The kids were great today.

My lessons went fairly well.

I had a pretty wonderful weekend, playing Dungeons and Dragons with my friends and my kids. We went apple picking and I did well in my axe-throwing league yesterday.

I didn't have a great day.

I have no rational explanation for it.

I could talk about how the geometry kids asked if we could finish working on the Gold and the Tiger and then just guessed which door to open rather than figuring it out. I could talk about how I'm nervous for the Math Team competition on Wednesday because I've had no permission slips turned in yet. I could talk about how I haven't been sleeping as much as I should. I could talk about how gross and grey the weather is today. I could talk about how my runs for the last few days haven't been great and how that's frustrating. I could talk about how I need to write both of my presentations for NCTM at the end of the month.

I could talk about how it's apparently National Grouch Day and I'm just celebrating.

The reality is that sometimes people just feel bad for no real reason. Today is one of those days. Anxiety is not fun.

## Monday, October 15, 2018

## Friday, October 12, 2018

### Day 31: Dom and Randy

Posted by
Justin Aion
at
4:08 PM

Once upon a time, two men were hired to work at a factory run by Func Enterprises

After several weeks of extensive training, Dom was given the assignment of sorting the raw materials and placing them on the appropriate intake belt of the factory. Those materials then traveled through the factory and were lovingly and expertly crafted into the various products made by Func. After passing through quality control, where they were checked to make sure they were up to the latest industry standards, the products were sent to Randy to be packaged and shipped out to customers all over the world.

Dom and Randy were both very good at their jobs and were both blessed with an innate curiosity. Neither man was content to simply and unquestioningly do his job. Instead, both men became interested in the inner workings of the factory.

In addition to the manufacturing process itself, Dom was deeply interested in the kinds of products that Randy packed based on what he delivered. Similarly, Randy was curious what kinds of raw materials went into the products that he was shipping.

Sometimes, Randy was able to tell exactly which materials Dom delivered just by the products that came through. Similarly, on occasion, Dom would know exactly which products Randy would receive based only on what he dropped onto the intake belts.

When Dom knows exactly what Randy is going to get at the other end, the relationship is a function.

When Dom doesn't know what Randy is getting, it's not a function.

When Dom knows what Randy is getting AND Randy knows exactly what Dom put in, not only is it a function, but it is a 1-to-1 function.

Eventually, both Dom and Randy moved on to careers in the lucrative field of illustrating mathematical concepts and within 6 months were able to retire to an island with white sand beaches, but neither man forgot the humble function backgrounds from which they came.

After several weeks of extensive training, Dom was given the assignment of sorting the raw materials and placing them on the appropriate intake belt of the factory. Those materials then traveled through the factory and were lovingly and expertly crafted into the various products made by Func. After passing through quality control, where they were checked to make sure they were up to the latest industry standards, the products were sent to Randy to be packaged and shipped out to customers all over the world.

Dom and Randy were both very good at their jobs and were both blessed with an innate curiosity. Neither man was content to simply and unquestioningly do his job. Instead, both men became interested in the inner workings of the factory.

In addition to the manufacturing process itself, Dom was deeply interested in the kinds of products that Randy packed based on what he delivered. Similarly, Randy was curious what kinds of raw materials went into the products that he was shipping.

Sometimes, Randy was able to tell exactly which materials Dom delivered just by the products that came through. Similarly, on occasion, Dom would know exactly which products Randy would receive based only on what he dropped onto the intake belts.

When Dom knows exactly what Randy is going to get at the other end, the relationship is a function.

When Dom doesn't know what Randy is getting, it's not a function.

When Dom knows what Randy is getting AND Randy knows exactly what Dom put in, not only is it a function, but it is a 1-to-1 function.

Eventually, both Dom and Randy moved on to careers in the lucrative field of illustrating mathematical concepts and within 6 months were able to retire to an island with white sand beaches, but neither man forgot the humble function backgrounds from which they came.

## Thursday, October 11, 2018

### Day 30: Bribery, Please

Posted by
Justin Aion
at
5:43 PM

My seminar was, once again, very well attended! Clearly, I've hit on something with the invitations and skill specific sessions. I thanked the kids for coming again and I'm thinking about having a snack for them in the future, although at random intervals so I'm not bribing kids to come to tutoring.

Now, if they want to bribe me...

I put a paper outside of my door inside a plastic sheet protector so I can write the schedule on it and have it be available when I'm not.

While I'm not feeling great about the progress that the classes are making through the curriculum, I am feeling very good about how well they are understanding it. The last few days have been intense and they've been asking great questions.

The algebra 2 kids were given a practice paper for rules of exponents and flew through it. The geometry kids took to the discussion of conditional statements very well and already began arguing in a more logical fashion.

I'm excited to have them be eaten by tigers tomorrow.

Now, if they want to bribe me...

I put a paper outside of my door inside a plastic sheet protector so I can write the schedule on it and have it be available when I'm not.

While I'm not feeling great about the progress that the classes are making through the curriculum, I am feeling very good about how well they are understanding it. The last few days have been intense and they've been asking great questions.

The algebra 2 kids were given a practice paper for rules of exponents and flew through it. The geometry kids took to the discussion of conditional statements very well and already began arguing in a more logical fashion.

I'm excited to have them be eaten by tigers tomorrow.

## Wednesday, October 10, 2018

### Day 29: Truth Tables

Posted by
Justin Aion
at
4:20 PM

Truth tables can be kind of dull, especially when your class is mostly asleep. The second class seemed to really like figuring them out, as did the third class. Perhaps they were slightly more interested when I told them that being able to determine the truth value of a compound statement would keep them from being eaten by tigers.

I think the plan is to make an answer sheet where kids have to make their decisions in pen and the one/ones who survive the longest will get some sort of prize. If I had a button maker, or had planned better, I would make a survivor button.

I'm very excited to work on conditional statements with them. If I had reliable access to computers for all 25 kids in my big class, we would also do basic programming.

The Algebra 2 kids have been working on rules of exponents and we spent yesterday and today looking at why the shortcuts work. I'm struggling a bit with the course sequence, but it will work itself out.

I'm having more and more students come to me for extra help. Most of them are either on my roster this year, or have been before, but not all. I have several kids who I never had in class who still come to me for help. I take this as a good sign.

I think the plan is to make an answer sheet where kids have to make their decisions in pen and the one/ones who survive the longest will get some sort of prize. If I had a button maker, or had planned better, I would make a survivor button.

**"My classmates were eaten by tigers and all I got was this stupid button!"**

I'm very excited to work on conditional statements with them. If I had reliable access to computers for all 25 kids in my big class, we would also do basic programming.

The Algebra 2 kids have been working on rules of exponents and we spent yesterday and today looking at why the shortcuts work. I'm struggling a bit with the course sequence, but it will work itself out.

I'm having more and more students come to me for extra help. Most of them are either on my roster this year, or have been before, but not all. I have several kids who I never had in class who still come to me for help. I take this as a good sign.

## Tuesday, October 9, 2018

### Day 28: You Are Cordially Invited

Posted by
Justin Aion
at
3:55 PM

After the assessments in Algebra 2 on Friday and various conversations with other teachers and administrators on how we can increase understanding and achievement, I'm trying something new.

My district has a seminar period at the end of each day from 2:30-3:00. I have always made myself available during this time (except when I have meetings) for students to come in for extra help. We aren't able to mandate that a student attend seminar, so I've been looking for ways to get kids to attend.

Since I am unable/unwilling to force students to attend extra help sessions, I invited them!

I have scheduled Skill Sessions after school on specific days and invited the students who are struggling with those skills to attend. All students who need to, or wish to, work on Skill 3 (I can write a linear equation of a line that is parallel or perpendicular to a given line) are cordially invited to attend seminar from 2:30-3 today in my room. Those wishing to work on Skill 4 (I can write and apply direct variation equations and proportions) should attend our session on Thursday.

All students are welcome at any time to work on any skill they wish, but the designated skills will be the primary focus on the announced days. I plan to do a remediation lesson and run through some practice problems.

I'm also thinking that in order for a student to reassess a skill, they will need to attend at least 1 session.

I handed out the invitations today and 4 kids showed up to seminar! We did a mini lesson and some practice and I thanked them for coming to spend time with me.

I was going to write about the specific lessons that I covered today, but I have pushed those a bit out of my mind for the moment and am thinking about how to improve these study sessions!

My district has a seminar period at the end of each day from 2:30-3:00. I have always made myself available during this time (except when I have meetings) for students to come in for extra help. We aren't able to mandate that a student attend seminar, so I've been looking for ways to get kids to attend.

Since I am unable/unwilling to force students to attend extra help sessions, I invited them!

I have scheduled Skill Sessions after school on specific days and invited the students who are struggling with those skills to attend. All students who need to, or wish to, work on Skill 3 (I can write a linear equation of a line that is parallel or perpendicular to a given line) are cordially invited to attend seminar from 2:30-3 today in my room. Those wishing to work on Skill 4 (I can write and apply direct variation equations and proportions) should attend our session on Thursday.

All students are welcome at any time to work on any skill they wish, but the designated skills will be the primary focus on the announced days. I plan to do a remediation lesson and run through some practice problems.

I'm also thinking that in order for a student to reassess a skill, they will need to attend at least 1 session.

I handed out the invitations today and 4 kids showed up to seminar! We did a mini lesson and some practice and I thanked them for coming to spend time with me.

I was going to write about the specific lessons that I covered today, but I have pushed those a bit out of my mind for the moment and am thinking about how to improve these study sessions!

## Friday, October 5, 2018

### Day 27: Grading...Ugh...

Posted by
Justin Aion
at
4:23 PM

The assessments went well for the students who have been working with fidelity. A few told me that they were confused, so I asked them what they had done to prepare. They admitted not much. I'm hoping that I can leverage these experience into helping them develop habits to succeed, if they choose to do so.

I am not going to judge their choices or their priorities, but if they wish to be successful in my class, I can help them with that.

By and large, the most common mistakes that I saw were careless ones. Students wrote "4 - 3 = 2" and similar transgressions.

While these are irksome, I'm not overly concerned about it. I don't honestly believe that they think the statement is true. I think it infinitely more likely that they didn't check their work, moved too quickly or something similar. Using standards based grading allows me to assign grades and feedback in a more comprehensive way.

In the section assessing the skill of solving absolute value inequalities, one student got the wrong answer for most of the problems, but still passed the section because the mistake were calculation-based. The work and thinking were clearly displayed, meaning that I was able to see that this student knew exactly what they were doing conceptually, but were careless with signs.

Two students showing the same wrong answers may get different scores based on how they obtained those answers. I understand there are arguments against this approach, most of which boil down to "in the real world, you're either right or wrong."

Setting aside the fact that I don't think that's always true, you can't argue about the "real world" and yet only allow students one opportunity to show understanding of a memorized topic. In the "real world" people get multiple opportunities to work on, improve and modify their products. In the "real world" people have resources at their fingertips, such as the internet.

I began writing a multi-paragraph rant here about the appropriateness of modern education in the scope of preparing kids for the "real world" and decided against it.

I have lots of assignments to grade, my ax-throwing league starts up again this weekend, the book I'm reading is starting to get great and I still have to run today.

I am not going to judge their choices or their priorities, but if they wish to be successful in my class, I can help them with that.

By and large, the most common mistakes that I saw were careless ones. Students wrote "4 - 3 = 2" and similar transgressions.

While these are irksome, I'm not overly concerned about it. I don't honestly believe that they think the statement is true. I think it infinitely more likely that they didn't check their work, moved too quickly or something similar. Using standards based grading allows me to assign grades and feedback in a more comprehensive way.

In the section assessing the skill of solving absolute value inequalities, one student got the wrong answer for most of the problems, but still passed the section because the mistake were calculation-based. The work and thinking were clearly displayed, meaning that I was able to see that this student knew exactly what they were doing conceptually, but were careless with signs.

Two students showing the same wrong answers may get different scores based on how they obtained those answers. I understand there are arguments against this approach, most of which boil down to "in the real world, you're either right or wrong."

Setting aside the fact that I don't think that's always true, you can't argue about the "real world" and yet only allow students one opportunity to show understanding of a memorized topic. In the "real world" people get multiple opportunities to work on, improve and modify their products. In the "real world" people have resources at their fingertips, such as the internet.

I began writing a multi-paragraph rant here about the appropriateness of modern education in the scope of preparing kids for the "real world" and decided against it.

I have lots of assignments to grade, my ax-throwing league starts up again this weekend, the book I'm reading is starting to get great and I still have to run today.

## Thursday, October 4, 2018

### Day 26: Blank Notebooks

Posted by
Justin Aion
at
3:52 PM

Tomorrow, there will be another assessment and the first major graded assignment for the Algebra 2 class. I am...nervous.

We've been hitting the material fairly hard and I know they are plenty capable, but I'm still nervous. The kinds of questions and the pace of work that has been happening in class over the past few days leads me to believe that there are some gaps in understanding, particularly when it comes to properties of linear equations, such as slope and the y-intercept.

I have my class open before school, at lunch and during our Seminar period, which is the last 30 minutes of the day set aside for tutoring or activities. My duty period during the school day is also tutoring when most kids have lunch.

I can't say that I've seen too many kids coming for extra help and this worries me.

The review packet was handed out on Tuesday and we've been working on it in class since then. It's due in class tomorrow and I think that the students who needed the practice the most put it off until tonight when they'll be unable to ask me questions.

Since I have the older kids this year than I have in years past, I'm being a bit more "rigorous" about my assessments and assignments. After our first assessment, many of the kids who wanted to reassess were shocked at how much work was going to be required before they could do so. They have to make corrections on their test and then do some more practice problems.

I am a brutal taskmaster, I know.

I don't want to be grading effort or habits, so I'm trying to find a way to incorporate those things into my assessments while putting the emphasis on the content.

I don't want to collect and grade homework unless I can give them meaningful feedback on it, but that may also have to change. I do like the idea of having a selection of homework that's all due together, rather than spacing it out, but would spacing it out make them more likely to do it?

Does that even matter? How do I make the homework meaningful when attempts are frequently not even made? How do we teach them the habits they need to have the outcomes they want?

What outcomes DO they want, besides "pass the class"? Should I set up a "mandatory seminar schedule"?

Tomorrow, before the assessments, I will be reminding them of all of the tutoring time I have available.

"The day before a test, I expect my room to be full."

I am hearing similar concerns voiced by other teachers, so perhaps we need to be working together to find a way to address this.

We've been hitting the material fairly hard and I know they are plenty capable, but I'm still nervous. The kinds of questions and the pace of work that has been happening in class over the past few days leads me to believe that there are some gaps in understanding, particularly when it comes to properties of linear equations, such as slope and the y-intercept.

I have my class open before school, at lunch and during our Seminar period, which is the last 30 minutes of the day set aside for tutoring or activities. My duty period during the school day is also tutoring when most kids have lunch.

I can't say that I've seen too many kids coming for extra help and this worries me.

The review packet was handed out on Tuesday and we've been working on it in class since then. It's due in class tomorrow and I think that the students who needed the practice the most put it off until tonight when they'll be unable to ask me questions.

Since I have the older kids this year than I have in years past, I'm being a bit more "rigorous" about my assessments and assignments. After our first assessment, many of the kids who wanted to reassess were shocked at how much work was going to be required before they could do so. They have to make corrections on their test and then do some more practice problems.

I am a brutal taskmaster, I know.

I don't want to be grading effort or habits, so I'm trying to find a way to incorporate those things into my assessments while putting the emphasis on the content.

I don't want to collect and grade homework unless I can give them meaningful feedback on it, but that may also have to change. I do like the idea of having a selection of homework that's all due together, rather than spacing it out, but would spacing it out make them more likely to do it?

Does that even matter? How do I make the homework meaningful when attempts are frequently not even made? How do we teach them the habits they need to have the outcomes they want?

What outcomes DO they want, besides "pass the class"? Should I set up a "mandatory seminar schedule"?

Tomorrow, before the assessments, I will be reminding them of all of the tutoring time I have available.

"The day before a test, I expect my room to be full."

I am hearing similar concerns voiced by other teachers, so perhaps we need to be working together to find a way to address this.

## Tuesday, October 2, 2018

### Day 24: The Sidewalk Is Wet, Therefore...

Posted by
Justin Aion
at
7:22 PM

We began our discussion of logic in geometry today. I want my students to be in the habit of backing up their claims with logic and reasoning, but that doesn't seem to be a priority in many math classes. As I have written about before, I believe there is too much emphasis on "answer getting" and not enough on WHY the answer is what it is.

The chapter on logic and reasoning in Geometry is, by far, my favorite.

For the last several weeks, I have frequently said that an justification I won't accept as a reason is "'cause it looks like one!" When I emphasize this point, I say that line in a faux British peasant accent and, much to my despair at the involvement of today's youth in the cultural zeitgeist, only one student has understood my reference.

Today, I began class with this following clip:

Afterwards, we had a brief discussion about how the argument and line of reasoning presented here has the flavor of logic, but is drastically missing internal consistencies. I know. I'm so much fun!

We talked about how making a statement that can be shown to be false through a counterexample usually wrecks whatever conclusions come after. Witches are made of wood because wood burns and so do witches, except we were able to list several other things that burn that are not wood and also not witches.

"If I look out the window and see it's raining, what conclusions can I make about the sidewalk?"

"That it will be wet."

"Great! Now, if I see that the sidewalk is wet, can I conclude that it was raining?"

"Not necessarily. Someone could have sprayed a hose, or dumped water or peed."

"Yes! Yes! Gross!"

After this, I introduced them to the idea of logical statements and conclusions through the use of THIS clip (which I also had to explain because "kids today"):

What are the implications of the question she asked? Would you have asked something else?

I may not be good at most things, but by glob am I good at improving their geek cred!

The Algebra 2 kids have another assessment coming on Friday so this week is a time for "review everything we've done so far and work on practice to solidify concepts."

I handed out the work I wanted them to do, then watched a student take 7 minutes to get a piece of paper from their binder, sharper a pencil, clean the edges of the paper turn the binder upside-down, get another paper, change pencils and then ask for help.

I've written before about the importance of starting a task and moving through it at a certain pace. I run into these same issues with my own children when I want them to clean their rooms or pick up their toys.

"Dad, this is taking forever!!"

"Of COURSE it's taking forever. In the past 10 minutes, you have danced with your sock, wandered aimlessly through the kitchen and sang to the cat. You haven't started yet."

With 40 minute periods, I'm really feeling the effects of the speed at which many of my students work.

I need to figure out how to fix it.

The chapter on logic and reasoning in Geometry is, by far, my favorite.

For the last several weeks, I have frequently said that an justification I won't accept as a reason is "'cause it looks like one!" When I emphasize this point, I say that line in a faux British peasant accent and, much to my despair at the involvement of today's youth in the cultural zeitgeist, only one student has understood my reference.

Today, I began class with this following clip:

Afterwards, we had a brief discussion about how the argument and line of reasoning presented here has the flavor of logic, but is drastically missing internal consistencies. I know. I'm so much fun!

We talked about how making a statement that can be shown to be false through a counterexample usually wrecks whatever conclusions come after. Witches are made of wood because wood burns and so do witches, except we were able to list several other things that burn that are not wood and also not witches.

"If I look out the window and see it's raining, what conclusions can I make about the sidewalk?"

"That it will be wet."

"Great! Now, if I see that the sidewalk is wet, can I conclude that it was raining?"

"Not necessarily. Someone could have sprayed a hose, or dumped water or peed."

"Yes! Yes! Gross!"

After this, I introduced them to the idea of logical statements and conclusions through the use of THIS clip (which I also had to explain because "kids today"):

What are the implications of the question she asked? Would you have asked something else?

I may not be good at most things, but by glob am I good at improving their geek cred!

The Algebra 2 kids have another assessment coming on Friday so this week is a time for "review everything we've done so far and work on practice to solidify concepts."

I handed out the work I wanted them to do, then watched a student take 7 minutes to get a piece of paper from their binder, sharper a pencil, clean the edges of the paper turn the binder upside-down, get another paper, change pencils and then ask for help.

I've written before about the importance of starting a task and moving through it at a certain pace. I run into these same issues with my own children when I want them to clean their rooms or pick up their toys.

"Dad, this is taking forever!!"

"Of COURSE it's taking forever. In the past 10 minutes, you have danced with your sock, wandered aimlessly through the kitchen and sang to the cat. You haven't started yet."

With 40 minute periods, I'm really feeling the effects of the speed at which many of my students work.

I need to figure out how to fix it.

## Monday, October 1, 2018

### Day 23: Changes Horses

Posted by
Justin Aion
at
4:11 PM

Each one of my geometry classes had a different homework assignment today.

Over the next day or two, we will be transitioning from the basics of points, line and planes, into more formal methods of logic and proof. One of the problems from their homework last night was a perfect segue to this.

"Given the following coordinates for points A, B and C, determine if these points are collinear"

I like this question a whole bunch as it allows me to illustrate that the phrase "it looks like it" doesn't really belong in mathematical debate.

We went through the idea of logical statement in a very informal way, with my tweaking their language as we went.

Me: What does it mean for 3 points to be collinear?

S: They are on the same line.

Me: That's true. More technically, it means there is some line that contains all three points. So what would we need to do to show that they are collinear?

S: If we found that line, we could show they are all on it.

Me: That's interesting. How do you think we could find that line?

S: ....

Me: How many lines are there that contain any two points?

S: Just 1.

Me: So, if we find a line that contains two points...

S: We see if the third one is on that line.

The first class seemed to a bit more practice with the actual calculations so their assignment for this evening was to do so. I set the other two groups to looking at the ideas of conjectures and what conclusions can be drawn from certain statements.

In looking forwards, I'm debating whether or not to do The Lady and The Tiger (modified to remove the misogynistic overtones of women as prizes).

The last time I did it, it went VERY well and the kids were pretty excited.

Over the next day or two, we will be transitioning from the basics of points, line and planes, into more formal methods of logic and proof. One of the problems from their homework last night was a perfect segue to this.

"Given the following coordinates for points A, B and C, determine if these points are collinear"

I like this question a whole bunch as it allows me to illustrate that the phrase "it looks like it" doesn't really belong in mathematical debate.

We went through the idea of logical statement in a very informal way, with my tweaking their language as we went.

Me: What does it mean for 3 points to be collinear?

S: They are on the same line.

Me: That's true. More technically, it means there is some line that contains all three points. So what would we need to do to show that they are collinear?

S: If we found that line, we could show they are all on it.

Me: That's interesting. How do you think we could find that line?

S: ....

Me: How many lines are there that contain any two points?

S: Just 1.

Me: So, if we find a line that contains two points...

S: We see if the third one is on that line.

The first class seemed to a bit more practice with the actual calculations so their assignment for this evening was to do so. I set the other two groups to looking at the ideas of conjectures and what conclusions can be drawn from certain statements.

In looking forwards, I'm debating whether or not to do The Lady and The Tiger (modified to remove the misogynistic overtones of women as prizes).

The last time I did it, it went VERY well and the kids were pretty excited.

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