I don't seem to have enough graded assignments to satisfy anyone.

The kids are unhappy because it means that the assignment they decided not to do is worth WAY more than they thought. The parents are unhappy because they think I haven't been updating grades, which translates in many minds to "not teaching."

I worry that to many people, the phrase "how is my child doing?" translates to "what is her/his grade?" I think those are separate things. I could argue that a student with a B is doing VERY poorly while one with a D is doing very well.

In any event, trying to work within our current system means that I need more grades. So pre-algebra had a quiz today.

Since we have double periods, I spent the first period going over homework and answering any questions that they were willing to ask. In the second period, we had the quiz. There were 15 questions on addition, subtraction, multiplication and division of fractions.

I asked them, when they were finished, to write at the top of the page how well they think they did.

The majority of the students thought they earned a C or below. Only one student wrote that she felt she earned an A. Tomorrow, we are going to have a talk (and I'm going to take their papers home) and write about why they felt they had earned that grade, how true it was to reality and what they could do in the future to improve both their grade and their perception of how they performed.

They did not do as well as I would have hoped. Very few passing grades and most of them are either careless errors, or using the wrong procedures at the wrong times. It's very hard not to think that the last two weeks were a total waste of time and effort.

In geometry, we finished the last trial of The Lady and The Tiger. I think when I do this again, I'll change it to a pot of gold to make it less sexist.

As this activity has progressed and we have talked about good reasoning versus faulty, I've been increasingly impressed with their logic. Today was, by far, the most difficult puzzle. They worked VERY hard and good reasoning, but all got eaten.

Afterwards, we looked at the scoreboard and I jokingly told the winning group that they were good, but everyone else failed for the year.

And two of my students LOST THEIR MINDS!

They began screaming about how they were going to go to the school board, etc. etc.

The rest of the class told them to calm down, that it was just a joke, but they were well into hysterics.

I have many feelings about this particular situation, but I don't have any idea how to sort them. What I DO know is that these two have been complaining about my class to anyone who will listen. The set of "anyone who will listen" does not include the majority of my students, so I'm not concerned about that.

I'm more concerned about how I can help those two students. I believe in the efficacy of my methods and I truly believe that, if given the chance, these two students would greatly benefit from the critical thinking and logical reasoning that I'm trying to promote.

I need to find a way to reach them and get them to give it a chance: to stop worrying about their grades and being more concerned about the learning.

An assignment about following directions was met with "Oh my god! This is so stressful."

I'm not sure how to break through...

## Tuesday, September 30, 2014

## Monday, September 29, 2014

### Day 24: Whose Job Is It Anyway?

Posted by
Justin Aion
at
4:13 PM

I want to write a post about a student's responsibility for learning versus a teacher's responsibility for teaching. I think about this frequently, mostly every time an administrator tells me that we need to be engaging our students.

I am 100% on board with this!

I think that what I do is engaging. I try very hard to come up with lessons that will catch the attention of my students and I try to make my assignments relevant to the tasks at hand. My students need practice working with our concepts, as do all students.

Rather than spending the 90 minutes of my class period grinding through practice problems, I try to incorporate activities that get kids up and moving, get them talking about math and thinking, get them working with their peers to answers important, relevant questions.

With two notable exceptions, I think I'm doing a fairly good job. The first one I notice is during 1st period. at 7:50 am, a large portion of my students are still asleep. Many have just rolled out of bed and aren't awake either physically or mentally. When I see them later in the day, they are up, alert and involved, but at 7:50, they simply are not with it.

"Shhh...it's time for learning..." |

A large portion of this group falls into the second category: assignments. Many of my students will engage in discussions in class in a very productive way, offering answers and contributing very positively to the learning environment.

Until it comes time to actually write something down.

My school has a homework policy, that being that teachers will assign regular homework. I have stopped grading homework regularly because, were I to do so, a large portion of students who understand the concepts and perform adequately on assessments, would fail my class.

In period 1 today, not a single student had done the assignment from the weekend.

Not a single one.

For the majority, this is due to lack of organization. They don't bring materials to class or take materials home. They are so good at compartmentalization, that when they leave my room, they often don't think about it at all until the enter again the next day.

This is something that I am used to and don't consider a phenomenon among my students alone. I know that, unless there is a concerted communal effort to help kids get organized, such as a study skills class, or a consistent homework sheet, students are terrible at this.

I don't judge at all! I am horrendous at organization. I am awesome at following check lists.

Now I just to work on writing good check lists.

So this is my struggle:

At what point is the student responsible for their own learning?

I am trying very hard to make my classroom a learning environment. I try to make it safe for students to experiment with academic methods and I don't force them to use whatever system works for me. The classes where I was least engaged were the ones where the teachers required that we copy things verbatim, or used a VERY specific format. (I'm looking at you, high school physics class!)

I tell them frequently that I don't care HOW they solve a problem as long as the method is valid and they understand what they are doing well enough to explain it to someone else.

At what point can I be comfortable to say "I've done everything I can to help this student. It's now his/her turn to do the work."

A few years ago, an administrator (not mine) told me that we need to meet them halfway. I partially agree with this. The phrase I prefer is "meet them where they are." In my experience with this specific subset of students, I have found that halfway is often not enough.

When someone has their back to you, you can't simply get closer. You have to tap them on the shoulder.

Ideally, we would never stop tapping. We would keep tapping until they turned around. Then we would encourage them to come with us, helping them run, or walk, or crawl, as far they needed us to help them.

In reality, we simply can't. Class sizes are simply too large to provide the individual attention that many students need or want.

I want to be clear on two points.

First, the metaphor above doesn't require that they come with US, simply that they move forward. If they don't know which direction in which to move, we can offer them choices. Under no circumstances do I think that my road is the only one and students who choose a different path are wrong. They are individuals with their own goals and desires. I don't need them to move in my direction, simply to move.

Second, I am not talking about academic achievement, but rather academic willingness. A student who is struggling, but working, I would start a war with Troy over! My purpose here is talk about those students who refuse to pick up a pencil. When I ask them to sit up, they stare blankly at me and put their heads down. When I ask them to get started on an assignment, they ask for a pencil, then let it sit on their desk.

I want to help them, but I don't know how.

"Make the lessons and assignments more engaging."

No matter how delicious the food happens to be, the person who refuses to put it in his mouth will never know.

No matter how engaging I make my lessons, at some point, the student has to do the work.

I don't know where that point is.

In VERY general terms, I think the graph of responsibility looks something like this:

As the years progress, teachers should be handing it off to students so that, eventually, we can be comfortable saying "You are now adults and you have to make your own choices."

Isn't the whole purpose of education that we are trying to develop capable, independent citizens?

I am conflicted.

Minnesota Teacher of the Year, Tom Rademacher used a much better analogy than I did.

```
@JustinAion @tritonkory It's kinda like trying to draw a straight line between where the beach starts and the ocean ends.
```

— Tom Rademacher (@MrTomRad) September 29, 2014

## Thursday, September 25, 2014

### Day 23: I Am LOVING These Rectangles!

Posted by
Justin Aion
at
4:50 PM

I'm ready for the weekend. Thankfully, we have a clerical day tomorrow, so I have put off all of my grading until then. I've also decided that I can't spend any more time explicitly teaching fraction addition and subtraction.

So today, we moved on to multiplication. Of all of the rectangle manipulation of fractions, this was the one that I had the most difficulty figuring out how to communicate. With addition and subtraction, we were taking rectangles with different sized slices, cutting them into equal sized slices and moving them around.

Multiplication was a little more complicated, so I started off simple.

Me: "If I have a problem like 2 x 3, what's happening here?"

S: "We are adding two, three times." (I swear to God this was said without prompting!)

The conversation went well from there. We talked about the difference between whole boxes (integers) and partial boxes (fractions) and how to manipulate them to solve a multiplication problem. After I moved a student from a talkative group, everything else went fairly well. Student participation was up and notes were being taken.

They even asked to do more and harder examples!

Their willingness to take notes makes me think that they were not doing so before simply because I wasn't explicitly telling them to. Hopefully by the end of the year, I won't have to, but if that's what it takes for now, I'll start the class by telling them to take their notebooks out.

In geometry, I started one of my favorite lessons! I had them watch this clip from Labrynth:

I paused it in the middle and asked them what question THEY would ask.

They tried every conceivable way to cheat. They wanted to ask two questions, or compound questions, or ask one to each door. When I realized they were having trouble with the concept, I picked two kids. I took four post-it notes and wrote True, Lie, Live, Die on them. I put the first two behind my back, shuffled and had a kid pick one, then did the same with the second pair.

Now, only those two knew who told the truth and whose door lead to certain death. Then students were able to ask them questions. After that, I talked about the idea of The Lady and The Tiger. Students were put into groups and asked which door they would pick.

Again, they tried getting around the rules, but I refused to ask any questions. We managed to get through 3 trials before the period ended and they were VERY excited to finish the days in the coming week.

One student was distraught because her team didn't have as many points as the other teams. She wanted to change teams and was worried that they were going to bring her grade down. We had a chat about how she could be helping them to improve.

I ignored her questions about the grade for the exercise.

Why can't we just do some things for fun and education? Why does it always have to be for a grade. I think I'm going to stop handing back assignments with grades on them, only giving feedback, and see how long it takes that class to have a breakdown.

I'm taking bets.

So today, we moved on to multiplication. Of all of the rectangle manipulation of fractions, this was the one that I had the most difficulty figuring out how to communicate. With addition and subtraction, we were taking rectangles with different sized slices, cutting them into equal sized slices and moving them around.

Multiplication was a little more complicated, so I started off simple.

Me: "If I have a problem like 2 x 3, what's happening here?"

S: "We are adding two, three times." (I swear to God this was said without prompting!)

The conversation went well from there. We talked about the difference between whole boxes (integers) and partial boxes (fractions) and how to manipulate them to solve a multiplication problem. After I moved a student from a talkative group, everything else went fairly well. Student participation was up and notes were being taken.

They even asked to do more and harder examples!

Their willingness to take notes makes me think that they were not doing so before simply because I wasn't explicitly telling them to. Hopefully by the end of the year, I won't have to, but if that's what it takes for now, I'll start the class by telling them to take their notebooks out.

In geometry, I started one of my favorite lessons! I had them watch this clip from Labrynth:

I paused it in the middle and asked them what question THEY would ask.

They tried every conceivable way to cheat. They wanted to ask two questions, or compound questions, or ask one to each door. When I realized they were having trouble with the concept, I picked two kids. I took four post-it notes and wrote True, Lie, Live, Die on them. I put the first two behind my back, shuffled and had a kid pick one, then did the same with the second pair.

Now, only those two knew who told the truth and whose door lead to certain death. Then students were able to ask them questions. After that, I talked about the idea of The Lady and The Tiger. Students were put into groups and asked which door they would pick.

Again, they tried getting around the rules, but I refused to ask any questions. We managed to get through 3 trials before the period ended and they were VERY excited to finish the days in the coming week.

One student was distraught because her team didn't have as many points as the other teams. She wanted to change teams and was worried that they were going to bring her grade down. We had a chat about how she could be helping them to improve.

I ignored her questions about the grade for the exercise.

Why can't we just do some things for fun and education? Why does it always have to be for a grade. I think I'm going to stop handing back assignments with grades on them, only giving feedback, and see how long it takes that class to have a breakdown.

I'm taking bets.

## Wednesday, September 24, 2014

### Day 22: The Pump Needs Priming

Posted by
Justin Aion
at
4:28 PM

Since my previous plan for pre-algebra (to have students devise problems and create a Tarsia puzzle for other groups) flopped so miserably, my plan for today was to give them a puzzle that I had devised. Working in groups of 3's and 4's, students would solve fraction addition and subtractions problems and match questions with answers to reassemble a square.

That was the plan, anyway.

In reality, only two of the groups managed to solve more than two of the fractions in the hour and of those two, neither was able to reassemble the puzzle.

The questions that they asked me made it seem as though we had never talked about this material. One student even went so far as to say "I've never seen this before."

I felt as though I was in the Twilight Zone.

"Take the case of Mr. Justin Aion: a middle school math teacher in a moderately sized school. To all appearances, he has a normal classroom with normal students. In reality, each night, his students are replaced by identical clones who have never attended his class before. Each day, the students are confused about seemingly brand new material, while Mr. Aion is confused as to why his students are so confused. But this is all par for the course when you have registered for a class in...The Twilight Zone."

I want them to be able to do independent work, but I'm not sure how to get there. When I stand in front of the class and ask them to complete the next step, anyone whom I call on is able to give me a good answer. But it seems that as soon as I say "Great! Now you do it!" someone performs a full format on their brains and they are completely lost.

When I'm giving individual attention and assistance, the majority of the students seem to be asking the same questions and making the same mistakes. Even when they take their notes out and go over step-by-step how we did previous problems, they seem completely lost, as though they are notes taken by other people for other classes.

I know that they are largely unfamiliar with this method of adding and subtracting fractions, but we've now been covering it for a week and I feel as though more of the concept should have been retained.

When beginning a new concept, I allow a certain amount of time for students grasp it. I try to work with them patiently until they do. Then, we build from that foundation to higher concepts. As time passes however, I start to have the internal debate about blame.

The old me wants to say "I've spent enough time on this. If they don't get it, it's because they aren't paying attention or doing the work. I need to move on."

The new me is saying "This is a new concept and I need to give them time to master it. If you spend enough time working with it now, it will build that foundation that you're looking for. Front-load the skills and the content will follow."

The guy sitting on my head dressed in red and white stripes is wondering if, after a week of attempts and ineffective teaching, they aren't going to get it and I should cut my losses and try something else. Don't move on to a different topic, but try a more traditional method to transition them."

Old me rebuts with "How many different ways do you have to teach a basic concept before you can wash your hands of it??"

New me claims that you can NEVER wash your hands of it. Furthermore, if they haven't grasped the concepts, then I didn't teach them.

The striped me says that we can't spend the year on a concept that they should have mastered in 6th grade, but neither can we really move on without it. Kicking the can down the road only hurts the students in the long run. Instead, I should move on to the next topic and incorporate this concept into future lessons.

And then in came 8th period. Instead of explaining the exercise and then getting frustrated, I started with a review of the process. I put two different types of problems on the board and we went through them as a class.

And then they worked. They worked well.

Perhaps the wells are not dry, but simply need to be properly primed.

That was the plan, anyway.

In reality, only two of the groups managed to solve more than two of the fractions in the hour and of those two, neither was able to reassemble the puzzle.

The questions that they asked me made it seem as though we had never talked about this material. One student even went so far as to say "I've never seen this before."

I felt as though I was in the Twilight Zone.

"Take the case of Mr. Justin Aion: a middle school math teacher in a moderately sized school. To all appearances, he has a normal classroom with normal students. In reality, each night, his students are replaced by identical clones who have never attended his class before. Each day, the students are confused about seemingly brand new material, while Mr. Aion is confused as to why his students are so confused. But this is all par for the course when you have registered for a class in...The Twilight Zone."

I want them to be able to do independent work, but I'm not sure how to get there. When I stand in front of the class and ask them to complete the next step, anyone whom I call on is able to give me a good answer. But it seems that as soon as I say "Great! Now you do it!" someone performs a full format on their brains and they are completely lost.

When I'm giving individual attention and assistance, the majority of the students seem to be asking the same questions and making the same mistakes. Even when they take their notes out and go over step-by-step how we did previous problems, they seem completely lost, as though they are notes taken by other people for other classes.

I know that they are largely unfamiliar with this method of adding and subtracting fractions, but we've now been covering it for a week and I feel as though more of the concept should have been retained.

When beginning a new concept, I allow a certain amount of time for students grasp it. I try to work with them patiently until they do. Then, we build from that foundation to higher concepts. As time passes however, I start to have the internal debate about blame.

The old me wants to say "I've spent enough time on this. If they don't get it, it's because they aren't paying attention or doing the work. I need to move on."

The new me is saying "This is a new concept and I need to give them time to master it. If you spend enough time working with it now, it will build that foundation that you're looking for. Front-load the skills and the content will follow."

The guy sitting on my head dressed in red and white stripes is wondering if, after a week of attempts and ineffective teaching, they aren't going to get it and I should cut my losses and try something else. Don't move on to a different topic, but try a more traditional method to transition them."

Old me rebuts with "How many different ways do you have to teach a basic concept before you can wash your hands of it??"

New me claims that you can NEVER wash your hands of it. Furthermore, if they haven't grasped the concepts, then I didn't teach them.

The striped me says that we can't spend the year on a concept that they should have mastered in 6th grade, but neither can we really move on without it. Kicking the can down the road only hurts the students in the long run. Instead, I should move on to the next topic and incorporate this concept into future lessons.

And then in came 8th period. Instead of explaining the exercise and then getting frustrated, I started with a review of the process. I put two different types of problems on the board and we went through them as a class.

And then they worked. They worked well.

Perhaps the wells are not dry, but simply need to be properly primed.

## Tuesday, September 23, 2014

### Day 21: A Confluence and Accidental Math

Posted by
Justin Aion
at
3:20 PM

Today, two of my three classes are taking CDT tests. The geometry kids will take them tomorrow. I wrote last year about how this is the only version of a standardized test of which I approve. It provides dynamic questioning and immediate feedback for both students and teacher, not about individual questions, but about topics that require strengthening versus topics of strength.

In addition to that, we have Open House tonight from 6:30-8:30. Since I live almost an hour from the school, this means that I won't be going home. I will be staying through at school for 14 hours today and will be facing parents in clothing that has looked as though I was at school for 14 hours.

It turns out that this coordination of events works very well for me because of the schedule that I've been keeping. Last year, I was at school around 6:15, which meant I had to leave my house around 5:30. So my alarm went off at 5. I get to school this early because I use the time before the kids show up to make the copies I need, make sure my room is ready and that I'm in the proper frame of mind for homeroom and the day.

This year, at the encouragement of @VeganMathBeagle, I've been doing T25 in the mornings. This means that my alarm has been going off at the unholy hour of 4:30. Those 30 minutes make a HUGE difference.

Today, however, since my homeroom students were going to be testing, the only prep I had to do in the morning was to get the room ready. I was able to sleep in until 5!

Knowing that I won't be home until close to 10 tonight made those 30 minutes oh so sweet.

As my students completed their tests, they went onto the game site that isn't blocked by our firewall, Cool Math.

For the most part, students play 3 specific games. Up until this morning, it annoyed me that they were playing these games. This morning, I started watching them. I realized that they were performing complex mathematical analyses without realizing it! So, here are the games:

This is a game where the characters (surprisingly) run. They move through levels of ever increasing difficulty. Why is this different from (and significantly superior to) Temple Run?

As the level progress, the characters have to start moving in 3 dimensions. They have to jump over, under and around the environment as it progresses towards them.

Then it gets even better!

A few levels in, the player is given the ability to rotate the environment around the character! Players are forced to make instant decision of rotation to ensure that a surface will be under the character when they land!

Students don't have any idea how much mental effort it takes to rotate objects in their minds before they do so in reality! In my opinion, this is a solid math game to help develop spacial reasoning.

This is a strategic puzzle game where the player moves a cube around a floating platform. As they move off of a space, that space falls away from the board pretending the player from moving backward. The goal is to remove all of the spaces and make it to the exit as quickly as possible.

As the player progresses through the levels, new obstacles are added, including blocks that create or destroy bridges, or blocks that have to be hit several times before they fall away.

This is very similar to another game that my students like called Bloxorz where a player has to move a 1x1x2 column around a platform to get it to slide into a 1x1 slot. In this version, players are not timed, but the number of moves taken is counted.

Both of these games do a great job of helping students to think about planning both ahead and backwards, knowing where they need to end up and how to get there in the most efficient fashion.

Planning and strategy are also highly valued in the last game

Players take on the role of a ninja in charge of painting a dojo. This ninja, however, can only move in straight lines until he/she hits an obstacle. There are colored pots around the board and specific colors that have to be placed in certain spots. The player must run over the proper color before the space will accept it.

This game, along with B-Cubed, does a great job with helping students to view unintended consequences. "Oh man! I needed that spot there!" or "Oops! The ninja ran too far."

I think we spend a ton of time as teachers forgetting that play is a form a learning. Free play has value, as does directed play.

To underscore this point, our music teacher, who I consider one of the best teachers in the district, uses Guitar Hero as one the stations in his classroom. When people (adults) give him complain that he's just having the students play a stupid video game, his response is to invite them to sit and play the drums.

They usually can't.

A greater teacher than myself could probably come up with a way to get students to some metacognition while they play. I would love to have some sort of assignment where they could play some of these games and then do a write-up about the math involved and their strategies.

I'm just not sure how to do it without A) ruining the game for the them, or B) having the assignment be "Do a write-up of the math involved in this game the strategies that you used!"

I think a fantastic test of SMP1 would be "What is the highest level you can reach on Bloxorz?"

Perhaps the assignment for this game play would be to have students record which game they are playing and what levels they have beaten.

What I found interesting was that the students who chose puzzle games like the ones described above seemed to do better on the test today than those who chose games that required no thought, but merely reflex.

I know that correlation doesn't imply causality, but I found it interesting.

In addition to that, we have Open House tonight from 6:30-8:30. Since I live almost an hour from the school, this means that I won't be going home. I will be staying through at school for 14 hours today and will be facing parents in clothing that has looked as though I was at school for 14 hours.

"Good Evening! I'm Mr. Aion and I am your child's math teacher this year!" |

This year, at the encouragement of @VeganMathBeagle, I've been doing T25 in the mornings. This means that my alarm has been going off at the unholy hour of 4:30. Those 30 minutes make a HUGE difference.

Today, however, since my homeroom students were going to be testing, the only prep I had to do in the morning was to get the room ready. I was able to sleep in until 5!

Knowing that I won't be home until close to 10 tonight made those 30 minutes oh so sweet.

As my students completed their tests, they went onto the game site that isn't blocked by our firewall, Cool Math.

For the most part, students play 3 specific games. Up until this morning, it annoyed me that they were playing these games. This morning, I started watching them. I realized that they were performing complex mathematical analyses without realizing it! So, here are the games:

**Run 2**This is a game where the characters (surprisingly) run. They move through levels of ever increasing difficulty. Why is this different from (and significantly superior to) Temple Run?

As the level progress, the characters have to start moving in 3 dimensions. They have to jump over, under and around the environment as it progresses towards them.

Then it gets even better!

A few levels in, the player is given the ability to rotate the environment around the character! Players are forced to make instant decision of rotation to ensure that a surface will be under the character when they land!

Students don't have any idea how much mental effort it takes to rotate objects in their minds before they do so in reality! In my opinion, this is a solid math game to help develop spacial reasoning.

**B-Cubed**This is a strategic puzzle game where the player moves a cube around a floating platform. As they move off of a space, that space falls away from the board pretending the player from moving backward. The goal is to remove all of the spaces and make it to the exit as quickly as possible.

As the player progresses through the levels, new obstacles are added, including blocks that create or destroy bridges, or blocks that have to be hit several times before they fall away.

This is very similar to another game that my students like called Bloxorz where a player has to move a 1x1x2 column around a platform to get it to slide into a 1x1 slot. In this version, players are not timed, but the number of moves taken is counted.

Both of these games do a great job of helping students to think about planning both ahead and backwards, knowing where they need to end up and how to get there in the most efficient fashion.

Planning and strategy are also highly valued in the last game

**Ninja Painter 2**Players take on the role of a ninja in charge of painting a dojo. This ninja, however, can only move in straight lines until he/she hits an obstacle. There are colored pots around the board and specific colors that have to be placed in certain spots. The player must run over the proper color before the space will accept it.

This game, along with B-Cubed, does a great job with helping students to view unintended consequences. "Oh man! I needed that spot there!" or "Oops! The ninja ran too far."

I think we spend a ton of time as teachers forgetting that play is a form a learning. Free play has value, as does directed play.

To underscore this point, our music teacher, who I consider one of the best teachers in the district, uses Guitar Hero as one the stations in his classroom. When people (adults) give him complain that he's just having the students play a stupid video game, his response is to invite them to sit and play the drums.

They usually can't.

A greater teacher than myself could probably come up with a way to get students to some metacognition while they play. I would love to have some sort of assignment where they could play some of these games and then do a write-up about the math involved and their strategies.

I'm just not sure how to do it without A) ruining the game for the them, or B) having the assignment be "Do a write-up of the math involved in this game the strategies that you used!"

I think a fantastic test of SMP1 would be "What is the highest level you can reach on Bloxorz?"

Perhaps the assignment for this game play would be to have students record which game they are playing and what levels they have beaten.

What I found interesting was that the students who chose puzzle games like the ones described above seemed to do better on the test today than those who chose games that required no thought, but merely reflex.

I know that correlation doesn't imply causality, but I found it interesting.

## Monday, September 22, 2014

### Day 20: Fractional Bellyflop

Posted by
Justin Aion
at
4:02 PM

After several days of working with fractions and rectangles, I knew my students needed more practice, but I didn't want to just give them a worksheet. We are constantly being told, and I agree, that the best way to learn is to do. So I had an idea to get them to "do."

Last year, I discovered the name of this type of puzzle:

The beauty is that there are no edges and every piece you place MAY be right, but it may mess up others and you won't know until the end. It can be infuriating, but it's also GREAT for practicing calculation.

This type of puzzle is known as a Tarsia Puzzle and dozens of teachers have written about using them in class. When I used them last year, I created one, cut the pieces out and had my students assemble them. My idea this year was to have the students do it!

Here was the thought:

"Your group will create 8 fraction problems with addition and subtraction. You will also come up with plausible, but incorrect answers. You will then put the right answers across from the problems on this diamond sheet that I borrowed from Kathryn, with the wrong answers along the outside. Then you'll cut them out and pass them to another group to solve."

What a cool idea! Get the kids practicing problems and solving puzzles!

And then, instead of a beautiful and graceful swan dive, this activity not only landed on its ample, patchy-haired belly, but actually missed the water entirely, hitting with a sickening splat on the concrete about halfway between the lifeguard chair and the concession stand with other pool patrons hiding their children's eyes and calling not for an ambulance, but rather a coroner and a clean-up crew.

Of the 7 groups in my period 1, only one did what I asked of them. The other 6 stared off into space or went back to talking about their weekends. My frustration and irritation mounting, I went to the different groups to tell them to get to work. It quickly became apparent that, despite what I thought was success on Friday, the majority of the students had no idea what to do and, if they were trying the activity at all, were doing it completely wrong.

I spent some time going between the groups, trying to push them in the right direction, offering encouragement and guidance. As soon as I moved to another group, the vacant stares returned, making me think that many of my students were the counterpoint to the Weeping Angels, in that they only moved when someone was staring directly at them.

It became clear that I needed to do some sort of intervention. I pulled the class attention back to me and we went over a problem on the board, not only the problem itself, but how we are using the rectangles to solve them. I offered no information, but instead had my students tell me what to do next. I had them give me the steps that we took, which I wrote down on the board as they told me.

I handed out a notebook to every student who didn't have one so that they could write down the information. Even if they weren't going to DO it, writing it would solidify the concepts better than just listening to me or their peers.

I asked several students to come to the board to demonstrate, but they refused. I hate when I'm the one doing all of the work in class partially because I'm lazy, but mostly because I know how much more they will learn when THEY do it.

We have trained them for so long that doing something incorrectly is such a terrible thing that it's better for them to not even try.

I will continue to encourage and praise effort, regardless of the results. I will continue to try to make my class a safe place to fail. I will continue to have faith that this is a goal that can be accomplished.

But man is it frustrating...

Last year, I discovered the name of this type of puzzle:

The beauty is that there are no edges and every piece you place MAY be right, but it may mess up others and you won't know until the end. It can be infuriating, but it's also GREAT for practicing calculation.

This type of puzzle is known as a Tarsia Puzzle and dozens of teachers have written about using them in class. When I used them last year, I created one, cut the pieces out and had my students assemble them. My idea this year was to have the students do it!

Here was the thought:

"Your group will create 8 fraction problems with addition and subtraction. You will also come up with plausible, but incorrect answers. You will then put the right answers across from the problems on this diamond sheet that I borrowed from Kathryn, with the wrong answers along the outside. Then you'll cut them out and pass them to another group to solve."

What a cool idea! Get the kids practicing problems and solving puzzles!

And then, instead of a beautiful and graceful swan dive, this activity not only landed on its ample, patchy-haired belly, but actually missed the water entirely, hitting with a sickening splat on the concrete about halfway between the lifeguard chair and the concession stand with other pool patrons hiding their children's eyes and calling not for an ambulance, but rather a coroner and a clean-up crew.

Of the 7 groups in my period 1, only one did what I asked of them. The other 6 stared off into space or went back to talking about their weekends. My frustration and irritation mounting, I went to the different groups to tell them to get to work. It quickly became apparent that, despite what I thought was success on Friday, the majority of the students had no idea what to do and, if they were trying the activity at all, were doing it completely wrong.

I spent some time going between the groups, trying to push them in the right direction, offering encouragement and guidance. As soon as I moved to another group, the vacant stares returned, making me think that many of my students were the counterpoint to the Weeping Angels, in that they only moved when someone was staring directly at them.

Don't blink. Don't even blink. Blink and they stop working. |

It became clear that I needed to do some sort of intervention. I pulled the class attention back to me and we went over a problem on the board, not only the problem itself, but how we are using the rectangles to solve them. I offered no information, but instead had my students tell me what to do next. I had them give me the steps that we took, which I wrote down on the board as they told me.

I handed out a notebook to every student who didn't have one so that they could write down the information. Even if they weren't going to DO it, writing it would solidify the concepts better than just listening to me or their peers.

I asked several students to come to the board to demonstrate, but they refused. I hate when I'm the one doing all of the work in class partially because I'm lazy, but mostly because I know how much more they will learn when THEY do it.

We have trained them for so long that doing something incorrectly is such a terrible thing that it's better for them to not even try.

The J stands for "Jay" |

I will continue to encourage and praise effort, regardless of the results. I will continue to try to make my class a safe place to fail. I will continue to have faith that this is a goal that can be accomplished.

But man is it frustrating...

## Friday, September 19, 2014

### Day 19: Gallery Walk

Posted by
Justin Aion
at
3:07 PM

The pre-algebra class did a few more examples of adding and subtracting fractions using rectangles and then I unleashed them to work independently, or in groups as they saw fit. I had written 5 fraction expressions on whiteboards around the room and gave each kid a half sheet of graph paper. The task was to pick a problem, solve it showing all their work, then get it checked out. If it was good, they were to tape their problem up on the board and get another sheet for another problem. As I did yesterday, I sat at a desk and helped any students who came over.

The main issue that I saw was, when adding 1/3 and 1/4, why we would use a rectangle that was 3x4.

Me: "We use that so we can cut one direction evenly into 4ths and the other evenly into 3rds."

S: "...so this rectangle should be 1 by 3?"

It was quite clear that I'm not as good at explaining things as I had hoped. In any event, I believe in the efficacy of this method and will continue having them practice it.

At lunch, our building behavior coach approached me about one of my students. This young man has a history of discipline problems in the school. When security goes around in the morning to collect kids to speak to the vice principal about behavior of the previous day, this kid is always snatched up.

For me, he excels! He works hard, he's polite, he asks good questions. He plays around on his phone and he talks to people around him, but he does what I ask and he does it relatively well. Once he leaves my class, however, his day goes downhill.

So I went to see him in In-School Suspension.

I knelt down by his desk and asked what he was doing. He started telling me about other kids and I stopped him. We talked about how he does so well for me and how proud I am of the stuff that happens in my class. He's doing what he needs to do and doesn't let other stuff get in his way, so why does he when he leaves my room?

I may also be breaking through to some of the geometry students in terms of their priorities. Their options today were to continue working in their notes, work on their recycles (revisions of last weeks test), start the chapter assessment that's due on Monday, or work on the mobile problems. I told them from the beginning that the mobile problems were not for credit, but were a transition to the next chapter on logic and reasoning.

Several students, upon being reminded that they weren't getting points for the puzzles complained that they did them for nothing!

"Not for nothing. You did them to help hone your skills of logic and reasoning. Those are infinitely more important than 'points.'"

I've been concerned that period 8 hasn't been grasping the concepts that I've been trying to teach and, as a result, have been acting up more and more. Today, during our gallery walk activity, I was able to move between groups, helping them to work on the rectangles and discovered something interesting.

The class is having a little bit of difficulty, but the majority of the issues are stemming from a very small group who, when they have difficulty, throw things at everyone else and generally make the classroom as unproductive as possible. I need a solution.

They are already separated around the room, but that means they just end up yelling louder and further. I think I'll be rearranging seats this weekend and will put that group all together on one side of the room.

Overall, I'm still struggling with the same issues that I have in past years. When I am sitting with, or talking to, a group of students, they are on the ball and doing great work. As soon as I move away to work with another group, they stop working and start distracting others. I feel as though I am constantly putting out fires and running back to stop kids from lighting more.

I'm glad it's the weekend. I have many phone calls to make to try to get some kids back on track and still more to praise kids for their hard work.

The main issue that I saw was, when adding 1/3 and 1/4, why we would use a rectangle that was 3x4.

Me: "We use that so we can cut one direction evenly into 4ths and the other evenly into 3rds."

S: "...so this rectangle should be 1 by 3?"

It was quite clear that I'm not as good at explaining things as I had hoped. In any event, I believe in the efficacy of this method and will continue having them practice it.

At lunch, our building behavior coach approached me about one of my students. This young man has a history of discipline problems in the school. When security goes around in the morning to collect kids to speak to the vice principal about behavior of the previous day, this kid is always snatched up.

For me, he excels! He works hard, he's polite, he asks good questions. He plays around on his phone and he talks to people around him, but he does what I ask and he does it relatively well. Once he leaves my class, however, his day goes downhill.

So I went to see him in In-School Suspension.

I knelt down by his desk and asked what he was doing. He started telling me about other kids and I stopped him. We talked about how he does so well for me and how proud I am of the stuff that happens in my class. He's doing what he needs to do and doesn't let other stuff get in his way, so why does he when he leaves my room?

I may also be breaking through to some of the geometry students in terms of their priorities. Their options today were to continue working in their notes, work on their recycles (revisions of last weeks test), start the chapter assessment that's due on Monday, or work on the mobile problems. I told them from the beginning that the mobile problems were not for credit, but were a transition to the next chapter on logic and reasoning.

Several students, upon being reminded that they weren't getting points for the puzzles complained that they did them for nothing!

"Not for nothing. You did them to help hone your skills of logic and reasoning. Those are infinitely more important than 'points.'"

I've been concerned that period 8 hasn't been grasping the concepts that I've been trying to teach and, as a result, have been acting up more and more. Today, during our gallery walk activity, I was able to move between groups, helping them to work on the rectangles and discovered something interesting.

The class is having a little bit of difficulty, but the majority of the issues are stemming from a very small group who, when they have difficulty, throw things at everyone else and generally make the classroom as unproductive as possible. I need a solution.

They are already separated around the room, but that means they just end up yelling louder and further. I think I'll be rearranging seats this weekend and will put that group all together on one side of the room.

Overall, I'm still struggling with the same issues that I have in past years. When I am sitting with, or talking to, a group of students, they are on the ball and doing great work. As soon as I move away to work with another group, they stop working and start distracting others. I feel as though I am constantly putting out fires and running back to stop kids from lighting more.

I'm glad it's the weekend. I have many phone calls to make to try to get some kids back on track and still more to praise kids for their hard work.

## Thursday, September 18, 2014

### Day 18: Rectangle? Damn Near KILLTANGLE!

Posted by
Justin Aion
at
5:35 PM

After how well the rectangle talk went with the pair of students yesterday, I decided to scale it up to the class. My students (and every student I have ever encountered) have tremendous difficulty understanding the concept of fractions and the work of manipulating them. Last year, I was introduced to the work that Fawn does with rectangles and I embraced it whole-heartedly.

I continued our discussion from yesterday in talking about equivalent fractions:

My plan was to spend the first of the double period talking about the physical realities of fractions in terms of rectangles and pizza. My favorite way to start any discussion of fractions is with the following scenario:

"We had a party this weekend and it was awesome! We ordered some pizzas from a few different places. At this party, Ki-Shawn eats 3 slices of pizza and William eats 2 slices. Who ate more pizza?"

It seems like a simple question, but I keep the discussion going until a students points out that they might be different sized slices, so just knowing the number of slices isn't enough for us to tell who ate more.

So I lay out some more information. We ordered 2 large pizzas, but they came from two different places. One place cuts their pizza into 8 slices while the other cuts theirs into 12.

The students can see that they ate the same amount of pizza even though they ate a different number of slices. This leads into equivalent fractions and how, if we want to talk about slices of things, we need to those slices to be the same size.

Today, a student suggested that we slice the pizza slices up smaller so they are all the same size.

Me: "What do you mean?"

S: "We could cut the bigger slices into 3 and the smaller slices into 2 each. Then they'd be the same size."

AMAZING! This let us go right through to where I wanted to be! We did several examples of this process. I was hoping they would catch it sooner so we could do some activity on the vertical non-permanent surfaces, but they were highly engaged and asking good questions for clarification.

8th period decided to spend some time looking up answers to our #Estimation180 warm-ups so 9 kids knew exactly what the answers were. I gave a long rambling talk about having multiple lottery winners from the same town and how that indicates cheating. When I was tired of being yelled over, I handed out a worksheet and told them I would be sitting at a back table working with anyone who wanted help. Several students flocked over and anyone who came to ask a question was invited to sit and join us.

By the end of the period I had almost a dozen students sitting around me with graph paper and white boards working on adding and subtracting fractions.

I'm pleased with the lesson and will continue it tomorrow. My fraction questions are up on whiteboards around the room. The plan is to have them do the work and then go hang their answers, creating a gallery walk.

I think it should be a good time!

I continued our discussion from yesterday in talking about equivalent fractions:

My plan was to spend the first of the double period talking about the physical realities of fractions in terms of rectangles and pizza. My favorite way to start any discussion of fractions is with the following scenario:

"We had a party this weekend and it was awesome! We ordered some pizzas from a few different places. At this party, Ki-Shawn eats 3 slices of pizza and William eats 2 slices. Who ate more pizza?"

It seems like a simple question, but I keep the discussion going until a students points out that they might be different sized slices, so just knowing the number of slices isn't enough for us to tell who ate more.

So I lay out some more information. We ordered 2 large pizzas, but they came from two different places. One place cuts their pizza into 8 slices while the other cuts theirs into 12.

The students can see that they ate the same amount of pizza even though they ate a different number of slices. This leads into equivalent fractions and how, if we want to talk about slices of things, we need to those slices to be the same size.

Today, a student suggested that we slice the pizza slices up smaller so they are all the same size.

Me: "What do you mean?"

S: "We could cut the bigger slices into 3 and the smaller slices into 2 each. Then they'd be the same size."

AMAZING! This let us go right through to where I wanted to be! We did several examples of this process. I was hoping they would catch it sooner so we could do some activity on the vertical non-permanent surfaces, but they were highly engaged and asking good questions for clarification.

8th period decided to spend some time looking up answers to our #Estimation180 warm-ups so 9 kids knew exactly what the answers were. I gave a long rambling talk about having multiple lottery winners from the same town and how that indicates cheating. When I was tired of being yelled over, I handed out a worksheet and told them I would be sitting at a back table working with anyone who wanted help. Several students flocked over and anyone who came to ask a question was invited to sit and join us.

By the end of the period I had almost a dozen students sitting around me with graph paper and white boards working on adding and subtracting fractions.

I'm pleased with the lesson and will continue it tomorrow. My fraction questions are up on whiteboards around the room. The plan is to have them do the work and then go hang their answers, creating a gallery walk.

I think it should be a good time!

## Wednesday, September 17, 2014

### Day 17: Defining Success and Rectangles

Posted by
Justin Aion
at
4:13 PM

I've been thinking very heavily about the conversation that I had with my geometry students on Monday. They are, in my mind, overly concerned with getting into college, to exclusion of all else, including the actual act of "learning."

I expressed my discomfort with this notion on Twitter and had a very interesting conversation about teaching and parenting with Kory Graham.

How do I help my students? How do I help my own daughters?

I think this is part of a much larger discussion about how we as teacher define success versus how the parents of our students do versus how the students themselves do.

A few weeks ago, I was asked for my opinions about Common Core and standardized testing by a reporter from the New York Times. One of the things that I told her was that I don't see how, effective or not, standardized tests can even be designed until we have a national, or state, or local conversation about the basic question of the purpose of education.

I don't know how we can create assessments until we have answers, or at least discussion, about the following questions:

What is the purpose of education?

What does success look like?

My thoughts on those are constantly shifting, which is why I have discomfort with my current assessment and grading practices.

I'd like to write more about this, but my head isn't on straight at this point, so I'll talk about my classes instead.

My pre-algebra student demonstrated proficiency with calculator use, about which I have mixed feelings. We are working with fractions, fraction to decimal conversion, and ordering rational numbers. I've been giving my students to the opportunity to do some independent work, but I think today may be the last day for that. The advantage was that I was able to sit with a few students and talk about ordering fractions.

As is the case with much of my brilliant lessons, I channeled Fawn Nguyen. I plan to spend the next week (month, year) talking about fractions in terms of rectangles.

As I was working with my students about how to compare 4/7 and 3/5, one of the girls started talking about how she learned to compare fractions from a previous teacher. Her explanation included phrases like "since the denominators are both odd" and "then you add the top numbers."

At that point, my eye was twitching so heavily that they had to call the nurse.

I should also state that, had she been able to solve the problem using this method, I would have been more likely to listen and try to figure it out, but she couldn't. Not only couldn't she solve the problem, but she admitted that the process didn't make any sense.

So we talked about rectangles. We did it slowly. It was a conversation, rather than a lecture. They took great notes and asked great questions. Perhaps most encouraging of all was what one of them said.

"I really feel like I learned something today."

I''ll admit that I've been lost for the last several days, feeling as though I was killing time and watching unproductive struggles. I think this could be a bit of interest that I can leverage into a more productive discussion of fractions.

I expressed my discomfort with this notion on Twitter and had a very interesting conversation about teaching and parenting with Kory Graham.

```
@JustinAion And I will admit, that I am a parent who really thinks/know that college is only option for my girls. It's a must. #dontjudge :)
```

— Kory Graham (@tritonkory) September 17, 2014

```
@JustinAion It's hard. I always want more for them, just need to realize their more might not look the same as mine. Such a fine line.
```

— Kory Graham (@tritonkory) September 17, 2014

How do I help my students? How do I help my own daughters?

I think this is part of a much larger discussion about how we as teacher define success versus how the parents of our students do versus how the students themselves do.

A few weeks ago, I was asked for my opinions about Common Core and standardized testing by a reporter from the New York Times. One of the things that I told her was that I don't see how, effective or not, standardized tests can even be designed until we have a national, or state, or local conversation about the basic question of the purpose of education.

I don't know how we can create assessments until we have answers, or at least discussion, about the following questions:

What is the purpose of education?

What does success look like?

My thoughts on those are constantly shifting, which is why I have discomfort with my current assessment and grading practices.

I'd like to write more about this, but my head isn't on straight at this point, so I'll talk about my classes instead.

My pre-algebra student demonstrated proficiency with calculator use, about which I have mixed feelings. We are working with fractions, fraction to decimal conversion, and ordering rational numbers. I've been giving my students to the opportunity to do some independent work, but I think today may be the last day for that. The advantage was that I was able to sit with a few students and talk about ordering fractions.

As is the case with much of my brilliant lessons, I channeled Fawn Nguyen. I plan to spend the next week (month, year) talking about fractions in terms of rectangles.

As I was working with my students about how to compare 4/7 and 3/5, one of the girls started talking about how she learned to compare fractions from a previous teacher. Her explanation included phrases like "since the denominators are both odd" and "then you add the top numbers."

At that point, my eye was twitching so heavily that they had to call the nurse.

I should also state that, had she been able to solve the problem using this method, I would have been more likely to listen and try to figure it out, but she couldn't. Not only couldn't she solve the problem, but she admitted that the process didn't make any sense.

So we talked about rectangles. We did it slowly. It was a conversation, rather than a lecture. They took great notes and asked great questions. Perhaps most encouraging of all was what one of them said.

"I really feel like I learned something today."

I''ll admit that I've been lost for the last several days, feeling as though I was killing time and watching unproductive struggles. I think this could be a bit of interest that I can leverage into a more productive discussion of fractions.

## Tuesday, September 16, 2014

### Day 16: Nose to the Grindstone

Posted by
Justin Aion
at
4:14 PM

After the conversation that I had with the geometry students yesterday, I had been thinking about the amount and type of practice that I've been having them do. While I think it's fair to have my class be a different style than what they are used to, I think it would be beneficial for me to offer a transition to the unfamiliar territory.

After reading the letters that I asked them to write this weekend, It's obvious that they are much more comfortable with working through lots of practice problems. Clearly, this is not true for everyone, but many expressed this concern.

So today, I gave them some options. I printed out several worksheets with practice problems from the current chapter. They could work on those if they wanted the practice. They could continue working in the guided notes, if they chose. They could work on revising their assessments from Friday.

I also told them that, if they chose to do so, they could waste their time. As long as they weren't stopping others from learning, they could spend the time as they wished. I explained that I am trying to move them in the direction of self-directed learning and being responsible for their own education. Since they are still 13 and 14, I don't expect that they will always make good, mature decisions, (especially because in my 30's I rarely do that myself) but I believe that there are lessons to be learned from failure and making bad choices.

And so I gave them those options and let them go.

The geometry kids, with a 10% error, all worked very hard on the assignment of their choice. I made myself available for those who had questions, or simply wished to talk things out. I was able to circulate and watch their efforts, talking to them as more of a peer than an authoritative figure.

THIS is how relationships get built.

And yet...

As I sat there, casually hanging out, waiting for students to engage me as they saw fit, I couldn't help but think that I wasn't teaching.

While I know that this is not true, the part of my mind that is a product of a direct instruction education was telling me that I needed to get up and address the group. I needed to be conveying wisdom or standing over kids while they work, like teachers do on TV.

I wonder what an observer would think if they walked into my room and saw me hanging out at a student desk. As much as I want to claim that I know (or at least think) that what I'm doing is in the best educational interests of my students, I wonder what a parent would think. What would an administrator think?

Why should I care? If I believe in what I'm doing, why do I care what other people think?

How long do I have to teach before I am truly confident in my work?

After reading the letters that I asked them to write this weekend, It's obvious that they are much more comfortable with working through lots of practice problems. Clearly, this is not true for everyone, but many expressed this concern.

So today, I gave them some options. I printed out several worksheets with practice problems from the current chapter. They could work on those if they wanted the practice. They could continue working in the guided notes, if they chose. They could work on revising their assessments from Friday.

I also told them that, if they chose to do so, they could waste their time. As long as they weren't stopping others from learning, they could spend the time as they wished. I explained that I am trying to move them in the direction of self-directed learning and being responsible for their own education. Since they are still 13 and 14, I don't expect that they will always make good, mature decisions, (especially because in my 30's I rarely do that myself) but I believe that there are lessons to be learned from failure and making bad choices.

These jive turkeys made bad choices today... |

And so I gave them those options and let them go.

The geometry kids, with a 10% error, all worked very hard on the assignment of their choice. I made myself available for those who had questions, or simply wished to talk things out. I was able to circulate and watch their efforts, talking to them as more of a peer than an authoritative figure.

THIS is how relationships get built.

And yet...

As I sat there, casually hanging out, waiting for students to engage me as they saw fit, I couldn't help but think that I wasn't teaching.

While I know that this is not true, the part of my mind that is a product of a direct instruction education was telling me that I needed to get up and address the group. I needed to be conveying wisdom or standing over kids while they work, like teachers do on TV.

I wonder what an observer would think if they walked into my room and saw me hanging out at a student desk. As much as I want to claim that I know (or at least think) that what I'm doing is in the best educational interests of my students, I wonder what a parent would think. What would an administrator think?

Why should I care? If I believe in what I'm doing, why do I care what other people think?

How long do I have to teach before I am truly confident in my work?

Overthinking is exhausting... |

## Monday, September 15, 2014

### Day 15: Communicating Philosophy

Posted by
Justin Aion
at
4:38 PM

This is my 4th year teaching 8th grade, my 6th year teaching in my current district, my 8th year as a classroom teacher and my 10th year working in some capacity in education.

I'm not sure how to teach. I'm not even sure what my style is...

In previous years, I would lecture and consistently utilize "I do, we do, you do" strategies.

Last year, I did much more project based activities, interspersed with lecture and group work.

This year, I have found that I'm giving the kids problems to work on, talking to the group very little and allowing them to work on their own or in small groups while I walk around and answer questions or guide them back on track.

I think there is value in all of these. I know which one I prefer to use, but I'm not sure that it's the best for my students.

In reality, I'm sure the answer is "a balanced mixture of all three approaches is most beneficial."

I like lecturing, but I don't want to be a lecturer. I love watching the kids solve problems at their own pace, but something deeply engrained in me makes me very uncomfortable with that.

I find myself constantly asking myself "is this actually teaching?"

So this is what I believe:

I feel that it is NOT the job of the teacher to simply share knowledge.

A teacher should be more than a textbook or a video.

"Christ! All he does is shows videos all day!" goes the conversation in the faculty room. Then we return to our classes and talk at our students for 45 minutes straight.

But we hold equal contempt for teachers who hand out worksheets and then sit at their desks for the whole period.

I feel that it is my job as a teacher to collaborate on learning with my students, helping them to explore their interests and become better critical thinkers.

What I have been trying to do has been to minimize the amount of time I spend talking and maximize the amount of time they spend working. Some of that work has been grinding through problems, but most has been abstract, critical and reflective. I am having them do writing and thinking about their process.

This shift in what they are used to receiving from a math class has split my students into three camps, that I can tell.

They have very little experience with efficient use of class time for independent or group work. For the most part, my pre-algebra students fall into this category.

For the most part, my geometry students fit into this category.

Perhaps it is misguided of me, but I would like this third group to grow. I know that my students are going to face such a variety of challenges in the coming years and, really, for the rest of their lives. They will not always have situations that are ideal to their learning styles or preferences. But that doesn't mean that they CAN'T learn that way.

We had a VERY long (both periods) discussion about the geometry quiz on Friday. Their homework over the weekend was to write me a letter about the class, telling me what they've learned, what they like and what they don't. The results were...interesting.

The students came in distressed that they had not aced the test on Friday. Much of what we discussed is in the preceding paragraphs. I tried to address their concerns and explain my view point and teaching style.

They expressed the sentiment that the world cares about grades, and so should they.

My counterpoint was that they should care about the learning, the knowledge and the skills. My claim was that if they master those, the grades will happen on their own and they will have the ability to build upon them.

We had many disagreements about educational philosophy and I hope that they felt as though I heard them. I tried very hard to express my sympathy for their points of view and to explain that my own.

I expect that we will have many such discussions over the course of the year. I know that I am different from any teacher that they have had before and, most likely, ever will again. I know that my teaching style doesn't work for everyone, so I'm trying to develop alternatives for those who need or want it.

Bree Murray introduced me to the format of the Recycle Assignment where students are able to correct their mistakes and talk about why they made their initial mistakes. I gave this to the geometry students and expressed that, since I care about the learning and they care about the grades, I would give them the chance to earn better grades by demonstrating knowledge and reflection. They seemed amenable to the process and I have faith in them.

There will be growing pains.

I just hope no one cuts my legs off to keep those pains at bay...

It was a long and exhausting day, but a good one.

I'm not sure how to teach. I'm not even sure what my style is...

In previous years, I would lecture and consistently utilize "I do, we do, you do" strategies.

Last year, I did much more project based activities, interspersed with lecture and group work.

This year, I have found that I'm giving the kids problems to work on, talking to the group very little and allowing them to work on their own or in small groups while I walk around and answer questions or guide them back on track.

I think there is value in all of these. I know which one I prefer to use, but I'm not sure that it's the best for my students.

In reality, I'm sure the answer is "a balanced mixture of all three approaches is most beneficial."

I like lecturing, but I don't want to be a lecturer. I love watching the kids solve problems at their own pace, but something deeply engrained in me makes me very uncomfortable with that.

I find myself constantly asking myself "is this actually teaching?"

So this is what I believe:

I feel that it is NOT the job of the teacher to simply share knowledge.

A teacher should be more than a textbook or a video.

"Christ! All he does is shows videos all day!" goes the conversation in the faculty room. Then we return to our classes and talk at our students for 45 minutes straight.

But we hold equal contempt for teachers who hand out worksheets and then sit at their desks for the whole period.

I feel that it is my job as a teacher to collaborate on learning with my students, helping them to explore their interests and become better critical thinkers.

What I have been trying to do has been to minimize the amount of time I spend talking and maximize the amount of time they spend working. Some of that work has been grinding through problems, but most has been abstract, critical and reflective. I am having them do writing and thinking about their process.

This shift in what they are used to receiving from a math class has split my students into three camps, that I can tell.

**1)**The first is those students who are used to lecturing from their teachers. These kids feel that if I'm not in front of the class, telling them how to do a problem, that I'm not teaching. They take the time that I give in class for them to work on practice problems as free time. I don't blame them or think that they are lazy because of this. I recognize that in the past, they have been conditioned to think that when the teacher stops talking, the class is over. They feel that doing the problems is a task for homework and, when given time to work on something in class, frequently respond with "I'm going to do it tonight."They have very little experience with efficient use of class time for independent or group work. For the most part, my pre-algebra students fall into this category.

**2)**Other students are used to grinding through worksheets and practice problems. These kids have great ability to work independently and, given textbook or worksheet problems, will solve them efficiently and happily. They are comfortable with assignments that read "do these 50 problems." For the most part, they prefer the type of teaching style that is "I do, we do, you do." They excel in situations where they are asked to recreate methods and strategies that have been shown to them. They take comfort in formulas and prescribed plans of action.For the most part, my geometry students fit into this category.

**3)**The third group is much smaller. These are students who preferred either lecture or worksheets, but received the other. This group wants to talk about the problems, discuss what they know and then practice independently. From these students, I frequently hear "alright, I want to try it on my own."Perhaps it is misguided of me, but I would like this third group to grow. I know that my students are going to face such a variety of challenges in the coming years and, really, for the rest of their lives. They will not always have situations that are ideal to their learning styles or preferences. But that doesn't mean that they CAN'T learn that way.

We had a VERY long (both periods) discussion about the geometry quiz on Friday. Their homework over the weekend was to write me a letter about the class, telling me what they've learned, what they like and what they don't. The results were...interesting.

The students came in distressed that they had not aced the test on Friday. Much of what we discussed is in the preceding paragraphs. I tried to address their concerns and explain my view point and teaching style.

They expressed the sentiment that the world cares about grades, and so should they.

My counterpoint was that they should care about the learning, the knowledge and the skills. My claim was that if they master those, the grades will happen on their own and they will have the ability to build upon them.

We had many disagreements about educational philosophy and I hope that they felt as though I heard them. I tried very hard to express my sympathy for their points of view and to explain that my own.

I expect that we will have many such discussions over the course of the year. I know that I am different from any teacher that they have had before and, most likely, ever will again. I know that my teaching style doesn't work for everyone, so I'm trying to develop alternatives for those who need or want it.

Bree Murray introduced me to the format of the Recycle Assignment where students are able to correct their mistakes and talk about why they made their initial mistakes. I gave this to the geometry students and expressed that, since I care about the learning and they care about the grades, I would give them the chance to earn better grades by demonstrating knowledge and reflection. They seemed amenable to the process and I have faith in them.

There will be growing pains.

No, not these... |

I just hope no one cuts my legs off to keep those pains at bay...

I'm so tired, but my skin looks amazing!!! |

## Friday, September 12, 2014

### Day 14: Technological Integration

Posted by
Justin Aion
at
4:14 PM

This past week, I started having my students recite the 8 Standards of Mathematical Practice before we start each class. I've been calling it the Pledge to Improved Mathematics because I don't have a better name yet. My geometry students asked whether they should put their hands over their hearts, like they do for the Pledge of Allegiance.

After some discussion, it was decided that a more appropriate gesture would be to place their hands over their minds.

So my classes now begin with student placing their right hands on their heads and reading the 8 Standards of Mathematical Practice.

A student who came in late asked if she had missed the Pledge and was very disappointed when we said that she had.

The other thing that we've been doing at the beginning of class is #Estimation180, as we did last year. This year, however, I've added a few new procedures. Going off the four steps that I'm emphasizing in all of my classes, the conversation goes something like:

Me: "What's the first question we ask?"

Students: "'What am I looking for?'"

Me: "And what are we looking for?"

Ss: "The number of staples in a single strip."

Me:

S: "How big the staples are."

S: "How long the strip is."

S: "How often the strip has to be replaced."

S: "How much it weighs."

Me: "Those sound like they would be very helpful in making good estimates. What are your estimates for the number of staples in the strip?"

I realized also that I don't have nearly enough grades in my book to satisfy my administration, so we had a quiz in all 3 classes.

The pre-algebra classes took a simple version of a test from the text book. It was 20 questions, multiple choice. I have very mixed feelings about multiple choice tests because, traditionally, they only provide the students "right" and "wrong." In an effort to incorporate more feedback, I decided that just because the test was multiple choice didn't mean that I couldn't use it to develop skills that I find important.

So the students took the tests.

While they were doing so, I handed out Plickers cards. Plickers provide a unique QR code to each student that can be turned 4 different ways to indicate 4 different answers. They are then scanned by a phone or tablet and the data is displayed in real time on the computer. I found out about this program this past summer at TMC when the amazing Pam Wilson presented about how cool it is. She was right!

Each student was assigned to a specific number and, once they had completed the test, we went over it. I had them hold up their cards to indicate which answer they had chosen while the display showed who I had scanned and who I had missed. The beauty of this was that no one knew what anyone else answered, but we were able to look at the data to see the distribution of answers. As the graph started to display, I asked the students if they thought it was a problem that we needed to go over as a group.

They quickly picked up that if the majority of the class had selected the right answer, they could ask me about it individually if need be.

Answers were revealed, kids cheered for themselves or sounded disappointed. I had them mark their own papers, keeping track of the ones they got right or wrong. I did the same for problems that more than 20% of the class got wrong so we could discuss them together.

Their homework assignment for the weekend was to take the test home and, as we have been doing for almost 2 weeks now, take the ones they got wrong, correct them and write an explanation of what they did. Doing so would give them the credit back for the ones they missed.

S: "Mr. Aion, can I just keep the score I have?"

Me: "Did you get all of them right?"

S: "Nah, but I'm ok with what I got."

Me: "If you didn't get a perfect, then you still have room for growth and improvement, right?

S: "Yeah."

Me: "Good! Then work on those."

Quote of the day: "They didn't cheat! It's called 'Number 8,' son!"

SMPs are sinking in!

After some discussion, it was decided that a more appropriate gesture would be to place their hands over their minds.

So my classes now begin with student placing their right hands on their heads and reading the 8 Standards of Mathematical Practice.

A student who came in late asked if she had missed the Pledge and was very disappointed when we said that she had.

The other thing that we've been doing at the beginning of class is #Estimation180, as we did last year. This year, however, I've added a few new procedures. Going off the four steps that I'm emphasizing in all of my classes, the conversation goes something like:

Me: "What's the first question we ask?"

Students: "'What am I looking for?'"

Me: "And what are we looking for?"

Ss: "The number of staples in a single strip."

Me:

**"What information might be helpful in order for us to make a good estimate?"**(Emphasis added because I think this is an incredibly good question, if I may humbly say so.)S: "How big the staples are."

S: "How long the strip is."

S: "How often the strip has to be replaced."

S: "How much it weighs."

Me: "Those sound like they would be very helpful in making good estimates. What are your estimates for the number of staples in the strip?"

I realized also that I don't have nearly enough grades in my book to satisfy my administration, so we had a quiz in all 3 classes.

The pre-algebra classes took a simple version of a test from the text book. It was 20 questions, multiple choice. I have very mixed feelings about multiple choice tests because, traditionally, they only provide the students "right" and "wrong." In an effort to incorporate more feedback, I decided that just because the test was multiple choice didn't mean that I couldn't use it to develop skills that I find important.

So the students took the tests.

While they were doing so, I handed out Plickers cards. Plickers provide a unique QR code to each student that can be turned 4 different ways to indicate 4 different answers. They are then scanned by a phone or tablet and the data is displayed in real time on the computer. I found out about this program this past summer at TMC when the amazing Pam Wilson presented about how cool it is. She was right!

I had them printed on blue cardstock cause it's purdy! |

They quickly picked up that if the majority of the class had selected the right answer, they could ask me about it individually if need be.

Answers were revealed, kids cheered for themselves or sounded disappointed. I had them mark their own papers, keeping track of the ones they got right or wrong. I did the same for problems that more than 20% of the class got wrong so we could discuss them together.

Their homework assignment for the weekend was to take the test home and, as we have been doing for almost 2 weeks now, take the ones they got wrong, correct them and write an explanation of what they did. Doing so would give them the credit back for the ones they missed.

S: "Mr. Aion, can I just keep the score I have?"

Me: "Did you get all of them right?"

S: "Nah, but I'm ok with what I got."

Me: "If you didn't get a perfect, then you still have room for growth and improvement, right?

S: "Yeah."

Me: "Good! Then work on those."

Quote of the day: "They didn't cheat! It's called 'Number 8,' son!"

SMPs are sinking in!

## Thursday, September 11, 2014

### Day 13: Classroom Cardio

Posted by
Justin Aion
at
4:59 PM

After the success of the whiteboarding activity in pre-algebra yesterday, I decided to try another variation today.

Last night, I went to Home Depot and bought two 4x8 pieces of 1/8 panelboard and asked the kind gentleman in that department if he would cut them for me. I ended up with four 2x2 whiteboards and twelve 1.5x2 whiteboards. (all units in feet) Those, added to the whiteboards that I bought last year, the ones I found in my classroom 4 years ago and the one so very kindly donated by Stephanie Reilly and Jen Silverman last year, brings my total to a whole bunch.

Yesterday, I barely had enough for each group to have one, but now, I have enough for each kid to have one and various sizes of each, ranging from Personal Pan to Big Daddy, to mix my pizza chain references.

After reciting the Pledge to Improved Mathematics and our #Estimation180 warm-up, I handed out 12 word problems and told them to get to work. But there was a catch:

They would only get credit for the problems on which I signed-off.

How would they get my coveted signature?

They had to show me how the obtained the answer. They could work in groups or individually. They could use the whiteboards or not. They could start on whichever problem they chose and work at whatever pace they wanted.

When they finished a problem and wanted it checked off, they would call me over and we would talk about it. If I liked what I saw in terms of work, explanation, picture, whatever, I would put a smiley face and my initials next to the problem. If I didn't have the time to get to them, I told them to keep the work somewhere, grab another board and work on another problem until I made my way to their workspace.

They did an incredibly good job with this assignment! They sectioned themselves into groups of 2, 3 and 4, spread throughout the room, snatched up whiteboards and got to work! I spent 70 minutes running between the groups asking probing questions and making them explain the work that I saw. They were eager to show me what they did and explain their efforts!

Along with the activity yesterday, I may have hit on a way to get them working consistently! At no point did I have to tell kids to get back on task because those who were off didn't get their papers signed and then had a ton of homework.

This group was VERY small. Several young women spent the first 15 minutes organizing lipstick and finding the best combinations for the day. I left them alone and devoted my attention to the ones who were working. After the initial grooming session, those girls got to work as well. Great questions were being asked and there was always someone to help.

I barely noticed that it was 85 degrees in the room and that I had sweat through my pockets!

My only real problem was that, since I was requiring that I sign every problem before they got credit, I had to be everywhere. I needed more me. This activity might be better with a co-teacher or an aide, but I'm still going to do it again, even if I'm alone. Also, I made several mistakes in the math and reading the problems since I was coaching on 12 different items at once. I tried my best to go back and correct it, but I know some slipped through.

It also helped me to see which students were really struggling with the concepts of translating words to numbers.

My absolute favorite part was that I was able to compliment students on their mathematical, problem solving and group choosing abilities. Genuine praise that doesn't feel forced is vital.

I think that today went a LONG way to building relationships with my pre-algebra students.

The geometry class is very...energetic. I like how enthusiastic they are about answering questions, but coming right out of lunch, it's hard to get them back in the mode of learning productively. I keep reminding myself that this is a different group of students from last year, but that's just not sinking in. I have to treat them differently because they have different needs and different dynamics.

Last night, I went to Home Depot and bought two 4x8 pieces of 1/8 panelboard and asked the kind gentleman in that department if he would cut them for me. I ended up with four 2x2 whiteboards and twelve 1.5x2 whiteboards. (all units in feet) Those, added to the whiteboards that I bought last year, the ones I found in my classroom 4 years ago and the one so very kindly donated by Stephanie Reilly and Jen Silverman last year, brings my total to a whole bunch.

Yesterday, I barely had enough for each group to have one, but now, I have enough for each kid to have one and various sizes of each, ranging from Personal Pan to Big Daddy, to mix my pizza chain references.

After reciting the Pledge to Improved Mathematics and our #Estimation180 warm-up, I handed out 12 word problems and told them to get to work. But there was a catch:

They would only get credit for the problems on which I signed-off.

How would they get my coveted signature?

They had to show me how the obtained the answer. They could work in groups or individually. They could use the whiteboards or not. They could start on whichever problem they chose and work at whatever pace they wanted.

When they finished a problem and wanted it checked off, they would call me over and we would talk about it. If I liked what I saw in terms of work, explanation, picture, whatever, I would put a smiley face and my initials next to the problem. If I didn't have the time to get to them, I told them to keep the work somewhere, grab another board and work on another problem until I made my way to their workspace.

They did an incredibly good job with this assignment! They sectioned themselves into groups of 2, 3 and 4, spread throughout the room, snatched up whiteboards and got to work! I spent 70 minutes running between the groups asking probing questions and making them explain the work that I saw. They were eager to show me what they did and explain their efforts!

Along with the activity yesterday, I may have hit on a way to get them working consistently! At no point did I have to tell kids to get back on task because those who were off didn't get their papers signed and then had a ton of homework.

This group was VERY small. Several young women spent the first 15 minutes organizing lipstick and finding the best combinations for the day. I left them alone and devoted my attention to the ones who were working. After the initial grooming session, those girls got to work as well. Great questions were being asked and there was always someone to help.

I barely noticed that it was 85 degrees in the room and that I had sweat through my pockets!

The kids thought I had peed on myself, which I thought was flattering, but silly. |

My only real problem was that, since I was requiring that I sign every problem before they got credit, I had to be everywhere. I needed more me. This activity might be better with a co-teacher or an aide, but I'm still going to do it again, even if I'm alone. Also, I made several mistakes in the math and reading the problems since I was coaching on 12 different items at once. I tried my best to go back and correct it, but I know some slipped through.

It also helped me to see which students were really struggling with the concepts of translating words to numbers.

My absolute favorite part was that I was able to compliment students on their mathematical, problem solving and group choosing abilities. Genuine praise that doesn't feel forced is vital.

I think that today went a LONG way to building relationships with my pre-algebra students.

The geometry class is very...energetic. I like how enthusiastic they are about answering questions, but coming right out of lunch, it's hard to get them back in the mode of learning productively. I keep reminding myself that this is a different group of students from last year, but that's just not sinking in. I have to treat them differently because they have different needs and different dynamics.

## Wednesday, September 10, 2014

### Day 12: Showing Vulnerability

Posted by
Justin Aion
at
4:17 PM

Several factors of frustration built up this morning before the students even came into the building. There were a few that were school related and a few that weren't. The end result was that I was already irritated and short-tempered by the time my homeroom got into my class.

This has happened before, so why was today different?

For whatever reason, it was just too much to swallow. Normally, I'm able to force it to the back of my mind and be present for my students, but no matter how I tried, I couldn't separate them from my frustration.

I responded to several students in ways that were not how I wanted.

They used to tell teachers that you shouldn't smile until after Thanksgiving. I suppose this was to establish the seriousness of education, or remind students that you are the authority in the room. I don't believe this. I believe firmly that relationships are what build education.

Students will work for a teacher they like, even in a class that they hate. I want my students to learn from me and they won't learn as much as they could if they hate or fear me.

So I talked to them about it. I told them that for reasons unrelated to them, I wasn't feeling great. I was annoyed and irritated, but it was by no means anything that they had done.

"I am feeling off today. I wanted to tell you so that you know it has nothing to do with you. There are other things going on that have me a little upset. I'm trying to keep it separated from here so that I can be the best teacher I can be, but if it leaks through and I seem upset, I wanted you to know ahead of time that it's not about you at all You guys are doing what I've asked and I greatly appreciate it.

"With that said, I would appreciate if you would be your normal charming selves and not pretend to be jerks."

My homeroom REALLY stepped up!

I want to be incorporating more presentations and explanations into my lessons, so I tried something new today. I broke the class into groups of 4 and assigned each group one problem from the homework. Each group got some whiteboards and markers and were told they would be presenting their problems. Each group used a different method to present, but all did a great job! I had the students applaud afterwards and will be emphasizing the importance of supporting each other.

At the end of each presentation, I asked the class to "tell me something that I love about what they did there." They always had something.

"You loved how they wrote down the 4 steps."

"You loved how they showed all of their work."

"You loved how they used a picture to solve the problem."

The only one I had to drag out of them was how, in the last picture, the group used a variable to represent the unknown quantity.

8th period did not do as well with this activity. There were several students who, not being in class yesterday to receive the assignment, tried to claim that they couldn't help their groups. I'm still having trouble modifying my expectation for a class that meets in 85 degree heat after a day of being cooped up in 85 degree heat. I allow them more latitude in terms of conversation and off task behavior, but I'm feeling as though the time for that is coming to a close.

I also think that the social make-up of that class is vastly different than period 1.

We talk a ton about differentiating lessons, but I would like to hear more about differentiated behavior expectations.

In geometry, while going over one of the examples, a student expressed that she felt defeated by the math. I thanked her profusely for her willingness to admit her feelings to others as I'm sure that other kids felt the same, but didn't want to say so. I also pulled up the link to this great post from Megan Schmidt. It talks about empathizing with students who feel this way.

In addition, starting yesterday, I'm beginning each class by having a student read the 8 Standards of Mathematical Practice. Eventually, I have the class recite it as a group. We make them stand and say the Pledge of Allegiance every day, so why not these?

I consider the 8 SMPs to be the Pledge to Improved Mathematics.

This has happened before, so why was today different?

For whatever reason, it was just too much to swallow. Normally, I'm able to force it to the back of my mind and be present for my students, but no matter how I tried, I couldn't separate them from my frustration.

I responded to several students in ways that were not how I wanted.

They used to tell teachers that you shouldn't smile until after Thanksgiving. I suppose this was to establish the seriousness of education, or remind students that you are the authority in the room. I don't believe this. I believe firmly that relationships are what build education.

Students will work for a teacher they like, even in a class that they hate. I want my students to learn from me and they won't learn as much as they could if they hate or fear me.

So I talked to them about it. I told them that for reasons unrelated to them, I wasn't feeling great. I was annoyed and irritated, but it was by no means anything that they had done.

"I am feeling off today. I wanted to tell you so that you know it has nothing to do with you. There are other things going on that have me a little upset. I'm trying to keep it separated from here so that I can be the best teacher I can be, but if it leaks through and I seem upset, I wanted you to know ahead of time that it's not about you at all You guys are doing what I've asked and I greatly appreciate it.

"With that said, I would appreciate if you would be your normal charming selves and not pretend to be jerks."

My homeroom REALLY stepped up!

I want to be incorporating more presentations and explanations into my lessons, so I tried something new today. I broke the class into groups of 4 and assigned each group one problem from the homework. Each group got some whiteboards and markers and were told they would be presenting their problems. Each group used a different method to present, but all did a great job! I had the students applaud afterwards and will be emphasizing the importance of supporting each other.

At the end of each presentation, I asked the class to "tell me something that I love about what they did there." They always had something.

"You loved how they wrote down the 4 steps."

"You loved how they showed all of their work."

"You loved how they used a picture to solve the problem."

The only one I had to drag out of them was how, in the last picture, the group used a variable to represent the unknown quantity.

8th period did not do as well with this activity. There were several students who, not being in class yesterday to receive the assignment, tried to claim that they couldn't help their groups. I'm still having trouble modifying my expectation for a class that meets in 85 degree heat after a day of being cooped up in 85 degree heat. I allow them more latitude in terms of conversation and off task behavior, but I'm feeling as though the time for that is coming to a close.

I also think that the social make-up of that class is vastly different than period 1.

We talk a ton about differentiating lessons, but I would like to hear more about differentiated behavior expectations.

In geometry, while going over one of the examples, a student expressed that she felt defeated by the math. I thanked her profusely for her willingness to admit her feelings to others as I'm sure that other kids felt the same, but didn't want to say so. I also pulled up the link to this great post from Megan Schmidt. It talks about empathizing with students who feel this way.

In addition, starting yesterday, I'm beginning each class by having a student read the 8 Standards of Mathematical Practice. Eventually, I have the class recite it as a group. We make them stand and say the Pledge of Allegiance every day, so why not these?

I consider the 8 SMPs to be the Pledge to Improved Mathematics.

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