Category Archives: Reflections

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.


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

Year 5: Week 1

This week was our first week of school – but before it even began I wrote this email to my principal on Sunday afternoon as I was move furniture:

As you know, I’ve worked pretty consistently over the summer to prepare for the school year knowing that I’d have [four preps]. However, this weekend has made me realize that we don’t have enough ready for me teach four preps adequately and I am already overwhelmed. 

This work isn’t easy – but doing it from scratch and meeting my high expectations for what I can do and what my students deserve for four different courses feels impossible. Plus, the responsibility to simply become a better teacher by changing 10% of my practice as recommended by Steven Leinwand (PDF). Unless that 10% is creating everything from scratch but that feels more like changing 70+% of what I’ve got….

As a department of two, with a supportive and former math teacher as Principal, we decided to eliminate one section I had with 8 students and split up our section of Algebra II into two classes of about 15 (it took us a week to figure out the logistics for the schedule and what course to split).
Good news: the other teacher in my department is experienced in Alg. 2 and I’m not. I also taught almost all of the students coming into my class on Monday. I also think that this decision helps the most students possible be successful this year.
Bad news: I still have four preps and might still feel overwhelmed.

While I predicted being overwhelmed and getting crazy confused with an intense schedule, I didn’t struggle this week as much as I thought. It might have been because after two days we knew that my first hour would be dissolved so I wasn’t nearly as concerned about it being perfect as other courses.

Algebra 1 in Summary: I spent two days building culture and routines. Students in my last period of the day were exhausted and I could not get them to talk to each other – until we got to content where I heard some whispers. The room was finally buzzing with conversations when we pulled out Desmos and worked with Function Carnival on Friday. Finally – mathematical conversations were happening! Hopefully these conversatiosn continue in less “exciting” tasks we work on.

My biggest concern in Algebra 1: I noticed by Thursday that almost all or at least a majority of the students who are participating/volunteering in class are the boys (a majority of both sections are boys). Spending the summer working with girls in the CompuGirls program with ASU has made me acutely aware of gender gaps in STEM education. I need to put structures in place to make sure their voices are heard and they feel supported to share. Secondary concern: Continuing to piecemeal a curriculum together from the interwebz – cause it isn’t what is best for students long term – I’ll reflect on that down that road later.

Statistics in Summary: After building culture and reading a syllabus, and introducing accountability structures about graduation, I had students create visual representations from our class survey and work on a simple M&M task. I mostly had these planned as “first week filler” in case schedules changed – which they did. However, I got to use it as a formative assessment of student understanding of statistics and how they chose to represent data. I got questions like “How do you make a percent again?” and I saw graphs with wacky scales. Super useful information on where to begin my work with them – and super useful graphs and experiences to reference later in the year.

My biggest concern in Statistics: Uh…this is a new course so what concerns me is finding a balance to make it work and not be boring. And, implementing technology that I’m barely familiar with is, as always, a concern and we’ll be using it a lot.

AP Calculus in Summary:   I’m fortunate to have taught these 20 kids last spring, but we didn’t spend any time building culture and getting to know each other. So, we spent three days doing that this week. It was enjoyable, fun and nice to ease into the course during the week. I’ve also implemented an accountability system.

Evidence: As we reviewed our syllabus I got these pictures as part of our summary that could only include 5 words and pictures:

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My biggest concern in Calculus: Flipping my class is off to a pretty strong start – but it will be time consuming. I believe this is what is best (saving the fun investigating for class of course) and class thus far has been much more engaging than in the past and focused exclusively on math instead of notes.

Algebra 2: Oh boy….we’ll think about this again next week.

On the bloggy side of life: I’ll be blogging more this year as a push to reflect more and add to our #MTBoS community. I’ve also pushed myself to become a part of the “Day in the Life” book team to help give myself and teachers a voice about what its like to be an educator. I’m hoping that the project forces me to not only be a better teacher, but by making days of my life completely public to make my life a little better and much more balanced – which needs to be a priority this year or I fear it could be my last in the classroom.

AP Calc: Final Reflections ’16

A few weeks AP scores came out and I wrote this draft from gorgeous Yellowstone national park. I’ve since returned to the desert, where today’s high is a cool 101 degrees.


Old faithful. Did you know the NPS gives a time for the geyser’s eruption – and gives a 90% confidence interval. Pretty nifty huh?

Right before students took the exam I predicted at least two passing scores (3 or higher). Scores weren’t too pleasant: passing percentage of the five students: 0%.
Initially,I took the result kind of personally – I thought they reflected upon me as a teacher
and as a person. I asked questions like “am I good at this? Do I know what I’m doing?” Then, I thought a little more rationally about the circumstances of the students mathematic education and senior so I found some relief. More importantly, I found ways to move forward:
1. I took over the class in January and students clearly hadn’t
learned everything they were supposed to in the fall. Trust me, you can’t teach all of this course in a quarter.
2. Almost all seniors took AP Calculus, regardless of readiness. That was a hot mess, and we addressed that by adding Statistics as another upper level course so I can Calc kids further and faster.
3. I didn’t have embedded ap exam practice or exams to use as a score predictor after spring break. This was the only benchmark I had to predict, and the tool didn’t cover all the content. Looking back, this gave me a bias lens to make predictions with.
While these results aren’t what anyone wants to see, it will be helpful for this year. I’m already:
1. Flipping instruction so there is more class time devoted to practice.
2. Moving to standards based grading so grades always reflect mastery,
instead of compliance.
3. I taught these students all last spring. I know what I taught them.
They know me. I know them. We should be able to begin much faster and
with a mission right from day one. That is really exciting.
4. I get to teach AP Calculus from August to May – which is the first
time since I’ve taught the course.
5. I’m embedding FRQs every Friday. I need an accountability system to
make sure we practice. And, looking at the data, my students underperformed globally most in this part of the test.
6. Rearranging the curriculum to both spiral and push transcendental
so to the end of the course instead of interspersed a la Jonathan.
This leaves me with three things to tackle before school begins in August 1:
1. Look at instructional reports coming out and seeing if what I
taught students did better on, or if it was all a wash (mostly for a
glimmer of hope that I know what I’m doing) Aside: I did this. And, while still underperforming globally, the gap was way way smaller for the content I taught. So – there is hope that I know what I’m doing. 
2. What and how often will interim assessments be to predict future
I’m still going to be advocating systematic change, but change has to start with what I have 100% control over, or in TFA speak, what is in my locus of control. Let’s make waves and see the ripple across our network.

End of Year Four

Today I wrapped up and checked out, ending my fourth year in the classroom. Unlike other years, there doesn’t seem to be as much of a finality to this year as every other year. I think there are two main reasons for that.

1) I switched preps almost completely in January when a teacher left. I never got all my classes going full-steam ahead. By the time we all found our groove we were gone.

2) I’m going on vacation for the 3 weeks before we start school and won’t be online/able to prep. I’m using June to bust out as much work as possible to make the next year smooth.

Even though it doesn’t feel like it is over, it is. I don’t think I made significant progress on my goals for the year – although others disagree. With that in mind, here are three big takeaways.

  1. Teaching is teaching. Students are students.
    1. I moved across the country this year to a school with a majority of latino/latina students, where in the past almost 100% of my students were black. I feared that I’d be starting over and not have some of the same skills – turns out that’s unfounded. Good teaching is good teaching. Students are students. Now, obviously, there are caveats to this to be a culturally responsive teacher and I’ve learned a ton but it was not a challenge this year.
  2. Problem/Project based learning and performance tasks are pretty darn awesome.
    1. I spent this year implementing and using performance tasks, which I’ve changed my implementation of throughout the year. My biggest take away is that these tasks have to be CAREFULLY scaffolded – not only within a unit but within a course. I saw students struggle because they were asked to do new work. That’s a growth I’m still working on. Long term, I unintentionally started all projects as group projects. In the second quarter onward, the task dictated the size of the group – and our last 3 projects in Geometry were all independent, and in August that wouldn’t have been possible.
    2.  Awesome parts: Once students begin an engaging project, all I did was manage behavior and answer questions. Students HAD to think differently about the mathematics and apply it. I have to be incredibly diligent about which questions I answer and how.
    3. Not so awesome parts: Assigning 3 projects in 3 preps simultaneously means 100 projects to grade. That’s a pain in the butt – and I didn’t get caught up for weeks. Class culture of waiting for answers is toxic with projects/performance tasks – and led to some students failing projects and therefore the course.
  3. Teaching gets easier.
    1. I’ve probably worked twice as hard this year as any previous year – but I know exactly what I want and find it with ease. I have teacher moves that have become pretty natural – but still need to add onto these and be intentional with lessons. Even though it doesn’t seem possible in year 1, teaching gets easier with time and practice – I just keep asking myself if that’s what I’m best at and what I want.

Back to writing unit plans….a.k.a. scouring the internet to find a place to start.

Two days out…

Two days from now is the AP Calculus Exam. My school offered the course for the first time this year, for our first class of seniors. Almost all of our seniors were enrolled, regardless of readiness which has not been best for our students. We’re adjusting for next year though by adding another senior level course.

Looking this year, of our 24 kiddos, 5 are sitting for the exam. I picked up the course in January so students have had a piecemeal experience in terms of curriculum and class culture. We’ve been going slow because of our a big skill difference and filling in holes from the fall (related rates was the last thing we covered…..a week ago). When students aren’t taking AP Exams this week, we’re working together through the 2008 Exam.  I know it isn’t the best review strategy ever, but I’m hoping that individual attention over these 3 days will help students feel more confident and brush up on skills.

I’m hoping for 2 or 3 passing scores, so between 40 and 60% of test takers. Heck I’d wager we have a good shot earning one or two of our schools first fives depending upon how the test shakes out. While I’m excited for students with a great chance of passing, I’m also intrigued by information from the other students taking the test – they represent a decent sample of what the “average” student in my class is capable of doing right now so I hope I can gain insights into improving the course for the average student.

Next year with a more targeted enrollment and kicking butt in the fall instead of January we’ll be in a better place. And a curriculum with a rearrangement of topics….and one teacher for the entire year…and an actual review strategy….

I’ve obviously got my work cut out for me to prepare Calculus for 16-17, but I’ll be looping up with some of my PreCalculus kids and can have a solid plan from day 1.

#NCTMannual: Final Reflections

This is the final in a series of reflections from my time at NCTM’s annual meeting in San Francisco. Wednesday, Thursday, Friday, Saturday.

It’s time to move up Blooms – as I’ve been reflecting and writing about almost every session I sat in, I noticed some bigger trends.

1. Curriculum

We often aren’t teaching the standards, we’re teaching a curriculum  (Graham Fletcher, Jason Zimba). We teach procedures because that’s what we were taught, not because it is what is best. While we should be critical of curricula we also need to have it (Max Ray-Riek)

2. Engagement

Real world isn’t all that. “SWBAT” isn’t king. Instead, curiosity should rule and will improve student outcomes/engagement. (Dan Meyer & Annie Fetter)

3. Assessment

Formative assessment is best when you look at strategies, not just a score. (David Wees)

4. Voice

We need to use our teacher voice. We need to be advocates for students, be radically inclusive, empower others and be heard in the “math wars” (Rochelle Gutierrez,Kaneka Turner, Robert Kaplinsky, Matt Larson). Teachers are the ground troops and need to speak up for all our kids, and for each other.  (This is reminiscent of Jose Vilson’s work). I need to find a voice (via Gail Burrill) and use it to amplify my own. My students need it.

5. Fear

In at least three sessions, in my reflection I noted that I was afraid to try things out without seeing it in person. I teach at a school with zero other full time math teachers. I’ll never be able to see anything that is a math focused skill. Students won’t know if I butcher something, but they’ll know if it’s a hit. I have to stop being afraid of new things in my classroom. It should be a place to experiment to become the best possible teacher – not the okay one I am today. Next year, it’s no fear. (Open Middle, Talking Points, not having a cohesive educational philosophy and Standard Based Grading stick out as clear things I’ve avoided because of fear).


Thanks to everyone who made #NCTMannual the amazing, reflective and powerful experience it was. I look forward to seeing and learning from y’all again soon.