On Task - Guided Notes Work Time Update

On Task Update:

Since the end of February, I have been using the on task tracker described in my Back to the Future post.

Students have interacted with the tracker in four ways:

1. Students and I co-created the “on task” criteria for work time:

2. Daily public tracking of the whole class:

Students earn a 4 (green) if they are meeting all the criteria and a 1 (red) if they are not meeting all of the criteria. I project this on the board during work time.

3. Weekly data overview:

I project this at the end of the week and we talk about the class goal for the week and progress towards it.

4. Individual reflections:
Students are  reflecting and setting goals for themselves.

On Task Reflection

My Analysis/Reflection:

Pros:

- (mostly) nonverbal redirection

- group goals and accountability: students have been reminding each other to be on task

- in general, work time has been more productive

- students have been motivated by my linking the class’s on task score to a related reward: the class earns the privilege of choosing seats if they meet the goal for the week

Cons:

- some students check out after they earn one red

- I can’t project anything else while I am tracking

- some students are only on task when then know that I am doing a check (which is better than nothing, but could be even better)

Moving forward:

When I started this, it was never my intention that this was something I wanted to do forever, or even for a long period of time. I wanted students go get into some good habits and then take the scaffolds away. So therefore, here is my plan for taking away the scaffold:

• Week 1: During work time, students do their own on-task check when I ask them. At the same time, I will be doing a check for them on my computer. At the end of the period, they should compare their perceptions with mine as well as calculate how on task they were. They will use this organizer to do that:

On Task Check	Are you on task?		Did Ms. Hansen agree with you? (Circle One)
	YES	NO
#1			YES              NO
#2			YES              NO
#3			YES              NO
#4			YES              NO
#5			YES              NO
#6			YES              NO
#7			YES              NO
Analysis	What percent of the time where you on task?		What percent of the time did you and Ms. Hansen agree?

•  Week 2: Students will self-assess in the same way as week 1, but I will not officially assess them. At the end of the week, students will reflect on the week and say whether or not they think they still need the checks to keep them on task.

•  Weeks 3 & 4: Check list only for students who need it.

NCTM Days 2 & 3

Three(ish) things I want to remember from the sessions I went to on Friday and Saturday

Building Student Understanding of the Mathematical Practices through IN-formative Assessment

Matt McLeod, Mary Wedon (EDC) 

 - Assessing students’ use of structure (MP7) through computation problems. In directions, write “avoid unnecessary computation”

- "Hidden Meaning" questions

- ex: 36(6⁵) is equivalent to 6⁷. Explain or show why this is true.

- "Chunking" questions

- ex: Simplify the following: 8(99²-4)+3(99²-4)-11(99²-4)

Fake-World Math: When Mathematical Modeling Goes Wrong

Dan Meyer

- There are 5 steps of modeling. Students do a lot of steps 3 and 4 in textbooks. We should be doing a lot more of 1, 2, and 5. Students don’t need to do all 5 steps every time you do modeling. Celebrate what students are contributing at each level through praise, one clap, etc.

            1. Identify the variables

            2. Formulate models

            3. Perform operations

            4. Interpret results

            5. Validate conclusions

- When modeling, we need to be honest about whether the math “works.” Have a discussion why the predicted height in cups with all accurate computation isn't the actual height in cups.

- Set up situations that require knowledge that students don’t have yet. This creates a need for a “bigger boat” (Jaws reference) before we give it to them.

Investigating the Pythagorean Theorem and Its Proofs

Robyn Carlin

- What is the definition of “proof” in the common core? Is it enough for students to be looking at examples and then making generalizations?

Reasoning Revisions Revolution

Patrick Callahan and Jessica Murk

- In having students work on problems you don’t know the answer to, you authentically cede authority and model reasoning and revision

- After having students/groups write and revise their own rules, having all students write the same rule down at the end defeats the purpose

- With peer feedback, the authority shifts from teacher to student. Feedback expectations:

            - it takes practice

            - giving feedback is not the same as being mean

            - think about what you would find helpful

            - avoid opinions

            - be specific

- Bongard problems

What do my students know? How do they know it?

Barbara Dougherty and Jeanette Olson

- Encourage students to show their thinking rather than show their work. In doing so you open the door for valuing logical reasoning over structured algorithms.

- Challenges of open response questions in progress monitoring:

            - students couldn’t explain

            - hard to score

            - students often skipped

- In multiple choice, options have different point values based on complexity of thinking required for the (wrong) option

Bringing the Standards for Mathematical Practice to Life In Classrooms

Ruth Parker

- Daily objectives are too fragmented of a way to learn math. Instead, there should be 6 to 8 units of study a year where you are looking at the same math on the first and last day of the unit (see Phil Daro on grain size). Then, students should be able to answer “what are you trying to figure out right now?” instead of “what math are you learning today?”

- Big mathematical ideas are never fully mastered. They deepen in complexity over time. Therefore, learners should encounter:

• fragile understandings
• periods of cognitive dissonance
• mistakes as sites of learning
• states of not knowing… yet

- Can You See? (Teacher starts by asking questions, then turns it over to the student)

            - 2/5?

            - 2/3?

            -1 divided by 2/3 ?

- Number Bracelets

- a way for students to gain addition fluency

- after doing an example or two, ask students to come up with their questions and explore them

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.