I had to revise my warm-up three times today because it was, apparently, too confusing.

I ended up with:

I've been wanting my students to work on solving problems, but I seem to be unable to get them there. The sequence of events goes something like this:

Me: "Here's an interesting question. Why do you work on it for a while?"

**crickets**

Me: "I don't want to give you any tips because I want to see where you go with this."

**crickets**

Me: "So...get started. Try something."

Students: "We don't know what to do."

Me: "So try something."

Students: "We don't know what to try."

Me: "Try whatever you think may work. Experiment. Explore."

Students: "But what if the answer is wrong?"

Me: "Then you've learned something. Try something else next."

Students: "What should we try?"

I don't blame them for this at all. There are deep problems with the educational system that praises speed and success on the first try over experimentation and perseverance.

Typing sentences like that make me feel old.

I'm not sure how to push that kind of thinking, how to support it and hope to foster growth mindset with people who think that if they don't get the answer the first time and get it instantly, they are too stupid to breathe.

Yesterday, one of my groups asked me a question about directions.

Students: "Mr. Aion, how are we supposed to solve this?"

Me: "When in doubt, ask Jane." (Note: Student's name is not actually Jane. I'm calling her Jane for the purposes of the post.)

S: "Are you saying we're dumb??"

Me: "No. You're very bright and that's sometimes your problem."

S: "What?"

Me: "Because you're bright, you think that you should instantly understand everything. You're great at a ton of things. You're not great at sticking with something until you solve it. Jane, however, is amazing at working at something until she gets it. She rarely asks me questions because she prefers to work things out on her own and she knows that she can. I know that you can do that too, but you don't believe it and so you ask me questions. When in doubt, ask Jane."

10 years of teaching and I still don't know how to balance support and enabling.

# Re-Learning To Teach

After several years in the classroom, I've decided that I want to be a better educator. These are my exploits and thoughts as I strive to rediscover my passion and purpose.

## Friday, December 2, 2016

## Thursday, December 1, 2016

### Day 66: Puzzle Pieces

Posted by
Justin Aion
at
4:01 PM

For the last few years, I've been presenting at national and regional conferences about the benefits of blogging as reflective practice.

Student: Mr. Aion, I can't see the board.

Me: You can move up. There are empty seats up in the front.

Student: I don't want to.

Last night, I submitted my first proposal for a session that was totally unrelated to blogging. I submitted a proposal to talk at the NCTM Regional conferences about using physical manipulatives in secondary classes.

Elementary school kids get to play with blocks and counters and toys all the time! Why not high school kids? I wrote up the proposal to be a workshop session, which is 75 minutes and will have participants develop lessons and activities in groups, covering various content.

If it gets accepted in either Orlando or Chicago, I'll have several months to figure out what and how I'm going to facilitate.

I have been trying to include as many physical manipulatives in my classes as possible, with mixed results.

I am deeply struggling with getting two of my classes to retain information. Much of it is directly related to the attention that they are paying (or not) in class. I've been working with them to increase the level of engagement when I'm not making direct eye contact.

Student: Mr. Aion, I can't see the board.

Me: You can move up. There are empty seats up in the front.

Student: I don't want to.

I was asked the same question four times in a row because, not only did they not hear the answer, they weren't listening to what the previous student was asking.

It's hard for me to tell the cause of this. If they are just not paying attention, it's one thing, but if that lack of attention is because they are concentrating too hard on what they want to be asking, it's something else.

I've been hearing similar stories from other teachers in the building. I find this encouraging because it means it's not just me or something I'm doing.

It's also discouraging because it means it's systemic.

There is a puzzle here and I'm just beginning to see what I'm missing.

## Wednesday, November 30, 2016

### Day 65: Trying Again

Posted by
Justin Aion
at
3:57 PM

When I first decided to use my Integrated Math class to work on Project-Based Learning, I knew that that there were going to be perils and pitfalls. I also knew that most of them were going to be mine.

Over the past month of so, my students have been working in groups to develop proposals, blueprints, budgets and presentations for a greenhouse on which the school and community would vote. The winning proposal would be built and filled with flowers, vegetables and herbs, and tended by students.

The presentations were supposed to be completed before Thanksgiving break.

They were not. I let them put the finishing touched on them during the long weekend and they presented today.

My main criticism for them was none of the presentations were of a quality that I would feel comfortable taking to local businesses to ask for donations.

I shoulder a HUGE amount of the responsibility for this. I made many assumptions about student time, ambition, drive and motivation going forward in this project and very few of them were accurate.

Things I should have done:

Organized our guest speaker MUCH earlier in the project (like day 3)

Held regular class meetings to talk about progress and problems

Held regular meetings to discuss expectations

Provided examples of business plans/proposals for them to model

Broken the project into smaller, bite-sized pieces

So...now what?

Do we take what we have, give grades and move on?

I think not. I think I'm going to use this as a growth mindset experience for them and for myself.

Tomorrow, we are starting over. Sort of...

Their assignment tonight was to brainstorm every aspect that would be needed to make this project a reality. Tomorrow, we're going to discuss what needs to be done, how we can achieve it, and break those tasks into smaller pieces.

Small, self-assigned groups will tackle each piece, including 3D modeling, research, design, presentation, budgets, etc.

We will move forward, we will continue to work and we will do so together.

I believe in this project and the students have shown great enthusiasm and interest in it. I will practice what I preach and learn from my failures.

We will try again!

Over the past month of so, my students have been working in groups to develop proposals, blueprints, budgets and presentations for a greenhouse on which the school and community would vote. The winning proposal would be built and filled with flowers, vegetables and herbs, and tended by students.

The presentations were supposed to be completed before Thanksgiving break.

They were not. I let them put the finishing touched on them during the long weekend and they presented today.

My main criticism for them was none of the presentations were of a quality that I would feel comfortable taking to local businesses to ask for donations.

I shoulder a HUGE amount of the responsibility for this. I made many assumptions about student time, ambition, drive and motivation going forward in this project and very few of them were accurate.

Things I should have done:

Organized our guest speaker MUCH earlier in the project (like day 3)

Held regular class meetings to talk about progress and problems

Held regular meetings to discuss expectations

Provided examples of business plans/proposals for them to model

Broken the project into smaller, bite-sized pieces

So...now what?

Do we take what we have, give grades and move on?

I think not. I think I'm going to use this as a growth mindset experience for them and for myself.

Tomorrow, we are starting over. Sort of...

Their assignment tonight was to brainstorm every aspect that would be needed to make this project a reality. Tomorrow, we're going to discuss what needs to be done, how we can achieve it, and break those tasks into smaller pieces.

Small, self-assigned groups will tackle each piece, including 3D modeling, research, design, presentation, budgets, etc.

We will move forward, we will continue to work and we will do so together.

I believe in this project and the students have shown great enthusiasm and interest in it. I will practice what I preach and learn from my failures.

We will try again!

## Tuesday, November 22, 2016

### Day 62: Patterns

Posted by
Justin Aion
at
4:12 PM

We spent all of my classes today talking about a single pattern from our warm-up.

In the Math 7, the discussion was about how we visualize this pattern and how it grow. In Pre-Algebra, I told the story of Gauss and finding the sum of the first 100 integers. As is usually the case when I tell a story, the students were highly engaged.

In Integrated math, this pattern moved us into a discussion of the math electives that we are trying to develop for the school. We ended up talking about Pascal's Triangles and polynomial expansion.

In first period, we talked about code-switching.

In second, we talked about the Alt-Right and the aspects of the election that the students didn't know about.

In third, we examined some of my favorite recreational math.

Overall, I very much enjoyed today and, while not directly related to the curriculum, we were solidly focused on Standards of Mathematical Practice 2 and 8.

I can think about numbers in many ways.

I can solve problems by looking for rules and patterns.

Also, I finished the last layer of polyurethane on my first bowl and turned a new handle for the crockpot!

In the Math 7, the discussion was about how we visualize this pattern and how it grow. In Pre-Algebra, I told the story of Gauss and finding the sum of the first 100 integers. As is usually the case when I tell a story, the students were highly engaged.

In Integrated math, this pattern moved us into a discussion of the math electives that we are trying to develop for the school. We ended up talking about Pascal's Triangles and polynomial expansion.

In first period, we talked about code-switching.

In second, we talked about the Alt-Right and the aspects of the election that the students didn't know about.

In third, we examined some of my favorite recreational math.

Overall, I very much enjoyed today and, while not directly related to the curriculum, we were solidly focused on Standards of Mathematical Practice 2 and 8.

I can think about numbers in many ways.

I can solve problems by looking for rules and patterns.

Also, I finished the last layer of polyurethane on my first bowl and turned a new handle for the crockpot!

## Monday, November 21, 2016

### Day 61: Cupcakes

Posted by
Justin Aion
at
4:01 PM

Today was designed to be a practice day for the Math 7 kids. We've been working on fraction division, which is admittedly, a difficult topic.

In the first class, I had a worksheet of practice problems.

They were a bit beyond reach. They would have been fine had we been doing "keep-change-flip" or the butterfly method or any of that nonsense, but since we've been using physical counters or pictures, they were a bit ugly. The kids got bogged down with the numbers themselves instead of the operations.

So I revised it. For the second class, I focused on word problems.

"Peter wants to make cupcakes. They take 1/3 cup of flour per batch and he has 7 cups of flour. How many batches can he make?"

We talked about the problem for a little bit before even bringing up the idea of division. We talked about it as a practical measure. If you want to make a bunch of batches of cookies or cupcakes, you need to make sure you have enough ingredients.

They got the solution to the problem without using fraction division and we talked about how that was fine.

The math should fit the problems. Problems shouldn't be invented to fit the math.

"You got the right answer and all of your work is valid, but I wanted you to use a different method, so you get an F" is one of the MANY reasons why so many kids hate math.

The sheet that I gave them had 10 word problems. I told them to read all 10 before deciding where to start. I told them that the problems lent themselves to fraction division, but however they solved them was fine with me. I told them they needed to show their work.

Then the period ended.

In the first class, I had a worksheet of practice problems.

They were a bit beyond reach. They would have been fine had we been doing "keep-change-flip" or the butterfly method or any of that nonsense, but since we've been using physical counters or pictures, they were a bit ugly. The kids got bogged down with the numbers themselves instead of the operations.

So I revised it. For the second class, I focused on word problems.

"Peter wants to make cupcakes. They take 1/3 cup of flour per batch and he has 7 cups of flour. How many batches can he make?"

We talked about the problem for a little bit before even bringing up the idea of division. We talked about it as a practical measure. If you want to make a bunch of batches of cookies or cupcakes, you need to make sure you have enough ingredients.

They got the solution to the problem without using fraction division and we talked about how that was fine.

The math should fit the problems. Problems shouldn't be invented to fit the math.

"You got the right answer and all of your work is valid, but I wanted you to use a different method, so you get an F" is one of the MANY reasons why so many kids hate math.

The sheet that I gave them had 10 word problems. I told them to read all 10 before deciding where to start. I told them that the problems lent themselves to fraction division, but however they solved them was fine with me. I told them they needed to show their work.

Then the period ended.

## Friday, November 18, 2016

### Day 60: Visiting Next Door

Posted by
Justin Aion
at
3:51 PM

The woman who teaches the Pre-Calc and Algebra 3 classes next door to me was out today. Her students kept coming to my room to ask me for help on their assignments. I eventually gave my own students an assignment to work on and just traded classes with the sub who was next door.

I had a blast!

There is something invigorating about running back and forth between two groups of students, one of which is working on function composition while the other is dividing fractions. It's interval training for the mind.

I've been thinking more and more about using my time in the wood shop to make fraction bars. The teacher who was in this room last left a game called Fraction Stax which has some pretty awesome pieces, just not enough of them.

I need to decide if I want to make mine like these, or more like the paper ones that my students have been using.

I also have a considerable amount of grading that I have to do this weekend. Using Standards-Based Grading means I have fewer grades that go in and I've been forgetting to actually do them. I also need to make up an assessment for the Pre-Algebra kids.

That's all for me this week. My daughter turns 7 today, so I'm going to spend some time with her and eat pizza and cake.

Here's the post I wrote when she was born.

I had a blast!

There is something invigorating about running back and forth between two groups of students, one of which is working on function composition while the other is dividing fractions. It's interval training for the mind.

I've been thinking more and more about using my time in the wood shop to make fraction bars. The teacher who was in this room last left a game called Fraction Stax which has some pretty awesome pieces, just not enough of them.

I need to decide if I want to make mine like these, or more like the paper ones that my students have been using.

I also have a considerable amount of grading that I have to do this weekend. Using Standards-Based Grading means I have fewer grades that go in and I've been forgetting to actually do them. I also need to make up an assessment for the Pre-Algebra kids.

That's all for me this week. My daughter turns 7 today, so I'm going to spend some time with her and eat pizza and cake.

Here's the post I wrote when she was born.

## Thursday, November 17, 2016

### Day 59: Downs and Ups

Posted by
Justin Aion
at
3:53 PM

Today was filled with an odd assortment of great things and deeply frustrating things. I'll write about the frustrating ones first so that I can end my writing on a high note.

Many of my students are struggling with timely task completion. I know that failing to understand certain concepts has a tendency to slow down work, and I'm alright with that. If you're having difficulty, I want you to work more slowly and carefully, to allow me to help you as you need.

At the same time, if I assign 20 problems to be done in 40 minutes and you get to number 6, we are having an issue that needs to be addressed. Similarly, I try to make my class as hands on as possible, but that still requires students to follow directions for an activity.

Several of the students in Math 7 and Pre-Algebra have been complaining about how they don't understand what's going on, but when I try to explain, or answer their questions, they are busy touching other kids or throwing things around the room.

Today's warm-up was mental math: 104 + 97

"What strategies did you use to solve this in your head?"

I was getting increasingly frustrated with numerous iterations of the following conversation:

"I just added it."

Me: "How did you add it?"

"I put the things together."

Me: "What does that look like in your head."

"It looks like adding."

Me: "Can you show us on the board?"

**write standard vertical column algorithm**

Me: "You did this in your head you visualized columns?"

"No. I didn't need to. I just did it."

So I put up a few examples of what I do in my head.

"I start at 104 and add 90, which brings me to 194, adding 6 more brings me to 200. I have one more left over to put me at 201."

They stare blankly at me.

"Or, I know that I need 3 more to go from 97 to 100, so I borrow it from the 104, leaving it with 101 on that side. 100 + 101 gives me 201."

At this point, I hoped the pump was primed and asked them how they had done.

"I just added them."

On the upside, some of the kids in Math 7 gave me amazing ways to think about this question.

One student said he pictured a square with 100 pieces and four on the end. Then he pictures a square of 100 with 3 missing. He moved 3 of the four to fill in the unfinished block, making one block of 100 and one of 101.

Fantastic!

On top of this, we continued working with our fraction bars on fraction division and it seems as though a large number of the kids are actually getting it, and more importantly, really enjoying it! I'm thinking that the next woodworking project will be to make a wooden set of fraction blocks.

I see much cutting and sanding in my future...

The other amazing thing that happened today was that my Integrated Math class was able to Skype with a landscape architect to talk about their gardening projects. Our superintendent let me know that she won a $500 grant to build a garden at the school, so the pressure is on. The groups were supposed to present today, but I think the Skype call made them rethink the way they were working on their projects.

I foresee much revision and hard work in their futures...

They were supposed to be presenting yesterday and today, but none of the groups were ready. I would rather take more time and have the products be of better quality.

YAY! I did it right! I wrote about the bad stuff first and the good stuff last and I feel great now!

Many of my students are struggling with timely task completion. I know that failing to understand certain concepts has a tendency to slow down work, and I'm alright with that. If you're having difficulty, I want you to work more slowly and carefully, to allow me to help you as you need.

At the same time, if I assign 20 problems to be done in 40 minutes and you get to number 6, we are having an issue that needs to be addressed. Similarly, I try to make my class as hands on as possible, but that still requires students to follow directions for an activity.

Several of the students in Math 7 and Pre-Algebra have been complaining about how they don't understand what's going on, but when I try to explain, or answer their questions, they are busy touching other kids or throwing things around the room.

Today's warm-up was mental math: 104 + 97

"What strategies did you use to solve this in your head?"

I was getting increasingly frustrated with numerous iterations of the following conversation:

"I just added it."

Me: "How did you add it?"

"I put the things together."

Me: "What does that look like in your head."

"It looks like adding."

Me: "Can you show us on the board?"

**write standard vertical column algorithm**

Me: "You did this in your head you visualized columns?"

"No. I didn't need to. I just did it."

So I put up a few examples of what I do in my head.

"I start at 104 and add 90, which brings me to 194, adding 6 more brings me to 200. I have one more left over to put me at 201."

They stare blankly at me.

"Or, I know that I need 3 more to go from 97 to 100, so I borrow it from the 104, leaving it with 101 on that side. 100 + 101 gives me 201."

At this point, I hoped the pump was primed and asked them how they had done.

"I just added them."

On the upside, some of the kids in Math 7 gave me amazing ways to think about this question.

One student said he pictured a square with 100 pieces and four on the end. Then he pictures a square of 100 with 3 missing. He moved 3 of the four to fill in the unfinished block, making one block of 100 and one of 101.

Fantastic!

On top of this, we continued working with our fraction bars on fraction division and it seems as though a large number of the kids are actually getting it, and more importantly, really enjoying it! I'm thinking that the next woodworking project will be to make a wooden set of fraction blocks.

I see much cutting and sanding in my future...

The other amazing thing that happened today was that my Integrated Math class was able to Skype with a landscape architect to talk about their gardening projects. Our superintendent let me know that she won a $500 grant to build a garden at the school, so the pressure is on. The groups were supposed to present today, but I think the Skype call made them rethink the way they were working on their projects.

I foresee much revision and hard work in their futures...

They were supposed to be presenting yesterday and today, but none of the groups were ready. I would rather take more time and have the products be of better quality.

YAY! I did it right! I wrote about the bad stuff first and the good stuff last and I feel great now!

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