Making Thinking Visible – Final Thoughts

About a month ago I was searching the library database for a book recommended by a fellow blogger. Our library didn’t have it, but Making Thinking Visible came up in the list. The phrase ‘Making Thinking Visible’ was thrown around a lot this past year at my school, and I never really knew what people were talking about. I do incorporate some think-pair-shares and writing with my students so assumed that I was probably more or less doing it. When I saw this title, I thought I could read the first chapter or two to be in the know. Much to my surprise, I’ve spent a month reading, re-reading, taking notes, and blogging about this book. I’ve really enjoyed this time to more deeply consider the acts of thinking and understanding and how to make these acts visible in my classroom. Below are a few quotes that really struck me.

  • Work and activity are not synonymous with learning
  • When classrooms are about activity or work, teachers tend to focus on what they want the students to do in order to complete the assignments. These physical steps and actions can be identified, but the thinking component is missing. When this happens the learning is likely to be missing as well.
  • …curiosity and questioning propel learning
  • …with the learner at the center of the educational enterprise, rather than at the end, our role as teachers shifts from the delivery of information to fostering students’ engagement with ideas. Instead of covering the curriculum and judging our success by how much content we get through, we must learn to identify the key concepts with which we want our students to engage, struggle, questions, explore, and ultimately build understanding. When there is something important and worthwhile to think about and a reason to think deeply, our students experience the kind of learning that has a lasting impact and powerful influence not only in the short term but also in the long haul. They not only learn; they learn how to learn
  • In using facilitative questions, the teacher’s goal is to try and understand students’ thinking, to get inside their heads and make their thinking visible. Again, it is switching the paradigm of teaching from trying to transmit what is in our heads to our students and toward trying to get what is in students’ heads into our own so that we can provide responsive instruction that will advance learning
  • How can we make the invisible visible? Questioning; Modeling an Interest in Ideas; Constructing Understanding; Facilitating and Clarifying Thinking; Listening; Documenting
  • Culture of Thinking: places where a group’s collective as well as individual thinking is valued, visible, and actively promoted as part of the regular, day-to-day experience of all group members.
  • Thinking routines are procedures that provide framework for focusing attention on specific thinking moves that help build understanding.

 

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

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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.

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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

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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.)

Thinking Routines – Synthesizing and Organizing Ideas (part 1)

Routines for Synthesizing and Organizing Ideas (Chapter 5)

1) CSI: Color, Symbol, Image (Capturing the heart through metaphors) – Nonverbal routine that forces visual connections

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Although a hard sell for math content, I think it could be used as a way to get to know students at the beginning of the year. I could ask them to represent themselves with CSI and explain the reasons for their choices. This could be followed up with teaching them MicroLab routine (I’ll detail that tomorrow), which is a reflection and discussion strategy. If this were completed on the computer and printed, it could be a nice bulletin board (check out my example below). Another option would be to use this as a means for students to reflect about their own performance at the end of a term, or use it as a means to discover how and what they think about math or learning.

CSI Example

 

CSI Template to use at the beginning of the school year. CSI Template


2) Generate-Sort-Connect-Elaborate: Concept Maps (Uncovering and organizing prior knowledge to identify connections) – Highlights the thinking steps of making an effective concept map that both organizes and reveals one’s thinking. “This provides structure to the process of creating the concept map to foster more and better thinking.”

Visible10 This could be used at the beginning of a unit to reveal prior knowledge or at the end to bring all ideas together. This would be great for any unit with many different components (e.g., functions and trigonometry units in Pre-Calculus; angle and triangle units in Geometry; linear equations in Algebra 1). During the ‘Generate’ phase the teacher could give students post-its or note cards to encourage more discussion during the ‘Sort’ phase. After they independently generate ideas, they could share with a partner to gather more ideas. If this is a small group activity, the teacher should provide large chart paper to help with the ‘Sort’ phase. The sort phase has the potential of generating great conversations as they organize the note cards and explain the connections that they are making. An extension of the ‘Connect’ phase would be for students to write a description of the connection on the line that they draw. This routine could be adjusted into a a whole class activity by using the whiteboard to Sort and Connect.

I’ve wanted to have students create concept maps as homework, but I didn’t know how to support them in that process. I think this is a great structure that I’m excited to try! After we’ve used it in class and they are familiar with this routine, I’m going to try it as a homework assignment, then the next day we would create collective concept maps.


3) Connect-Extend-Challenge (Connection making, identifying new ideas, raising questions) – Key synthesis moves for dealing with new information in whatever form it might be presented: books, lecture, movie, and so on

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“Ideas and thoughts are dynamic, ever deepening and growing, and that’s a big part of learning is attending to the information we take in.” p.133

In some units this could be an ongoing class routine. After each exploration or activity we could do the ‘connect’ and ‘extend’ phases and create a unit list of connections. At the end of the unit we could revisit this list identifying common themes and important ideas that surfaced over the course of the unit. Teaching this routine would require a lot of modeling so students learn to produce strong connections. A lesson idea from the text is a sorting activity with examples of “OK Connections” and “Strong Connections”.

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Some sentence starters could be given to help students as they begin. A few examples, Connect – “This reminds me…”, Extend – “This added to my thinking because…” or “I used to think…Now I think…”, Challenge – “This makes me wonder…” or “This surprises me because…”

Once students are familiar with this routine, I think it could be used for homework. If using it for a homework assignment, I would add a component to start where they summarize what they learned in class that day, then Connect-Extend-Challenge.


**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 first 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.)

 

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

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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 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

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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.”

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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.)

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.

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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

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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

A Map of Thinking – Part 2

As I mentioned yesterday, I’m working my way through the book Making Thinking Visible by Ron Ritchhart, Mark Church and Karin Morrison.  Since the main objective of this strategy is to reveal what our students are thinking so that we can further their learning and dispel misconceptions, then it makes sense that we should first be very familiar with the types of thinking. The authors divided the types of thinking into two main lists based on the thinking goal. The first list is focused on thinking moves involved in understanding. The second list is focused on another group of goals, specifically solving problems, making decisions, and forming judgements. Because this is not a hierarchical list, I wanted to make a non-linear representation of these lists to help me wrap my mind around it and to refer to when I’m lesson planning. Below are a couple screen shots of the prezi that I created for the second list. The screen shots of the first prezi are on yesterday’s blog post.

As I was thinking about this list of thinking moves, I kept thinking about the Standards of Mathematical Practice. Has anyone thought about these connections or done any work to connect them?

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A Map of Thinking for Understanding

My thoughts on the book Making Thinking Visible by Ron Ritchhart, Mark Church and Karin Morrison. – continued

The questions – “What kinds of thinking do you value and want to promote in your classroom? What kinds of thinking does that lesson force the students to do?”

The challenge is posed to teachers – to step back and consider, what do I want the students doing mentally? What type(s) of thinking? When I ‘stepped back’, I wasn’t sure exactly what my choices were. I could flounder around a bit, throw out some ideas, but I wasn’t very happy about that. And neither were the authors. What they found is that teachers would often flounder (making me feel better), then ask if the answer was found within Bloom’s taxonomy. Well, it is and it isn’t. They worked to put together a couple of lists to make visible the forms, dimensions, and processes of thinking. They say time and again that these lists are not comprehensive and could be fleshed out further. But, these lists will help us determine the types of thinking that we are going to later work to make visible in our classrooms.

The lists are broken into two ‘Maps of Thinking’. The first is based on thinking moves to aid in understanding and the second to solve problems, make decisions, and form judgements. I was struck by this concept and wanted to wrap my head around these thinking moves. I also wanted to create some sort of document that I could have nearby as I’m lesson planning. Below is the document I created for the first list (link to the prezi below). The second document will come along soon.

Understanding Map

 

Understanding2

A Map of Thinking involved in Understanding Prezi

 

 

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’

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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

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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

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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.

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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)

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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

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