Ch. 7 Homework Reflection

Aside from the white boards propped all around my room,

The change in how homework was handled was probably the biggest change.

Pre-covid I would take completion grades on practice.

Students were to "complete" the practice before we moved on.

After reading this book, it became crystal clear how this completion was happening.

Students were completing it JUST TO HAVE IT DONE.

The purpose of practicing and becoming more efficient in the new skills

Was not even on their radar.  

Simply getting it done, whether by copying another's work or just putting reasonable answers,

Was acceptable in their eyes

And MILES away from the purpose I had in mind.

During hybrid and remote learning,

I quickly realized that I had to take a grade on every little thing mentioned in Google Classroom.

It didn't take long to realize that the math grade was reflecting work ethic and responsibility

Instead of any true understanding of the concepts.

And then along comes BTC!

No more grades for any learning that occurs in the classroom.

Whether at the boards or in Check Your Understanding situations,

Students did as many problems as they wanted,

Knowing that any problems not completed would be good practice for learning the concepts.

But it was not required.

The focus quickly shifted to understanding the material 

And away from having to complete all the problems.

We talked a lot about how many problems were needed to learn and apply a new skill,

And how this number could fluctuate from person to person,

And from concept to concept.

Another change was the availability of the answer sheets.

For every Check Your Understanding, answer keys were posted around the room.

Students could check their work as often as they liked.

The questions prompted from this approach were much more specific

And the amount of thinking during this activity was increased immensely.

It was interesting when new students would join our class.

When these students realized the answers were there for their taking,

They became very excited...anticipating the ease of completing the assignment.

When they eagerly asked if they could copy the answers,

And when I answered, "Sure!  Go ahead!"

My students were quick to clarify that copying would not help them understand the math.

And then when it came time for the quiz where they could show off what they learned,

The person copying the answers would have a hard time!

Oh how I loved this shift in thinking!!!

My only conundrum with all this centers around the Simulation Trainer in my math curriculum.

The simulation trainer is totally a mimicking activity.

And as the book points out, "mimicking has limitations and is antithetical to the kind of thinking behaviors that thinking classrooms are trying to foster".

To incorporate both ideas, we use the Data/Computation problem at the boards.

And then the simulation trainer is done individually as a Check Your Understanding of sorts.

After every problem, is a video of how to solve it.

Repetition.

But I will be honest,

I do see thinking decrease during this time.

I will have to keep thinking how I can best use this component in a BTC classroom.

By the end of the year, students were reporting that they liked this "new" way of grading.

66% of the students liked it.

28% of the students had no opinion either way.

Only 7% did not like it, stating that they would like other opportunities to improve their grade.

Some of their comments to explain why they liked (or didn't like) about grades not being taken for class learning.

"It made me more relaxed and confident about this class and made me feel better about making mistakes."

"It allows me to make mistakes and learn from them and not get a bad grade because I didn't understand it."

"I loved how I could just learn so much and write it down and not have to get graded on it till the test. I believe it really helped me succeed in your class."

"It's learning. It shouldn't be graded."

"Because then people were working slow and not fast."

"It made my grades stay high and it made it seemed easier and less stressful."

"It makes the class seem like less of a thing we have to attend and something we WANT to attend."

When asked how they used the answer keys...

88% used them to check their work

76% corrected any mistakes they made

66% used the answer to help them figure out the problem

I loved it as well as the grade finally reflected true math understanding.

The number of semester F's fell considerably this year with only 1 semester F in the fall.

Last year we had a total of 9 F's for the entire year

And during that crazy hybrid/remote year??? 15 F's!  

Ch. 6 Giving Tasks in a Thinking Classroom

Our math curriculum has a 7-10 minute review called Test Trainer.

It is to be done at the beginning of each class period.

However, this year, I changed it to the last 10 minutes

So we could best utilize that first five minutes to get the task up and going.

Before this new curriculum and implementing Test Trainer,

I had always just jumped in to the lesson,

Somehow sensing before reading about the research that backs it up,

That engagement early on in the class period is optimal.

Just ask my principal...it's because of this mindset that I forget to take attendance!  

Oops!

Anyway, by pushing Test Trainer to the end of the day,

We noticed some positives and negatives.

The students liked it at the end, 

As they reported that their minds were already primed for math

And they thought it was reflected in how they did.

However, there were MANY times when Test Trainer just did not happen.

The problem or the whole group discussion took priority

As learning would reach its peak at about the time we should have been shutting down for TT.

At the beginning of the year, 

I did give the tasks outloud with the students standing around me.  

However, with this group,

Having them all in such close proximity,

The talking increased!

I tried various other ways...

Giving the instructions verbally while they sat in their table groups,

and giving verbal instructions after moving them to their boards.

Both had their downfalls.

At their table groups, they were still seated

And not as plugged in had they been standing.

At the boards, they were standing,

But much more interested in visiting with those in their group.  

Maybe it was just this group.

Maybe it was a call to revisit expectations.

Whatever the case, this is something easy that I can work on next year.  

Ch 5 Reflection - How We Answer Questions

I will be honest,

Some days my answering student questions is better than other days.

And it may depend on how much time was allotted for the problem.

The more time allotted for struggle, the better my questions.

I did see more keep-thinking questions as we went through the year.

Especially when it came to thin-slicing.

They always wanted another problem to try.

I also heard questions such as, "would this work with negative numbers?"

To try to keep students thinking my go-to questions centered around the following list.

"What do you think of this answer?"

"Why do you believe it is correct?"

"Will this always be true?"

I also did the walk away method quite often.

Or I would position myself in the middle of the room,

Simply watching and listening,

Before starting my rounds.

Things to remember for next year.

Respond to Is-It-Right-Questions with 

"Me telling you that it is right is worth almost nothing. 

If you can tell me that it is right, however, that is worth everything."

This is such an important piece of all the strategies,

That this short reflection is a surprise to me. 

However, with having a discovery classroom prior to this,

This type of questioning students was already in place. 

By having six whiteboards going, 

The questions I asked were more specific to each small group,

Essentially moving thinking even farther.  

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.