PD with Dan, creating intellectual need

This past week was workshop #2 with Dan Meyer, who was invited by the NYCDOE to conduct a three-part PD series. It’s not every day that you get to attend a workshop with him, so I’ve decided to capture each of my experiences. More on workshop #1.

Too make a long story short, it was another outstanding experience. Dan Meyer never ceases to be thought-provoking. He presents the sort of stuff that stays with you long after you get back to your classroom. Here are the details.

The focus of the session was creating intellectual need in our classrooms. He’s advocating for the learning of mathematics that doesn’t need to real world, job world, or even related to student interest. His argument was based on the work of Guershon Harel (article here). Dan believes, and I do too, that we can meaningfully engage our students by creating headaches in our classroom for our students. We shouldn’t be in the business of imposing mathematics where it isn’t wanted or welcomed. I’ve read his headache-inspired posts from his blog, so it was really cool to get to experience first hand his thoughts on the matter.

He hooked us by running through a series of small activities that are examples of creating intellectual need.

  • Little expressions. This creates a need for combining like terms and efficient calculation techniques.
  • Controversy. This creates a need a need for how we communicate and represent mathematics a series of operations.
  • Memory Game. He flashed first a 9-digit number and then a 16-digit number and asked us to remember as many digits as possible. Created a need for scientific notation, an efficient means of mathematical communication.
  • The $20 Bet. He wrote down a number and gave a volunteer ten attempts as guessing what it was. If they could guess his number, he’d give them $20 (he only had $5 though). After each guess, he let the volunteer know if their guess was too high or too low. His number ended up being 87.21! This creates a need for different number families and their relevance.
  • Parallel Lines. Creates a need for precision when calculating and representing two parallel lines. The coordinate plane rescues us.

We then explored two of Guershon Harel’s five components of intellectual need: the need for computation and the need for communication. These two needs were directly tied to the five activities that Dan shared. More on the five intellectual needs here.

Dan mentioned that there are three questions that he asks himself when he attempts to design experiences that create intellectual need.

  1. If [x] is the aspirin, then what’s the headache?
  2. Why did mathematicians invent [x]? Can I put students in that place even for a moment?
  3. How can I help students view [x] as powerful, not punishment?

A common theme throughout the day was how we should get into the habit of turning up the dial slowly. You can always give more information to your class, but you can never take it away. SO TRUE. This connected well with session 1, specifically the use of the white rectangle to remove information and increase access. The introduction to a lesson (the Do Now) was emphasized as a critical phase of creating intellectual need – students must be able access the content however inefficient their means may be.

The afternoon began with an activity creating a need for proper labeling and name-giving in geometry. Dan had a bunch of random points on the screen and had two volunteers each choose one and attempt to describe which point they’d chosen to the other person. Another headache ensued. For the 2nd person, he labeled the points with A, B, C, … and the aspirin was given.

We then were broken up into groups and were given a scenario. They all showcased the opposite of what a needs-based classroom looks like. We were asked perform a makeover. We jigsawed it back together, read the summary of each prescribed remedy from Harel, and everyone in our original group shared. What stemmed from the conversation was awesome: developing a need for the algebraic form of a function. The Points Desmos activity followed, emphasizing the usefulness of inequalities when representing all points that satisfy a given set of conditions.

Lastly, we explored Polygraph as a way of creating a need for math-specific language related parabolas. This was great.

Other interesting bits:

  • The word student means “to take pain” in some language (can’t remember which)
  • Whenever students laugh during an activity, you know their pain has been relieved
  • Algebra is sophisticated version of trial and error
  • Math pedagogy aside, I’m always find it compelling how Dan manages his audience. He greets everyone at the door. His warm use of “friends” and “colleagues” whenever referencing the audience makes everyone feel a sense of togetherness despite being strangers. I also liked his use of the phrase “For those of you that have the answer, say it out loud.”
  • After discussing the need for the algebraic representation of a function, Dan referred to algebra is “a more sophisticated form of trial and error.”

Dan’s Google Doc of the session.


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The need for estimation and the estimation wall

For the last few months, I’ve really been buying into the power of estimation. It has changed how I teach in a dramatic way. Let me set the stage.

In December, I gave my students this problem on a checkpoint:


I wish I would have taken photos of some of their work. A few gave answers like $340. Others were in the ballpark of $34,000. To say I was disappointed is an understatement.

But to make a long story short, too many of my students made absolutely no sense of the problem. Sure, they knew that a given formula needed was to be used, but in terms of logical answers goes, they were lost. Key skills like using context clues and relevant information, compare/contrasting, drawing from prior experience, and – most notably – number sense, were completely absent in their responses.

Upon handing back their papers the next day, I did everything but rip the SmartBoard of the wall. They felt my disappointment in their responses. I made sure they did. The most disappointing part was the fact that I’ve seen this sort illogic amongst my students for years and have never strategically addressed it…until now. One student even boldly asked, how do you expect us to think logically if we don’t practice doing it? She was SO RIGHT. I was expecting them to do something I hadn’t outwardly emphasized or taught. More on this situation here.

Around the same time, I attended a workshop led by Dan Meyer and remember him asking for estimates for the answer to a problem. It wasn’t his goal for us to better understand the usefulness of estimation, but somehow that was a big takeaway for me. I think it had much to do with the context Dan created and how worthwhile the too low, too high, and just right estimates were to help us make sense of the problem.

Ever since, I’ve been opening class with an estimation challenge at least three times a week . Estimation 180 has been my go-to. The kids love it. Besides addressing the issues I described above, I’ve been intrigued by how the estimation process itself leads to a variety of other conversations related to the context.

For example, this estimation on the capacity of the soda can prompted a meaningful discussion around why the soda can contains more than the stated 12 fl oz that’s printed on the outside of the can.


What’s the capacity of the can (oz or ml)?

Could it be manufacturing error? Or maybe the carbonation bubbles are causing the measured volume to be greater than expected? Or better yet, maybe Coke is out to get us all by covertly filling our cans with even more sugar or, in this case, artificial sweeteners? (Conspiracy theory anyone?) These sorts of tangents abound whenever I post an estimation challenge.

Anyhow, take all of my in-class success with estimation coupled with my knowledge of Jonathon Claydon’s estimation wall and I decided create a space in the hallway outside of my classroom to encourage the entire school to dive in. Hence, the estimation wall (first edition):


The wall consists of several estimation challenges and their associated question, each taped to piece of construction paper. Underneath the construction paper is the answer.

Soon after I completed the wall, here’s what could be seen. Woohoo!


The creation of the estimation wall also served a different, much bigger purpose. It is much bigger than myself and it revolves around school culture. I realized pretty quickly this year that beyond high-stakes exams and AP courses, my school has no real mathematical identity. There are no mathematical initiatives, no clubs, no field trips, no electives. Though it has mathematics in its title and its one of its founding principles, mathematics is not publicly championed at my school for its creativity, wonder, beauty, and usefulness.

I’m on a mission to change that. The sort of cultural shift I’m envisioning at my school will take time, but we’re a small school…so I’m determined to make a difference.


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Random groupings

popsicle sticks

I recently had an epiphany. It came from Ilana Seidal Horn.

I was reading her book, Strength in Numbers, and she was addressing status in the classroom. Her definition is status is the perception of students’ academic ability and social desirability. Here’s an excerpt that blew my mind.

Unless we address underlying conceptions of smartness, we risk reverting to the commonly help belief that group work benefits struggling students because smart students help them. As long as we have a simplistic view of some students as smart and others as struggling, we will have status problems in our classroom. Students quickly pick up on assessments of their ability. For example, when teachers arrange collaborative groups to evenly distribute strong, weak, and average students, children will figure out that scheme and rapidly learn which slot they fill….If mathematics is rich enough, the strengths of the different students come into play, rendering the common mixed-ability grouping strategy useless. (p.29)

Truth. Talk about unraveling so many years of my teaching career in one paragraph.

A day later I noticed this tweet from Frank Noschese:

Bam. Just like that I was finished with strategic grouping.

Each seat in the room is assigned a number and every Monday students select a numbered popsicle stick upon entering the room. I’m coining them destiny sticks.

Screen Shot 2017-03-06 at 3.14.06 PM

This week, after the first go around with the new approach, I immediately got lots of “this is a great idea” and “I love this!” from the students. Full steam ahead.



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Day in the Life: February 24, 2017 (Post #8)

I’ve decided to chronicle this school year through my blog. It’s part of Tina Cardone’s Day in the Life book project. This is the eighth post in the series.

5:45am | Rise and shine. This is fourth consecutive Day in the Life post that is not a teaching day for me. The New York City Public Schools are on midwinter break this week. Traditionally public schools in US have two weeks for winter recess for Christmas and New Years. Instead, we only get one week and get the other week off in February. I love it.

I make coffee and read. Right now I’m in the middle of How to Bake Pi by Eugenia Cheng and Strength in Numbers by Illana Siedal Horn. I read some of the latter and sip my coffee for about half an hour and then hang out with the family for a while and eat. I also begin drafting this post.

8:30am | Today I have my Renewal Master Teacher interview with Math for America. It’s scheduled for 10:40am, so I get ready to leave. Am I nervous? A little. But my experiences with MfA have been so uplifting these last four years that I would say I’m far more excited than nervous. I have a lot to share. More on this later.

I shower and I’m out the door just before 9.

9:15am | I’m on the 5 train. I tap out more of this post on my phone and read more of Strength in Numbers.

After a few minor delays, I arrive at Union Square at 10:10. I have enough time to grab a muffin and apple from the farmer’s market and do some people watching for the next 20 minutes. I walk down the MfA offices for my interview. I don’t wait long. After a minute or two I’m called in.

11:10am | I walk out of the interview feeling pretty good about how things went, but you never know. It was really laid back. More like a conversation than an interview.

I’m meeting with another MfA teacher to map out an upcoming workshop we’re running next week. We meet up at the City Bakery and talk. We wrap up around 12:15pm and I head out to grab some lunch in the area. I get a salad from Chop’t and lounge at Union Square. The weather is stunning, 70 degrees with plenty sun. A total gem. After soaking up some rays and watching some skateboarders attempt trick after trick, I head to the train.

1:00pm | I’m on the 4 train headed uptown, back home. I brought both books with me, and I’m feeling rather mathy on the ride home, so I crack open Eugenia Cheng.

1:45pm | I’m back in the ‘hood. I run a couple of errands. I want to simply be outside for the remainder of the afternoon because it’s so nice, but I have to get some work done today so I meander back home.

3:15pm | This school year I’ve been putting off work on my National Board Certification Component 2 submission. Now that the MfA renewal is officially complete and out of my mind, I want to channel a lot of energy towards prepping and completing the submission. It’s a beast and it’s going to need my full attention to tackle.

I decided early in the year that I wanted to showcase my deserted island activity for it, but yesterday realized that I wanted to use some of my intro and graphing logarithms material for the submission. Well, after a solid hour and forty-five minutes of deep thinking, I’m still unsure about the route I want to take. Mind you I haven’t even begin writing up the 10+ pages that the submission requires…I’m still deciding on the activities. It’s due May 17. Pray for me.

Despite sitting in front of my computer for all that time more confused than ever, I do manage to make it back outside for more fun in the sun. Family time. The best time.

9:00pm | I’m in the middle of watching the Raptors and Celtics on ESPN and can’t seem to keep my eyes open. Off to bed I go.

1. 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?

I am concerned about my NBCT submission. I would have really liked to have my two required activities pinned down by this point in the year, but I don’t. With that said, I know how I think. I’m a slow, grind-it-out sort of person. Things don’t usually hit me in a flash. So although I didn’t walk away with the answer today, I know that my time investment brought me closer to finding it.

2. 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?

To close the first semester at the beginning of this month, I had my students complete a “report card” for my teaching. I asked many questions and there were different trends in every class, but one commonality was their dissatisfaction with how I pace the course. I got the same feedback last year.

I say that to say that I came to the realization that I must slow down. Moreover, I realized that, as is, I’m not going to finish the algebra 2 curriculum. It’s not realistic. This is a result of me adapting to the new set of standards and confusing myself along the way. Needless to say, Its been a rough go.

Anyhow, my students need exposure to the entire curriculum for the Regents exam. My solution to this dilemma is to organize video lessons for my students to watch that will introduce the material that we won’t cover in class. The students will watch the videos at the own leisure outside of our regular lessons. This is very disappointing – especially because the videos will cover of the entire statistics and probability units.

3. 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.

This relational moment doesn’t pertain to any specific person. Rather, it’s about an organization – Math for America.

It’s remarkable just how different of a teacher I am after four years being given a MfA fellowship. My relationship with MfA has grown from one of deep admiration and respect to one of deep trust and responsibility. Summarizing four years worth of immense growth into a thirty-minute interview today wasn’t possible, but I hope the interviewers got a sense of my deep-seeded gratitude for how MfA’s impact on my career. I’ve been mindful of giving back to the community these last four years – beyond merely facilitating workshops and completing surveys. It’s the absolute least I can do for all that they’ve given me and my career.

There was interesting moment during the interview. I mentioned that I felt somewhat guilty applying for renewal because even if I wasn’t picked up for renewal, I would still take advantage of the MfA community by means of the Emeritus program – which doesn’t include the stipend. I’m certain that there are teachers new to MfA that would only be interested in applying and joining the community because of the stipend. In this way, I expressed that I openly accept not being offered a Renewal Mater Teacher fellowship. In fact, I questioned whether I should even apply for the fellowship in order to make space for someone new who otherwise might not get the opportunity.

4. Teachers are always working on improving, and often have specific goals for things to work on throughout a year. What is a goal you have for the year?

In my last DITL post I was disappointed at how little I was integrating instructional routines into my teaching, one of my big goals for this year. I’m proud of the fact that since then I have pushed myself to use at least one instructional routine in all of my classes…with more on the way. Things have slowed down at school and as a result I’ve been able to process the curriculum in a more structural way. I must keep at it.

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

In order to help bring a much-needed culture of mathematics to my school, I’m pumped about starting an after school math club. I surveyed my students and there is definite interest. I even attended a workshop to help me get it started. My hope is to have some initial meetings before the close of the school year. Worst case, I get things off the ground next year. Either way, I took concrete steps this month to make it a reality.


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Man, you talk about teaching as if it were love


Today is Valentine’s Day. I don’t really celebrate it, but it hit me that I recent conversation would make for the perfect post for today.

A couple weeks back, a group of colleagues and I were sitting around having a conversation about the teaching profession at my school. We talked about a lot of stuff ranging from our views on professional development, the transition that comes with changing schools, how to best reach struggling students, among other things.

I can’t remember exactly what I was talking about, but at one point I finished my thought and one of the relatively younger teachers in the group told me, in a matter-of-factly sort of way, “man, you talk about teaching as if it were love.

Wait, what? Did he just drop the L word?

He probably didn’t think twice about his remark, but I was caught off guard.

I never thought about it, but he was right. The moment was an unexpected self-realization. I was, and often do, talk about teaching like I would talk about love. It’s not far-fetched to say that most people would equate “talking about love” to expressing deeply held emotions that one holds for someone or something. I don’t want to sit here and try to define love, but I think it’s fair to say that it means to be strongly connected by means of admiration and devotion. It indicates an unbreakable bond and profound respect. It means embracing the inevitable struggle and hardship attached to the subject of your love.

All of that, and more, reflects the feelings I have for teaching and the teaching profession. It’s not just a job or career for me, it’s a relationship. It can be too heavy at times for certain discussions, but hey, it’s coming from a great place. A place filled with love.

Happy Valentine’s Day.


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