Monthly Archives: April 2016

#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.


#NCTMAnnual: Wednesday

This is a series of posts reflecting on my time at NCTM’s Annual meeting in San Francisco this April. Post 1, Post 2, Post 3.

Since I got into San Francisco Tuesday night, I decided to attend NCTM’s research conference since it was open to me. I also prefer to scope out places before I have to be somewhere so I felt way more comfortable Thursday when “teacher” sessions started. As a warning, of any of the days at NCTM annual, these reflections are the most likely to be inaccurate so feel free to take anything with a grain of salt, but my blog is for me not you 😛


How Research into Second-Language Learning Might be useful to Mathematics Educators: Brent Davis

Davis argued that there are three types of teachers: Standardized education where knowledge is a series of things, Authentic/Reform Education where knowledge is about personal interpretations and connecting to create webs of knowledge. The third group is a group in between. This inbetween group is where most teachers are, but they don’t self identify as strongly with where their classroom lies. These teachers aren’t completely reform teachers but instead their inbetween state makes them easy critics of “traditional” educators.  Davis’s talk made me self reflective about my current position and philosophy as an educator.

Personal takeaways:
– I currently speak this middle language and isn’t very coherent
– I need to become more internally consistent – my beliefs should match my classroom and once again…they currently don’t. They both need work to give me a stronger voice.

Mathematics and the African American Males’ Graduation Success: Stuart

Stuart looked at black graduates from HBCUs and PWIs to see how different things impacted their college careers. When interviewing individuals, the only significant variable was having a relationship with a professor – which was  more likely at an HBCU than a PWI. Students were also more likely to talk to faculty about career plans at HBCUs than at PWIs.

I went to this session to be a more informed advocate, and left that way. The information and discussion wants me to advocate for smaller institutions that cater to first generation students, or at least make sure students will are informed in their choice (I don’t think they currently are as informed as possible about kinds of colleges and universities).

Instructional Practices related to Students’ Conceptions of Mathematics: Grady

Grady studied a teacher who taught an Algebra 1 in 2 years course and looked at how he pushed his students to change conceptions of mathematics to a more coherent body of work.

A couple quick take aways:
– the teacher gave problems without context, but were easily relatable to students. They then built the context into the problem and worked it from there
– The teacher went down any rabbit hole to address student thinking and insight
– Most of class was spent on review, diving deep into a very few concepts
– the teacher kept going back to basic understandings every time a concept came up by making connections and repeating explanations. He also designed the course to provide a continuous review of content.

Personally, if I teach our remedial math course next year, I’ll look back at these take aways for personal implementation and reflection.

#NCTMannual: Saturday

This is a series of reflections based on my time at NCTM’s annual meeting in San Francisco. Part 1, Part 2.

By Saturday, I was whomped, but kept going because I only had a few solid hours left to experience NCTM. Of all the days, I walked out of the most sessions this day. But, some of my favorite sessions were this day.

Beyond Relevance & Real World: Dan Meyer

I didn’t attend Dan’s session because I knew he’d be posting it online. With other PD not being posted/easily accessible I attended other PD. Resources

My takeaways from watching his talk today:
– We have to ask students FOR questions to invest them
– Wrong answers and best guesses/estimations improve student outcomes.
– it is in our best interest to redefine “real world” mathematics in the broadest sense to engage students. Just because there’s a picture or a word problem doesn’t actually push for better student engagement.

The Life-Changing magic of Tidying the Math Curriculum: Jason Zimba

Jason spoke to a lot of the same issues of Graham Fletcher’s #ShadowCon16 from the day before. As an author of CCSSM, it was interesting to hear him speak and tear down some of the assumptions and critiques around the standards. His biggest push was not to teach too many methods or procedures.

On methods he noted that some things “go stale” and that what is easiest for students may not help them with later mathematics. Other methods we teach should complement not replace the standard algorithm.

On procedures, he admitted that procedures have a place – for procedural tasks. However, they don’t belong to be taught to answer conceptual questions (like the vertical line test). If we teach a different procedure for every problem, students will be overwhelmed and think math is a series of procedures instead of a coherent body of work.

Finally, Zimba called us to “pursue ultimate simplicity” in our curriculum to advance students.

Personal Take-aways:
– Curriculum needs to be carefully vertically aligned, with knowledge of what is to come to bet promote student learning
– Think about when I teach things as a procedure (which I do) and reflect on its effectiveness (hint: it isn’t 97% of the time)

Assessment Structures that Work: New Visions for Public Schools

If you can’t tell, I have an assessment addiction because mine kinda suck, and I’m still not happy with how I use assessments in class. David Wees and Erik Laby friends however made such a challenging topic so simple. This hour was one of my favorites of the week.

My “Why on earth hadn’t you thought about this before?” moment was how they code formative assessment based on strategy and track it. Then use that data for the entire unit. When I’ve done that before for a MARS task it was just short term, never long term/unit wide preassessment. They’ve created (and shortly will share) rubrics that give us data on strategies, not scores to improve instruction.

They also designed a common curriculum for teachers in their work to have common conversations. Their breakdown is: Course -> Units -> Task (initial task on prior knowledge with a non-traditional rubric) -> Teachers teach the big ideas of the unit however they feel is best -> Formative Assessment -> Re-engagement tool -> then a “balanced” assessment. This wasn’t a sales pitch, but I think I’ll be an advocate for adopting their model 9-12 because so much of their work just makes sense. And, they have done all the hard work we can’t improve.

And, I had some great conversations with my neighbor and she pushed my thoughts and recommended Dylan William’s work on formative assessment She also said that I seem to be doing good things – it’s the little things that make you feel good 🙂

Resources: Handout PPT Website

Personal Action steps:
– Ensure whatever we adopt of 16-17 has a strong formative assessment already built in that is simple to use
– Become consistent about formative assessment
– Think about the thinking students are doing at the beginning of a unit and use that as a way to bridge their thinking to what they need to be doing.

#NCTMAnnual: Friday

This is my second in a series of posts breaking down my time at NCTM’s annual meeting in April 2016. Here is the first.


Ignite talks are 5 minute bursts of passion by educators. I won’t recap them all, just those that moved or pushed me. Ignite was a pretty solid way to start my Friday.

Michael Fenton

When presenting a problem, consider adding a sequel because students are already invested, we can push boundaries and we can learn more about the work by pushing beyond. We also have to know when to stop, teachers have to solve the problem before putting it in front of students and we should take what works from before and apply it again.

Andrew Stadel

Time is a dirty, dirty word. We need to use the highest leverage things in our classroom because we only have so much time with our kiddos. What are the highest pieces of leverage we can use during our class? Andrew proposed: Talking less so students can talk more, do less rote problems and more problem solving and finally blend different parts of instruction together as students work through a problem instead of having discrete parts. (Follow the discussion online at #classroomclock)

Annie Fetter

People can’t understand solutions to problems they don’t have and therefore STUDENTS CANNOT ANSWER QUESTIONS THEY DO NOT HAVE. She also said that students may believe that mathematics is something done to you, not something you do. We have to believe and promote a culture that every student has ideas about every math problem, which will increase their engagement and learning. She pushed us to replace SWBAT with students will be curious about….

Max Ray-Riek

Max shared with us that when you reflect on a lesson someone else has implemented and written about online, you are thinking critically about the lesson and how to improve it. This kind of thinking is what promotes student outcomes. While Max pushed us to become blog addicts, he also said that students need a coherent curriculum. My school doesn’t – I’m just a blog addict cut-pasting things together. It’s atrocious and a huge problem. I’ll be addressing it this summer because what we have is not okay.

Tracy Zager

Mathematicians work together in fluid ways, 4 authentic ways mathematicians share

  1. Working alone (think time, before ready to talk to anyone else)
  2. Thinking partnership: Could we work on _ together? Can I run something by you?
  3. Cross Pollination: Share ideas from different people
  4. Math Disputes: I think I hear what your saying but I disagree because, listen to others
  5. Peer feedback/critique: Can you prove me wrong?

Big takeaways:
-there’s a need for a coherent and longitudinal curriculum that will outlast me
– Sequels are an underused tool in my repertoire
– Structure to a group activity/purpose will promote better reasoning and ideas when a student then recognizes that they need help. And what kind of help they need
– My classroom clock is running on better time this year in the past, but it still needs to be reworked.
– Students have to be asking questions about the mathematics (A great followup to this is Dan Meyer’s presentation)

Digging into DOK with Robert Kaplinsky

When you walk into a room 10 minutes early and there isn’t a seat left in the house, you know the presenter is a rock star…at least in the math community. Robert was one of those sessions – and didn’t disappoint. I didn’t a seat, but I did get a push to push student thinking my classroom by increasing the Depth of Knowledge.

Reflecting upon the work, I realized that in many of my classes, there’s a clear jump from basic computation questions to bigger 3-act math/math tasks. And there isn’t much opportunity for play or experimentation like open middle problems. Many days, my class doesn’t have much cognitive demand, and that’s a problem. A big problem.

Moving Forward:
– Plan for students to do deeper level work to build up their knowledge
– Use open middle tasks
– My students can do it. I need to let them.

I did implement my first Open middle problem in Geometry this week. It went okay…but I fit it in over three days instead of devoting a chunk of instructional time to it. I definitely feel that there’s a skill in implementation that I don’t yet have. The task also took way way longer than I anticipated…but did help reveal some misconceptions about student understanding. There’s also a class culture around these types of problems I have to address – but it is not just my class my entire school has an apathy/engagement problem. Hopefully more consistent implementation  of problems like these will be helpful.


Rewards and challenges of Standards Based Grading

I’ve considered implementing SBG for a couple terms and just never have had the guts (or been together enough to be ready for it). Matthew Grinwis and Michael Manganello gave simple, concrete ways they have slowly implemened it in their work. 

Their take aways: SBG allows for better feedback, students talk about topics and know their deficits. Biggest struggles were sharing information with parents, creating standards, designing/grading unit tests and creating re-test assessments. They also eventually created a generic rubric, score each question on the rubric then take the average for the final score on the topic.

Personal takeaways:
– Take risks, do it. Stop making excuses Winfield
– Scoring each question on the rubric is actually brilliant and would solve my current problem
– So much of what I grade now isn’t a measure of student learning and that needs to change. (As I have hours upon hours of grading to catch up on from being gone for two weeks).

Handout PPT


A Brief History of Math Ed: Lessons for Today

Matt Larson, President of NCTM, gave an expanded version of his Ignite talk from the morning. He pushed that we need to stand up as educators and stop swinging between procedural knowledge and application – both are good and both are necessary for student success. He called us to do three things to address this “Pendulum Swing”: 1) Recognize that we have the same goal as previous generations – to educate students 2) realize that mathematics is multidimensional, not necessarily what people were exposed to in school 3) Parents respond best when we discuss the need for critical thinking and problem solving skills. We need to help people separate standards from curriculum, help critics see strategies and finally be advocates for research based strategies.

– My voice is needed, not only in Arizona but in NCTM, #MTBoS and AATM.
– We’re in this together

Developing Problems that Evoke & Assess the SMPs:

I started in this session, but left early because I saw that #ShadowCon16 had a huge line and I didn’t want to be turned down like I know people were earlier in the day for Jo Boaler.

Biggest takeaways:
– design and implement an algebra 1 assessment that focuses on how students use structure to solve problems, instead of struggling through problems.
– Two kinds of structure were “Chunking”  where you treat objects as a single number and “Hidden meaning” Where you can re-write a problem to reveal different properties
– When looking at student work, it shows the students first inclination and what they are most comfortable with not all that they are capable of.


A series of 10 minute talks by leading folks in our field. NCTM’s website about the page is here, pushing us to take action after the conference together.  I have one complaint about #ShadowCon16 1 Some presenters repeated their presentations in large part from earlier in the week. I get why, but I would’ve known that I could’ve been somewhere else during the earlier block. This wasn’t an issue in 2015 because ShadowCon was created because people got snubbed. Now that it was sanctioned this seems like an unexpected hurdle for the team to conquer.

Robert Kaplinsky shared his powerful story and called us to empower others. Personal response: See below.

Gail Burrill: Called us to ask deep and meaningful questions about deep topics. And never say anything a kid could say, but instead probe them to have conversations themselves.
CTA: Find a “mentor” voice and keep them in your head. After class, think about what would have happened if you listened to that voice and try to make a change for the future.
Personal Response to the CtA: I’m going to find that voice over this summer and follow Gail’s advice. Why summer? I have just 4 weeks left of school and want to frame my entire 16-17 school year around my “voice” of choice.

Kaneka Turner: Pushed us to invite others into the world of mathematics. Without an invitation, we are excluding others who so desperately need to be included.
Personal response to the CtA: As we hire our new math teacher for 16-17, my goal is to be radically inclusive, empower and invite them into #MTBoS and help them grow.

Brian Bushart: Bring joy into mathematics classrooms. His presentation resonated with me because as I teacher higher and higher levels of math there is significantly less joy.
Personal Response to CtA: Bring play into my precalculus classroom as we discuss continuity through an open middle problem. Long term: Embeded more play – students LOVED playing with polygraph earlier this term – it shouldn’t go away.

Rochelle Gutierrez: Once again, a rockstar in our midst. Her call was for us to stand up for students and be an advocate for them, and possibly against the system.
Personal Response: We are redesigning (or dare I say designing) a scope and sequence and choosing courses to offer our students. I want to be an advocate for flexibility of placement, allowing students not placed on the AP track in grade 9 could find a way to be on that track later in their mathematics career.  I am also pretty sure I’m going to ask to teach our new statistics course for seniors and design it around social justice issues. (And yesterday at our staff PD, I pushed back that our school’s guiding principles don’t mention our students culture or being culturally relevant, which I don’t think I would’ve done two weeks ago).

Graham Fletcher: Discover something within our standards for our courses. Then reflect and see if there is anything we are currently teaching that isn’t in the standards (ie simplifying fractions)
Personal Response: Well…our entire curriculum needs to be (re)designed so as I find out which courses I teach in 16-17, I’ll be digging in deep to the standards and reflecting upon Graham’s call.

My two sentence summary doesn’t do the work justice, so ShadowCon16 talks are being released in the coming weeks:


#NCTMAnnual: Thursday

Earlier in April, I have the privilege of attending NCTM’s annual meeting in San Francisco. I’m going to spend the next bit breaking down the sessions I attended and being more concrete about my next steps as an educator.

Math Mistakes and Error Analysis: Diamonds in the Rough with Andrew Stadel (@mr_stadel)

Within 30 seconds of beginning Andrew began by using Matt Vaudrey’s “Music Cues“, which I considered implementing this school year. While I did like using them to bring people back together, I didn’t like using them during think time – I kept getting distracted. More importantly, seeing it happen makes me reflect on deciding if I want it in my classroom next year in some fashion.

Andrew broke up his session in three parts and ways to use error analysis. Our essential question when thinking about mistakes was if a student makes a mistake, what do we do next? While I do use mistakes frequently, Andrew pushed us to make routines a norm where we use errors to drive students and conversations forward. Thinking about what’s next this seems like a good routine in a class. Quick take away: Teachers in samples re-wrote/created mistakes instead of direct student work. I think that’s a culture improvement from what I do now.

Moving Forward:
– Be regular about routines about mistakes
– Music Cues?
– When applicable, re-write student mistakes to avoid embarassment
– Experiment in Class – I can’t see everything before I do it so be BOLD

(Digital Resources here.)

Mathematics Teaching as Social Justice

Presented by Rochelle Gutierrez

I was excited by this session, and Rochelle blew me away me with her talk. Within five minutes, she (rightly) critiqued PARCC, Pearson, current thoughts on race and countless other things. She used blunt, truthful language to accurately describe what our students face. I left inspired to become a much more significant actor of social justice though what I do instead of just being a part of a system.

Moving forward:
– Rethink everything I do and why
– Challenge assumptions we make about math education
– Be an advocate for students

Mathematical Practices in AP Calculus

The 2016-17 AP Calculus course is changing slightly and I wanted information about how, why and what’s next for students. Not the most exciting hour, but certainly important.
Quick highlights:

  • 95% of AB is staying the same
  • L’Hopital’s rule is being added back to the curriculum
  • College board made explict the bigger picture thoughts that students in AP and in Pre-AP courses need to be doing. They essentially mirror the SMPs of CCSSM, but are a little more explicit.

Moving Forward:
– Keep this in mind as I rewrite/write curriculum for the SY16-17
– Use CollegeBoard Resources as I redesign

Talk Moves and Structures for cultivating MP3 with E. Statmore

I’ve heard plenty about Talking Points and why it works – but had questions about format, how it looked and in general was pretty uncertain about the structure. I attended her session knowing what was being preached, and still had an enjoyable time. My table (with John Berray) amongst others had a little difficulty conceptualizing the point and wanted to talk through the mathematics instead of following the structure. Grappling with talking points with others was so helpful – it made us think carefully about designing the Talking Points and the purpose. I had questions about ELL students being successful because I feared their difficulty with abstract concepts, but Statmore relieved my fears, saying the structure was helpful (especially “No Comment”). Hearing that she groups students homogenously was also a relief – that seemed to eliminate a lot of my fears. Final kick in the bucket: “Talking points isn’t about getting the mathematics right, it’s about speaking, listening and changing your opinion” I thought the goal was to come to a common understanding about the mathematics (which would be great) but instead the focus is on LISTENING and taking turns and the soft skills students need. Statmore took all my fears, crumpled them up and threw them away.

Moving forward:

  • FInd more examples of Talking Points from #MTBoS
  • Think about HOW to implement this structure in 16-17 (course? frequency? purpose?)

Digital resources