The final countdown…

Today is our final working group session, as we’ll be sharing our working group products (this blog) tomorrow. Today was also our final small group Reflection of Practice session, and tomorrow we’ll be doing a whole group wrap up. 3 weeks really goes fast!

Over the last two days, we spent time reflecting on Peter’s presentation. A few interesting thoughts came out of it:

  • During group work, the teacher has limited interactions with the students aside from questions to manage flow or correct cruel behavior. Ideally, a teacher is not even correcting off task behavior (because flow is being managed by interesting problems).
  • Meaningful notes resonated strongly with us.
  • We feel like this system would be hard to implement daily, especially at the start.
  • As we are all teachers in the U.S. in the room, we’re wondering the balance between oral instructions and group work and the common core emphasis on literacy and individualized testing.
    • It was shared with us that the goal of a thinking classroom is not to spend the entire time doing small group work, but there is a chance for students to go back to their seats and work on a handful of check for understanding questions independently, which was not made fully evident during our discussion. Dylan shared this document on Twitter later in the evening which addressed a lot of the questions we have around this.

Another interesting “Aha!” moment is that while there is a lot of research behind thinking classrooms, not everything has been proven through research (yet).

After reflecting, we did a small group activity with the following problem:

You have a 5×5 board which has 5 coyotes and 3 sheep. The coyotes can move like Queens on a chessboard, which is apparently not like this:

Image result for queen waving gif

The goal of the game is to place each coyote and sheep in such a way so that after one move, ALL sheep will be safe. In groups, we worked through this problem. After about 10 minutes, we came back together to share out “What’s hard about this problem,” and then we spun the room, with one group member moving to the left and one group member moving to the right. We continued working on the problem for a few more minutes, with no groups figuring out a solution yet (for reference, it’s apparently searchable).

We wrapped up the conversation today, and were charged with thinking about the following prompt:

How do we create an environment where challenge is not merely accepted, but expected?

After we spoke about this for a few moments, we were presented with the following quotation from Lajos Posa:

At a certain point students realize the joy of struggle, thinking with their own brains, what it means to look for a road, find it, and reach the goal. What it is like to think freely, with the hazard of getting lost, but with the possibility of the unusual, individual, surprising.

Our very own Robin shared a perfect analogy afterwards. My loose paraphrase is as follows: It’s kind of like walking on a treadmill in hill mode or hiking. In both, you’re walking and getting a workout, but hiking allows for the potential of the unusual and surprise.

With that statement, we transitioned our thinking to assessments in the classroom, discussing three categories of assessments:

  • Isomorphic: What most of us already do (teaching to the test with a focus on individual learning)
  • 2 part tests: Students take an individual mixed question test (short response with justification, 5 open ended questions and 2 extended responses). The next day, students take 30 minutes in a group to re-do slightly modified versions 2 conceptual multiple choice questions, 2 open ended questions and one extended response questions. Students final grade is an average of 75% of their individual test and 25% of their group test, assuming the group test grade is higher than their independent grade.
  • Pre/Post test: A teacher gives a test at the start of the unit, and again at the end of the unit. The test grade is then a measure of how much growth the student shows.

We had a lot of different thoughts about these assessments, and how they can help to show understanding as well as where they may falter (time consuming, not showing all student’s thinking accurately, understanding the implementation, etc).

After talking about the categories of assessment, we spent some time thinking about different types of assessments, which provided a different definition versus what I’m used to using:

  • Formative assessment: formative assessment should be focused primarily on informing students about where they are and where they’re going in their learning. This will require a number of different activities, from observation to check-your-understanding questions to unmarked quizzes where the teacher helps students decode their demonstrated understandings.
  • Summative assessment: Summative assessment should focus more on the processes of learning than on the products, and should include the evaluation of both group and individual work. Summative assessment should not in any way have a focus on ranking students.
  • Reporting out:  Reporting out of students’ performance should be based not on the counting of points but on the analysis of the data collected for each student within a reporting cycle. The data need to be analyzed on a differentiated basis and focused on discerning the learning a student has demonstrated.

Again, this led me to a few more questions than it did answers, as the processes for implementing these philosophies were not made abundantly clear. It does open up an opportunity to re-consider my assessments and figure out how to find the balance between figuring out what students know and meeting all of the additional institutional norms within my class, school and district.

How do you use assessments in your classroom to ensure you have evidence of learning? 


Note: This will likely be the last post for a bit on here until we’ve had a chance to digest everything we’ve learned and start implementing the practices in our classrooms. We’ll likely have posts throughout the school year, both about what we’ve learned through implementing these practices as well as dispelling our learnings through other channels and professional learning communities.



Thinking Classrooms with Peter Liljedahl

Today at RoP we had the pleasure of Peter Liljedahl coming in and facilitating a thinking classroom.

The session started with Peter asking each of us to come pick a playing card, and then stay close to him. After everyone had a card, he told us a story (verbally) about two containers. The larger container was mostly full of water, 20 inches tall and 12 inches wide. The smaller container was empty, 18 inches tall and 10 inches wide. As the smaller container enters the larger container, water fills in to the smaller container. The question, then, is how much water is in the smaller container at the end? Once he posed this question, he sent us on to our groups based on our playing cards to think about the program on our vertical surfaces, one marker per group. Roughly 40 minutes later, we came back together and Peter asked us several additional whole group questions, with time to discuss with the people nearest to us. Peter modeled several teacher moves throughout this process; my group kept hearing about Peter checking in with others and realized he did not speak to us the entire time (though, he most likely checked in – we were so wrapped up in problem solving that we didn’t notice).

Peter then had us sit down and took us through the research he did to develop these routines. About 15 years ago, Peter observed a classroom, and noticed that students were not thinking, and the teacher was planning her teaching on the assumption that students wither would not or could not think. “Everywhere I went, I saw the same sort of behavior,” he told us; students in rows, the teacher at the center of the classroom doing the thinking. The classrooms he went to, visiting across all different types and grade levels of schools, looked more alike than they did different, as they all followed the institutional norm, which he described as a non-negotiated norm.

To help make the move to thinking classrooms, Peter and his team created 2 week action research cycles in over 40 classrooms over a 13 year period, aimed to break down those non-negotiated norms and increase student thinking. As a result, Peter categorized 14 opportunities for student thinking along with the optimal practices:

Opportunities for Thinking [Optimal Practices for Thinking]

  1. Problems [Begin lessons with good problems]
  2. How we give the problem [Use verbal instructions]
  3. How we answer questions [Answer only keeping thinking questions]
  4. Room organization [Defront the classroom]
  5. How groups are formed [Form visibly random groups]
  6. Student work space [Use vertical non-permanent surfaces]
  7. Autonomy [Foster autonomous actions]
  8. How we give notes [Have students do meaningful notes]
  9. What homework looks like [Use check your understanding questions]
  10. Hints and extensions [Manage flow]
  11. How we consolidate [Consolidate from the bottom]
  12. Formative assessment [Show where they are and where they are going]
  13. Summative assessment [Evaluate what you value]
  14.  Reporting out [Report out based on data (not points)]

Peter suggested that if we use thinking classrooms, we minimize learned helplessness, which we as teachers help promote by answering all of our students’ questions and robbing students of autonomy.

Of course, when reading 14 idea shifts, it’s good to have a starting point, and Peter has found through his research which order of moves makes the most impact in the first year:

First: Start with good problems, form visibly random groups, and use vertical non-permanent surfaces.

Second: Use verbal instructions, defront the classroom, answer only keep thinking questions, use meaningful notes, and foster autonomous actions.

Third (where the learning really happens):Use hints and extensions to manage flow, consolidate from the bottom, assign check your understanding questions. 

Fourth: Communicate where students are and where they are going, evaluate what you value, and report out based on data.

After sharing this high level overview, Peter took some time to answer questions. One of the areas he focused on that I found of particular interest was his idea of meaningful notes. He showed this visual, which makes me rethink all of the note taking I ask students to do:


He suggests, instead to give students time in class to jot down the key ideas that students are writing for their own, future, dumber self. He also referenced Laura Wheeler’s course packs for her classroom, which are 5 double sided sheets of paper with a box for each key term/skill a student needs to know by the end of the year; students receive their note catcher at the beginning of the year and then fill it out throughout the course. Students are asked to write down notes they find meaningful based on the work done during the class period, and have a few moments at the end of classes to fill in their notes as they best see fit based on the work they’ve done. It’s certainly an interesting idea that I’d be willing to try (also to help minimize paper usage in my classroom!!).

Have you implemented practices from thinking classrooms? What’s your best advice beyond what Peter has shared? 

N.B.: a more detailed description of this post can be found on Peter’s website under any of the “Building Thinking Classrooms” presentation links here (his presentation from today was not up yet).


Encouraging Student Listening

Talking Points

(If you haven’t heard of the Talking Points activity yet, Cheesemonkey gives a great breakdown here.)

I’ve used Talking Points at the beginning of the year before to uncover student learning mindsets and to hear a little about their predispositions for math. Here are the Talking Points I used:

  1. When working together on math, if one person knows what to do, they should let other group members try first.
  2. Being good at math means being able to do math problems quickly.
  3. Getting a problem wrong means you’ve failed.
  4. A person is either good at math or bad at math.
  5. Drawing a picture is always helpful when doing math.
  6. Math is easier to learn when it involves the real world.
  7. There is always one best way to do math.

While these conversations were good to hear, I thought they did little to build on students’ current thinking. They felt a lot more like me, throwing statements (that I felt had obvious answers) out to my students, and waiting for them to come to what I felt were the correct conclusions. I think my students must also have felt there were correct answers and were just saying what I wanted to hear. In short, it felt artificial.

While combing MTBoS this week, I uncovered that Brian Miller uses the Talking Points protocol differently. He uses them to develop a classroom culture of listening. His Talking Points are:

  1. It’s impossible for other people to tell if you are listening.*
  2. Talking is more important than listening.
  3. Group activity can be good for learning.
  4. Listening and thinking are different things.
  5. Learning to listen and collaborate well with other people is important.
  6. If you think someone is wrong about something, it is more important to tell them right away than to listen to their reasoning.
  7. Everyone can learn to be part of a learning conversation.

*This one is his favorite. Mine too!

But I think one of the reasons Miller’s Talking Points activity seems less artificial is in his whole class reflection after the activity. He asks his classes,

Do you feel like you were being listened to? Why?


Were you listening to others? Do you think they knew you were listening?

In his words, “the conclusion at the end is that just listening is not enough.” These reflection questions urge his students to convert the thoughts on listening they just discussed and turn them into actions that will enhance their classroom community. Reviewing the Talking Points that I’ve used, I wonder what reflection questions I can ask about them to achieve a similar outcome!

Students Summarizing Students

From Research in Practice,

This summer, when I or a student put forth an idea, I regularly followed it with, “who can summarize what so-and-so said?” Or (even better), “so-and-so, can you summarize what so-and-so just said?” Following the models of Lucy West and Deborah Ball, I carefully distinguished summary from evaluation. “Not whether you buy it, just the idea itself.” When dipsticking the room on an idea, I would also make this distinction. “Raise your hand if you feel that you understand what was just said; not that you buy it, just that you understand what they’re trying to say.” Then, “leave your hand up if you also buy it.”

Two weeks ago, I wrote about using language that supports students seeing the class as a learning community. One way to do that is to frame classroom discussions as ways to build consensus. Moreover, looking at discussions this way encourages students to construct viable arguments and critique the reasoning of others.

I love this idea of asking students to summarize one another and am looking forward to implementing it more in my classroom this year. I’ve lived with a secret fear that students who are paying attention to the class discussion will find the summaries repetitive. (I find it hard to distinguish between my preferences as a learner and best practices for students when I’m the teacher.) Happily, Kelly O’Shea reminded me of the importance of not falling into The Right Thing, Said Once trap.

Do you wish your classroom was more like a community?

Building a strong community is something I like to have in my classroom. I have given some suggestions from a PD, PCMI, research, and activities I have done in my own classroom to help give you some ideas of different things you could try in your classroom.

Group work is a great way for students to learn from each other and builds community in the classroom. I will list different types of activities you can use in your classroom to build a strong community.

Let start with quick and easy ways to build a strong classroom community.

  • Plan get-to-know you activities the first week or two of school
  • Work as a class to create classroom norms or expectations
  • Conduct a beginning greeting (should only last a couple of minutes)
  • Random seating – have students sit by different students each week or bi-weekly
  • Have students sit and work in groups, so they can work cooperatively.
  • In groups assign students different jobs and rotate these jobs.
  • Periodically invite students to eat lunch with you.
  • Print off “Math About You” posters (I have attached a copy of the one I use)

In my classroom, I have done many of the ways listed above and they really do help to get students talking to each other and help them feel as a community. I really want to have better systematic random seating and groups. During PCMI Reflection on Practices, we have used random seating by picking a playing card. How this works is the suit of the card tells us where to sit and the number represents the vertical non-permit wall groups we work in; I like this ideas because it it truly random. I am excited to try this and blog later how it works.

Through a previous PD from Dr. Sharroky Hollie and his book Culturally and Linguistically Responsive Teaching and Learning, I have listed his suggestions and activities for building a strong classroom community. I have used some of these in my classroom and they do help build a community in my classroom. I want to incorporate more of them and incorporate things I have learned from PCMI.

Design Culturally Responsive Classroom using these five ways; which helps build a strong community in your classroom.

  1. Know your students well – academically, socially, and emotionally. Learn about their families, culture, and interests. Go to an event (sporting, band concert, choir,etc.) they participate in and cheer them on. You would be surprised how excited they are to see you and it shows them you really care.
  2. No matter the subject matter build on your students’ life experiences – Current or real-world problems helps students make good connections with the curriculum and they will care more about what they are studying.
  3. Create a classroom learning community – Help students feel safe and comfortable in your classroom with not only you but also with their peers.
  4. Have high expectations for all students – Incorporate Growth Mindset and help your students feel competent and developing.
  5. Understand your own culture identity – reflect on how your handle discipline and classroom management. Show our students that you are caring, honest, and human.

Culturally Responsive Classroom Activities

Let Me Hear You – Students actively respond in unison to speaker either verbally or with movement (or both) to either an improvised or pre-taught “call”

Pick-a-stick After the teacher poses a question, students think about the answer silently. After sufficient thought time, the teacher picks from a group of sticks that represent each student.

Roll ‘Em – Students are divided in groups of 4-6. Students think about a posed question as the teacher rolls two number cubes. One number cube represents the table/group number and the other number cube represents the seat number. The student sitting in the seat represented by the rolled number cube answers the question. Rolling of the number cube can continue until a sufficient number of answers are heard.

My Turn, Your Turn – This turn-taking protocol is utilized in several protocols for participation and discussion. It is an explicit way of indicating when “jumping in” is not appropriate and reminds students that their turn to talk and ask questions will follow soon.

Give a Shout Out – Students softly shout out responses all the same time. The teacher can record shout-outs on the board, if appropriate. Posed questions can require either one correct answer or a variety of short answers.

Moment of Silence – This is an explicit time for total silence, including on the part of the teacher.

Train or Pass It On – Students call on one another to answer and/or ask questions. Students should not raise their hands to be called on and should be encourages to call on a variety of people in the classroom. Students can also “pass” on a question they do not want to answer by calling on another student for help. This is called “pass it on,” (they must repeat the answer).

Raise a Righteous Hand – Students raise a hand/fist to volunteer information that is specific to their experiences.

Whip-Around – Each student in the room takes a turn responding with quick answers to a posed question. The order should be based on seating in order for the teacher to avoid having to constantly facilitate the direction of the students answering. This should go very quickly around the room, so the question needs to be appropriately precise as well.

Numbered Heads Together – Students are divided in groups of 4-6 and numbered. When asked a question, they work together to find the best answer. When called together again, the teacher rolls a number cube and asks the students from each group with the number rolled to stand. Each student then represents the group and reports its answer.

Think Pair Share – This involves a three-step cooperative structure. During the first step, students think silently about a question posed by the teacher. Individuals then pair up during the second step and exchange thoughts. In the third step, the pairs share their responses with other pairs or the entire group. It is usually a good idea to have the individuals asked to share with the whole group to explain what their partner said in order to promote good listening skills.

Merry-Go-Round – Each student takes a quick turn sharing with the team a thought or reaction to something posed by the teacher. Responses should be quick 1-5 word phrases in order to keep it going quickly and keep thoughts concise.

Put Your Two Cents In – Each student has two cowry shells in use as talking pieces. In groups of four, each student takes a turn by putting one cowry shell in the center of the table and sharing his or her idea. When everyone has shared once, each student then puts one more cowry shell in at a time and responds to what someone else in the group has shared. (I agree with….. because ……. or I disagree with …… because ….. )

Circle the Sage – The teacher polls the class to see which students have special knowledge to share. Then, those students (the sages) stand and spread out in the room. The teacher then has the rest of the classmates go to one of the sages, with not work members of the same team going to the same ages. The sage explains what he is=or sheknows while the classmates listen, ask questions and take notes. All students then return to their teams. Each in turn explains what he or she learned. Because most have gone to different sages they compare notes. If there is a disagreement, they stand up as a team. Finally the disagreements are aired and resolved.

Give One Get One – After thinking or journaling about a topic, students are asked to get up and find someone across the room with whom to share their thoughts or answers. STudents are thus receiving an idea in exchange for giving one.

Three-Step Interview – Each member of a team chooses another member to be a partner. During the first step, individual interview their partners by asking clarifying or interview question. During the second step, partners reverse the roles. For the final step, members share their partner’s response with the team.

Jigsaw – Groups of 4-5 students are established. Each group member is assigned some unique material to learn and then teach to his or her group members. To help in the learning, students across the class focusing on the same material get together to decide what is important and how to teach it. After practice in these “expert” groups, the original groups reform and students teach one another. Tests or assessments can follow.

Team-Pair-Solo – Students do problems first as a team, then with a partner, and finally on their own.

Partners – The class is divided into teams of four. Half of each team is given an assignment to master to be able to teach the other half. Partners studying the same material go to one side of the room and consult with one another about the material and how to best teach it to the other half of their team. Teams then go back together, with each set of partners teaching the other set. Partners quiz and tutor their teammates. The team reviews how will they learned and taught and how they might improve the process.

Corners – Each student moves to a corner of the room that represents a teacher-determined alternative or point on a scale. Students discuss their choices in their own corner and then listen to and paraphrase or debate ideas and opinions from other corners.

Send-a-Problem – Each student writes a review problem on a flash card and asks teammates to answer or solve it. Review questions are passed to another group to be answered.

Silent Appointment – After the teacher poses a problem/question to be discussed, students make “silent appointments” with each other by making eye contact and nodding to indicate that an appointment has been made. Students then go to their appointments and share. The teacher should then review with the whole class by asking what students heard that was shared by others.

Musical Share – This is similar to Give One, Get One. The teacher poses a question and turns on music. Students move/dance around the classroom until the music is turned off. Students discuss the question with whomever they are closest to when the music is turned off. The teacher resumes music and the process continues until they have had enough opportunities to share.

Roundtable – Each team uses a single sheet of paper and pencil and, in turn, responds to a question or problem by stating their ideas aloud as they write them on the paper. The paper is then passed around the table until time is called. Team members are encouraged not to skip turns, but if their thoughts are at a standstill, they are allowed to say “Pass” rather than turn the brainstorm into a brain drizzle. Thus, there is almost universal participation in Roundtable.

Inner-Outer Circle – There should be two circles, with the outer-circle students facing inward and the inner circle students facing outwards. Students in the outer circle begin by asking the student facing them on the inner circle a question. The questions may be prepared by either the students themselves or the teacher. Once the inner-circle student has had an opportunity to answer, either the outer or inner circle rotates and the process is repeated until a full rotation is made. Then, the inner circle has the opportunity to ask questions as the outer circle responds, and so forth.

Round-Robin Brainstorming – One person in each team is appointed as the recorder. An open-ended question is posed and students are given time to think about answers. After the think time, members of the team share responses with one another round-robin style. the recorder writes down the answers of the group members. The person next to the recorder starts, and each person in the group gives an answer in order until time is called. A person may “pass” if needed, and provide input on the next rotation after he or she has had time to think.

Great and Respond/Tea Party – Provide each student with an unfinished sentence, question, or prompt to which a response can be made> As the teacher calls out or displays particular settings/situations, students walk around and use appropriate greetings to greet each other, read their prompts, and respond to each other in turn.

If you have used any of these or want to add anything you have used to build a strong community in your classroom; please comment.


Accountability, Day 2

After a nice weekend break, we continued our delve into accountability. On Friday, we focused on the tenet that everyone participates, and today we shifted gears to the second tenet of “listening matters.” In thinking about accountability, Horn suggests that this goes beyond assignments, but is a list of norms, or acceptable ways students are acting in a classroom in order to fulfill their obligation to learn, which ties very closely to active listening.

To model active listen, we completed a few activities in small groups.

First, we were given a set of graphs (based on the NY Times column What’s Going On in This Graph) and asked to write a short paragraph entailing the context, theme, our interpretation, and questions that were raised for us while including at least four data points of the graphs we chose. After we wrote our anonymous paragraphs on graphs ranging from categorizing Denzel Washington films, to what Americans versus nutritionists consider to be healthy, to the value of each World Cup’s team’s bench and starters, we were asked to switch papers with another table to give feedback. Each participant received the paragraph of another participant who focused on the same graph, and we used the following sentence stems to help craft our two pieces of feedback:

  • The work addresses blank in a way that is understandable and makes sense because…
  • The description might have more details or clarification, such as….
  • The work uses appropriate statistical language, for example…
  • I am a bit confused about…

After receiving our feedback (at this point in a classroom, the goal would be to have students implement the feedback), we had a round robin discussion about how peer feedback can help to increase accountability. Some ideas that came out of my room included liking the use of sentence starters to help students provide feedback, providing a venue for students to write down their thinking, allowing students to be in conversation with the work, having a shared experience with others in the classroom through written work and feedback, and the ability to call out strong student written feedback to continue helping students craft this skill. Some concerns that were brought up include students may feel anxious about individual writing and feedback (so an alternative could be poster feedback or a gallery walk) and thinking about what students will do with the feedback (revisiting what we discussed last week).

During the discussion, I was thinking this might be a great routine to utilize in my classroom when we work on our bulletin board projects. At my school, I need to have roughly 9 pieces of typed student work across three different tasks or questions. Student work is graded on a problem solving rubric, and all work that scores above an average of 3 is posted in the hallway. I’d love to implement this routine, allowing students to create a first draft and then receive feedback from their classmates who are working on the same task. My hope is then all students would be able to strengthen their answers from the feedback and see additional ways of thinking, forcing me to make tough decisions about which pieces to hang!

The next strategy we looked at is Peter Liljedahl’s “Smudged Math” routine (which Dylan talks about in more depth here), which is very similar to the “Bleep” routine I’ve seen Kara Imm of Math in the City present (more on that in a bit). In this activity, we were presented with problems with some numbers missing, forcing us to think critically. These problems lower the floor, allowing all students an entry point, but have a high ceiling in that multiple extension questions can be asked. After we each had a few individual moments to look through a series of smudged problems, we used visibly random grouping to share our thinking at the VNPS boards. Before going up to the board, we were tasked with reporting back an idea we heard from another presenter to our home groups. Most people felt like this activity would help to address all of the components of accountability, in that the smudging allows for all students to participate (low floor), forces us to play the role of listener as we need to report back (listening matters), and has us keep our conversation focused on the mathematical concepts as we were explaining our problem solving approach and potential extension questions.

Tying back to the idea of strengthening my bulletin board projects, I actually used the “Bleep” strategy to complete a mixed review project, which filtered in to the boards. For each of the three tasks, I displayed a math problem students had seen before winter break with the numbers bleeped out. We read the problems out loud as a class, and said “bleep” for every unknown. I then asked students to jot down what they noticed and wondered about each problem (beyond the missing values), and then create a strategy to solve the problem that would work no matter what values we had. Students then chose which problem they wanted to explore more, which became their piece. Selfishly, I made each of the questions about my pup and the school comfort dog, Buttons, and used it as a way to put lots of pictures of him up on my bulletin board.


We ended the session with an independent reflection, focusing on two of the questions at the end of the Accountability chapter in Horn’s book. We invite you to consider your own classroom as well:

  • What gaps exist between what you say you value and what your students do in your classroom?
  • What structures or routines can you incorporate that might help you teach your students new ways of being in math?





Day 9: Accountability

Today we did our last RoP group switch (only one full week left here – time certainly flies)! In switching we groups, we also switched to our last tenet that we’ll explore from “Motivated,” which is accountability.

In Horn’s book, she defines accountability as follows:

Accountability refers to the structures and routines that oblige students to report, explain, or justify their activities. Often reduced simply to assessment, accountability goes beyond how we grade to encompass the routines and norms that enjoin students to participate in particular ways in classroom life. When students feel a sense of investment in and accountability to their classmates, for example, this changes the risk-benefit calculus, leveraging positive peer pressure to increase participation.

As teachers, one of our goals is to make students feel like they are part of a community and are also accountable for their own learning.

Ideally, if you were to enter a math classroom, you would hope to observe:

  1. Every student participating in the task
  2. Students actively listening to each other
  3. Focused conversation on mathematical ideas

In order to help build these characteristics, we observed several routines that we can take back to our own room in order to build accountability.

To start, we were provided with a set of student work contain errors, and a protocol students were asked to follow:

  1. Read each piece of sample student work carefully.
  2. Try to understand what they have done. You may want to add annotations to the work to make it easier to follow.
  3. Think about how the work could be improved. Take turns explaining your thinking to your partner.
  4. Listen carefully and ask clarifying questions.
  5. When your group has reached its conclusions, write your answers to the questions [on the bottom of the paper].

After taking some time to read through the procedure and look through the sample work, we watched this video on Teaching Channel. We liked how students were focused on the mathematical process of the work, as well as the organization and process of their classmates (being able to identify these elements can help to build competencies for students), and thought there was the ability to create a safer space for risk taking for some students. It was mentioned by at least two groups, however, that there was a clear gender dynamic amongst the group focused in the video, and the girl did not have many opportunities to be heard. Perhaps prior to starting an open discussion, the teacher could have set up a round robin protocol to ensure all voices are heard, pushing the routine to ensure that everyone participates.

The second routine we tried was entitled “Whose solution is the best and why?” and focuses on the work that Chris Luzniak has done with claims and warrants. We were provided with 4 sets of correct student work and debate with our group using the following sentence starter: “My CLAIM is _________ and my WARRANT is _______.” At our table of 6, each participant chose a different student work as the best work and gave supporting reasons, which made others re-consider their answers after the fact. Once we debriefed, we watched this video of Luzniak’s procedure in action. One participant, Paul, mentioned that there is another element to the procedure that we didn’t use, in that students stand up to share their claim, and then the next student summarizes the previous claim before sharing their own. Amy mentioned that ongoing research has suggested that standing up and having debates increases participation and learning. Josie connected this technique to cross curricular techniques of providing a claim with evidence and reasoning, which is one way to modify this routine. Jake mentioned from his previous student teaching work with Luzniak that the format comes from debate format, and Kristen shared a reference from when she saw a mini course at MfA: the argument is a statement made with sound reasoning, which is comprised of two parts – the claim (the controversial statement being made) and the warrant (the justification for the claim). At our table, Sean suggested that adding an additional layer to the mix would be for a group discussion to occur and have a reporter share a peer’s claim and warrant (versus the student who developed the argument).

Our last routine for increasing student participation was completing a number talk, which actually became an algebra number string. In this instance, we were asked to solve a system of equations in our head and then share our strategies. One teacher move that I’m going to take back home with me is the idea of holding up the number of fingers for the number of ways you have figured out how to solve the problem, versus simply holding a thumbs/hand up once you have your method. As people shared their method, they were scribed on the board and became great references to refer back to as the level of difficulty in solving the problems increased.

As someone who consistently gets feedback during observations on increasing questioning and discussion, I’m happy to add these routines to my tool kit. Of course, in order to do this I’ll need to ensure the questions I ask my students allow for multiple ways of thinking and representations.

How do you encouraging participation and discussion within your classroom? What routines work best for you and how do you roll them out?



How to Help Students with Test Anxiety

How do we help our students with test anxiety?

What is test anxiety? The Anxiety and Depression Association of America (ADAA) defines test anxiety as an extreme nervousness about taking a test and categories it as a type of performance anxiety. This is a serious problem with students in school. However, as teachers we can help students with this type of performance anxiety. Before teachers can help students, we need to know why students have test anxiety and the symptoms.

According to ADAA.

The main causes of test anxiety:

  • Fear of failure
  • Lack of preparation
  • Poor test history

In my classroom, I have seen all of these play a part in test anxiety. All of my students want to be successful even if they say they do not care or want to do well. The lack of preparation, usually out of their control, most of my student’s home life is very difficult and they have to either work, watch small siblings, or sometimes even take care of their parents (due to illness, drug use, etc.). And the lack of preparation during class time is usually caused by poor math classroom experience and poor test history. This is where it is important for me to help struggling students as much as possible while they are in class, so they will be prepared for the test or quiz. I also try not to put too much emphasis on quizzes or tests. This week we have seen a way one teacher tries to help test anxiety by not grading students tests, but highlight where they made a mistake. I really like this idea, because it will cut back on the stress of “the grade” and focus more on positive feedback, what error did I make, and how can I fix it. I am very excited to try this technique in my classroom this coming year. If you have done this, please share your experience.

Have you ever wondered why a particular student always needs to go to the nurse or the bathroom before you hand them their test? This is a symptoms of test anxiety. Below are more symptoms:

  1. Physical symptoms – This includes headaches, nausea, diarrhea, excessive sweating, shortness of breath, rapid heartbeat, lightheadedness, and feeling faint. More serious cases include panic attacks.
  2. Emotional symptoms – Which includes feelings of anger, fear, helplessness and disappointment.
  3. Behavioral/Cognitive symptoms – Difficulty concentrating, thinking negatively, and comparing yourself to others.

Some ways I try to decrease test anxiety is by having a plan of letting students take their test in a smaller environment, even if they do not have accommodations. I also have students sit alone at a desk by themselves, so they do not have to worry about the person beside them. Before I pass out the test/quizzes I remind students that the test is not worth much compared to all the work they will be doing all quarter (or semester) and it’s to see if we can move on or need to reteach. I also tell students at the beginning of the year I do not accept IDK or I don’t know and not to put a huge “x” through the problem, but to show me everything they know about the problem, even if it is in words. I try very hard not to put too much emphasis on the tests/quizzes. If a student wants to go to the nurse, I allow them or if they need to go to the bathroom, I allow them (one at a time). I ensure students I will answer questions on test/quizzes without giving them the answer. I also help some struggling students by prompting them by asking questions, so they can get started and feel reassured I know they can answer the questions.

Here are some tips for teachers to help with test anxiety (from the article: How Teachers Can Help Students Cope with Test Anxiety).


  • Ask student where their fear is coming from
  • Try to understand why the student is experiencing test anxiety.
  • Keep things in perspective
  • In the big picture, one test is not going ruin a students career. So keep it in perspective and let students know.
  • Prioritize classroom preparation efforts
  • Make sure you give students adequate time to prepare for the test by reviewing.
  • Teach effective test-taking strategies
  • By teaching test-taking strategies, it will easy the anxiety. Practice this with students, this will increase their confidence in taking a test.
  • Focus on the positives
  • Help them reflect on past positive experiences. Maybe when they answered a question correct in class and just remind them they can do the test.
  • Empower students with simple strategies to reduce anxiety
  • Basic anxiety-reducing techniques; such as, deep breathing techniques or seat stretches.
  • Help students create a study schedule
  • Let students know when they can come get extra help. Either before or after school or maybe during your prep.


If you know of different techniques you have used in your classrooms that has helped, let us know by commenting on the blog.