The Power of Choice

For today's lesson, I offered the students a choice in the problems they solved.

We talked about closing our gaps,

With one of our gaps being fractions.

We also talked about where our lesson ended yesterday,

Solving operations with integers.

Today's assignment held problems with positive and negative fractions

As well as some fun integer puzzles.

Every small group chose to start with the fraction problems.

People.

In all of my years,

Students will shy away from fraction problems.

They will groan.

They will throw fits.

They will refuse.

Today...

They chose fractions.

#smallwin!

The Locker Problem Takeaway

Today was the Locker Problem.

Our last non-curricular task.

My takeaway?

Students need to feel comfortable taking a large problem and making it smaller.

Most of my groups concentrated on how to display the 100 lockers.

This slowed down their thinking progress.

During consolidation, we looked at how our brains work better with a smaller snapshot of the problem.

Which, in the long run, can. ultimately get us to the answer!  :)

Ch 10 Reflection: Consolidate a Lesson

This is probably my favorite part of BTC.

Bringing the discussion full circle. 

The one thing that stuck with me though,

Was to level to the bottom.

How many times did I level to the top,

The place where we all needed to get to,

Only to have it flop, with everyone feeling frustrated.

By starting with the bottom of the tiered problems,

The ones that everyone successfully solved,

We were able to get everyone on the same page,

And then could slowly work our way through the more challenging ones...

And get more students where we needed to go in the process!

One thing that I need to work on is keeping the students standing next to their boards.

I started to have students sit back down at their tables, but according to the research, this drastically diminished the thinking.

Gallery walks.

I tried these.

What I learned is that I need to have a specific goal for the walk.

What specifically should they be looking for?

Are they comparing methods to find similarities?

Are they looking for differences?

Are they trying to find misconceptions or mistakes?

Something to work on this year!

Ch 9 Reflection - Hints and Extensions

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

This is my goal.

Every lesson.

Facilitating this optimal experience can get a little tricky though at times.

Especially when frustration sets in.

Either on my part or the students.

Three things to remember when aiming for an optimal learning experience.

1) Clear goals

2) Immediate feedback

3) A balance between the ability of the doer and the challenge of the task

Creating clear goals seemed to get better each time.

I learned quickly where loopholes would be found

And addressed those head on as we headed into a task.

Immediate feedback was sometimes right on point

And sometimes left me feeling like I was playing whack-a-mole.

I soon realized that when I was found running around the classroom

In a state of total frustration,

It was actually because the task I had selected was not balanced between the ability and challenge level for the student.

As I got better with creating thin slicing learning activities,

I started to see the magic happen.  

Not only were students being more successful

Because the challenge was very small between each task,

The frustration levels decreased dramatically.

And then a wonderful moment would appear that would take me by surprise.

STUDENTS WANTED A HARDER PROBLEM!

The excitement at being able to solve more difficult problems was amazing!

You could hear it.

You could see it.

And I, as the teacher, just revelled in the moment.

This is what I had been seeking.

My goal for this next year is to create more thin slicing opportunities.

For some concepts, it's super easy.

For others, it takes more time to set up a series of problems.

I conducted the thin-slicing lessons usually two different ways.

Sometimes, I would have the problems written out on cards,

And as students completed one, I would hand them another as I made my rounds.

This was beneficial as I could address mistakes and misconceptions for each small group

Without having to drag the entire group into the discussion.

Groups could keep working at their own pace,

Slowing down only when they started to struggle.

Other times, each group worked the same problem at the same time.

This allowed for quick little popcorn whole group discussions as we compared the boards

Before starting on the next problem.

Ch. 8 Reflection...Student Autonomy

Students were soooooo used to going to the teacher when things got challenging.

They didn't trust themselves.

They didn't trust their classmates.

But it all boiled down to one thing...

They didn't want to take the time to think.

Couple that with the teaching of not copying from others,

And students seemed at a loss of how to move forward.

Many class discussions had to be had

On what using others' thinking looked like,

What it meant,

And ultimately, how it could be helpful for everyone's learning!

We talked about the benefits of looking at other boards when the going got tough.

How was this helpful?

Students could find validation in what they were trying.

Students could discover multiple methods they may not have thought about.

Students could compare solutions or strategies

Which would then prompt more thinking on who was correct and where was the mistake.

One thing I need to work on,

Is how to use student autonomy to keep the problems flowing. 

Students are quick to erase once they have solve a solution.

It would be beneficial,

Especially during thin slicing problems,

That seem to be solved at a greater rate of speed,

To always keep the previous problem up on the board,

To allow for other groups to see the problem and keep moving.

To do this...

1) Have the problems numbered for easy reference between boards

2) Students MUST write down the problem before trying to solve to help communicate with other boards that are needing to move on.

3) Encourage just copying the problem and start solving on their own before assessing how the answer was derived.