Day 81: The Day Before

'Twas the day before Christmas (break)

And all the school

Movies were played

By teachers who were cool.

In the hallways kids skipped

On the way to their classes.

They had brought in nice treats

To share with the masses.

Holiday cheer

Was spread far and wide.

"OMG! Nice sweater!"

"Thanks! Nice antlers," they cried!

They chatted and talked

Holiday plans, they did spill.

"I'm sleeping in."

"Me? Just Netflix and chill."

But over in math class,

Mr. A knew his biz.

The last day of school?

Perfect time for a quiz!

"It's not that I'm mean.

It's not that at all!

But we wait till January,

You'll have forgotten it all!"

He quizzed with compassion

And cheered them all on.

"You got this," he cried!

"You guys are the bomb!"

When tests were completed,

And the scores were all in,

They had performed really well!

Now THAT was win!

As grades were entered,

The bell, it did chime.

The students escaped

For 10 days of free time!

As he watched from the window

As they all walked away.

It's said that his heart

Grew three sizes that day!

He'd made a few lists.

He'd checked them all twice.

They were not lists

Of "naughty" or "nice."

His textbooks and notebooks

Were secure in his tote.

The chance that he'd work

Over break? Mmmmm...remote.

He waved at the kids

As they all walked off into the day

Then he shouted "I'M FREE!"

And cartwheeled away!

Day 80: Multiple Lessons

Both Math 7 classes had the same lesson today, with vastly different activities.

One class was at the board and did mini-presentations as they practiced combining like terms.  We had conversations about how they arrived at their answers and the types of strategies we used.

The other class worked in short bursts on a worksheet of the same material and we gathered back together as a group to discuss their thoughts.

Both groups did incredibly well with the activities and, in hindsight, I would do it the same way.  It bothers me slightly that I had a group of students doing worksheets.  There is enough evidence that shows that the benefits of repetition of problem sets in math class are short lived and ineffective.

Getting students to have deeper discussions about how they think about numbers and how they apply their strategies is a much better way to solidify the learning.

80 days in, however, I'm still encountering an incredible amount of resistance to that deeper thinking.  They will grind through a list of problems for an entire period.  They will complain about it the entire time, but they will do it.

More cognitive activities, they claim to love, but getting them to actually complete them has been a struggle.

If they are going to insist on doing work at their desks, maybe I need to look into getting some pedal desks.

For my own growth as an educator, I need to work on developing better transitions from rote memory and guided practice to exploratory learning.

Tomorrow we will have a quiz the skills with which we've been working for a week.  I honestly have no idea how it's going to go.

Day 79: Taking Stock

When we came back to the topic today, it was as though they had never heard any of the words before.  They put their hands up to answer questions, but when I called on them, they refused to answer, insisting that they had no idea and wanted to answer a different one.

"I get that.  Let's try this one though."
"No."

Also, I think that the blog is moving away from the original reason that I started it.  I don't think I'm doing enough reflection.  I don't want it to be just a chronicle of my day, but rather a chronicle of my thoughts.

It may be time to re-evaluate and re-center.

Day 78: Productive Distraction

A good or interesting question from a student can completely derail my lessons.  I have tremendous difficulty saying "that's a good question about something I find interesting, but we need to talk about exponents, so hang on to it."

Instead, I say "that's a good questions, so I'll talk about it for a bit and then follow the tangents until the bell rings."

In my first two sections of Pre-Algebra today, we had and excellent lesson about the angles formed when two parallel lines are cut by a transversal.  The kids were involved and good discussions were had.  We talked about the reasoning behind every statement they made when I followed every answer with "how do you know?"  They were willing to give their reasoning in ways that I hadn't truly seen before.  It could be due to the low-entry nature of the activity and how it was more logic and vocabulary than what they traditionally think of as math, but either way, I'll take it!

Even the Math 7 classes went well today.  Our work with combining like terms took longer than I had planned, but we were having excellent discussions about reasoning and representation.

"If I have 5x+2, why can't I just put those together to get 7?"
"At my house, I have 3 tomatoes and 2 plums.  If I cook 2 tomatoes and my wife buys 2 more plums, what do we have?"
"1 tomato and 4 plums."
"Could I say I have 5 plums?"
"No. They are different things. You can't put them to.....oooooooooh!"

Then 8th period came in and, after doing our warm up, a girl raised her hand.

"Mr. Aion, I've always wondered. How do they build bridges?"

30 minutes later, we've watched 2 videos from OK Go and are talking about the science behind space movies.

I don't always get side-tracked, but when I do, every student in interested and I'm left wondering how I can get that level of interest during my content activities.

Day 77: On Point!

Another 2-hour delay today means I get to impose another false sense of urgency on my classes.  I gave structured tasks to the Pre-Algebra and Math 7 classes and they rocked it! It was beautiful!

In Math 7, we are talking about combining like terms and using that to simplify expressions.  I put this up on the board and asked what they thought they could do with it:

After a minute or two, someone suggested using the circles to group things that looked the same.

From there, we combined those terms and work talked about simplifying expressions.


In Pre-Algebra, we kept talking about the angles formed from parallel lines and I asked the kids to do the following problems:

They did them!  They did them well and they did an excellent job of justifying their answers by using the vocabulary that we've discussed in class!

This was an excellent end to the week.

Day 76: Delay

A 2-hour delay always makes for a great day.  While kids crave routine, they also crave disruption to that routine.  We had a late start and the classes were in different order than normal.

Everyone was in a pretty good mood and we got a ton of stuff done in my classes.  We continued talking about parallel line and angle vocabulary in Pre-Algebra.  In Math 7, we starting to seriously discuss algebraic expressions.

I'm not sure if it was the disruption in the schedule or my own sense of shortened-period urgency, but all of the classes were attentive and on point.

So...how about another delay tomorrow?


My favorite interaction today:

Me: "What strategy did you use to mentally solve 13 times 9?"
Student: "Well, this is what I did, but it's probably wrong..."
Me: "Don't say that! Have confidence!"
Student: "Alright. I'm POSITIVE it's wrong."

Day 75: A Proven Fact

"Mr. Aion, my pap came over last night and saw my grades, which are good except for math and science.  He told me that it was ok because girls aren't as good at math and science.  He said it was a proven fact."

While I managed to resist the urge to challenge her grandfather to a fistfight, I did go off on a prolonged rant about setting expectations for young women.  I cited Katherine Johnson, Mary Jackson and Dorothy Vaughan as examples of women who helped put humanity on the moon.

I pointed out that, with one exception, every science teacher in the building was female.

I encouraged her to, every time someone claims something as a "proven fact", ask that person for the source of their claim.

There are only about 3 things that I can think of that men can do better than women:

1) Write history books in their image

2) Subjugate half the population of the world

3) Pee standing up

Over the years, many parents have asked me what they can do to help their children do better in math class.  My response has become: Stop saying you are bad at math.

You are not bad at math.

You may be out of practice at calculation, but you're not bad at math.

Every day we are presented with problems and situations that we have not encountered before.  We use information that we know and our past experiences to overcome these obstacles.

THAT'S math.

When parents tell kids that they, too, were never good at math, they think they are creating empathy.  "I don't want my child to feel alone in this respect" is an admirable goal.  The problem is that it doesn't build empathy.  It provides an avenue for them to quit.

It opens the door to the thought "Mom/dad wasn't good at math and they turned out ok.  I don't need to be good at it either."

There is a world of difference between being bad at math and being bad at math class.

This situation, however, goes a bit beyond that.  This feeds into the gender-based stereotypes that marginalize and minimize the accomplishments, achievements and abilities of women and girls.  It hobbles the child before she can get out of the gate.

You cannot achieve something that you can't dream and comments like these kill dreams.  Even if they come from a place of love in an attempt to make someone feel better for not being as good as they would hope, it's harmful.

It boils the deficiency down to one that cannot be overcome.  "You're bad at this because of who you are" is damaging on multiple levels.

The person giving the message may be implying love and support, but they are conveying limitations.

My daughter came home with her first report card from kindergarten last week.  Her school uses an assessment system that reports students as "approaching expectations," "meeting expectations," or "exceeding expectations" in the various skill areas.

My daughter was meeting expectations in all areas, save one.  The final category was the one that I consider the most important.  If she were going to score poorly in any aspect, that would be the one that would cause the most concern.  If she were going to exceed in any aspect, that would be the one that would give me the most pride.

In the area of "Consistently works on a task/problem until a solution/resolution is found," my daughter earned "Exceeding Expectations."

I want so many things for my children.  I want them to be happy, to be healthy and to know they are loved.  I want them to support others and know they are supported themselves.  I want them to be self-reliant and strong.

I want these same things for my students.

And I will not stand by idly when someone tells them that something is out of their reach because of race or gender.

Day 74: Back in Rows

It's about this time of year that I move the kids from groups back into rows.  I don't like having them in rows all facing the front for a few reasons.  First, I don't setting the implication that it's MY class.  I want it to be OUR class.  Second, in spite of the fact that the norm for public school classrooms has been lecture-style teaching for thousands of years, that doesn't seem to dawn on the people who install writing surfaces.  Mine are scattered around my room making it difficult to justify facing students in any particular direction.

I prefer my students to work in groups, learning how to work as a team, using each other as resources to grow and explore.  Inevitably, around this point in the year, I move them back into rows because I'm not seeing the type of progress I'm looking for in that regard.

I put the rows in pairs so there will still be collaboration, but hopefully, more on-task collaboration.  At least for today, I got acceptable results.

In light of my revelation about empathy last week, I need to appreciate that my students have a certain level of comfort and familiarity with lecture-style learning.  Moving them away from that without at least paying tribute to their desires seems unfair.

I'm also restructuring my lessons a bit as well.  We will still be doing exploratory learning. I'll be sending them into the jungle, but now I'll give them a bit of a tutorial on how to use the compass.

Teaching needs to be responsive, not just to the needs of the students, but also to what they are willing to do.

I don't like having my room in rows, and I'm going to work to move back to groups by the end of the year.

The transition back into rows was a bit earlier this year than previous years.  I'm not sure if that says more about the students, or more about me.  Reading that post from 3 years ago makes me wonder how much I've changed as an educator in that time.


It also makes me wonder if, as a self-professed "progressive educator," my aversion to having the kids in rows is based anything more than principle.

Being aloof is part of my mysterious nature

Day 72: Empathy

My new district occasionally hold class meetings.  This is a half hour session where they kids are broken into groups of 20 and each teacher gets a group.  It's much like a mentoring period where we discuss issues that are going on either in the school, the world, or their lives.

Each teacher approaches this time differently.  The other math teacher in my hallway and I often use it to show TED talks and facilitate a discussion afterwards.  Today's talk about was titled "Math is the hidden secret to understanding the world."


I picked it because it was math related, but also because it hits on the topics that I've been trying to emphasize with my students, specifically viewing problems from different perspectives.

Antonsen does amazing things with the concept of 4/3 and the various ways that it can be represented.

"My claim is that you truly understand something if you have the ability to view it from different perspectives."

This is a much more eloquent way of thinking about understanding than my go-to quote, "If you can't explain something to a 6-year old, you don't understand it."

He took his talk to a place that I wasn't expecting.  He spoke about the importance of different perspectives and brought it around to empathy.

"When I view the world from your perspective, I have empathy with you."

I was using this talk to get my students to understand where I was coming from with my educational philosophies.  So many of them believe that I'm not teaching because I don't lecture and I ask them to explore and learn on their own.

I have been getting frustrated with them for not understanding what I have been trying to do and my frustration has moved me towards being a much worse teacher.  I have been losing my patience much too quickly and getting annoyed much too easily.

I was hoping to help them build empathy, but wasn't doing the same myself.  I started out the year doing well, I believe.  I knew that my teaching style was very different from what they had experienced.  I knew that the new curriculum was different from what they were used to and would take adjustment.

I expected them to come along but I didn't understand just how far they would have to travel.

I have not been seeing enough from their perspective.


I have a considerable amount of work I have to do this weekend, not the least of which is reevaluating the needs of my students NOW instead of focusing on what will serve them best in the future.

"You'll thank me later" is not a good was to structure lessons and throwing students into the deep end of the pool is not the way to teach them to swim.

I'm not giving up, I'm not doubling down.  I'm stepping back, taking a breath and diving back in.

Day 71: Grades and Mathemagic

I screwed up.

I'm a numbers guy, and I screwed up the numbers!

One of the more difficult aspects of doing Standards-Based Grading inside of a traditional grading system is the conversation.  How do you equitably convert a 4 point scale to a 100 point scale?  In SBG, a 2 isn't failing, but means basic understanding of the concepts.  In a traditional system, this usually means a C (70-80%).  A straight conversion would put the 2 at a 50%, which doesn't accurately represent the level of understanding in the course.

When I set up my scale, I set the conversions as follows:

4 ⟹ 100%
3 ⟹ 85%

2 ⟹ 70%

1 ⟹ 50%

0 ⟹ 0%  (This is reserved for students who missed a test or didn't answer a question)

With this scale, my classes were averaging 73% overall.  This is a little lower than I would like, but well within reasonable parameters.

Except for the mistake that I made.

My new district doesn't use 70-79% as a C, 80-89% as a B and 90-100% as an A.

The scale we use is:

A ⟹ 92-100%

B ⟹ 84-91%

C ⟹ 76-83%

D ⟹ 70-75%

F ⟹ Below 70%

This isn't a major difference, but it meant that my points didn't correspond to the appropriate grade.

So I changed them!  I changed them for every student, in every class, for the whole year.

4 ⟹ 100%
3 ⟹ 88%

2 ⟹ 80%

1 ⟹ 50%

This change brings the class averages back into line with the appropriate letter grades.  This was entirely my mistake and it didn't occur to me to do this until today.

I accepted responsibility for it and asked my students for forgiveness of the oversight.



In 8th period, something incredible happened.

The warm up today was for students to come up with a strategy to solve 14*16 mentally.  Through most of the day, students had ideas to break the numbers down in multiple ways, the most common being breaking 14 into 7*2, 16 into 8*2, then 7*8 is 56 and 56*4 is 224.

At the end of the day, a kid came up with an odd strategy:

"I took the 4 from the 14 and added it to the 16, making it 20, so I had 10*20 which was 200.  Then I multiplied the 4 and the 6 to get 24, added it to the 200 and got 224."

I looked at him skeptically.

When students develop their own strategies and algorithms, they may stumble on the right answer without having a valid mathematical reason.  This happened with a few other strategies that students offered.  When I tried the previous ideas using different numbers (24*26) it fell through.

With this strategy, it worked!  So I tried a different pair of numbers. And it worked!  With 28*35, we added the 8 to 35, multiplied 20*43 to get 860.  When we multiplied the ones digits (8*5) it didn't work, but it DID if we multiplied 8*15 (15 being the difference between 35 and 20.)

What was that about?? Does it work with any pair of 2 digit numbers?  Like a good mathematician, I realized that I needed to do a general proof.

I started by setting up general terms for 2 two-digit numbers (10x1+x2 and 10y1+y2) and multiplied them.  Then I went through the process that the student described with the general terms and, lo and behold, it works in general!

My favorite part of this was that I was doing this proof and exploration while students watched, letting them see my excitement, my methods.  The pre-algebra students saw the algebra I put on the board and, while they found it a bit intimidating, many of them were interested and wanted to me to explain what I was doing.

Math isn't magic.  It's the language with which we describe reality.

Day 70: HexBiscuits

Yesterday, I introduced the following problem to my Math 7 students.  They struggled deeply with it, but in the productive way that I would have hoped.

Today, I reassigned the problem, but I was a little more clear about my instructions.  They were to make as many many biscuits as they could with the materials available.  They could make part of a biscuit, but couldn't make smaller or bigger ones.

After this second explanation and the encouragement to "try whatever you think might work" they did some pretty incredible stuff.

There were a bunch of different approaches they could have used and too many of them got bogged down by the numbers rather than the concepts.  For future reference, I used hexagons to demonstrate how I would solve this problem.

 Since the denominators in my problem were 2, 3 and 5, I decided to use 30 hexagons to represent a cup.  This means I have 100 hexagons of mix and 80 hexagons of milk.

 The recipe called for 1 1/2 cups of mix and 1/2 cup of milk for each batch. (45 hexagons of mix, 15 of milk)

Each batch made 5 biscuits, so I divided my hexagons into 5 equal piles. (9 hexagons of mix, 3 of milk)

 To keep with the context of the problem, I saw that each biscuit took 3/10 cup of mix and 1/10 cup of milk.

 At this point, I could have pulled out groups of 9 mix and 3 milk hexagons, but I decided to do it in batches instead.

I separated as many whole batches as I could and set them aside.

 From what I had left over, I pulled out 9 mix and 3 milk hexagons to make another biscuit.

At this point, I didn't have enough mix left for even a whole biscuit, but I could make 1/9 of a biscuit!

To prove how many I could make, I broke the batches up into individual biscuits, giving me a total of 11 1/9 biscuits.

Now, in addition to wishing I had biscuits, I also wish I had white hexagons...

Day 69: Hehe..."69"

The Pre-Algebra students have been struggling with ratios of similar figures so today we did direct instruction.  I had them open the three resources that we've been working with and I jumped back and forth doing different examples.  I color-coded them and the students followed along.  They weren't excited, but they were interested and paying attention.

The students in Math 7 are struggling deeply with application.

I took a lesson from Robert Kaplinsky and asked them to work in groups.

"With the recipe and the given ingredients, how many biscuits can I make?"

In 20 minutes, not a single group finished and very few even made headway.  I made sure to tell them that they didn't need to solve it any special way, but rather a way that made sense to them and that they could explain.

Several of the groups had trouble getting started.  Several had trouble making sense of the problem.  Several had difficulty figuring out which operation I wanted them to use.

A few had some pretty great ideas on how to work this problem, but were unable to complete it in a reasonable period of time.


After school, I was speaking to another teacher about this issue and he had an interesting observation.

"Our generation just wanted to explore and we were forced into rote memorization.  We want these kids to explore and they want rote memorization."

I'm not sure that I agree with this as my students are explorers of their interests.  The trick is figuring out how to get them interested in my content.

Day 68: Repetition

Which One Doesn't Belong?

Our Monday warm-ups have been images like this.  The students are asked to justify why each of the four objects/shapes wouldn't belong in the group.  Sometimes the differences are easy.

Some, not so much.

Today's warm-up took us to some interesting discussions of symmetry, color and optical illusion.

It looks to me as though the shape in the bottom right corner is three-dimensional, folded together like the top of a box.  The bottom left corner is the only shape where the most distance point of the shape is facing in, instead of out..

The discussions went well until I had 4 students in a row give me the exact same reasoning.  This wasn't because they cheated off of each other, but rather because they weren't paying enough attention to notice that 3 other students had said the same thing.

This happens repeatedly.  It's the Inception of answers.

For the love of God, fall down!

I spoke with another teacher at length about this and she said she sees it in other classes as well.

I think I need spend more time asking students to "put her answer in your own words.  What did she say?"



Kids have learned bad habits. Is it better to move them on knowing they aren't ready, or hold them back and make them hate school, thinking they are stupid.

It's almost like grouping kids by manufacturers date is tremendously detrimental.

Day 67: Ask Jane

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

I ended up with:

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

Me: "Here's an interesting question.  Why do you work on it for a while?"
**crickets**
Me: "I don't want to give you any tips because I want to see where you go with this."
**crickets**
Me: "So...get started. Try something."
Students: "We don't know what to do."
Me: "So try something."
Students: "We don't know what to try."
Me: "Try whatever you think may work.  Experiment.  Explore."
Students: "But what if the answer is wrong?"
Me: "Then you've learned something.  Try something else next."
Students: "What should we try?"


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

Typing sentences like that make me feel old.


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

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

Students: "Mr. Aion, how are we supposed to solve this?"
Me: "When in doubt, ask Jane." (Note: Student's name is not actually Jane. I'm calling her Jane for the purposes of the post.)
S: "Are you saying we're dumb??"
Me: "No. You're very bright and that's sometimes your problem."
S: "What?"
Me: "Because you're bright, you think that you should instantly understand everything.  You're great at a ton of things.  You're not great at sticking with something until you solve it.  Jane, however, is amazing at working at something until she gets it.  She rarely asks me questions because she prefers to work things out on her own and she knows that she can.  I know that you can do that too, but you don't believe it and so you ask me questions.  When in doubt, ask Jane."


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

Day 66: Puzzle Pieces

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

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

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

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

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

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

Student: Mr. Aion, I can't see the board.
Me: You can move up. There are empty seats up in the front.
Student: I don't want to.

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

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

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

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

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