NCTM Day 1

The sessions I attended and three things I want to remember from each one.

Incredible Math Tasks! Supporting the Productive Struggle in Learning Mathematics

Bill Barnes and Jenny Novak

- Five Practices for Orchestrating Productive Math Discussions by Stein and Smith

- Choose a learning target and find a task that matches it, then:

- anticipating, monitoring, selecting, sequencing and connecting

- Resources at Howard County Wiki

Building Middle Grades Ratio, Proportions, and Proportional Reasoning Essential Understandings

Travis Olson, Hannah Slovin, Melfried Olson

- Keala makes pizza at a rate of 3 pizzas in 5 minutes. Casey makes pizza at a rate of 4 pizzas in 9 minutes. Who is faster?

- You cut 2/5 of a piece of a board. The piece is ¾ of a foot long. How long is the whole board?

- Two solving methods I hadn’t thought about:

(2/5)x = 3/4 Scale up both sides by 2 ½ (2/5)x = (3/4)(5/2)

(2/5)x = 3/4 (1/5)x=(1/2)(3/4) 1x = (5)(1/2)(3/4)=(5/2)(3/4)

Developing Fractional Reasoning through Number Talks

Ann Dominick and Sherry Parrish

- Fractional Reasoning: Distinct numbers, parts of a whole, denominator, numerator, equivalence

- Comparing Fractions: benchmarks, unit fractions, distance from whole, compare numerators, compare denominators

- Whole # Multiplication: Partial products, doubling and halving, repeated addition, breaking factors into factors

Getting Students to Pose Powerful Questions

Jane M. Wilburne

- When you ask a question, you are more interested in finding an answer

- People don’t ask questions when they are angry/upset/troubled/victimized, other people around them have more knowledge/power --> intimidation, can’t formulate a question, haven’t felt supported in the past, lack of time

- Promoting classroom questioning: model questions, multiple platforms for students to ask and answer questions, invite questions, safe environment, plan for questioning (prompts)

Getting Students to Argue in Class with Number Sense Activities

Andrew Stadel

- Is the circumference of a Nalgene bottle greater than its height? Students improve their justification each time in first explaining to someone who agrees with them, second explaining to someone who agrees with them, and third convincing someone who disagrees with them, all while using the sentence frame: “I believe the circumference is {less than/equal to/greater than} the height of the bottle because _______”

- Each answer faces in a different direction, once they are done justifying, get the option to choose direction change

- Sentence frame for justifying prediction “I noticed ____, so I _____”

Tasks That Build the Essential Understandings in Middle Grades Algebra

Zandra de Araujo, Barbra Dougherty, Fay Zenigami

- Tasks:

• g - 227 = 543. g - 230 equals what?
• Write an equivalent expression for 5 - 7m
• d + 1 is less than d + 3. Is this always, sometimes, or never true?

- Flexibility, Reversibility, and Generalization problems

- Essential Understandings in Practice book coming out in the fall

Teachers as Designers: Mindset and Multidimensional mathematics in Classrooms

Jo Boaler

- even if you are not aware of making a mistake, your synapses will still fire because you are making a mistake (or possible because you are thinking hard?)

- pose the problem before teaching the method

- (first) week of school tasks

ShadowCon

Michael Pershan

(I sadly came in at the end of this, so he was the only speaker out of six that I saw)

- Problems with our hints: too vague, kill thinking, don’t have reasons, we improvise too much

- For better hints: add context, add reasons, be just specific enough. Example: If you’re dealing with lots of data it can help to make a table to help us notice patterns.

- Call to action: plan some hints, try them out in the classroom, and share them

Back to the Future - Guided Notes Work Time

Group Work Update

After two months of explicitly teaching group work, I feel like we are on a pretty good trajectory. In order to stay on this trajectory, I think I need to continue to in-detail plan at least one group work task a week. When planning group work, here is what I am seeing as the essential elements:

•  An individual doing-math element and a group doing-math element, both with accountability.
• A focus for the process part of the group work that is taught/discussed at the beginning and assessed with evidence from the student and/or teacher. This is even more powerful if it is continuously reinforced by me throughout group work and if there is a discussion about it at the end.
• Giving reminders/specific directions to particular roles during the task. This requires thinking through the particulars of what each of the group roles will do for this particular task.

Guided Notes Work Time

With group work going pretty well, I would now like to turn my attention to maximizing productivity during work time where students are not working on group-worthy tasks. Most of this time, this work comes after I do a mini-lesson and while students are working on problems in a guided notes packet. Depending on the day, these problems fall somewhere on the continuum from low cognitive demand skills practice to high cognitive demand procedures with connections. In order to start planning how I will modify and explicitly teach this structure, I did a modified form of the Back to the Future protocol. This protocol is a way to identify and address obstacles in getting from where you are to where you want to be.

Back to the Future Protocol

My goal: Students will productively use work time to think through problems that help them meet the day's learning objective. They will be self-motivated by a sense of urgency/importance about what we are doing.

Project into future (Describe in present tense what it looks like when you have achieved your goal):

As I finish the mini-lesson/launch, students ask any last questions that they have about the notes and/or the directions. I then tell them to get started working with a couple minutes of private think time. I am standing in the front of the room and I see all of the students pick up their pencil, read the first problem, and start independently working. No one raises their hand because they know that questions need to wait until after private think time. After a minute or so, I start circulating, and I can see that students are marking up the first problem, flipping back to their notes, writing down key information, or any of the other strategies we have talked about. Once I can see that everyone has gotten started, I let them know that now is a time to check in with their partners and keep working. Still no hands go up. I hear several students ask someone else at their table a specific question and the person looks at the other person’s paper and answers, even if it means pausing in what they are doing. I see several students continue to work independently but know that when they get to a point where they have a question or need to check their answers, they will ask their classmates. The students continue to work through the packet. All conversations are about math and they are building on each other’s ideas and challenging each other in a respectful way if they disagree. When a question comes up that a whole table gets stuck on, they call me over and show me what they have done so far. They have a specific question that everyone can articulate. This continues for about twenty minutes. Sometimes students are working independently, sometimes they are talking with each other about the math. While they work with a sense of urgency, the goal is not just to simply complete the assigned problems. Instead, students are trying to truly understand the big idea from the day.

“Look back” from future (Describe in past tense where are you starting from aka what my classroom looks like now):

Before I really started focusing on guided notes work time, I often had a slow start to students reading and working on the questions. Instead, they would be talking about whatever was on their minds--sometimes the math at hand, but sometimes the basketball game from the day before, or the weather outside, or what happened at lunch. When I would redirect them to get back on task and focus on the math, they would tell me that they were working and talking. While this was true--most of the time, some math work would get down on the page--there was no sense of urgency in terms of completing it. Many students would call me over with individual questions and be frustrated that their group members wouldn’t talk to them about their question. Some students would also start really productively and then get distracted and start chatting either with people at their table or across the room.

Connect and Obstacles (Describe in past tense how how you got from the past to the future):

Obstacle #1: Lack of a sense of urgency about meeting the day’s objective. 
Students and I had a discussion about the purpose of doing practice problems after the mini-lesson/launch.  They talked about having a sense of urgency not necessarily in finishing, but in gaining the understanding/skills of the day. This goal for the day was obviously communicated through the objectives and also in terms of me verbally setting goals based on time frames.

Obstacle #2: Slow start and lack of stamina in keeping focused on the work. 
I had students get into the habit of always starting with several minutes of PTT. I publically tracked who immediately got to work in starting with PTT and continued to publically track at random intervals for who is on task. Students defined what “on task” looked like and set up weekly goals.

Obstacle #3: Individual questions/Not asking each other questions/Not using their resources. 
I went back to really reinforcing the question protocol (see the Other Days section of this post) and explicitly taught the strategies that it mentions.

Obstacle #4: Whatever math students were supposed to be doing was less interesting than the other things they wanted to talk about. 
I figured out how to hook them better when we started a topic. Also, even if they were doing practice, the renewed sense of urgency from a firm deadline and learning goal helped them stay focused.

Group Work Update

Introduction:

So it’s half way through the year and once again, I am thinking pretty deeply about group work and how to teach and sustain it in my classroom. From September until December, I had students sit in pairs. I launched roles for the pairs and the question-asking protocol (see my previous entry) in September. However, I did not continue to reinforce either of those, so they fell out of use. Coming into January, I decided that I wanted to re-launch group work. I moved my desks into groups of four and reintroduced my question protocol. I changed the partner roles into group roles, adapting language and ideas from here. I structured the first two weeks of class in January to explicitly teach and build these routines. Since then, I have been trying to do at least one lesson a week where I plan a task and a structure that relies on the group roles and (hopefully) teaches the students more explicitly about how to use them.

Here are the group roles that I am using. Facilitator is split between two people if there are four in a group and is done by one person if there are three in a group.

NAVIGATOR — focus on GROUP INTENTION

Keep the group pointed in the direction of reaching a shared understanding:

•   read instructions aloud

•   enforce norms

•   resolve conflicts, find compromises

•   organize production of high-quality group deliverables to turn in

FACILITATORS — focus on GROUP PROCESS

Keep the process of collaboration running smoothly:

Person A:

•   watch progress & the time

•   make sure the group meets its deadline

•   lead the process of filling out the group self-assessment questionnaire to turn in

Person B (if your group has only 3 people, Person A should also do these roles):

•   get the work off to a fast start

•   make sure everyone participates (turn-taking)

•   make sure everybody has good written record of work

RESOURCE MANAGER — focus on GROUP RESOURCES

Get what your group needs:

•   get & return all needed supplies

•   organize the group to ask a group question of the teacher (make sure that anyone in the group can state the shared question)

•   call the teacher over for group questions

•   organize clean-up

(As a side note, when I launch group roles next year, I would like to have the group roles cards also have sentence frames for each role.)

I am also currently participating in a 5-session workshop where I am thinking about group work in my classroom as well as group work in others teachers’ classrooms. For this group, I had to present a success (using this protocol) and I chose to talk about my introductory lesson for group roles. I somewhat unexpectedly found this a really useful exercise. I have a tendency to focus on the challenges I am having and figuring out how to change or fix them. Not only did focusing on a success make me feel more confident about my teaching, presenting it and hearing responses from other teachers helped me identify what made this lesson so successful. This will make me a better teacher because now I know what I should keep doing.

I started with some of the context above, along with some pictures of my classroom set-up and overall norms.

Structure of the lesson:

I started this part of class with a brief re-introduction to the idea that we would work on some problems that really lend themselves to group work. For these problems, we would use group roles. Each person had a role taped to their table and spent a couple of minutes doing some individual writing about what their role was. We then had a brief discussion about why group roles might be helpful and what might be challenging about them. The pros of group roles that the students talked about were that everyone has something to do and it holds everyone accountable. They identified the challenges that some people might not do their role or that some people might accidentally or purposely do someone else’s role.

Then, I launched the problem to the whole class. This was my version of Nathan Kraft’s version of the oreo problem. I gave some initial information during the launch (I eat only the filling in oreos, my sister eats only the cookies. We had a box of double-stuff oreos and wanted to know who was getting more calories). In the spirit of Ilana Horn’s Strength in Numbers, I handed each table a task card with the additional information they needed, the questions, the final product details, and how they were being assessed.

Task card:

The Oreo Problem!
The questions - How many calories are in one cookie? - How many calories are in one single filling? - If Ms. Hansen eats the filling from a Double Stuf oreo and her sister Emy eats the two cookies, who ate more calories?	The product The table will create a poster that has… - a diagram to represent the problem information - a system of equations where both variables are defined - the work done to solve the problem - answers to all 3 questions
Assessment Your grade will be based on… - group work grade based on norms and table roles - mathematics on the poster - individuals will describe their contribution to the group work
The information
One serving: Three Oreo Cookies 160 calories		One serving: Two Double Stuf Oreo Cookies 140 calories

As they started the problem, I put up a "participation quiz" on the board where I wrote down +’s and –‘s for the group. 

This is also from Strength in Numbers and I have used participation quizzes periodically and pretty successfully throughout the fall. Once they got the task card, groups had about forty minutes to work on the problem and create a rough draft of the final product.  Finally, I had them go back to their individual writing and reflect on their contribution to the group and how they had done with the group roles.

Here are some of the rough drafts that were produced by the groups:

  

And here are some of the individual writing that students did before and after the group work time:

Reflection

Here is what I identified that made this a successful class period:

• I had done participation quizzes in the past and they have been a really good tool for getting groups back on task—in this lesson I felt like the participation quiz was extraneous. Students didn’t need it as a reminder to do what they needed to do. This meant I was able to confer with groups more.
• All students were participating. I have one student who rarely produces any work. The facilitator at his table repeatedly re-engaged him.
• There was a group of 3 who really had trouble listening to each other. Their facilitator was not able to smooth things out between them. I went over, had each of them write what they were thinking individually for about 5 minutes. Then, I stood there while they explained to each other their thoughts. They ended up going with the ideas of someone who has very little social capital but had a great math idea.
• Two of the students who are the most distracted and struggle the most were absent. I am still trying to figure out the best way to engage them in group work.
• With prompting, the resource manager made sure that the group had discussed any questions before asking me and that everyone knew what the question was.

Here are the successful elements that were identified by the other teachers in my workshop:

• The participation quiz was a strong visual reminder to students on how they were contributing.
• Reflective writing at the beginning and the end allowed students to think about their role and then reflect on how they contributed. This led to more individual accountability.
• Students relied on each other as resources, not just the teacher.
• This lesson was part of a sequence that built up group work (even thinking as far back as the fall) rather than throwing everything at the students at once.

The teachers in my workshop also asked me some very useful questions:

1. Was it the plan all along to start small and build up with group work?
   Yes. This has been the plan since the summer. Both this fall and in January I planned out how and what order I was going to introduce different elements of group work.
2.  Did they have any individual time to work on the math task?
   No, they did not have any individual time to work on the math task before talking about it with ttheir groups. Given the nature of having the navigator read the instructions, I am finding it awkward to then have them do individual work time and then have them go back in the group. Based on this question, the next group work activity I did, I gave an agenda to groups and had the facilitator monitor a couple minutes of private think time for everyone in the group.
3.  Did they actually do the group roles? Was it strict about who did what role?
   In this class they did some of the group role things (navigator reading aloud, resource manager organizing the questions, facilitator watching the time and making sure that everyone had a copy of the work). As they were going, I occasionally gave directions to a specific role. For instance, when I gave time checks, I specifically called out the facilitators and told them to make sure that their group was on track. I was also strict about people doing their own role. Eventually, I would be fine with more fluidity of the roles as long as they are all getting them done. But while the kids are still being introduced, I think it is important to keep the roles distinct in order for everyone to be held accountable. This question and discussion prompted me to think about how I could structure tasks to teach more deeply into the roles. At this point, I am trying to do at least one a week where one of the main objectives is for students take ownership over their roles and continue to increase the effectiveness of group work.

Joyful Learning - Vignette 1

I am currently part of a group of teachers who are investigating joyful learning. The essential questions of our group are as follows:

• What does the “pursuit of joyful learning” mean to us-- as learners and as educators? Why is it important?
• What does it mean to teach with “joy” in mind? (students owning, driving and expressing joys of learning?)
• What does joy sound like and look like? 

As part of our investigation, we have done some writing about experiences of joy in our own learning. Here is my response to the prompt: 

What is one salient memory or example (recently or as far back as childhood) where you were both driven and excited about learning something hard? 

To give some context, this learning experience took place during the math content methods class I took as a preservice teacher. I was student teaching Monday through Thursday and then we met for three hours on Thursday evening.

It was Thursday afternoon after a full week of teaching and we were sitting in content methods class. Our teachers had realized early in the year that what gave us energy in this class was doing math. And so like most weeks, we started class with a math problem that was related to whatever we were learning about that day.

We were focusing on geometry that week and they selected the following math problem:

You have a cake that is a rectangular prism with a square base. It is frosted on the top and each of the four sides. You want to split the cake into seven equal sections, where each section has the same amount of frosting and the same volume of cake.

We started working individually, each on our own separate piece of chart paper. On the paper, we were documenting our thinking, rather than trying to make a presentable product. This was a habit that we had gotten into over the course of the year and one that we wanted our students to do as well. The problem, though fairly straightforward in its set-up, was hard. The challenge and interest came from the corners and the frosting on the sides of the cake. Although I don’t remember exactly what I did during that initial private think time, I likely chose dimensions for the cake and calculated the volume as well as the surface area of the frosting. I probably thought about a circle and how much simpler (and more boring) the problem would be if it were a circular cake.

After some time to grapple with the problem on our own, we started working in partners. Again, I don’t remember the specific details of what my partner or I said or did. But based on how partner work generally went in that class, I would guess that we both shared what we had worked on so far, and asked questions of each other in order to both understand and probe each others’ thinking. This then gave each of us a direction to keep working or something new to try. We probably then continued to work individually, but would periodically check in, because sharing our ideas helped us thinking more clearly and creatively. Our teachers watched what we were doing. They also asked us questions so that they could understand. In talking with them, it pushed our thinking, just like talking to our partners. They, however, did not indicate how they had solved the problem, or if we were on the “right track.” We were the ones who were doing the heavy lifting of thinking.

There are particulars that I do remember from this day, though, that made it stand out from the other content methods classes. This is the only problem from the whole year that I did not come up with a solution for during class. Our teachers had us share out specific parts of our strategies to the rest of the class. One of my classmates, who taught under the same mentor teacher as me, had figured out a solution. I remember her being so proud and borderline smug (we all knew each other well enough at this point that it was allowed to be borderline smug) that she had come to a solution. I remember being annoyed and jealous that I hadn’t been able to figure out a reasonable solution in the time that we were given.

The feelings that we had were not destructive or harmful to the learning or the relationship we had with each other, though. They were part of friendly competition that rested on the solid foundation that we had set up as a community. I trusted everyone in that room to know that I was trying my best and that I did have interesting/useful ideas about math and teaching. I know that I believed that of everyone else in the room. I also knew that they were there to support me no matter what. Throughout the year, they had seen me at my lowest points, just as I had seen them. In those times, they had helped me figure out how to pick myself back up and keep going. So we could have a little friendly competition and boasting because of that.

The last thing that I remember clearly about that problem and that day was that even though one person had figured out a solution, none of us were satisfied at the end. The solution was inelegant. It brute-forced a way for everyone to get the same amount of cake and the same amount of frosting. We were all convinced that there was a more elegant way to split that cake into 7 equal pieces. Despite having a solution, we wanted to keep working on the problem in order to find a better one.

Looking back at what I remember from this class, there are so many elements that made us both driven and excited to work on this problem. Here are the elements that I notice that I want to work towards in order to foster joy in learning mathematics in my own classroom:

1. Our teachers intentionally structured class to start with something they knew was engaging and gave us energy.
2. The problem we were looking at was simple to understand but challenging to solve.
3. We all had some time to start the problem on our own.
4. We weren’t trying to make a final product as we were solving. The documentation we did was a record of our thinking.
5. My partner and I both found it useful to talk to each other about our work because explaining our own work and hearing someone else’s ideas pushed our thinking on the problem.
6. We had the freedom and the self-regulation skills to move back and forth between individual thinking and discussing our work with partner.
7. We, the students, did the majority of the thinking. Our teachers supported us, but I still have no idea how they solved the problem, or if they knew a more elegant solution than anything we came up with.
8. I was interested in what the other groups had tried. This was facilitated by what our teachers had us share with the whole group, but was primarily because everyone shared a different idea that as a class pushed us closer to a solution.
9. We all trusted and respected each other. We had built relationships where every single person was valuable to the group.
10. The competition that we felt with each other pushed us all to do our best.
11. Despite having found an answer, we still wanted to work on the problem. We valued other parts of the solving process (elegance, succinctness, being able to articulate ideas) more than having a solution.

Tackling Group Work - Part 2

Types of Task

I believe that not all activities are suited to the type of group work that I described in my previous entry on group work.  For example, doing problems to practice a particular procedure does not lend itself to collaborative group work. While students benefit from asking each other for help, this type of discussion is usually asymmetric—a student who understands the procedure is helping a student who does not yet understand a procedure. The group work that I particularly want to foster in my classroom is more symmetric and involves all students sharing possible ideas and then together trying at least one of them out.

In Strength in Numbers (in case you can’t tell, I am pretty obsessed with this book), Horn suggests the following about “groupworthy tasks”

• task focuses on central mathematical concepts or ideas
• task require some interpretation
• task provides multiple ways of being competent in problem solving
• task is done in a group, which bolsters students’ interdependence
• task is designed in a way that provides individual and group accountability
• during collaborative learning time, only group questions
• have clear evaluation criteria

These criteria overlap with the QUASAR description of “doing mathematics.” These tasks...

• require complex and non-algorithmic thinking
• explore the nature of math concepts, processes, and/or relationships
• require analysis of constraints and connections
• may involve some level anxiety due to unpredictability

I would like to commit to doing this type of task at least once a week. Some weeks this task will be intimately related to the content we are focusing on. Some weeks it will not be related at all, but will build other mathematical problem-solving skills (ex: diagramming, working backwards, developing a strategy when there are no hints for what the strategy should be).

Problem-Solving Days: Groupworthy Tasks

In general, I imagine that we will usually do some sort of problem launch for the whole class.  Students would then have a couple of minutes of PTT to start the problem on their own. This should not be enough time for any student to solve the problem or feel like they’ve solved the problem. Instead, it would be enough time to start thinking about a strategy for solving the problem. Once PTT is up, then the group work begins.

Here’s how I envision students starting a problem together after private think time:

• each person explains their ideas(s) so far
• each person makes sense of partner’s idea: what did they do and why did they do it
• partners compare their ideas: similarities and differences      
• partners evaluate their own and each other’s ideas
• partners choose some next steps to try together

As they continue to work together, I imagine that there is a lot of exploratory talk. Here is a description that I think is important, again from The Value of Exploratory Talk.

“In exploratory talk, listeners gain the benefit of hearing a speaker’s tentative thoughts. Feedback from listeners may require a speaker to elaborate their point of view, to perhaps cast it in a clearer, more persuasive form—or even to change their mind. Talk of an exploratory kind is thus not only useful for an individual to sort out their thoughts, it can also help two or more people to solve problems because they are sharing ideas (some of which may only be partly developed) in a genuinely collaborative interaction.” (66)

Students may find that they would again take PTT at points during the work time. But they would continue to check back in with each other and follow the steps from above.

Supporting Students in Successful Groupwork

In looking and thinking about CI group work roles (see Strength in Numbers and here), two things were important to me. First that everyone pulls their weight, and second that responsibilities were not artificially divided when shared accountability would be more appropriate. Therefore, pulling from the different CI roles, I came up with the following for partners:

Partner Work Norms and Responsibilities

Facilitator: - read instructions aloud - get the work off to a fast start - watch progress and time	Resource Manager: - call the teacher over if there is a question - get and return needed materials
Both students will enforce partner work norms: - Everyone gets a turn to talk and everyone listens - Explain your reasons so that everyone understands - Respectfully challenge and build on each other’s ideas - Make decisions together after everyone has shared - Everyone contributes to documenting and/or presenting

I also wanted to offer students some guidance in how to talk together once they have taken some PTT.

Partner Work Protocol

Steps	Sentence Stems
1. Each person explains their idea(s) so far	“What were you thinking?” “What did you do?” “I started by…” “I tried… because…”
2. Each person makes sense of partner’s idea: what did they do and why did they do it	“Can you explain that to me in another way?” “What did you mean when you said…?”  “Why did you…?”  “How do you know…?” “I don’t understand…” “I have a question about…”
3. Partners compare their ideas: similarities and differences	“My strategy is like yours because…” “This part is different because…” “Our ideas connect if…”
4. Partners evaluate their own and each other’s ideas	“I agree/disagree with… because…” “This makes sense/does not make sense because…” “I got a different answer because…”
5. Partners choose some next steps to try together	“What are you thinking now?” “I think…. is a good start because…” “I think we should try… together because…”

I will also have various class structures/teaching moves to support students in working collaboratively while having individual accountability.

Most of these ideas are from Strength in Numbers. Here are explanations of ones that I had not heard of before:

Task card: Students share the problem/directions would also have evaluation criteria, students do not write on it or turn it in

Participation quizzes: Teacher calls attention to particular groupwork norm(s) and then publically tracks all groups on the norm.

Check points: Before the group can continue, someone randomly selected by teacher answers a few key questions.

Group quiz: Group has 4 questions to answer and everyone records on their own paper. Teacher chooses one randomly to grade and all group members earn that grade.

Shuffle quizzes: Teacher takes every group member’s paper, shuffles, and then chooses one. That person has to explain for the group.

Other Days: Non-groupworthy Tasks

When we’re not doing “groupworthy tasks,” my students will still sit in partners. They will be allowed/encouraged to work with each other, but it will be less structured than groupworthy task days. The following will always be my expectations and will be taped to all sets of desks.

Table Work Norms Help! I don’t know what to do!
Before asking a teacher… - look back at your notes (ex: first page of packet(s), similar problems, reference sheets) - ask someone at  your table - try something even if you’re not sure it will work	When you ask a teacher… - all people at your table must be able to say the question - you should have evidence of something you’ve tried - all people at the table must be involved in conversation with the teacher
Norms: - you have the right to ask anybody at your table for help - you have a duty to give help to anybody who asks - helping is not the same as telling - stay focused on your table’s work

 The most important thing to me in the above is that there is a protocol for asking me questions that makes the students think and use each other as resources first. The norms that make this possible are that everyone has the right to ask for help and a duty to give help when asked.