My plan:

- Math Maintenance on Mondays, Tuesdays, and Thursdays. This is a spiral review strategy from Kathryn at ‘i is a number’. I can tweak what I’ve used in the past to this more organized and deliberate method. (Thanks Kathryn!)
- We have a shortened schedule every Wednesday, which not only results in less instruction time, but also more rambunctious students. Therefore I need a Do Now that is engaging and thought-provoking. I’m going to project a photograph or video of math in the real world. I have a lot of these in relation to architecture from being a Fund for Teachers Fellow a few years back, so that will be a good place to start. I’ll use the ‘I Notice, I Wonder’ and Headline strategies, which encourage students to look closely, make observations, and promote curiosity.
- On Friday, I will incorporate Estimation 180 to build number sense skills and get students talking.

Monday through Thursday will be completed on this handout. On Friday, they will estimate in their notebook so they can track their progress week to week. I included an explanation of how I grade Do Now’s on the bottom of the handout as a reminder.

- Attendance – you are in your seat and started when the bell rings (1 pt)
- Effort – you work hard until the Do Now buzzer rings. (1 pt)
- Excused absence: complete missing problems for homework (1.5 pts.)

The Do Now is worth 2 points per day. There is occasional push-back about the attendance point, which they discover is non-negotiable. I don’t mind being tough on this because it gets students to my class on time. If they’re late there is no argument, just my best ‘I’m disappointed’ look and a point deduction.

Filed under: Teaching Math Tagged: Do Now, Estimation 180, Notice & Wonder, number sense, Planning, Routines ]]>

- 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.

** **

Filed under: Teaching Math Tagged: Making Thinking Visible ]]>

**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]

* **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 time

*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.)

Filed under: Teaching Math Tagged: Making Thinking Visible, PD Meetings, Pre-Calculus, Student Talk ]]>

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

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.”

*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.)

Filed under: Teaching Math Tagged: Homework, Making Thinking Visible, Planning ]]>

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.

Filed under: Teaching Math Tagged: Attendance, Homework, Interactive Student Notebook ]]>

The general layout: On Monday, I will give three assignments. I expect one assignment to be completed a night for these three days, but they can choose the order. These assignments will provide guided opportunities to reflect on their learning, make sense of their notes, introduce new content, and explore ideas that interest them. My hope is that the flexibility and choices will increase student engagement and promote personal control for their learning. For the Thursday and Friday assignments they will practice skills that they are ready to tackle independently.

**Assignment A**: Watch an assigned video about this week’s topic. There will be a written component to this assignment depending on the video. I’m not sure what exactly, but it will have an open-ended question and something factual (e.g., writing the examples).

**Assignment B**: ISN Reflection 1 – Students will choose from a list of thinking routines to make sense of the notes/examples that week. (I plan on creating an ISN page with a list of routines and strategies from which they can choose. Coming soon…)

**Assignment C:** ISN Reflection 2 – Students will choose from a different list of thinking or writing routines to make sense of the notes that week.

**Throwback Thursday**: On this assignment they will practice skills learned earlier in the year. My intention is to build their retention of the previous skills. I plan to include the relevant ISN page number to encourage them to use this resource if they get stuck. I want to include a self-assessment element to accompany each skill that will help us both see how they are feeling about that skill. In the first term I cover skills necessary for the state test in May, so I hope to build their confidence in these areas through repetition and increase the rigor as the year goes on. I will methodically choose these problems to ensure that I am rotating back through all the skills. I will collect and grade these assignments, record their progress and re-teach as necessary.

**Fundamental Friday**: This will be a set of problems from this week of work. I will deliberately choose problems that I have witnessed students complete accurately in class, but with which they need more practice. I will give a small weekly quiz on Wednesday, which will help me determine appropriate practice problems. My hope is that they will feel comfortable solving these independently at home and that I can move away from some of the major homework issues from before (read more here). My goal is to have the correct answers listed either on that handout or online, so they can monitor their progress and not repeat errors.

** ISN Logistics** – Assignments A,B,C and Fundamental Friday will all end up in their ISN. A,B & C will be on a tri-fold paper (see draft below). They will turn this in as they walk into the classroom and I will read/stamp/return during the Do Now activity. I will collect these on Thursday to record their scores and give feedback. On Friday, they will glue these into the next page open page of their notebook. They will complete their Fundamental Friday practice problems on the facing page and on the next page if needed. These pages will not be labeled with a page number, but rather as “HW”. This will keep all of our page numbers the same and allow flexibility for students that need more space. Throwback Thursday will be the only homework assignment that will not go into their notebook. They will have a folder that stays in the classroom that will house their assessments and Throwback Thursday assignments. I will allot time every Monday to answer questions for Thursday and Friday’s assignments.

All of this is a work in progress – I would love to hear your thoughts and suggestions!

Filed under: Teaching Math ]]>

*“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…

Filed under: Teaching Math Tagged: #eduread, Homework, Reflection ]]>

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.

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.

*from Fires in the Mind by Cushman

Filed under: Teaching Math Tagged: #eduread, Debra J. Pickering, Homework, Research Based, Robert Marzano ]]>

Filed under: Teaching Math Tagged: Reviews, Student Talk ]]>

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.I 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?

Filed under: Teaching Math Tagged: Anchor Charts, Do Now, Homework, Isosceles Triangles, Reviews, Student Talk ]]>