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


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


“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”.


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.)



Interactive Student Notebook Calendar



I wanted to create a calendar for our Interactive Student Notebook this year. This is going in the front of their notebook, and we will refer to it regularly. I wrote in our weekly quizzes which will help them to plan ahead, reduce the occurrence of the question, “We have a quiz today???”, and will also hold me accountable for giving weekly quizzes. I also included a little box on each page for a monthly report. My plan is for them to record their absences and averages by category here.

Here are my 3 big reasons/hopes for including this calendar:

1) Attendance – at our school we are working on decreasing student absences, which is a huge problem. I’ve found that my students often don’t realize how often they are absent and/or they don’t realize the impact of being absent once every week or so. There is also a really, really big problem with students arriving significantly late to school, which kills their performance in their first period class. I already make a connection when a student returns from an absence and when they come late to school. I’m going to follow that up by having them to record the absence/tardy in their calendar and reminding them to pick up their missing work. Also, at the end of the month, we will record their absences for the month in the monthly summary. My hope is that this visual reminder will help raise their awareness of the pattern and become powerful tool when discussing grades.

2) Homework – I’m going to have them record the points they earn for homework each day to help students recognize their patterns (both positive and negative). I will use this calendar as one resource when I have connect with students about their grades.

3) Planning – we used to provide planners for students but this was cut a number of years ago due to a reduced budget. Very few of my students use a calendar or planner of any sort. I want to start teaching them the soft skills of using a calendar to plan ahead.


ISN Calendar – Full Page


ISN Calendar – One Month

A Homework Philosophy

I often reflect on how I implement homework (post here), and I am consistently disappointed. Although I do change it up now and then, my go-to tactic is to assign a set of practice problems based on that day’s instruction. We don’t have enough textbooks to send home with students (I’m not a fan of our textbooks anyway, so the limited number doesn’t really matter), so I either create or search for decent handouts to give for homework. Some of the practice handouts I’ve created are pretty good – asking students to reflect on what they learned, describe processes using math language, identify errors and write directions, etc. Unfortunately creating high quality homework assignments like these is extremely time consuming, and realistically, there is not enough time to do that for every assignment. And even when I’ve assigned the most creative and relevant handout, I can, without a doubt, count on hearing these three things the next day:

  • “I didn’t do it.” For some students, it’s a matter of time, motivation, circumstances, or a host of other reasons. I find this concerning, but that’s an issue for another day. What is within my power are the students that didn’t understand the lesson well enough to complete the problems. They went home, stared at the paper for a few minutes then shoved it back in their bag. Or even worse, when they left class they already knew there was no point even trying because they didn’t get it. This is definitely an indicator of a poor homework choice on my part.
  • “I did it…but I think it’s all wrong.” I find this particularly troubling because they are usually right; it’s all wrong. They’ve just spent a solid chunk of time practicing an incorrect method and now they’ve really got it down! AHH!!! So now, I need to try to “un-teach” that error and “re-teach” the correct method. Again, this indicates a poor homework choice on my part.
  • “I did it and it was SO boring.” I honestly don’t hear this very often, but I know some students are thinking it. They mastered the skill on the first couple problems, and diligently continued through the rest without being challenged or learning anything new.

What I would love to hear is, “I’m glad we practiced that more. Now I really get it!” Wishful thinking? Maybe. However, I believe that I can get closer to this ideal, and I definitely need to move further and further away from what I normally hear. With all of this in mind, I’ve been thinking a lot about my homework philosophy. I’ve never really given this particular “philosophy” much thought before and now that I have, I foresee a dramatic shift come September. Hold onto your hats…

Actively Think and Reflect about Math

Holy cow! Crazy, right? Stick with me…it seems so obvious but up until now my ideas about homework were very narrow. What I wanted was for my students to practice what we did that day or practice a host of things before a test. Practicing is part of it, for sure. However, to ACTIVELY think is what I really want. And, too often (see reasons above), the level of mental activity when completing practice problems is super low. And there are so many amazing ways to promote active and engaged thinking that could zest up the routine and connect with different learning styles! With this adjustment, I can implement some of the thinking routines (from Making Thinking Visible posts one, two, three, four) to help my students make sense of the content (bonus points for teaching great thinking tools for all content areas). In addition, homework assignments can become lessons in how to study on their own (make a set of flashcards, rewrite notes in a more concise way, other creative stuff that I haven’t thought of yet).

Reflection is also a key component to learning. If I can teach my students in class and through homework assignments to thoughtfully look back to that day’s lesson and make connections to previous concepts, this could be huge for their retention and engagement. Because we use Interactive Student Notebooks (ISN), I think the reflection piece can easily be woven into the routine. In class when we reach a question about a previous topic, I direct them to their notebooks; they search for the page, read and find an answer. In the past, I regularly told them to use their notebooks to study and help them on their homework, some did and some didn’t. So although this became part of our classroom routine, it didn’t translate into a homework routine. Homework assignments that require them to use their ISN to refer back to that day’s lesson will teach them to reflect on what they’ve learned and can extend this learning as well.

If asked before this summer, I would have ended the phrase differently – analyze and reflect about the day’s lesson. However, as I’ve read and thought more about homework, I think this is too narrow (again). Don’t get me wrong, I do want them to think about the day’s lesson, but I also want my students thinking about math in general. I want them to see math in the world around them, to problem solve, to notice patterns, to explore mathematical ideas that they find interesting, etc, etc, etc. So that’s why opened it up to actively think and reflect about math.

In tomorrow’s post, I will detail my budding plan

#EduRead: The Case For and Against Homework

I stumbled upon the blog “Read…Chat…Reflect…Learn…” and the #eduread article from June 18 “The Case For and Against Homework” by Robert Marzano and Debra J. Pickering. I read the article, the discussion tweets, and few other blog posts, which gave me a lot of rich material to consider! I’ve been thinking about the how’s and why’s of homework for years, and for the first time I’ve been able to dedicate some uninterrupted time and thought to it, and I think I’ve reached a few conclusions. (This will probably translate into a series of homework blog posts – one and two.)

Before I add in my two-cents, below are a few quotes that stuck with me from the article:

  • Homework has decades of research supporting its effective use.
  • Cooper and colleagues’ (2006) comparison of homework with no homework indicates that the average student in a class in which appropriate homework was assigned would score 23 percentile points higher on tests of the knowledge addressed in that class than the average student in a class in which homework was not assigned.
  • Perhaps the most important advantage of homework is that it can enhance achievement by extending learning beyond the school day…. The study found that “students abroad are required to work on demanding subject matter at least twice as long” as are U.S. students (National Education Commission on Time and Learning, 1994, p. 25).
  •  Certainly, inappropriate homework may produce little or no benefit—it may even decrease student achievement.

Although I’ve never toyed with the idea of not assigning homework, the research presented in this article made me even more convinced of its weight. It’s so important to keep our students thinking after the school day ends, both for the good of the individual (building their mental muscles) and the community. Yet to ensure our students are actually thinking after school, we need to be deliberate in choosing appropriate and effective homework assignments.

Research Based Homework Guidelines -Marzano & Pickering

I found two lists to help teachers in this process in a number of different articles and blogs. The first list is from a section of the “Research Based Homework Guidelines” by Marzano & Pickering. The other is from the book Fires in the Mind, “Four R’s of Deliberate Homework” by Cushman. Each contains four key components, the first three from both lists overlapped, but the fourth components differed. I grouped the first three pairs together below to preserve the wording in case one speaks to you more than the other. Then I listed the fourth components separately. Note – I identified Marzano & Pickering’s list with a “+” and blue text. Cushman’s list is identified by a “*” and red text.

1) Introducing new content + Readying themselves for new learning *
I played with this a little over the last few years by ‘flipping’ the classroom and assigning online videos and activities for a week here and there. I fell back into old habits and didn’t stick with this even though it worked pretty well. I found that some students that previously did not do any homework loved this and completed it every day. It was also good for my English Language Learners because they could re-watch a video if they had difficulty with the language. I’m sure there are means other than online videos, but I can’t think of any right now. Ideas?

2) Practicing a skill or process that students can do independently but not fluently + Repetition and application of knowledge and skills *
This has been my go-to method although I didn’t apply an essential piece: they need to be able to do the work independently. Some could, some couldn’t. I’m sold on committing to ensuring that they are ready to practice independently before I send these assignments home. This will definitely be a big adjustment for me, but so very important!

3) Elaborating on information that has been addressed in class to deepen students’ knowledge + Reviewing material learned earlier *

This brings to mind one type of problem that I give regularly (and seemed to make a big difference). I ask students to identify the error is a worked example, then explain how to complete the problem correctly. Any other ideas?

4a) Providing opportunities for students to explore topics of their own interest +
Now this is not something I’ve ever done. I’m wondering if I could find a way to implement this component as a long-term homework assignment. Has anyone tried this?

4b) Revising their work *
I’m not in total agreement with this for math homework. At least in regards to quizzes and tests, I’ve found that when a student has a mistake that student needs teacher-support to ensure accurate revisions of this work. I suppose if the student received enough support and/or feedback in class to address their mistakes, then homework revisions could be a possibility.

Homework-Alternatives*from Fires in the Mind by Cushman


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?

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! =)