Polynomial Division: An #OpenMiddle Problem

In Precalculus, we’ve just wrapped up our work with polynomials – including long division. I was definitely not looking forward to this topic – I haven’t taught it before (or been taught it formally) and the #mtbos had me a little bit.

On our practice set, at the bottom I added this problem as an extension for students who completed the traditional practice set:


I got some interesting responses that made me pretty pleased- but I didn’t (and haven’t) check these for accuracy.

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What I didn’t want to do verify all of them….so instead I had students do it! I typed up the questions onto a worksheet and passed them out to class the next day. Their assignment: Yesterday students created these problems and claimed there was not a remainder. Choose four problems and determine if the students are correct. This was a solid move – I didn’t have to check all the work and students got more practice.


Next time I need to wrap our work back together before assessment. Most students did really well on the assessment but closure could have brought this activity to the next level. We also could have given feedback on how to improve their work (One thing you did wrong was… etc.). I will also include more time for all students to create a problem to feel more invested in the work we did on the second day of instruction.


Day in the Life: October 8

This year I’m part of an MTBOS community sharing experiences of our year together to reflect and grow.

Today is October 8 – Saturday and the first day of fall break. Arizona does this awesome thing where there is a week off in the fall just like spring break. It is drastically needed to spend some time away and recover from a challenging first quarter.

7 am: Wake up without an alarm. One of my best friends is in town for a wedding. This was the first time we’ve had a chance to chat since he arrived Thursday night because of wedding duties and school for me. We talked about our lives and how his PhD program was kicking his butt – he’ll make it though.

9:30 Take my friend to the pre-wedding gathering because it was about 10 minutes from my apartment. Small world right?

11: Made it back to my apartment and started grading. Our first quarter ended yesterday so I was working to finish grades before my vacation to Florida. I worked until about 6 pm (with some breaks, watching football and being pissed on twitter about Donald Trump’s ridiculously misogynistic comments). Trump definitely derailed my plans to be finished work because I’m pretty pissed that someone who could say those things is still in the running for President. I finished all the grading, but still have comments to upload for students.

After 6 I ended the day by continuing to watch football and then continuing to read “For White Folks” – a book on what white folks can do to make their students more successful and feel more included in our classrooms. Dr. Emdin shares his perspective and is making me think critically about my classroom, my biases and how to improve my most challenging courses.

Teachers make a lot of decisions throughout the day.  Sometimes we make so many it feels overwhelming.  When you think about today, what is a decision/teacher move you made that you are proud of?  What is one you are worried wasn’t ideal?

No teacher moves – Saturday!

Every person’s life is full of highs and lows.  Share with us some of what that is like for a teacher.  What are you looking forward to?  What has been a challenge for you lately?

Looking forward to fall break. I’m hopping on a plane to go to Tampa to see my parents for the week.

I’m still struggling to find a balance between personal and professional lives but there’s a glimmer of hope on the horizon 🙂

We are reminded constantly of how relational teaching is.  As teachers we work to build relationships with our coworkers and students.  Describe a relational moment you had with someone recently.

Personally, I love that one of my best friends is here in town. I haven’t seen him in years and he’s a pretty awesome dude.

Professionally, I had to have our dean have conversations with multiple students to the office for making a suicide pact in my class for all to hear (it turns out in jest, but not appropriate either way). While I told them I had to follow up with administration legally they were pretty bummed and upset that I couldn’t understand it was a joke. I continued to emphasize that mental health and suicide is personal – not a joke – and our class needs to be a safe space for everyone. I’m hoping that my honest and firm stance will allow them to understand it is unacceptable and allow them to have a greater empathy for others.

What have you been doing to work toward your goal?  How do you feel you are doing?

  1. Survive with four preps, and do a good job for our students.
    1. I’m surviving…that second part? I don’t think I’m doing a good job at all….
  2. Close lessons to summarize student thinking
    1. This hasn’t happened intentionally or consistently in weeks. Break should give me a chance to refocus
  3. Continue to increase student engagement and cognitive workload
    1. Nope. Hoping break gives me a chance to make progress. My fourth hour (the remedial class) gives me biggest concern because students are not engaged or making progress.

What else happened this month that you would like to share?

This conversation I wrote about earlier because it has slowly transformed my classroom based on survey’s we took before break.

Day in the Life: September 8

This year, I’m part of an #MTBoS community recording the stories of our day throughout the year. Follow us throughout our journey at #DITLife.

Earlier this week I was pretty sick and went to work Tuesday even though I probably shouldn’t have. I was super happy that I woke up this morning at 4:45 and stayed up – which is moving in the right direction. Hopefully I’ll be able to start going to the gym again because I really liked those slow mornings and working out. But, I’ve been sick and before then my class schedule went insane :/

After lounging, showering and prepping, I left for school at 6:15 and was the first person to arrive 15 minutes later. I unlocked the building and gates to get ready for the day. While coming into the teacher work area (we have a communal space with desks for all of us by the copiers) I graded assessments from Precalculus from the day before. Once I finished inputting those grades and making sure I had copies for the day, I grabbed a laptop cart and rolled it down the hall to my room.

First hour began at 7:40. We’ve been working in precalculus with increasing, decreasing and positive and negative intervals. There’s been a challenge getting students to understand that increasing does not always mean positive so we focused today on using Desmos to see that visual relationship and color-coding graphs to represent our increasing/decreasing/positive/negative intervals.

8:46 Second hour Algebra 1 was focused on applying information we learned about parent functions earlier in the week by creating a graphs that met different criteria and then practicing using the different properties of functions we know. The english-language-learners in class have definitely struggled, even with a bilingual co-teacher, since it is such a vocabulary heavy unit. I’m still trying to find the best ways to support them and be successful as they learn both English and mathematics.

9:50 My AP Calculus class has finally got to the point where I introduced the power rule for differentiation to make their lives a million times easier. I left class because I had to go to the bathroom and told them to “Fill up the board with as many problems like the ones you’ve been doing. When I get back I’ll find their derivatives in 2 minutes.” Not only did students give me insane functions with exponents of 100, but by leaving up my mental work they were able to see how I was taking derivatives. Definitely increased the excitement in class and we’ve had much more understanding than last years. Even though this isn’t a rigorous proof, we’ve got it down and can apply it.

10:51: Right after this class come announcements every day. Recently, half a dozen heard back from Arizona State University and were accepted – and a ton of them were already in my class. I taught all those who were accepted last year – and most were in my room for Calculus and I’m so proud of all the hard work they’ve done.

Thursdays are special days, where all students go to lunch together followed by a 30 minute tutoring block. Students self select a class they need additional help in or are requested by a teacher. Instead of my normal set of 13 10th grade boys, I had a group of 8 students working on make up work for Algebra 1. One of the students in my tutoring block was T – a new student. I got him caught up on our work for Algebra 1 by giving him a notebook and having him take notes from the week so he’d be ready for class Friday. I also had a chance to check in with him one-on-one before he came to my class later in the day.

In tutoring block I also this interaction with a student
Student: “Is that a hickie on your face?”
Me: “No, I have a skin condition….not a hickie. See, it makes my elbows look funky too” [shows elbows]
Student: “I have kidney stones”
Me: “I hear those are painful”
Student: “Just kidding, I just know someone who has kidney stones”
Me:”Let’s get back to work…”

After that interesting conversation, my day normalized with my next course starting at 12:00. This class is for struggling learners and we always begin with a number talk. We’ve been focused on composing and decomposing numbers to multiply…and haven’t made much progress. I’m keeping the faith and being explicit about thinking…hoping that it helps long term.

We worked on solving mobile puzzles from EDC. One problem required a student to split 24 into two equal groups. I asked her to do that and she started giving me random numbers. I handed her 24 rulers and asked her to split them into two equal groups. She still looked at me like I wasn’t making sense, so I modeled what “two equal groups” meant. After giving her some time working, I circulated back through and worked through the problem with her, using rulers as manipulatives because it was what was handy. I didn’t walk into class today expecting that struggle, but we worked through it together.

Finally, my planning period at 1:00. Since I missed my check-in meeting with my Principal earlier in the week on Tuesday (it was the day after Labor Day and I forgot) I met with her and chatted about the need for manipulatives and more SPED support from our contractor in my fourth hour class.

I checked in with our Dean because earlier in the day I saw and took a paper in a backpack hat had the following written on it:
“Drink hot bleach”
“Go eat dog shit”
“But what if I don’t?”
“Then too bad”
I didn’t know why those comments were written, but they don’t belong on another person’s work. The Dean said she’d follow up with the student whose paper it was and let her know she was concerned….we’ll see what happens there.

I had a student hunt me down and ask for make up work. I got him extra copies and then made my next video for AP Calculus so I could post it for homework.

2:10: sixth period arrived. Or, 22 rambunctious students came into my class. In 60 minutes, students earned 26 consequences. Everything from juggling glue sticks, to walking around the room instead of heading back to a seat to continuing conversations which prevented us from learning new content. The work we were doing was just a new way of looking at previous learning, but it took us so long to get through it we barely finished the content. I left class frustrated and overwhelmed – what I’m doing isn’t working and consequences don’t seem to make a difference.

After school, our counselor and I forced a student who wants to apply to MIT to actually make progress on his application since he hasn’t on his own for weeks. (It isn’t that hard to email someone to set up an interview….). I stopped by our principal’s office again to share my exasperation with my sixth period – we decided to try snacks as another incentive to see if that will help us change behavior. I met with the coordinator of MAES from ASU to see how they could partner with us this year. We decided if it would be awesome if they could come and help us build robots since we plan on competing this year. When that concluded, I went back to my room where a couple boys were continuing to build our future robot. At five I sent everyone home so I could go home too.

At home at 5:30, I cooked dinner, relaxed and did absolutely nothing else. Long days do that to you.

Teachers make a lot of decisions throughout the day.  Sometimes we make so many it feels overwhelming.  When you think about today, what is a decision/teacher move you made that you are proud of?  What is one you are worried wasn’t ideal?

While I’m not proud I had to do this, I am proud of how I took the note from a student’s backpack. I saw the paper hanging out of  a student’s backpack, noticed it had a different name on it who wasn’t in class and had those disturbing comments on it. I slid over, silently, grabbed it and put it on my workstation to look at closer later. I don’t think she even noticed. I kept the incident itself completely uninteresting instead of blowing up or questioning her in the middle of class. I think if I had less experience that could have ended in lots of eyes hearing a conversation that none of us needed to have during Algebra.

My sixth period can quickly turn toxic….and I haven’t found a way to make that passion and energy productive. Every time I give 20+ consequences in a class of 22 it concerns me that I set a negative tone for the class that could have dramatic ramifications for their future since this is a ninth grade course. So much depends on this year and their futures shouldn’t be determined exclusively by not facing forward or listening to directions and right now that is what it feels like.

Every person’s life is full of highs and lows.  Share with us some of what that is like for a teacher.  What are you looking forward to?  What has been a challenge for you lately?

I think teaching while being sick is one of the hardest possible things – you just want to be able to turn off a little part of your brain but when you do crazy happens. I’m looking forward to the weekend to recover fully.

We are reminded constantly of how relational teaching is.  As teachers we work to build relationships with our coworkers and students.  Describe a relational moment you had with someone recently.

Tutoring block today had a couple moments I hope that can build into something more. First, I tried to be really intentional and personal with our new student. I know how hard it can be to transfer and that he didn’t have an easy freshmen year last year. I’m hoping that by being kind, gentle and a human being right off the bat will help him get adjusted and be more successful. Second, I was intentionally vulnerable with the student who asked about my “hickies.”He’s a student that has been struggling to stay on task and I want to build a relationship to work with him to make class work for him and his needs. I’m hoping that by me being honest and open he’ll feel comfortable doing the same and share anything as it becomes relevant.

I’m also reminded of working after school in the office, pushing a student to make the next steps on his MIT application.

What have you been doing to work toward your goal?  How do you feel you are doing?

  1. Survive with four preps, and do a good job for our students.
    1. New course load that is more reasonable. Still surviving. Adopted a new curricula so I could better serve students.
  2. Close lessons to summarize student thinking
    1. This is still a low priority in planning – it just takes time but I definitely feel like I’m making progress on this front slowly.
  3. Continue to increase student engagement and cognitive workload
    1. Currently no progress has been made…and I don’t that. Sixth period needs more engaging work but I’m overwhelmed so I plan quickly, which isn’t always the most engaging tasks. Hopefully I’ll be better balanced this next month.

What else happened this month that you would like to share?

Well….my schedule changed for the third time in 5 weeks so I now teach 4 preps in 5 sections – but I teach Precalc instead of statistics which I’ve done before so I can do it much quicker and know what I want students to know. I also told my principal if we didn’t make changes to make it more sustainable I’d quit – going into week 3 of school I had a meltdown where I was working. We’ve made changes for the better – now were looking at long term, more sustainable solutions. #smallschoolproblems


Love and #BlackLivesMatter

This week Terence Crutcher and Keith Lamont Scott were shot and killed by cops. I read about Keith’s death in bed and was upset – I couldn’t sleep. I realized I could stay silent, or I could tell my students, who are almost all Hispanic or Black, how upset I was. I decided I could no longer be silent. I remembered Jose Luis Vilson’s saying that he told his students he loved and cared for them the first day of school and realized it was the least I could do. So that’s what I did.

With my  juniors and seniors we started off class as normal with 5 ACT questions. After checking our answers, I had them direct their attention to these graphs – looking at ACT performance, broken down by race/ethnicity from the 2015 ACT Report (PDF).


I asked “What do you notice? What do you Wonder?” After a minute of think time we shared out. A couple of things that stood out:
– Students noticed how well Asians performed in comparison to others
– Students noticed that Hispanics and African Americans underperformed nationally
– One student pointed out systematic racism and wondered what the impact that has on their performance.
– “What resources do they have that we don’t? How can we get them?” was the most disheartening wonder…because sometimes it feels that we have so little and I can’t get them everything they deserve.


Calculus’ Discussion

Here my classes diverged. With my precalculus class, I talked about why we work hard (to combat systematic racism, to make gains and improve our community). I told them I cared for and loved them. But, I didn’t have the guts to tell them why I told them today.

Calculus started the same way – then I asked”Why do you think we are looking at this today?” Students said things like “To motivate us” “To show us where people like us score.” While I validated them, I then told them the real reason.

I’m tired of black men being shot at rates that exceed that of whites.

I told my students that it feels like there is so little I can do so far away, especially as a white male. I told them how we, right now, might not be able to make the change we need, but we can make an impact on these ACT statistics by working hard. Then they, as well rounded, educated people from the community can make an impact and make much more significant change within their community than I can.

Then I said: “In case you haven’t heard recently, you should know that I love you, I appreciate you”  Then I started crying so no one could understand me. I tried again:”I love you, I appreciate you. Even if no one else says it at school, we all care about you. We wouldn’t be here if we didn’t.”

I tried not to make too much eye contact cause I was crying, many of them were too.

I didn’t make too much of my conversation, since after we went back to finding implicit derivatives. I didn’t know if it made a difference to them, but it made a difference to me.

After school, I checked in with our secretary and two of my students were chatting with her. She said that students had already told her what happened in class that morning.  One of the students said “I’ve never made a teacher cry” I said with a smile “Not until today” As I left, the secretary said “But that was a good cry.” She was right.

Then, two days later at our whole staff meeting another teacher well respected by students mentioned that Juniors and Seniors were touched and moved by our discussion of both data and Black Lives Matter.  Once again, I was and am surprised that our ten minute divergence from math was that impactful enough to share with another person my students respect.

Was our conversation perfect? No. Has it made a bigger impact than I could possibly imagine? Yes.

Starting Over in Week 6

This year I planned on using GreatMinds Eureka Math curriculum (a.k.a. EngageNY) for Algebra 1 since I was going into the year with four preps and thought it would be better than what else we had (nothing). I wrote semester exams based on the course map and then started teaching. As I talked to colleagues and opened each lesson, I became more and more disappointed in what Great Minds had to offer me and my students. I began taking each lesson’s objective and then turning to the #MTBos Search engine, my google drive and my own mind to create each and every lesson. I wanted a resource that would make my life easier and provide some sort of coherence- not increase my workload and decrease coherence.

I was left without guidance on the rigor that was expected of students, and this past week feared that I wasn’t teaching the standards, but instead was just teaching Algebra stuff without a bigger picture in mind (which was true since I was focusing on procedural knowledge anyway. And while that is a “my bad” I do think that GreatMinds is partially at fault since I spent so much time redoing their work quickly, instead of pushing myself and my students to think deeper.)

After this week when I looked at my plans, the standards and said “Am I even supposed to be teaching this?” I couldn’t find good answers about inequalities- but what I did see was that I wasn’t using my time well and that class is/was too procedural. I’ve decided to reboot the course and follow the pacing of a more trusted curricula we have access to that doesn’t suck butt, with the long term goal of seeing if it is something to adopt formally. So, we’re rebooting, starting over – Unit 1, Chapter 1, Day 1 – on the sixth week of school.

I definitely have struggling learners who will benefit from seeing the content again and cycling through the math we’ve already done with a different flair. I’ll definitely benefit because I don’t have to write every lesson for the next 150 days. I’ll also benefit because I have the privilege of not ever going back on the GreatMinds website ever again.

Sucky parts: We’ve spent five weeks making progress and now we’re taking a step back to make leaps forward. Oh, and I wrote two semester exams that I won’t be using anymore. But those are #SunkCosts and it is essentially now or never for SY16-17. My kids deserve better than EngageNY and that’s what they’re going to get.

P.S. Dear Illustrative Mathematics team,
Please finish your 6-8 curriculum work, then move on to high school. I trust you and that your curricula will be worth the space it will take up on my Google Drive. Other free curricula don’t even meet that standard.
– A not-so-secret admirer

My Favorite Test Question

Flipping my Calculus classroom has been quite the adventure in the first three weeks. I love that my students are engaging with my videos and we can spend so much more time practicing instead of taking notes. I’ve also been able to prioritize building culture – if that’s weird drawings, bad puns or my greeting of “Hello” – which some students are obsessed with. Flipping my class allows me to be me a little more easily because I feel that I have time and I’m looking at how every person and group is working on mathematics

This culture has bled into our first test – I added my new favorite test question. I read about this somewhere on the #MTBoS in the past year

“7. Draw a picture of an elephant in/on a spaceship”

Below, are my favorites:

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Day in the Life: August 8th

This year, I’m part of an #MTBoS community recording the  days of our lives. Follow us throughout our journey at #DITLife.

Monday, August 8th 2016, our sixth day of school

5 am: Wake up, shower, pack lunch eat breakfast. During breakfast I was reading through blogs on feedly and read about a practice routine I wanted to implement later in the year. I made a mental note to record it in my planning binder on my desk later that day (Triples by E. Miller)

6:07 – Leave and drive to school. I have been leaving unnecessarily early since I’ve moved across town…in part because I forgot when I woke up last year and I’m waking up earlier. Not mad about it

6:30 – I arrived at school and set up for the week by organizing papers and copy all the work for the week for AP Calculus.

6:45-7 I had a meeting with our Director of External Affairs about a grant for our robotics team we are starting this year.

At 7:20 I headed to my room to set up and get ready for the day. Good news – our school was doing NWEA MAP assessments in math classes Monday and Tuesday so I didn’t have lessons to plan for. Bad news – my first period changed to an Algebra 2 class so we could split a larger course and make better use of our man power in the department.

During the morning, most of my day was preparing and proctoring the test with all three of my classes. However, a few highlights stand out. I heard back right away about our grant – earning us $750 to get started. Then, a generous donor doubled our funding – giving our fledgling team $1500 within 6 days of school. I also connected our new assistant principal to Students Today Leaders Forever – the group we organized our spring trips through last year so they could begin a conversation.

After three periods, at 10:56, my lunch period begins (and my first bathroom break). Only four teachers have first lunch and two of us chill together in the work room. We chatted about our weekend and also about our student she had in the morning – R. He wasn’t being too successful in english class and I was wondering if it would transfer to my class.

At 11: 28 our lunch ends and we meet with our advisory – which for me is all 13 of our sophomore boys. We passed out grade reports (that were mostly blank after just the first week of school) and behavior reports (also mostly blank which is a good thing). The boys then balled up their reports and started playing trashketball – and eventually it got out of hand so I had to put an end to that.

12:00 – 4th period begins, which is statistics for me. They began their MAP test and I input grades.

1:01 – Fourth period ends, planning period begins. I chatted with our Principal about moving a few more students into my very small (11 student) Algebra 2 section – the week before we planned on moving 15. Turns out that there were more gridlocks than we thought but we identified some key students to see if we could move them. We did find two students that are both in my advisory and had been in my class before that we could move to improve culture in our class. I then went to my room and prepped for all the AP Calculus videos for my flipped class for the week, waiting for sixth hour to begin.

2:10 – sixth period begins. It began fine…then at about 2:40 the chromebooks went hay-wire and started turning on accessibility features like high contrast and zooming in. I was able to fix it for some but most of our momentum went out the window. I closed down the test session and hoped we could fix it for the next day. I didn’t have students plug in computers – which was a bad call – and I did it instead.

I also had a small incident with the student my colleague and I chatted about during lunch – he isn’t meeting our expectations and is distracting others. I moved his seat right in front of me and I probably wound’t have done that without that brief check in during lunch.

3:10 students are dismissed. I created and uploaded videos for calculus onto our course website. I also added the practice strategy I read about earlier in the day to my planning binder.

4:20 I left school for the post office. Turns out, they close at 4:30 and I was a few minutes late because of after school traffic from the larger high school nearby. I couldn’t get stamps to send in a bill – but I did drop off my early voting ballot for the fall primary.

5:00 Made it back to my apartment and finished the West Wing – watching the end of season 7. I warmed up dinner (I’ve become a Sunday cooker)  and watched Olympic swimming from 6 until 8. During my Olympic adventure, a student who transferred into Calculus emailed about how he didn’t have access for the homework assignment. I gave him an alternate assignment via email for him to complete and told him that assignment we’d make sure he had access to the next day.

8:30 – I went to bed and continued reading my book. By 9 p.m. I was asleep 🙂

Reflection Questions:

  1. Today didn’t have too many instructional decisions because it was all computer based testing. The one decision I was able to quickly and efficiently come to was sorting through and temporarily resolve the computer issues. I had to use lots of management skills, calm students and also try to figure out what was happening. While students didn’t respond perfectly, there wasn’t nearly as much chaos as there would have been earlier in my career.
  2. One big thing I’m looking forward to this year is our robotics team. The mentor last year didn’t get it started but we have super excited students who want to take part. Today we received $1500 between grants and donations – without much effort. I’m excited by the opportunity it holds for us. My biggest challenge is that I have been  taken on a new course that I haven’t taught and we don’t yet have a curriculum for. So…that makes me nervous. You don’t have to be a mathematician to realize that four courses with little resources for the most part, five sections and one planning period is a lot and will be a challenge.
  3. We’ve been working on building a family and fun atmosphere in our sophomore advisory since it is the first year we are all together. Both today and other days we can both joke around, enjoy each others company and know when to turn it down to get through important information. The boys are crazy, but I love them 🙂
  4. My goals for the year:
    1. Survive with four preps, and do a good job for our students.
    2. Close lessons to summarize student thinking
    3. Continue to increase student engagement and cognitive workload
  5. Anything else to share? Not yet – but as things settle I’ll have a better perspective on both this first month and these first few weeks.