Ch. 4 Furniture Arrangement Reflection

This will be a short reflection

As not much changed in my classroom based on this chapter.

I already had 4 tables that seat four students per table,

And two tall tables for two students each. 

With a whiteboard on the east wall 

And a large TV on the south wall,

There really was no front to the classroom to begin with.

My desk is in the back corner of the room.

Although I do have a table in the front corner where the document camera sits,

It's usually just used to hold materials and handouts needed for the lesson.

When something is needed to be projected,

Then the focus turns to the "front" part of the room.

I use a seating chart so students have a home base when entering the classroom.

These table groups are used when we don't have random groups at the boards.

This also helps when I have a sub teaching my classes.

One of my thoughts though is I could switch up the table groups as well 

For days when we aren't at the boards.

With the boards, I do find myself moving around the room 

when bringing the group back together for whole group discussion.

With the rich math on the vertical white boards,

Attention is directed to various methods of solving the same problem,

Misconceptions and questions from the group.

We have also used what's on the boards to help clarify our rough draft thinking

As we try to figure out what a particular group was thinking of trying.

Ch. 3 Reflection: Where Students Work

Let me just summarize this up quickly.

Vertical white boards have changed my teaching.

Vertical white boards have increased the amount of thinking in my classroom.

Vertical white boards have made math accessible to everyone.

Vertical white boards have helped students develop a growth mindset.

Vertical white boards made learning fun!

In fact, I had one class who would ask every single day..."Boards today?"

And when my answer was YES, the students would cheer.

Yes. 

You read that right.

They would cheer to do math.

Markers was the one thing that we struggled with.

We went through A LOT of markers.

Markers seemed to walk off at times to other boards.

Next year, I will make a greater effort to allow only one marker per board.

To help with this, I bought broom holders that I will attach to the boards.

Another change we will be making next year 

To help with our functions and graphing unit,

Will be to attach large sheets of laminated graph paper to the boards.

This way, students can complete problems 

And everyone can see their work.

Speaking of seeing the work on other boards,

This developed into a useful tool as time progressed.

We started the year with conversations of how valuable it was 

to look at all the boards when solving a problem.

At first students felt like they were cheating.

But as we progressed through problems

They started to realize how useful the other boards could be to get unstuck.

Any idea...even an idea that isn't correct,

Could be the catalyst of correctly finding a solution to the problem. 

Thinking also was increased with viewing others' boards.

As work and possible solutions were compared,

Students had to think through their thinking to justify their solution.

When asked about using the vertical white boards in their math learning, 

here's what the students had to say.

The best part of working at the boards...

"After working on a problem we get to discuss what we did."

"The best part about boards is it is 2 or 3 brains thinking instead of just one."

"It's not as boring, because you can discuss what you're doing with your partner and pick how to approach it rather than having to do it one way."

"Getting to see what other people are thinking."

"As you call it when you have 'ohhhh' moment and understand."

"That's usually when I learn the most."

"You get to see things from other people's perspective and you get to hear and see how to do things differently."

"You get to watch other people do math and see people do math different than you so you learn how to do some new math."

What is not liked about working at the boards...

"You can get paired with people that don't want to talk so it's hard communicating."

"Getting partners that don't want to work."

"The teacher couldn't be at everyone's whiteboard."

"I didn't like everyone looking at my board when I didn't know what I was doing."

"The time limit. I think it's better to have a little bit more time to solve or check the problem."

"Feeling rushed."

How did the boards help (or hinder) your math learning...

"They help because I can see where I went wrong by looking at other boards."

"The boards help me because it lets me picture the problem better."

"You can get rid of mistakes easily."

"They help us put our information down instead of just trying to keep track of it in our heads."

"It helps when you get feedback from others to see if you did it right."

"It helped by changing the way I look at math."

(Whoa.  That's huge.)

When a problem was solved at the boards, how did you feel?

"Awesome...like I accomplished something."

"It makes me feel great and I want to do another one."

"It made me really excited and made me feel good like I can actually do something."

"It makes me feel like I conquered the math problem."

"It made me feel good and want to try to keep solving math problems."

"It made me feel good and confident about the next one."

One of the true tests of this is when students that rarely engage

Are seen up at the boards working away.  

My principal, on more than one occasion,

Has walked in my room and was surprised to see so-and-so totally engaged.

Now that is a testament of the power of where students work.

Ch. 2 Grouping Reflection

We started the year creating random groups by handing out playing cards.  

This worked pretty well.

I would adjust the cards for every class.

But I soon tired of handing out and then collecting them all again.

While it probably only took a minute,

It was too much time being non-productive in my eyes!

Surprisingly, we never lost a card!

If I were to use cards in the future,

I would stick a library card pocket on every board for the cards,

Making collecting them easier as I move around the room.

We switched to the app Team Shake.

I had read about this app on the Building Thinking Classrooms Facebook group.

What a quick way to create truly random groups!

Plus, I could discreetly shake my phone to create a new set of groups 

if I happened to notice a pairing that wouldn't work that day.

We never had more than three at a board.

And even then, this sometimes was too many

As the third participant would sometimes take the passive seat in the learning process.

A couple hurdles that we had to get over with random groups was

1) the concept of being kind to others, even if you don't want to be in their group

2) not wandering to other groups to talk to friends

When these things happened, we would revisit the group expectations

and the importance of being kind and being able to work with others.  

Students reported on the reflection survey their thoughts about the random groups.

"I like them because it shows you different people and their struggles with the problems so you can help them."

"I felt like I just got partners that didn't do anything or people I just didn't get along with."

"It depended on who you are working with for it to be a good learning experience."

"[Random groups] were good because I could get help or my team could get help."

"Random groups are better so we don't just choose our friends."

"It was great because you didn't have the same people all the time."

"It would help us know more about each other and it helps cause it's a different person trying to explain it if you don't get it."

"I liked it because you got to share info with people you've never met before."

"It was nice because not only did you get to see how other people learn, it really helps you learn how to work with others."

"I disliked random groups because I would get people that would mess around."

I will continue to incorporate random groups next year.

To help with working with and getting to know others, we might need to use more 

  1) Kagen Cooperative structures and 

  2) Get to know you activities at the beginning of the year.

This might also need to be repeated when classes switch for the second semester. 

I might also incorporate a peer rubric of sorts.

(Was this mentioned in a following chapter?)

The rubric would help students remember the expectations when working at the boards.

Just off the top of my head right now...

--> Contributes their thinking/ideas

--> Asks questions of the group

--> Utilizes the marker when it's their turn

--> Stays engaged at the group's board

--> Respects those in the group

Students could rate themselves and also rate the peers in their group.

For each expectation, students would assign a number.

       2 -- Expectations were met on a consistent basis

       1 -- Some expectations were met and some need work

       0 -- Most expectations were not met 

I would not use this as a grade, but as a tool for growth.

After collecting data for a week/month, I would share averaged scores with each student. 

Chapter 1 Student Reflection: Types of Tasks

Four sentences in Chapter 1 grabbed my attention the first time I read the book.

"Students will get stuck.

They will think. 

And they will get unstuck.

And when they do, they will learn --

they will learn about mathematics, 

they will learn about themselves,

And they will learn how to think."

In my end-of-the-year survey,

I wanted to see how students perceived their own thinking.

I was seeing waaaaay more thinking than from years past.

But what were they seeing?

How were they reflecting on their learning?

I was pleasantly surprised to see that students were seeing their learning in the same way I was.

For them to be aware that they were thinking through the math problems,

Then they were probably aware that they were learning these very math concepts.

Which was another question on the survey.  :)

For 64% of my students to feel like their learning was greater than in years past,

Was proof that the vertical white boards were being seen as a valued tool

in the thinking, and ultimately, learning process.

When students explained their thinking for their overall learning,

I was blown away by their answers!

"It was greater because I was more focused."

"I'm getting good scores from my quizzes and I'm understanding problems better."

"I learned more standards than I have in previous years."

"There were different ways of learning how to do something"

"Last year and the years before, I really struggled with keeping up and understanding mat.  It was my hardest subject. But this year I really started understanding and enjoyed doing the math and gained confidence."

"Math is my worst subject but I am definitely doing better at it now."

"I never really picked up math this well until this year."

"I feel like I'm not the best at math but I do feel like I'm getting better."

"I can remember what we did at the beginning."

"I feel like learned quite a bit this year, because I paid more attention."

"You filled some of the gaps [in my learning] that I needed filled."

 

When asked what strategies they [the students] relied on when they got stuck...

"I just restarted and tried different ways."

"I looked at the other boards to see how they were solving it."

"I would THINK about what we did in the classroom."

"I would talk about it to find what was wrong."

"I would look [through my work] from the beginning for any faults and skim through until I got to the part we messed up on."

"Ask other people for how they understood the problem."

"I would try to find another way to solve it."

"I would ask for help."

While this data and the many comments do not simply address the Type of Tasks that Chapter 1 addresses,

This data is in direct response to the three sentences that started this whole journey.

I wanted to increase mathematical thinking in my classroom.

And from what I've shown here,

I believe that happened.

When the Math Teacher Teaches Reading...

My students have struggled reading all year long.

I believe they can read, 

But they just don't like it.

I have worked really hard to get good, interesting books into their hands.

And this has helped.

Somewhat.

As a reader myself, this "inability" to read for 30 minutes at a time

Has been a thorn in my side all year long.

Students need to be able to read.

Students need to be able to read for longer periods of time.

Students need to understand what they are reading.

Maybe this is the problem???

Soooo...once library books were due back in for inventory,

I had to find something to fill the time.

Why not go over reading strategies one last time before high school?

With copies of Leonhard Euler in hand,

And a blank piece of typing paper in the other,

We started reading.

Outloud.

Paragraph by paragraph.

Stopping at predetermined various points.

Our focus was going to be on practicing what good reading looks like.

We first paused to draw a visual from the Biographical Information.

They could pick any point that a picture had popped into their head while we were reading.

We took a little time to discuss the pictures 

and how they were similar and different than others in the class.

Our next stop was in the Contributions section of the reading.

A mathematical concept was described,

One I knew my students could identify with,

And I wanted to see if they could picture it.

It involved labeling a triangle's sides and angles.

This was very eye opening as I saw connections being made to Pythagorean's Theorem!

Another stop was also in the Contributions section.

It had mentioned pi and how Euler was responsible for this symbol.

Students had to write about what this section made them think of.

Another opportunity to connect to their mathematical learning this year.

Finally, we got to the Quotation.

"He calculated just as men breathe, as eagles sustain themselves in the air." ~ Francois Arago

We dove deeper to figure out what the author was trying to say here.

The responses were amazing!

"He was always doing math, like it came natural to him."

"He did work easily and he worked all the time."

"Breathing is easy so he is saying that's how easy math is for him."

Today, as we finish up the piece,

We are going to focus on the following areas.

1) Write one or two sentences to summarize what you read in the Anecdote Section.

2) What thoughts do you have when Euler had to settle the argument between two of his students?

3) Can you picture all the places Euler taught?  (Look at a map to get a better understanding of the area he worked in)

4) After reading three sections: The Pillaged Farm, The St. Petersburg Fire and The Smart Pencil, connect character traits of those in the writing with our pillars (respect, responsibility and growth mindset).  Where do you see each of these?

5) Finally, in the Birth of Topology section, Euler creates his own visual of a real life math problem.  How does his drawing connect to the real life situation?

Measuring Growth

State assessment scores came out yesterday.

This was the day I had been eagerly anticipating. 

I couldn't wait to see how the use of vertical white boards

Impacted learning in my classroom!

As my eyes scanned through the scores,

Searching for my data,

My heart plummeted.

We had scored below the state average.

The high hopes I had to see an increase in learning

Just wasn't meant to be.

What could I have done differently in my teaching?

What gaps still exist?

Should I have used a more traditional approach of instructing?

Would incorporating homework again be the fix all?

What would the scores have been had I NOT implemented the Thinking Strategies 

as outlined in Building Thinking Classrooms?

As I crawled out of the pit of disappointment,

I realized that the state assessment is just one snapshot of my student's learning.

Growth was shown by our daily Test Trainer (MidSchool Math math curriculum).

While I would have liked to have seen more growth,

(What teacher wouldn't???)

I couldn't ignore the fact that growth was evident.

I also checked our Fastbridge scores.

Again, the students showed growth.

My take away from all this?

Change takes time.

There is more than one way to measure success.

Look for the positive in all things.

Student Reflections - What Life Lesson Did you Learn in Math Class this Year?

One of my learning goals does not even center around math.

I want my students to walk out of my classroom 

more prepared to be a productive addition to our community outside these four walls.

I always ask at the end of the year,

What life lesson did you learn in math class this year?

This year's responses literally made me tear up.

Is it because of the climate change in our classroom with vertical white boards?

Is it a post-COVID thing?

Is it this group of students?

Whatever it is, this teacher's heart is all warm and fuzzy right now!

"Mistakes are okay."

"To discuss stuff to other people to understand it better."

"To not look at something and say it is too hard."

"That you will have to work with people you don't like."

"Don't ever give up."

I"t is ok to fail but not give up."

"If I try hard and give it my all I can be smarter than I ever though I was."

 

"That life is just a learning lesson."

"Everything has an equation!"  (LOL!)

"Things don't always go the way you plan."

"To use information wisely and to learn from your mistakes."

"Everyone has their strengths and weaknesses."

"Not everything comes easy."

"Things may seem hard because you don't want to do it, but they can actually be fun."

"There is always more than one to fix a problem."

"There are multiple ways to solve math problems and there are multiple ways to solve life problems and many ways work so you should always listen to everyone's ideas."

"It takes respect to gain respect."

 

Don't mind me...I'm just over here tearing up a bit.

BTC Chapter 1 Reflection: Types of Tasks

The end of the year just begs for reflection.

And after implementing Thinking Classrooms,

The list of changes and what went well keep swirling in my mind.

So to organize my thinking, 

I plan to reflect on each chapter. 

Soooooo....

Let's start with Chapter 1: What Types of Tasks We Use in a Thinking Classroom

What Went Well (with changes in red)

It is imperative to start with non-curricular tasks to set up the expectations of VWBs (Vertical White Boards).  We started with the Painted Cube problem the very first day.  While it was a good problem and tied in nicely to upcoming 8th grade standards, I might switch it out next year.  The Tax Collector problem is a good one to get conversation going at a level everyone feels comfortable in.

We also did the problem finding solutions for 1-20 with only four fours.  This was excellent to review the order of operations in a non-traditional type lesson.  

We did the Palindrom problem.  The students really got into this.  I would like to dive deeper into this problem so see where it can go.  

Lastly, we completed the Locker Problem which was also a good one.  

Our first attempt at using curricular tasks was when we reviewed operations with integers.  I used a missing number puzzle to really emerge them into thinking about what happens with adding and subtracting negative numbers.  Once I got to understanding thin-slicing problems better as the year progressed, this would have been an excellent way to extend thinking and get more practice in.

The non-curricular tasks definitely did their job in propelling students to WANT to think.  Many times, especially here at the end of the year when I threw a couple of non-curricular tasks at them, the students DID NOT WANT TO STOP for the discussion piece.  They wanted to KEEP THINKING!!!  This was my entire reason for moving to a Building Thinking Classrooms approach.  I wanted more thinking happening in my classroom!

Things to Think About for Next Year

I need to get better at extending the problem.  For example, in the Tax Collector problem once they figured out they could beat the Tax Collector, we then moved on to the question: What is the largest amount you could make?  After they figured that out, we extended it to 24 paychecks.  

Do I still continue the Simulation Trainer lessons from MidSchool Math, when all they are is essentially mimicking a task??? At this point, I believe that I can continue to use this component of the curriculum if I make a valiant attempt to push their thinking and fluency afterwards.  This can be ONE problem that extends the learning.  Or it can be the Check Your Understanding (Practice Printable).  But my goal will be that if the Simulation Trainer is used, we spend more time on a rigorous problem(s) afterwards.