Building Thinking Classrooms: Ch 9 - Hints and Extensions

Since curriculum tasks are the main staple in a math room,

Creating sequences of curricular tasks help students to think more 

And ultimately cover large amounts of content in a short amount of time.

"If we are thinking, we will be engaged."

"If we are engaged, we are thinking."

Goal is to keep students in the flow

By finding the task that meets them where they are at.

Not too challenging.

Not too easy.

Timing matters as to when we increase the challenge.

To do this, 

CREATE SEQUENCES of problems. 

Teacher: If I add three to my number, the answer is 12. Thumbs up if you know my number.

Calls on student when enough thumbs are up for the answer.

Teacher: If I double it and add three my answer is 15. Thumbs up if you know my number.

Calls on student when enough thumbs are up for the answer.

Teacher: Before I give you the next one, we have to learn how to write what I just said.

               x + 2 + 3 = 15

Teacher: And before I give you the next one, there are three rules for this task.

1. You can use a calculator.

2. If you use a calculator, you must write down on the whiteboard what you are typing in.

3. You have to check your answer by putting it back into the calculator.

Here's your next one

              x + 3.014 = 7.22

Randomizes groups and send them off to work.

Rest of the sequence

x - 15.1 = 7.88

x * 4.25 = 24.8

x / 1.356 = 4.02

x * 2.5 + 3.67 = 18.3

Variation can only be seen against a backdrop of non-variation.

The increase in challenge from one task to the next is incrementally small.

Just pushing the envelope a little bit in each step, which helps keep the students in flow.

Changing engagement can also maintain flow.

If a group has answered wrong, or even if they are right,

Simply ask them if they would bet $100 on their answer...and then walk away.

They just went from DOING to JUSTIFYING.

When they call me back to EXPLAIN, they are required to articulate their thoughts for an outside audience.

To further increase the challenge, I may point them to a group to TEACH them something.

And finally, at the pinnacle, having them create a new task for a group.

REMINDER! To avoid falling into stop-thinking questions, use these instead.

1. Why did you do that?

2. Can you tell me what you are doing here?

Question 1

What are some of the things in this chapter that immediately feel correct?

I love the subtle variations to build confidence in students' ability to solve curricular problems!  My mind was already making plans to create these sequences this summer so I have something to rely on when the school year starts.  And then I saw Question 2 and 3.  Don't worry, I will have several sequences ready to rock and roll. 

Question 2

Pick a topic that you have just finished teaching, and try to build a sequence of incrementally more challenging tasks that cuts through a part, or all, of the topic.

Created sequences for solving one- and two-step equations for rational numbers (decimals), rational numbers (fractions), and rational numbers (integers).  This will be very helpful as students struggle with all of these concepts. 

Question 3

Now do the same thing for the next topic you will be teaching.

My next focus will be

• Pythagorean's Theorem

Question 4

Think about a topic that you believe is brand new to students. What is the minimum set of instructions that you need to give in order to prepare students to be able to think their way through the first task you would ask them to do? What can students learn from this first task?

Pythagorean's Theorem.  I would do the Discovery activity where students find out what the theorem actually is.  From there, I would give them problems for finding the missing side lengths.  

Question 5

Do you think your students have developed the autonomy they need to allow them to help themselves to stay in flow? If not, reread Chapter 8, and think about how you can continue to further their growth in this area. This does not mean you can't start to play with creating and maintaining flow. Flow is a great context in chich to keep working on mobilizing knowledge to building students' autonomy.

We shall see.  You can bet I will be reviewing these notes and the chapters in the book as I implement these new ideas!

Question 6

Have you seen instances where your groups exhibit tremendous perseverance or patience while working in a thinking classroom setting? If so, could they have done this at the beginning of the school year?

I have seen this.  Students will make comments of "I feel so accomplished" or they won't want to leave to go to their next class.  I have used non-curricular tasks to establish class norms in the past years, but I love how these non-curricular tasks have a purpose to create more thinking opportunities, which also has been my ultimate goal.  Now I will have the tools to make it happen!

Question 7 

What are some of the challenges you anticipate you will experience in implementing the strategies suggested in this chapter? What are some of the ways to overcome these?

Creating sequences that go step-by-step.

Creating the atmosphere for students to "steal" the next problems.

Building Thinking Classrooms: Ch 8 - Fostering Student Autonomy

Look for moments where a group can get what they need from another group.

THE KEY IS TO NOT SAY OR SHOW SOMETHING ANOTHER GROUP CAN.

Use this when two groups have different solutions

Or when they have the same solution but used different methods.

Question 1

What are some of the things in this chapter that immediately feel correct?

I like the whole approach of don't say anything that a kid can say. 

Question 2

Have you already given your students autonomy to interact across groups? Have they taken advantage of this autonomy to the degree that you wish?

With sitting at tables, students don't really have access to this.  I did see students looking for hints when we did the Build It activity here at the end of school, so I do see a need for it.  

Question 3

What other ways might you foster autonomy beyond what is mentioned in this chapter?

Googling vocabulary definitions

Ask 2 before asking the teacher

Question 4

This chapter focused on the nurturing of independence through the fostering of autonomy. Have you found any other ways to nurture independence?

This year during our Test Trainer time, autonomy was encouraged when students didn't know what a question was asking them, to google it and learn from what they read.  In some cases, as in a stem-and-leaf plot, I would have to tell them what to google so they could answer the answer on their own.  This seemed to work quite well, and the concept of googling to find out information crossed over into areas of the lessons as well.

Question 5

What is your feeling about mobilized knowledge versus groups doing the work on their own?

I'm okay with this.  After all, this is all during the learning phase.  If we can get the culture where students value their learning, are thinking, and get excited about learning...using check-your-understanding instead of practice, vertical thinking boards, and random groups...more math learning has to happen!

Question 6

What are your feelings about the possibility for the proliferation of errors in a classroom where knowledge is being shared between groups?

This is just an excellent opportunity to iron out misconceptions.  The use of "My Favorite Mistake" could be the focus of a whole group discussion.

Question 7

What are some of the challenges you anticipate you will experience in implementing the strategies suggested in this chapter? What are some of the ways to overcome these?

I'm anticipating there will be a lot of copying answers, but this can easily be overcome by showing and EXPLAINING their work and thinking. 

Building Thinking Classrooms: Ch. 7 - Homework

Homework, or practice, is a thing of the past in my classroom.

As or Right. Now.

The problem with practice problems is that 

• Students don't do it anyway
• They cheat to get it finished
• They get help in some way...but the help is just to complete it, not to understand it
• They try it on their own, but mimicking takes a front seat in this approach.  Any problem where mimicking can't be utilized most likely won't get solved

Taking points for homework is also off the table.

More cheating occurs (23%) when points are taken then when no points are put in the grade book (2%)

But that is the only good new for not taking points.  

The students not doing it increases from 25% to 38%!!

Question 1

What are some of the things in this chapter that immediately feel correct?

I had already changed my working from "homework" or "assignment" to "practice".  I also had taken away the "zero mark" if it wasn't completed, giving only 100% to those completing their practice.  In fact, during the pandemic, I was also offering up answer sheets for immediate feedback. So after reading the research on why students don't complete their work, this change to check-your-understanding makes a lot more sense and seems a logical direction for me to. 

Question 2

Which of your students do their homework, and which do not?

The students that do their homework in class are those that grades are important to them (or their parents).  They want the gradebook to reflect that all work has been completed with high marks.  I suspect there was a lot of cheating on some, to be able to achieve this.  

The students that do not do their homework are the same every year.  You can pick them out.  Grades are not important to them.  Completion or checking things off a list, are not in their rolodesk.  

Question 3

Of those who do their homework, why do they do it? If you consider yourself successful at getting students to do their homework, what message are your methods sending to your students? That is, why do they do their homework, and who is it for?

As mentioned in Question 2, the students that do the homework have a self-drive to get high grades or to have everything completed.  The message I am sending them is the same one that drives them as well.  They are doing it for me, their parents, to cross it off the list, but it isn't being done for understanding the material any better. s

Question 4

Contrast your answers to Question 3 with the reasons for why you want your students to do their homework.

I want students to do their homework ,

• so they can practice the skills
• so they can make mistakes to move their thinking
• so I can see where the troublesome spots are
• so I can see where their level of understanding is
• so they can work together to solve a problem

Question 5

In this chapter, it was mentioned that practice invokes mimicking. What are your thoughts about practice as an effective learning tool? Is this what you want your students to do?

My biggest concern as I was reading this chapter, is what will I do with the Simulation Trainer!  That is totally a mimicking exercise!  It is the same problem over and over again.  "Mimicking has limitations and is antithetical to the kind of thinking behaviors that thinking classrooms are trying to foster."

Question 6

What do you think about the reality that some students may choose not to do, or not do all of, the check-your-understanding questions? How will you cope with this?

I liked the idea of allowing students to work in whatever groups, wherever they want to.  This means they can work on their own, with others, at the tables, or at the vertical surfaces.  I can see the Practice Printable being a good resource for check-your-understanding.  

Maybe an idea would be if students are struggling with the Printable (I will have to change the name of these!!!!), then that student could go to the Simulation Trainer.  But even as I type this, I know this is not the answer for promoting more thinking for that student.

Question 7

What are some of the challenges you anticipate you will experience in implementing the strategies suggested in this chapter?  What are some of the way to overcome these?

With all the little changes I've made along the way, I see this new way, Check-Your-Understanding fitting in quite nicely.  

Will I have enough opportunities to get grades?

Will SBG become a more prevalent thing as I walk around the classroom observing math understanding?

Building Thinking Classrooms: Ch. 6 - When, Where, and How Tasks are Given

Question 1

What are some of the things in this chapter that immediately feel correct?

Give tasks in the first 3-5 minutes to optimize thinking.

This is always my goal and why I was such a failure at taking attendance!  

However, this year we have been using Test Trainer during the first 7-10 minutes.

I see this changing. 

Test Trainer will be able the thinking activity.

It may be the last thing they do each day,

Or a transition activity in the middle.

Question 2

Think about your teaching when students are sitting in their seats.  How many are really paying attention to you?  If a teacher were standing in the back of your class and was able to see what your students were really doing, what do you think they would see?

I can see now that sitting is a really passive way of learning.  Add that to proximity questions, and students have a ride down easy street for their math learning.  Love the idea of standing for instructions.  

If a teacher were standing in the back of the classroom they would probably see students drawing, zoning out, or trying to talk to their neighbor.

Question 3

What is it about the students standing in close proximity to you that changes the way they pay attention to you?

Proximity has always worked as a classroom management tool, so why not use it as a way to promote thinking!  By standing, students are already more focused.  And with the teacher in the middle of it giving only verbal directions, attention should increase.

Question 4

Think about how often you are verbal, only verbal, in your current practice. Don't just think about when you talking to the class as a whole, but also when you are interacting with the students one-on-one or one-on-few?

I am not a verbal learning, so rarely am I only verbal.  I usually had a text copy of the activity that students could refer to as the instructions were given verbally.  And as the book pointed out, this is not effective to promote thinking.  I will definitely be trying the verbal and write only pertinent information on the board to see how that goes.  

Question 5

Think about how often. you are verbal in your interactions with people outside of the classroom. What are the circumstances in which being verbal is not enough, and you need to demonstrate, point, or write something to help with the interaction? What is it you show, point to, or write in these circumstances? How does that compare to what you write for students in your current practice?

With the MidSchool Math curriculum, to introduce a problem, there is a always a video.  In a sense, one could say that is verbal.  As I introduce the data/computation piece, instead of having them refer to a page in their workbook (which we won't have anyway next year), I can instead introduce the task verbally by writing on a specific whiteboard at the front of the room (that students will not be using, the important data they will need to use. 

Question 6

What will be the hardest part of trying to be verbal when giving a task?

I can see students wanting to engage in their own conversations with each other if they are standing in close proximity to each other.  

Question 7

What are some of the challenges you anticipate you will experience in implementing the strategies suggested in the chapter? What are some of the ways to overcome these?

Figuring out how to use this concept with the new curriculum.  

Building Thinking Classrooms: Ch 5 - How We Answer Questions

This chapter had excellent information and suggestions for what to do with student questions.

Students perceive their job as a student is to ask questions.

And the job of the teacher is to answer these questions.

While this is true in theory,

It's the types of questions that we need to be focusing on.

Question 1

What are some things in this chapter that immediately feel correct?

I totally recognized the PROXIMITY questions.

Questions from students while I'm in the area to make them look like they are on task,

But questions they themselves could easily answer.

"Removing" myself for the first 3-4 minutes to avoid these proximity questions will be my first line of defense.

Question 2

The introduction talked about institutional norms being a potential source of student disengagement and lack of thinking in the classroom. This chapter talks about the way we, as teacher, answer questions as contributing to students' not thinking. In what other ways do our interactions with students reduce or remove their need to think?

For many many years, I have been answering student questions with a question.

My thinking being that if I asked them a question back, they would have to think through the process.

However, here lately, I have started to wonder if my questions were too leading,

And actually taking away the ability for them to do the thinking. 

Question 3

Many of the practices for building thinking classrooms discussed to this point are ways in which we can create environments that get students to think. The practice discussed in this chapter, in many ways, is the opposite of this. In this chapter, you learned about ways to avoid doing things that stop thinking. What other practices stop thinking?

Reading, going over directions prior to the activity.  Instead, I should have students read the directions, consult with their group, and then ask questions of me for items they don't understand.  By going over the directions together, students tune out knowing that someone in their group will know what to do. 

Questions 4

What are some of the challenges you anticipate you will experience in implementing the strategies suggested in this chapter? What are some of the ways to overcome these?

Recognizing the proximity and stop-thinking questions when they happen.  I will need to create a cheat sheet of the list of go-to questions (see below) until they become second nature. 

1. Isn't that interesting?

2. Can you find something else?

3. Can you show me how you did that?

4. Is that always true?

5. Why do you think that is?

6. Are you sure?

7. Does that make sense?

8. Why don't you try something else?

9. Why don't you try another one?

10. Are you asking me or telling me?

Remembering when answering a question with a question to walk away so the stop-thinking questions don't start up again.  If walking away seems to abrupt, simply smile at the student to encourage them and acknowledge the question, and then walk away.

Building Thinking Classrooms: Ch 4 - Arranging the Furniture

Classrooms that are organized and symmetrical

Convey the message that these traits are important for mathematics.

"Defronting" the classroom is essential to getting students to focus on each other

Instead of the teacher.

How my room is arranged now.

Other possibilities that could work to free up space for vertical thinking areas.

Possibility #1                                                                                            Possibility #2

Possibility #1 still has a "front" for the white board, but with chairs around the tables, it doesn't have the symmetrical feel as what I currently have.

Possibility #2 is still very symmetrical (I'm a math teacher...this is hard!), but it is harder to determine where the front of the room is.

Question 1

What are some of the things in this chapter that immediately feel correct?

I get the whole non-symmetrical thing but it truly goes against every fiber in my body.  I'm willing to try whatever though to see how it goes.  

Question 2

Think about the way the furniture in your room is currently arranged. Is that for your benefit or the students?

The arrangement of the furniture in my classroom is so I can get get to every table as students are working.  If we move to vertical spaces, this won't be an issue, and table placement can be anywhere really.  My only concern is being able to see the TV for the Immersion videos.  That is one fixed point that can't really be changed unless I have students watch the videos independently.

Question 3

What is it you like about the way the furniture is currently arranged? Why do you like it?

It's symmetrical. It's how I've had it for years!  

Question 4

Think about other arrangements that you have seen. Why would a teacher prefer that?

I am not a single desk in rows fan.  Tables are much better for collaboration...which also means they contribute to extra talking, but creating the proper learning environment usually helps with this. 

Question 5

In this chapter I talked about straightness and symmetry. What else in a classroom, and in teaching practice, might be governed by a desire to have things be straight and symmetrical? What, if anything do you like about this? What message does this send to students?

My whiteboard is very constant.  Weekly calendar, learning goal, quiz schedule.  This sends a message to students about consistency and order.

Posters on my wall are purposefully placed.  Often symmetrically. 

Question 6

If we think about the fact that everything we do send a message to the students, what is the main message that students hear from your practice? Is this the message that you want to be sending them?

Intended message:

Everyone can learn math.  Our brains are all wired to learn.  

Question 7

What are some of the challenges you anticipate you will experience to implementing the strategies suggested in this chapter? What are some of the ways to overcome these?

Excessive talking with closer proximity

Movement around the classroom

Building Thinking Classrooms: Ch 3 - Where Students Work

Vertical Non-Permanent Surfaces

Yes.

YES!

YESSSSSS!!!!

I love love love this idea.

Now to figure out how to incorporate it into my classroom.

One marker per group.

Subtly rotate the marker.

Teacher has different colored marker.

Use numbers to match random groupings

So groups know where to go.

Question 1

What are some of the things in this chapter that immediately feel correct?

As mentioned above, I love the idea of vertical boards.  I had thought about simply removing the chairs and having the boards on the table, but if vertical surfaces produce more thinking, I bet I can make it work.

I have always loved when we use whiteboards to show our thinking, and already have five large boards in my room.  These could be incorporated propped up in various areas of my room.

Question 2

What must change in your room in order for you to gain the wall space necessary to get all of your students working on a VNPs?

If I could find extra classroom-sized whiteboards to prop up on my counters, I could easily gain enough vertical space for all the thinking that's going to go on.

I could use one of the small table whiteboards to put my calendar items on each day, freeing up the one large whiteboard in my classroom for two groups.

Question 3

Which strategy for moving the marker around did you like the best and why?

I liked the strategy "never write down your own thoughts".  This will increase communication and collaboration.  I also like subtly moving the marker to a different student after visiting each group.

Question 4

In this chapter, you read about the notebook as a catchall -- the place where we default to having students do their work. Think about all the different types of things you ask students to do in their notebooks. Which of these, other than doing thinking tasks, can you imagine having your students doing on VNPs?

Things we use notebooks for...

--> Notes

--> Practice - some could be on the boards

--> Examples - students make up their own examples

--> Reflections

Pictures of boards/thoughts that students want to save could be taken, printed off and put in notebooks.

Question 5

What else happens in your classroom that can be enhanced by having the students work on a VNPS?

The data/computation piece could be done on VNPS.  As a whole class, we could watch and discuss the Immersion piece before moving to the D/C piece on the whiteboards.

Question 6

What are some of the challenges you anticipate you will experience in implementing the strategies suggested in this chapter? What are some of the ways to overcome these?

Excessive talking?? Establish expectations and goals.  Be consistent.

Copying?? Keep track when this is happening and see if it decreases as students become more confident.

Building Thinking Classrooms: Ch 2 - Forming Collaborative Groups

Visual random groupings work best.

Use playing cards so students can see which group they are in and where to go 

(have tables pre-marked...use fish numbers and A, 2, 3, 4, 5, 6

Groups of 3 is optimal.

Change groupings every day to increase thinking.

Question 1

What are some of the things in this chapter that immediately feel correct?

I have been using random groups for years, however, I have been making the random groups and telling the students that they are randomly created.  I like the idea of handing out playing cards so that students can see the randomness and know that tomorrow their group will change.

Question 2

What is the worst combination of students that can come together in random groups? What is this perception based on? Is there any possibility that this could go well?

The first thing to pop into mind is that a group of all weak students could end up together.  But, this could be a good thing as they won't have the pressure for contributing ideas to students they deem smarter than they are.  Kagan suggest heterogenous 

Question 3

Can you think of some students who would benefit greatly from visibly random groups?  Why would they benefit?

Based on the research in the book, I totally believe that all students will benefit from random groups.  By not having the pressure of having to pick groups or fall into "undefined" follower roles, more thinking is sure to happen!

Question 4

Can you think of some students who will likely not enjoy random groups? Would it still be good for them?

My independent thinkers may not like to be switching it up all the time.  But I do believe that being able to communicate and share with others is a needed skill for the future workplace.

Question 5

What are some of the challenges you anticipate you will experience in implementing the strategies suggested in this chapter? What are some of the ways to overcome these?

I can still see students complaining about their groups.  I will just point out that groups will continue to change each day.