Monday, October 15, 2018

Day 32: For No Reason

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.

Friday, October 12, 2018

Day 31: Dom and Randy

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.

Thursday, October 11, 2018

Day 30: Bribery, Please

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.

Wednesday, October 10, 2018

Day 29: Truth Tables

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.

"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

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!

Friday, October 5, 2018

Day 27: Grading...Ugh...

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.

Thursday, October 4, 2018

Day 26: Blank Notebooks

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.


Tuesday, October 2, 2018

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

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.

Monday, October 1, 2018

Day 23: Changes Horses

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.

Thursday, September 27, 2018

Day 21: Self-Control

I think I'm keeping myself under better control.

As I've written about repeatedly, I have a tendency to get distracted by something interesting in class and go WAY off topic. Sometimes this is a valuable learning experience and sometimes I use the excuse that I'm building a space where students want to be.

Today I was much more deliberate about staying on topic as we were taking notes. I was deliberate about deriving the distance formula from the Pythagorean Theorem.  I deliberately chose specific examples to build up to linear inequalities.

As someone who teaches in a much more informal style, this was difficult for me.  I enjoyed it, but I finished the day having accomplished almost none of the other things I wanted to do and I was completely exhausted.

"Justin, aren't teachers SUPPOSED to plan out their lessons in great detail?" you ask.

"That's an excellent point, but I think there's something you're forgetting."


Wednesday, September 26, 2018

Day 20: The Power of Duran Duran

One of the first things that a student said to me this morning was "can we do board work today?"

"Heck yes!"

I had planned to have them doing some practice problems, but saw no reason why they couldn't be done on the white boards, so we did!

After going over a few questions on the homework, I had them pick spots on the boards around the room and gave them some problems to work on.  My instructions were:

Do as many as you can
If you finish a problem and feel good about it, move on to the next
You don't need to check in with me unless you have questions
Recap my markers when you're done
They did an amazingly good job with three of these four.  The kids who were pretty solid on the material were able to talk about their different methods of solving inequalities, discussing where the shading should go and pushing each other to justify answer.  The kids who were struggling a bit were able to ask for help and get the attention they needed.  Since I was roaming around the room, the ones who needed help but didn't (couldn't) ask for it were still able to get their needs met as I was able to see them struggling much more clearly.

I also realized that we needed some music, so I played an '80's Britpop playlist in the background while they worked.

I know how regularly I say "I should get the kids up at the board more" but I really should get the kids up at the board more.

Sadly, I can't REALLY do it in my one geometry class since there simply isn't enough room.

The geometry classes in general are starting to really move along. It's taken me a while to figure out what they need in terms of pedagogy and I'm sure it will take more time to get where I want to be, but we're moving in the right direction and I'm really pleased.


I've been making a conscious effort to keep a smile on my face and greet the students by name and at the door as much as I can. I stand in the hall between classes and say good morning to everyone who walks by.  Former students have been coming by for extra help before and after school and during their study halls.  I am feeling pretty good about my place in the community for the students.

Teaching isn't just about content transfer, but about building a community of learners.  I hope that I am doing what I can to build that positive and trusting environment.

Tonight, I am attending a school board meeting to receive a grant for ZomeTools.  I'm pretty pumped about it, but I'm worried that I won't get home for my 9 pm bedtime.

I suppose we all make sacrifices for our students.

Tuesday, September 25, 2018

Day 19: Reluctance to Experiment

I have many areas of weakness as an educator.

I don't deny this fact.  It's something that I attempt to work on each day, partially through my interactions with students discussing their needs and partially through the self-reflection that is this blog.

One of my major areas of weakness seems to be understanding the gaps in prior knowledge for my students and modifying my lessons accordingly.

I find that I spend an inordinate amount of time on back-filling skills and concepts and I am attempting to analyze exactly why.

I think that much of it comes from the normal attrition of skills that happens over time. While we are several weeks into school at this point, many kids are still in summer mode.  Today, two separate students asked me specific questions about the homework and then didn't realize when we went over their questions.

It can be a bit disheartening.

In addition to this, I'm very much struggling with my morning classes simply because of the time.  Research on circadian rhythms has shown that adolescents needs up to 9 hours of sleep each night. It also discusses how those adolescent biological clocks don't let them get to sleep before 10 or 11.  This research has suggested that delayed start times for schools would lead to increased engagement.

My 11th and 12th graders are asleep well into my 3rd period.  In addition to this, the make-up of my roster just happened to work out where the most low-key kids are enrolled in my morning classes.  Even when I see them later in the day, they are always very chill.

My more boisterous students just happened to be enrolled in my afternoon classes.

This quirk of rosters makes for a bit of a roller coaster day, leaving me exhausted at the end.


So, what I am doing about the lack of background knowledge?

I've started being MUCH more deliberate about the examples and problems that we do in class.  Many of my students are not used to independent style learning, which means that when I hand them an assignment or task and say "go! Let me know if you need anything" that many of them shut down.  This shut down comes from either the lack of understanding of expectations during this time, or the unfamiliarity with what to do when they get stuck.

"How you doing? It's been 20 minutes and I see you're on number 2."
"Yeah, I didn't what to do, so I just stopped."

I found that the major stumbling block in the geometry classes is a solid understanding of the visuals of what we are trying to find.  The skill of translating phrases into pictures in order to understand what's happened in the problem is a difficult one.

I fear that I've been relying too much on the "here you go" approach without respecting how uncomfortable many of the students are with the experimentation that comes with problem solving.

"I didn't know what to do."
"What do you THINK you do?"
"I don't know."
"Ok. Try something."
"Like what?"
"Like anything. Throw some numbers around and see what happens?"
"I don't know what to try."
"So you've said, Dear Liza."


I'm not sure how to overcome this discomfort. Our warm-ups have helped a bit, as has my emphasis on asking kids to explain their thinking and validating those thoughts.


In middle school classes, you sort of expect a certain amount of hand-holding. It takes much of the year for me to teach my students to take risks with their mathematics.  It's very frustrating to be having to do the same thing with the older kids.

With that said, there are a ton of students who are great at the experimentation.

I need to find ways to keep them challenged and engaged while I help the rest get over their fears.

Monday, September 24, 2018

Day 18: Wrong is Wrong, Right? Wrong!

It was, overall, a pretty good day. I handed back assessments, showed my colorful grade book to the students and had them Notice/Wonder about it.  They identified which skills we needed to readdress as a class, and which needed to be covered on an individual basis.

I reminded them again how reassessments would work and what they needed to do in order to take them.

I also talked about importance of showing their work using one of the examples on the assessment.

There were a large number of students who gave the answer to this question as "3."  With no context, this could have a been a random number, conjured from the ether by sacrificing a protractor, inscribing a ouija board on a coordinate place and asking the spirit of Pythagoras for the answer.

This wrong answer provides me with no clue as to the thinking or understanding of the student.  Under the current grading system, this answer would earn a 5. It shows an acknowledgement of the problem, but with no demonstration of the concepts that were covered in class.

Unless, they showed me how they arrived at this wrong answer.  This would make the answer any less wrong

Unless it DOES make it less wrong.  While 3 isn't the answer the question I asked, it IS the answer to an intermediary question, that being "what is the value of x?"

Showing how they arrived at the answer of "3" tells me two VERY crucial pieces of information:

1) Whether the kid actually knew what was going on, or if they had stumbled upon the number.

2) That I need to make sure I address the issue of answering the question that I'm asking.


While the original answer would have received a score of "5," the second answer, with the demonstration of thinking would receive an 8 or 9, indicating mastery of the skill for which I was testing (I can use the Segment Addition Postulate to describe how segment lengths relate to each other) but also recognizing that the work wasn't perfect yet.

With this being the first exposure to Standards Based Assessments for many of my students, I wanted to take the time to demonstrate what I am looking for and explain why I'm being picky about what I want.


All too often, we hear complaints from students claiming that they studied, but what they studied wasn't on the test.  There aren't "tests" like these in real life (except in academia, which is, arguably, not real life). So if we are going to insist on testing in this fashion, rather than having practical exams, then we need to make sure that we are assessing the skills and habits that we are teaching and emphasizing in class.

School is confusing enough without having arbitrary goals going unexamined and unexplained.

I may be wrong, but I don't think it's too much trouble to explain to students not only what we want and expect from them, but why we expect it.

Friday, September 21, 2018

Day 17: Assessment Drawings

All of my students too assessments today. A very few seemed to struggle, but the vast majority did an amazing job! The mistakes that were made seemed primarily to be ones of calculation rather than concept.

I was very careful to ensure that my grading aligned with the skills I was assessing.

I explained this to the students before the test and reminded them that if they show their work, then I'm able to see where they went wrong and that could be the difference between "You don't know what you're doing," which is a score of 5, and "You got this, but need to check your calculations" which is a score of 8 or 9.

I made sure to leave feedback where appropriate and did my best to interpret their meaning as well as their answers.

Even better, I added something at the end of each test. In the blank space at the end, I asked students how they thought the class was going, or to draw me something interesting.

I was not at all disappointed and will be doing that again for every assessment.








I don't mean to brag, but my students are pretty awesome.

That's a lie.

I totally mean to brag.

Thursday, September 20, 2018

Day 16: Students Are Better Than Clippy

Tomorrow is the first Standards-Based assessment that many of my students will take.  The job of class today was to remind them how the process goes, what the assessment will look like, how they will be scored and then give them the remainder of the time to practice and ask questions.

They utilized the time incredibly well and several stayed after school to work together.

I, on the other hand, had a wildly unproductive day as I spent most of it trying to get the formatting of my assessments the way that I want them.

Reason number 49,244,036 why I love Twitter:


Turns out, the answer was "Yes! They COULD answer some questions for me."

But, in true Microsoft style, they answered questions I didn't ask, such as how to place a picture in Word when using a MAC. They linked me to a generic FAQ site that was 90% unrelated to my query.

So it turns out that Clippy is alive and well! He is now running the Microsoft social media account.

I promise that I didn't scream profanity in a room full of students.

Wednesday, September 19, 2018

Day 15: Assessment Incoming

This Friday, I will be assessing skill in all of my classes. I've given the Geometry classes about 3 days notice and about 2 days to the Algebra 2 classes.  We have spent that time working on practice and taking the opportunity to ask questions and clear up misconceptions.

My worry about their performance is the same as it always is.  I am concerned that they won't read directions or show their work. I am concerned that they will make simple calculation errors that will make the problems MUCH more difficult, increasing their frustration and causing the reinforcement that they are bad at math.

The truth is that they are NOT bad at math.  Their logical processes and thought structures are very good. What they lack is the language to express their thinking.

For the last two days, the Geometry classes have been defining the vocabulary that we've been using and will be using going forward. I made the point to them that I didn't want text-book definitions for the terms, but rather an accurate explanation in their own words, to help them to better understand the concepts.

A "segment" is a part of a line with defined end points.  "Perpendicular lines" are two lines that cross at right angles.

There is an argument to be made about semantics and technical definitions, but as I stated in my post about notation, I would rather they be able to express their understanding than to get bogged down by memorizing definitions.

With each definition, we also draw a picture, looked at notation and gave examples.  There were distinctions that we drew, such as between supplementary angles and a linear pair.

I was hoping to play Headbands with them tomorrow to review quickly before the quiz, but I also want to make sure that we have time to answer any last minute questions they may have.
"You are good at deductive reasoning and what you get when you put more than one angle together!"

40 minutes is not enough time.

Tuesday, September 18, 2018

Day 14: Misplaced Stress

I am very much enjoying my classes. I am looking at areas in which I can improve both my planning and my instruction, but overall, I'm pleased with how they are going.

With that said, there is a very brief period of my day, entirely unrelated to my classes or my students, that is the source of a disproportionate amount of my stress.  I am examining ways to mitigate this, but as of now I am unclear on what to do.

I had a conversation with a supportive coworker today that helped me to pinpoint some areas for improvement and shed some light on the reasons for my anxiety.  It's going to be a process.



I'm also noticing an interesting phenomena in my Algebra II classes.  I gave an assignment yesterday for students to practice solving equations with 1 variable.  With no exceptions, my students fell into one of two categories: they either blew through the problems (accurately) and asked what was next, or they became hopelessly stuck on the first one and spent 15 minutes trying to solve it.

There was no middle ground.


Looking at the questions, they were remarkably similar to those given today by the Algebra 1 teacher to his classes as well as bearing a striking resemblance to the ones I gave to many of these same students in Pre-Algebra.

Why do we teach the same problems over and over again and why is there no retention of this information?

A good friend who is working on her doctorate reminded me that OF COURSE there is no retention of this information.  The process of solving equations doesn't really make a ton of sense and is often put out to a level of abstraction that makes it difficult for students to relate to.

The process of solving an equation is disjointed and unconnected to any tangible concepts.  This goes slightly better when we use a physical representation, such as a scale balance, but ultimately this process has the same faults.

I am doing what I can to put in more concrete questions and lifting the restrictions of "write an equation that represents this situation."  Instead, my directions are that I want to come up with an answer that makes, using whatever process makes sense provided that it is mathematically sound and they explain it.

To illustrate this point, we did a series of problems today that read something like:
Stefan left school and drove to his friends house. Eugene left school 2 hours later. He drove at 40 km/h for 3 hours and arrived at the same time as Stefan. How fast was Stefan travelling?

The traditional process would want students to set up an equation relating the various speeds and times.

As a class, we talked about how they would solve this problem if they weren't forced to make a single equation. What if they solved it like they would solve any problem outside of school?

We solved it one piece at a time, picking apart what we knew and finding things we didn't.  When we finished, I showed what the traditional process would look like and we talked about whether one was better than the other. One way was better for generalizing and was more efficient, but the other helped students to understand why we were doing what we were doing.


I prefer the second way as I would rather they have understanding, trusting that efficiency will come later.  I wish I had more time. 40 minute periods are not enough...


Monday, September 17, 2018

Day 13: What's Important?

I put up a question on Twitter today, seeking advice from other math teachers on an issue of precision:

How important is this distinction?


Specifically, what I'm concerned with here is the amount of emphasis that should be placed on the distinction between congruence and equality.

My understanding has always been shapes/segments/angles are congruent while the measures of those objects (lengths, angle measures, etc.) are equal.

As usual, when I put this question out to my teacher community, I received back a wide array of constructive answers that forced me to think about my goals for the class.

On one end, one of the major focuses from the National Council of Teachers of Mathematics has been an emphasis on precision of both work and language.  As a result of this, it's important to teach students the precision language that is used by mathematicians.


On the other end, there is the work of students making themselves understood without bogging them down with the semantics.  As Brian pointed out, he isn't 5'10", he's a human being.  At the same time, when he says "I'm 5'10"" you'd be hard to pressed to find someone who would say "Nice to meet you, 5'10"! I'm Justin!"
Before the discussion, I was heavily leaning towards the view and reasoning expressed by Christopher Danielson:



Yes, the precision is important. Yes, students should be exposed to how mathematicians speak and express their ideas, but I also don't want to lose student interest over semantics.

I feel as though this may be the math-specific version of:
"Can I go to the bathroom?"
"I don't know! Can you??"

If what you're teaching is the difference between "can" and "may," then this is an important distinction to draw.

Along these lines, I want my kids to know and use proper notation, but I don't think it's the most important aspect of the lesson.

I've settled somewhere in the middle.




I, too, will model appropriate use, making corrections where I see them. I want kids to get used to seeing the difference between congruence and equality.  As the year goes on, I may become more strict about the usage, but for now, I think I'll simply settle for modeling.

I have enough things on my plate that I don't think I need to add this.


But I may be wrong...

Thursday, September 13, 2018

Day 11: Exhausted on Purpose

I noticed something interesting today.

My energy and attitude are staying at pretty high levels during my classes, but I'm finding more and more that as soon as class ends, that changes drastically.


I'm finding that the conscious effort of maintaining the high energy and positive attitude is emotionally draining.

With that said, I feel the need to clarify 2 things:

First, the energy and attitude aren't fake. I'm not putting on a show for the students, nor am I pretending to be happy when I'm not.  The effort comes from continuously looking for how to make the best of whatever situation may arise.  Rather than expressing disappointment when only 1 student has completed the assignment, I am using it as an opportunity to talk about decision making.

"I know that you all have things going on. I'm not going to harp on you about your homework because you need to be making choices based on your goals and needs. If you want to understand this material, you're going to have to practice it."

I am trying very hard to honor who they are as people and not just as students. In middle school, it seems more important to emphasize the school as, in theory, their parents are taking care of much of the rest.  As junior and seniors, many of them have jobs and activities, or are responsible for younger siblings.

In addition to this, we talk about getting students ready for the real world, but if we don't allow them to make decisions about what to prioritize are we actually doing that?

Second, the energy and effort spent to maintain this level of involvement is, in my opinion, 100% worth while. I am doing what I can to provide my students with an environment in which they feel safe and comfortable asking questions and taking risks. Students greet me in the hallway with a smile, a handshake, a high five or a fist-bump.

Teaching is about building relationships, otherwise you might as well be an audio book or video playing in front of the class.


At the end of each class, I am exhausted and am tempted to take a nap before the next group comes in, but I don't plan to change what I'm doing any time soon.


Wednesday, September 12, 2018

Day 10: Multiple Pathways

One of the major hurdles that we have to overcome in math class is the misconception that there is one right way to get the answer.

Unfortunately, due to the pressures of the amount of material we are supposed to cover and the limited time in which to do it, we often opt for the "fast way" rather than helping students to understand the how and why.

I've encountered several math teachers who require students to complete assignments using specific procedures and take off points if they find the answer a different way.

I'm not going to judge their pedagogy, or criticize this approach except to say that those are not the skills I choose to emphasize.



I'm lying.  I think this is a terrible way to teach. I think it fosters hatred and confusion for mathematics in students who think differently.  There is no one way to do mathematics and grading students on whether they use your preferred method assesses compliance more than mathematical understanding.  I understand that there are times for this, but if a kid can get to the answer and explain how they got there using mathematical methods, should I penalize them for that?

In any event, once this habit has been formed for students, it's very hard to break.  In my experience, this manifests itself in two main forms:
  1. Students asking "is this how you're supposed to do it?" Occasionally, this a conceptual question, but more often they are really asking "is this how you want me to do it," expecting a single path to be the right one.
  2. Students glancing at a problem and immediately giving up, claiming they don't know what to do.  What this frequently indicates for me is that they think there is a single procedure for each problem and they can't remember it.  In this world view, it makes sense to give up. If there is only one path and I don't know that path, what's the point of trying? Requiring a single procedure in mathematics discourages them from experimentation and trying to "figure it out."

Trying to combat this takes a serious effort.

Today, to help the Algebra II students remember what they know about working with proportions, I had an opportunity to do exactly this.

When presented with a proportion that contained variables on both sides of the equal sign, many of the students fell back on memorized procedures, some of which only work in specific cases, others of which would always work, but made the problem needlessly complicated.

We did the problem at least 5 different ways.  I wrote so that everyone could see the work and so that multiple students could provide feedback as needed.

Each time we went through the problem, students would ask what we do and I replied with "what do you WANT to do? What's your instinct? What do you see?"

No matter what their response was, I wrote it on the board (as long as it was mathematically sound). We played with numbers until we ended at the same spot.

I loved it! There was a ton of "what if" discussions and, since I was the one doing the writing, the risk to the kids was minimal.


There can be great value in working deeper on fewer problems, especially if it's being used to value student thinking.

Tuesday, September 11, 2018

Day 9: Perspective: A Play in One Act


Scene: A classroom
Students are working on pattern recognition


Mr. Aion
Tell me about this pattern

Student 1
It looks like a plus sign

Mr. Aion
Awesome! What else?

Student 2
Each time it's adding one block to each side

Mr. Aion
Say more about that

Student 2
It starts as just a square, but each side of that square has another square on it.  In each new picture, another square is added

Mr. Aion
Cool. What about the next one? What will that look like?

Student 2
It will be a square in the middle with 4 squares in a line on each side

Mr. Aion
Do we agree?

Students nod and murmur approvingly

Mr. Aion
Alright, so what about the 10th step? What will that look like?

Student 3
It will have 21 squares each way

Mr. Aion
**smiles cunningly** 21? Step 1 had 1, Step 2 had 2. Tell me how you counted 21

Student 3
It's makes a plus sign and there are 21 squares going up and down and 21 going back and forth

Mr. Aion
**looks around to rest of class** Thoughts? This isn't at all how we were examining the pattern. What do you think?

Brief discussion ensues where students ask clarifying questions.

Mr. Aion
Since day 1, we have been talking about how mathematics is a language. Everyone speaks it to a certain degree, but our goal is to become fluent. Student 3 had an idea that was different from the rest of ours, but she was able to make her thinking understood, turning an answer that, on the surface, was wrong, into a class discussion about perspective.  While there are answers that may be incorrect, it's important not to discount results that are different without examining the thinking behind them.

Math is more than calculation. Math is discussion, debate, argument and exploration.


**Bell Rings**

Students climb onto their desks.



Students
Oh Captain, My Captain



**Curtain falls**

Monday, September 10, 2018

Day 8: Cracked Expectations

We are beginning Algebra II with a review of linear equations.  This was a topic that was covered in Algebra I, Pre-Algebra and Math 7.  This means it should be a breeze of a review.

It's not going as smoothly as I would like, which is alright.  I don't have a problem with the kids struggling with this topic because I understand how much material was covered in those classes and how long it has been since they worked with the concepts.

It does, mean, however, that I needed to readjust my Monday plans.

Instead of "Any questions on the homework? Cool! Let's start the next section" we ended up with "Anyone do the homework? No? Ok, let's talk!"


We had a brief conversation about how as they get older, the onus of learning passes more to their shoulders.  I explained how I don't want to give them absurd amounts of work just to prove that they know it, but if they aren't doing what I do give, then I don't know what they know.

There are a few reasons why students don't complete assignments on time:

  1. They don't understand the material and then give up
    • If this is the case, then I need to know about it. Students who are lost can become insanely frustrated. (I saw this last week with my own 2nd grader, but that's it's own post) I want a level of frustration that makes them feel they can accomplish a task if they just knew one more thing, and so they go find that thing. This is a difficult balance and I'm still working on it.
  2. They forgot
    • Bruh, get yourself organized! You have a school issued planner to write down your assignments and you can always shoot me a message over Remind. In addition, if they are subscribed to my class using Remind, they get notifications for any assignments I give.
  3. They don't want to
    • As a crappy student myself, I totally get this. I spent WAY too much time thinking that I knew what was going on in class only to get to the test and discover that I was wrong. I sympathize with this completely, which is why I've tried to minimize the amount of out-of-class work I'm assigning and making sure that what I do assign is relevant.  My plan has been to do mini-lessons and then give them time to practice the skills in class where I can help them.  This has been working well in theory, but the majority of the students who REALLY need the practice have been taking too long to get started and too long to complete the tasks, making themselves believe that 10 practice problems will take 6 hours.  ANY task can take forever if you don't start it!
  4. Extenuating circumstances
    • Mom/dad/grandparent/sibling is in the hospital, they are homeless, they have to work 6 hours a day after school, they have to babysit siblings, etc. etc..  I am, in no way, judging these reasons. Many of them are incredibly valid and many of our students live lives more complicated than I can fathom.  Everyone has their own struggle.

I think that, moving forward, I will need to be much more deliberate about my classroom structure. Today, I gave extension activities to the few students who completed their work for today.  The rest of the students and I went over some examples in great detail.  I worked on some problems using a very clear format and engaging my kids, rather than just having them copy the answers.  I also tried to make it clear that my going over these things wasn't a punishment at all.

It was an opportunity for them to learn note-taking and to create a resource for themselves that they could reference as we delve deeper into the content this year.

I will also admit that this strategy changed over the course of the day. I asked my morning students to work more independently and by the afternoon, I realized that they needed a bit more structure.

Unfortunately, we aren't a point yet where I can say "here's the assignment, go to it" and they will.  I have several students who need me there with them, giving them support and encouragement.  I don't mind doing those things, but too many need that at the moment for independent work to be productive for more than one or two.

We will get there! I have faith in my students and myself.

Friday, September 7, 2018

Day 7: Beep Beep!!


All aboard the struggle bus!

I started most of my classes with the following statement:

Today is day 7. For the last 6 days, I have tried my best to be upbeat, energetic and excited. Today, it's not working for me. I'm not sure if it's the heat, or the lack of sleep, or just the normal stress of starting a new year, but I'm on the struggle bus today.  I need you to understand that it has nothing to do with you.  I don't want you to think that my mood, which is obviously depressed from what it has been, has anything to do with how you have been participating, acting or working. You are all champs and have been doing great work since day 1.  Some days you just aren't feeling it and, for whatever reason, that's me today. I'm sorry for that and I will try to do better.
 In addition, the weekly warm-up sheets are coming in and I'm seeing student responses to "I wish Mr. Aion knew..."

The vast majority are either random and funny, or very encouraging.

"I am enjoying this class this year"
"It's ok to not be energetic all the time."
"I would smile at his jokes, but I cut my mouth and it hurts to smile."
"He is one of the coolest, respectful teachers."  (Seriously)

There are, of course, a few that are discouraging

"I used to think I was better at math than most people, but now I've been knocked down a peg."
"I used to think math was easy, but now I know it's not."

Since I am a human being who is currently working on myself, I am WAY over focused on the negative comments, despite the fact that they are vastly outnumbered.  Is it in the nature of humans to look at 99 successes and see 1 failure, or are teachers more susceptible to that mentality?

The goal for next week is to get kids up out of their seats, or working on activities as much as possible.  I want the Geometry classes to start doing constructions and I'm going to browse my resources for a good Algebra 2 activity.  I avoided it this week simply because it has been too hot to ask people to move around.

Overall, it's been a great week and I'm thankful for the kids I have in class.

Time to nap until Monday!

Thursday, September 6, 2018

Day 6: What the Buck-et

I've taught geometry several times before this year.  In all of that time, I would say that the aspect of the course that my students find most challenging is the ability to visualize the shapes without having a physical manifestation.

I'm not sure if this is due to the lack of abstract visualization in the K-12 curriculum, or it's simply an insanely difficult skill.

When we begin to study 3-dimensional shapes in 5th and 6th grade, we hit on the idea of nets as representations of objects.  When I did the cereal box project last year, this was, by far, the most difficult aspect.  Students had tremendous difficulty figuring out what their box would look like when they were unfolded and, similarly, struggled with how to create a net for a box of a desired shape.

We had a VERY long talk in geometry today that dealt with moving from lines to planes.  We talk about each wall in the classroom, as well as the ceiling and floor, can be seen as a plane. Things written on those walls are contained in that plane.

Where it usually falls apart is when we're deciding whether three corners of the room that are NOT all on the same wall happen to be on the same plane.

"Are points E, D and B co-planer?"


"They aren't on the same plane because they are on different walls."
"They are because you can draw a line between any two of them."
"They are because you can make a triangle between them."
"But that triangle isn't on any of the planes."

How do you get students to realize that ANY three points can make a plane? How do you get them to SEE that plane when one isn't there?

I tried drawing it.  I tried having them picture a mesh net between those points.

After they left, I realized I needed a bucket.

I have several small rectangular crates in my room to hold pencils and markers at each table.  I held one up as a physical representation of the space. It allowed me to turn it around and have the kids look inside.

I needed a bucket.

If I had a bucket, I'd bucket in the moooo-oooorning.
Get out of here, you three!
If I had had a bucket, I would have filled it with water.  Then I could put the crate in it, using the water level as the representation of the plane!  Is there a way to submerge the crate such that those three points are on the surface of the water?

I come up with great ideas for yesterday's lessons!

I'm taking a bucket of water to class tomorrow!

Wednesday, September 5, 2018

Day 5: Lesson Plans?

Well, that didn't take long!

Something about the best laid plans...

I managed to fall behind my lesson plans already.  To be fair, our schedule has been messed up by having early dismissals from the heat.  I was also reminded that I have a tendency to ramble when I find an interesting topic.

In geometry, we were defining terms, specifically points, lines and planes.  We were talking about what it means for something to be three-, two-, one- or zero-dimensional. I was reminded of one of my favorite ideas in geometry, which is that two-dimensional objects (like squares) can be seen as the projections or shadows of three-dimensional objects (like cubes).  Similarly, one-dimensional objects can be seen as the shadows of two-dimensional objects.

Extracting from this, it's a great way to ask students to visualize that they (three dimensional objects) are merely projections of some other four-dimensional object.

"Mr. A, what's the highest level math class you can take?"

Philosophy!"


In other, more reflective, news, I'm having difficulty realizing that my 3rd period class is my 3rd period.  I keep thinking it's 4th and I keep getting shocked when kids come after they leave.

No worries though. I have 175 more days to get it right.

Tuesday, September 4, 2018

Day 4: Lesson Plans

Due to concerns about heat, our district, as well as many of the surrounding districts, closed school early today and will do so again tomorrow.

As much as I'm disappointed to be losing some of my classes so early in the year, my intense desire to fall asleep in front of an open refrigerator tells me that it's a good idea.


In spite of the heat and humidity, my students worked very hard for me today.  I've been scouring various curricula and picking the things that I like in order to try to organize these classes that I haven't taught in many a moon.  I'm also making a concerted effort to be more organized than I normally am.  This is helped along by our new mandate to have lesson plans available for the next week should someone ask for them.

The plans themselves don't have to be anything absurd, just a basic outline and topic list so someone could grab the folder and teach the class in case of emergency.

This is the 12th year full time classroom teacher.  Including the two years that I spent working on my Master's Degree, this is the first time when I have been told to make lesson plans that meet the needs that I set out for myself.

In all previous years, when lesson plans have been mandated, a specific format was chosen and implemented district-wide, regardless of whether aspects of it were useful to individual teachers.

Anyone who has attended an education program can attest to the fact that the required lesson plans would make Tolstoy say "that's a bit much."

As a result of this, I have almost never taken lesson plans seriously.  I would spend hours on a format that was filled with information that I didn't find helpful and would only confuse me further.  In addition to that, they were almost never checked.

A former colleague went a year without changing the plans, only modifying the date before they were submitted.  She was told that her attention lesson plan submission was exemplary.

She even turned in several plans that were laced with profanity, or contained excerpts cut from fiction articles.

No one noticed.


I am not opposed to lesson plans.  I am, however, deeply opposed to assignments that serve no purpose except to check a box.

When we were told that we would be required to have lesson plans on hand in the classroom, I'll admit that I grumbled and planned to look for the old plans from years ago.

This weekend, I actually started doing just that and quickly realized it was a mistake.

Lesson plans in the past have not been helpful to me, but this was a chance to make them so.  With the ability to choose the format, I was able to make it what I wanted.  It is very minimalist, but contains what I'll need to keep my classes moving at a good pace.

I need structure.  I need time tables and check lists and to-do's.  I wander off task in my content, hitting things that are interesting, but not necessarily helpful to my students' learning.

I am glad to be writing lesson plans again.


Education programs, instead of forcing students to write 35 page lesson plans, should be teaching them how to develop their own planning style, selecting the items that are important and productive for them.

I stuck with my lesson plans today and will continue to do so.


At least until I see something shiny.

Friday, August 31, 2018

Day 3: FRIDAY!!!

Well, I'm exhausted...

We only had 3 days of class this week, but I've been going full blast! In addition to getting up before 5 am, being in an 85 degree (and up) classroom for 8 and a half hours, getting home to take care of my own kids, and running a 5k each day, I've been pouring on the high energy during my classes.

It was so important to me to make this first week a good one, not only for me, but for my students.  Knowing that the room was going to be a bit toasty, and that math would be happening in it, I knew many of the kids would be coming to me with some ... demeanor concerns.  I don't blame them.

I will get them up and moving around when it cools off a bit, but for now, I wanted to create an air of fun and interest in my room, demonstrating the beauty that is mathematics.

I THINK I've done that.  It's hard to tell, simply because the nature of high school students is so different than that of middle school students.  It will take me a bit of time to relearn how to read my audience, but so far I think I'm heading in the right direction.

What you do during the first few days will set a tone. What kind of tone do you want to set? Do you want the students to be in charge? Do you want them to be afraid of you? To love you? Do you set a tone of cooperation, or one of domination?

I'm making a conscious effort to use names of everyone I address and to keep a smile on my face as much as possible.
WELCOME TO MATH!!!

I managed to write back to every student this week on all of their name tents.  It has been time consuming, but very worth it.

We are babysitting for a friend tonight, so I need to run before that happens and then I plan to sleep until school starts up again on Tuesday.



Thursday, August 30, 2018

Day 2: Still Hot, Still Cool

It hit 90 in my room again, but it was another great day!

We began looking at procedures with our daily warm-ups and recitation of the 8 Standards of Mathematical Practices. I gave a brief explanation of the Standards-Based Grading system that I use and answered any questions that they happen to think of right then.

Then we were off into content!

I explained to both classes (Algebra II and Geometry) that mathematics is a language.  It's insanely hard to learn a language by simply reading the dictionary.  Those who wish to become fluent regularly engage in conversation with native speakers, learning the conjugations and idioms.

Math is no different.  In order to learn math, we have to engage with it beyond simply using the operations.

We need common language.

In Algebra II, we started a card sort activity that was..ahem...appropriated from Jonathan Claydon.

Student groups were given 24 cards, consisting of 8 terms, 8 equations and 8 graphs.  With no help from me, they were asked to put them into 8 piles of 3 cards each, matching term to equation to graph.

I reminded them that it has been a few months and so they shouldn't panic if they don't know it right away. 90% of the groups ROCKED it! They dove in, using different strategies, pulling out the ones they knew (linear, absolute value), picking ones that seemed to go together (f(x)=log(x) and "logarithm") and using process of elimination to find others.



After about 10 minutes, we stopped to talk about how they could figure out which graphs went to which equations if they didn't remember what they looked like.  None of the groups had built a table of values, but when I asked this question directly, they almost all said that you could plug in numbers and graph it.  We did some examples on the board before the bell rang.


In Geometry, we worked on defining terms and notation that we will be using throughout the year. I gave them a check list to try, knowing that most of the notation was beyond what they had covered yet.  Several students asked "what's notation?"

When it became clear that I wasn't going to give them the answers, that I wanted them to struggle, most stopped asking me anything more than clarifying questions. They worked in groups for a bit and when I began to sense the frustration level getting too high, I stopped them.  We looked at the board and built the beginning of our vocabulary notes as a group.

Even in the heat, the kids were engaged and working hard!

I had them fill out the second day of their Name Tents (Ask me a question) and I managed to respond to all of them before I left school!

They were great questions, but a few stuck out to me.

It's a shame that no one will be able to read my response.

I think this is going to be a pretty darn good year!
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