with 10 big ones. Over the course of two weeks, the students encountered a different topic each day for the Do Now (all review). I asked an open-ended question for the Think-Pair-Share/Do Now Activity. During the discussion, I recorded their responses on chart paper to capture their ideas on a student-genterated anchor chart. These remained posted in the classroom for the students to refer to during other review activities. There are a few examples below.


ReviewPoster_2-D figures

ReviewPoster_Measuring Parts of Triangle

ReviewPoster_Types of Angles

ReviewPoster_Angle Relationships

Exam Reviews, Student Talk, and Anchor Charts

I dedicate the last 3 weeks or so to a culminating project so I’ve tried to find a (good) way to fold in review during this time without losing too much momentum on the project. I really liked my most recent attempt in which I used a series of Do Now’s and Homework’s to tie together the review topics. I’ll explain the process by referring to the example below, which addressed Supplementary Angles and Isosceles Triangles.

I structured each Do Now to contain 4 components including individual think time, sharing in pairs and a whole class discussion. (This did take longer than my normal allotment for Do Now’s, but it was worth it to me.)

First, the students would individually recall facts from the Previous Topic (e.g. Supplementary Angles), which we had reviewed in both the Do Now and Homework yesterday. Once they wrote these facts they could crosscheck it with the previous Do Now if they were unsure.

Second, they would move on to Today’s Topic (e.g. Isosceles Triangles). The task was always to write down 3 statements that they know or think they know about the topic. The second part of the statement allowed them the freedom to write something down even if they weren’t 100% sure. I would challenge them to do this just by memory, but they could refer to their notebook if necessary. During this time, I would circulate and snoop like crazy to get a feel of how far they could get before opening up their notebooks. This helped me to gauge what they still remembered about the topic and if I would need to work in a mini-lesson.

Third, they would share their statements to their partner and add any new ideas that surfaced during this conversation.

Fourth, I would bring the class back together to share out. During this discussion, I recorded their ideas on chart paper.

Lastly, practice problems to accompany Today’s Topic were for homework that night. The homework problems were similar to examples in their notebook from earlier in the year. On the Do Now was a box to record the page number, which hopefully spurred them to look to their notebook as they practiced that night.

The next day we would repeat the process, starting with the previous topic (e.g. Isosceles Triangles) for step one, then add in a new topic. I continued this process for 10 days then stapled these together so they had all their work in one place.

There were a couple things I really loved about this review set up. Through the discussion, we created a student-generated anchor chart for every topic on the exam. I kept these anchor charts posted in the classroom until the day before the exam. As we worked through the topics and we taped poster after poster to the walls, the students began to realize how much they learned that year. =) It also helped them determine the topics they needed to study the most. I loved that every day’s lesson had a few key elements worked in already – individual recall, sharing with a partner and a collaborative discussion to review for the exam.ReviewPoster_Isosceles Triangles1I normally would have focused only on big ideas and wouldn’t have added the examples to an anchor chart. Yet the discussion led to a request for an example, so this may not be but it did the trick.

*How do you review at the end of the year? If anyone else ends the year with a project, how do you work in a review?

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.)

Thinking Routines – Introducing and Exploring Ideas (part 1)

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!

Day and Night

Thinking Routines – Digging Deeper

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’

photo 1

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

photo 3

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

Claim, Support, Question

Math Idea from text – introduce a math problem with a variety 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

photo 2

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.

photo 1-1

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)

photo 4

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

photo 2-1

Math applications N/A; Possibly use for an advisory lesson


July Blogging Challenge

I came across a blogging challenge, and I’m going to try this out. I’m a regular reader of math teacher blogs, and I’ve been trying to work up the nerve to jump into the ring.  The challenge suggested to start with a reflection on the past school year using the prompt, START/STOP/CONTINUE, and I think that’s a great way to begin.

3 things to START:

  • A couple years ago I used a lot of photos (art, architecture, etc) to launch lessons, but that fell off this past year. I want to start doing that again.
  • Planning lessons and activities with a focus on making thinking visible and the type of thinking in which I want my students engaged (inspired by a book I’m reading Making Thinking Visible by Ron Ritchart)
  • Regularly reviewing previous content and connect it to the new material.  I found that the students struggled to retain some of the content, especially vocabulary, after we moved on to a new unit. I occasionally would give ‘Throw Back’ homework assignments that would bring up some of these topics and the students appreciated it. I want to start this right away next year, and implement it weekly.

3 things to STOP:

  • Traditional homework problems…I’m finding that many of my students either don’t do homework, copy it from someone else, or end up solving the problems incorrectly and form bad habits. I’m still thinking about how (flipping, written reflections…), but I know it needs to change.
  • Over-booking each lesson. I tend to be overambitious in my lesson planning resulting in us working to the bell (which is good), but I then sacrifice the summary or exit ticket (which is bad). I need to either stop overbooking OR stop things early to get to the summary.
  • Feeling pressured to move on at the end of the unit. I got away from spending time with the students reviewing their tests at the end of the unit. I want to incorporate both test corrections and a written component at the end of each unit.

3 things to CONTINUE:

  • Interactive Student Notebooks! This was my first full year trying out this method of note-taking, and I’ll never go back! I used it in both Geometry and Pre-Calculus. The students loved it, I loved it, and it had a great impact on their learning experience!
  • Games and activities that increase student talk. I started incorporating more pair work at the end of the year focused on practicing content and verbalizing their thoughts. The students were engaged, talking about math, and happy. =)
  • A problem-solving strategy that I regularly implemented this year, Notice and Wonder. It really helped to develop my students’ confidence with open-ended and word problems. Notice & Wonder Record Sheet

Thanks for the challenge! Day 1 completed! =)