This is supposed to be good for me

Everyone says it’s helpful/reflective/cathartic/instructive to write about lessons that flopped, and I guess I don’t disagree.  But there’s something very uncomfortable, clearly, about seizing upon an idea, envisioning its unfolding in your classroom, doing the [sometimes huge amount of] prep work, and either watching hopelessly as it sinks like a lead balloon or flailing about to keep the ball rolling.  (Okay – sorry for the overindulgent metaphors were in that last sentence.)  And I’m still not sure the lesson was as complete a disaster as I thought it was.  I’ll let you be the judge along with me as I reflectively recount it.

When I read Lisa B’s wonderful post about introducing key vocabulary in her geometry class, I immediately knew that I wanted to try the same thing with my students.  She was helpful and generous, sharing her files as well as a step-by-step description of her procedure.  We had spent the first four days of class estimating, analyzing visual patterns, preparing our interactive notebooks, and exploring the idea of justification through folding paper.  This lesson seemed the perfect way to dig into the content while preserving a cooperative and constructive atmosphere.  I created the vocabulary strips with our new laminator (thank you, donorschoose!), photocopied a pile of Frayer Models, and scripted the introduction in my mind.  I was ready to go.

The Laminatorrrrr

The Laminatorrrrr

Microsoft Word - Contract p. 2.docxI had not given out my course contract during the first few days of school because all the other teachers were doing that in their classes, and I couldn’t bear the glazed eyes of students who had heard the same speech 5 times already.  But now it was the sixth day of school, the contracts had been returned by the Copy Center (the other reason I hadn’t yet distributed them), and it was getting late to disseminate written expectations.  I thought I would do a brief ‘scavenger hunt’ as a class warm-up, highlight the class rules that might not have appeared on other contracts (my famous Rule 0 – No Grooming), and transition directly to the activity.  Needless to say, the contract review took longer than I had planned, which is not necessarily a bad thing – expectations should be said out loud in your classroom, even if they have been said in others.

Microsoft Word - Widgets.docx copyBorrowing shamelessly from Lisa, we successfully completed “What is a Widget?”  The students seemed to grasp the idea of example versus counterexample.   I modeled how to complete a Frayer model using the word ‘ray’, realizing that they would not be able to define ‘angle’ without that term first.  I also realized that many students did not know certain notation conventions – for example, that equal numbers of tick marks on segments or angles signify congruence.  I have very patient and cooperative students in my 2nd period class (the first class in which I tried this lesson), and we worked through these kinks together.  But by the time they got to work on writing their own definitions, there were less than 15 minutes in the class left.

Despite the warm-up with the Widgets and my modeling, the students seemed reluctant to proceed similarly on their own.  Almost every table (there are 8) required a significant amount coaching to write their definitions, and to use the counterexamples in identifying characteristics.  I told the students we would jump right into the activity the following day, in the hopes that they would complete at least half the list.  I had originally planned having them swap definitions with other groups, but not enough work had been completed for that to be an effective activity.

The following day was Geometry textbook day – determined by my assistant principal, and mandatory.  Textbook distribution involves sending a group of students to the book room (two floors down) where they wait in line with students from other Geometry classes, and upon receiving a stack of books, return to the classroom.  The students completed their book receipts, got their books, and continued working on vocabulary.  I asked them to put the books away and develop their definitions in the same manner as the day before – through discussion and observation.  But when I read this definition, I realized that some of the students were using IMG_3954their textbooks, and asked them to stop, repeatedly.  Let’s just say, I didn’t get 100% compliance with my request.  But with 8 tables and 34 students, I wasn’t able to control this.

By the end of the second class, most of the students were on their second sheet of Frayer models, which meant they had completed at least 6 definitions.  I observed that my efforts at getting the students to talk to each other about the vocabulary were only moderately successful, and that some students, who were not engaged in conversation, spent most of their time copying the examples and counterexamples.  As I moved around the classroom and talked to the students, I also realized that many of them were missing some of the finer points of the definitions – that supplementary angles did not need to be adjacent, for instance (and defining adjacent – that was a hugely difficult task for most) – and that misconceptions were showing up in some of their work.


Some definitions are better than others…   IMG_3960  

I collected all of their    work (three classes times 34 students times 2 sheets each = a lot of definitions).  I brainstormed my next steps with a colleague, who suggested I look for the best definitions from all of the classes, and put together a ‘master’ which the students could use to create the final Frayer models to go into their notebooks – an idea which I think will give credit to the students who understood the activity and provide solutions for those who struggled with it.  And it won’t be me spoon-feeding them the definitions, or having them copied directly from the textbook.

But after two class periods and a whole lot of prep (not to mention the work to come), I am not sure what was accomplished.  I know that these concepts will need to be re-introduced and carefully reviewed.  Have I laid the groundwork for that?  Or have I seeded the geometric field with misconceptions?  And I’m not sure what I would do differently.  IMG_3956Would it have worked better if my classes were smaller?  (You know the answer to that – of course, it would have.)  Clearly the addition of the contract review and the interruption of textbook distribution distracted from the task at hand.

I want to understand this better, because I don’t want to spend the prep time and energy, as well as the classroom time and energy, on activities that I can’t execute properly, or that may not benefit the kids.  If my goal is to guide them through constructing some geometric meaning for themselves (rather than delivering it directly), I want to make sure that they are learning.

And so another week begins.



My trusty cart loaded with supplies, ready to go.

When I described what interactive notebooks are today, using Sarah Rubin’s excellent Prezi, 35+ students became very quiet – all three times.  When they began selecting duct tape and paper for their notebook covers, it was if the room became a meeting of the Teen Scrapbooking League.  In all three classes, the students went at the task with enthusiasm, and abandon. photo 2

I am not as experienced or efficient at this process as some of my MTBoS colleagues, so the initial set-up will take 2 days.  But I am excited by the willingness of these students to follow where I lead.

The best part?  We haven’t even done anything yet, and one girl came up to me after class and said, “I want to thank you for using these notebooks.  I can never take good enough notes.”

Worth all the scraps of paper and balled up duct tape.

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P.S. My co-teacher hard at work, duct-taping that notebook into submission!

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You can do math even if you’re schvitzing

Maybe because the summer was so meteorologically pleasant.  Maybe because the windows to the lovely new classroom [which I am privileged to teach in] only open 6 inches at the bottom per NYC Department of Education building code.  Maybe because the 75-year-old school building went from having a handful of people in it to having 4,000.  Maybe because I’d rather be on a lake in Vermont any time.

The start of school felt particularly painful to me this year for any one of the above reasons.  Yesterday at the conclusion of what will probably be the easiest day this term (the periods were only 25 minutes long), I couldn’t see straight.  Actually, I’m pretty sure it was the heat and humidity.  But at the time, I felt like I had lost my classroom mojo, and wasn’t even sure where to look for it.    I envisioned myself barely scraping through the remaining 160+ days of the school year.

I came home, hydrated and cleansed myself, and began to go through the feedback name tents from my students.  And, predictably, their voices, in the form of their calligraphy and questions, cheered me.  Several students asked my age (one sly student asked when I graduated from high school), one asked what my favorite ice cream flavor was, and another asked where I shopped for earrings.  But most of the questions fell into two categories,  which speak to what all students would like to know at the start of a class –  ‘What is expected of me in this class?’ and ‘Will I be able to do it?’  I answered over 100 questions, but the task actually cheered me – I teach because I love math and students (several asked that question as well).  The exercise heartened me for Day 2, which was actually quite awesome, although equally sweaty.

The theme of the Geometry classes was Communication.  We opened with the Pick-a-Point activity lifted from Dan Meyer’s video, and expanded the discussion to include selections using lines (thank you, Quadrant Dan!).  Interestingly, the students didn’t use the letters in the second screen – at least not specifically.  For example, one student said, “It’s the point between A and X.”  I loved their willingness to keep up the challenge.

We then moved on to a Talking Points activity.  I was quite nervous about this; I’ve read several blog posts (Cheesemonkey, for example) since Twitter Math Camp about this, trying to envision how the activity works in real time, and practiced – in my mind –  how to break down the big ideas and directions.  I have to thank Amy Fine over at It’s Fine in the Middle; her clear description of how she ran the activity in her briannaclassroom helped me tremendously.  So this morning, even in the swampy morning heat, I took the plunge, and the kids did me proud.   Everyone participated, and they adhered to the No Comment rule without prompting.  I’ve had many of these students before (this is an off-track/repeater course), and it is gratifying to see their personal growth.  And when we were finished and shared out, lovely Brianna hit the nail on the head – “You can hear better what people say because you aren’t trying to talk.”

Back to Back Drawing

Back to Back Drawing

The class finished with Back-to-Back drawings, an activity in which one student describes a picture to another, who has to draw it purely from their description.  I think having just completed a listening activity contributed to the success of this exercise.  Here are some of the results – and I know the students who were drawing didn’t peek!

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IMG_3867Algebra 2 was equally enjoyable, albeit sweatier (these classes were in the afternoon).  I  used a lesson plan that I had written for a class in graduate school, but never implemented; I came across it while cleaning off my desk before the start of school.  After a quick review of the Real Number System (and hinting that there were other numbers which were outside it), we held the IMG_3858Rational Number Challenge.  First, students in teams of 4 were given a list of 20 numbers in all different formats – fractions, decimals, words, constants – and had to order them from least to greatest.  The winning team received one free homework pass (they thought this was FABULOUS).  The groups immediately became engaged and cooperative, and there was a lot of great math talk going on about how to organize the task.

After we had a winner, the real challenge began.  Here is what the rules were:

Untitled copyAgain, I was impressed with the engagement and focus given the unpleasant conditions.  And it was fascinating to watch the different teams work.  One team stacked all the Pawns in one corner and pulled them out one at a time to order them.  Other teams moved students around while they stood in line.  And again, the winning team was thrilled with their free homework passes – even though there is no homework yet.

IMG_3863IMG_3859  IMG_3872

I was just as sticky at the end of the second day of school as I was at the end of the first day, but no longer felt quite as desperate.  If we can have a great day under these conditions, imagine how well we’ll do when the air circulates again.

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Feedback Name Tents – Student Voices


Tomorrow is the big day.  I’m pretty anxious after watching everyone else go back, have their great first days, great first weeks.  It’s given me the opportunity, however, to borrow and adapt liberally – so thank you all.  I’ve been crediting and thanking on Twitter all along, so I hope you all know who you are.  This is the game plan:

We have very brief periods because of program and MetroCard distribution, so I have two objectives.  The first is for each student to create a ‘feedback name tent’ the wonderful idea that I borrowed from Rachel Rosales last year.  They are such a great way to connect with the students individually and quickly.  (Here is a sample my daughter made.)   photo (7)The second goal is to collect student information.  Thanks to Kristen Fouss, I created my first Google Form survey.  Then, with a little help from Kathryn Freed and @algebrainiac1, I was able to print QR codes with which the students can access the surveys.  I will bring the iPads to class for those students without Smartphones.   We only have 25 minutes per class, so with first day attendance, supply distribution and brief introductions, I’ll be happy if both of these tasks are completed.

On Friday, I have more interesting plans.  In Geometry, the theme of the day is Communication.  We will start with a “Pick A Point” activity as a warm-up, work through a Talking Points exercise as an introduction to cooperative groupwork, and finish with some ‘Back-to-Back’ drawing.  I’m hoping the big takeaways will be the necessity for active listening and clarity in expression.  My Algebra 2 students will be piloting a lesson on the real number system which I wrote as a graduate student (but never had opportunity to use). In teams, the students will be given a set of twenty numbers to put in order from smallest to greatest.  The numbers will be in scientific notation, radical form, written in words, expressed as fractions – you name it.  We’ll try several rounds.   I would like to open the lesson with some constructive talk about groupwork, but I’m not clear on whether I will have time do a Talking Points activity here. [I'd love feedback from anyone reading this who participated in that workshop at TMC14.]    I’m looking forward to both of these lessons –  I feel very positively about how they set the tone for the work to come in both classes, and am predicting high levels of engagement.

I’m saving my course contract for next week; I can’t bear to do it in the first two days when the students are hearing the same thing in every other class.  I’ve transformed by Geometry contract into something I consider much more attractive than the usual laundry list.

Wish me luck!

Get set…

(subtitled In Response to “For the start of this school year, I am excited about…” at

This morning, I read Andrew Shauver’s blog post (highlighted above) which motivated me to let go of my ‘so long to summer’ gloom and look forward with enthusiasm.  In that spirit, I offer the following list of things about which I am either excited or anxious (or both) as the 2014-15 school year begins.

  1. My newly crafted Geometry course – I have been given the opportunity to teach a new geometry course (entitled Geometry Fundamentals) which is “Regents-optional” for the students.   I spent the summer working on the curriculum map, seeking hands-on/discovery-based activities to supplement and/or replace much of the direct instruction I have used in the past.  It will definitely be a challenge – the students in this class are those that have struggled with math classes in the past, and a new course means writing new curriculum – but I excited to implement so many of the strategies that I don’t usually have time for in Regents Geometry classes, as well as using Interactive Notebooks.
  2. A second pass at Algebra II – I wasn’t satisfied with how this course finished up last year; besides the Regents results which were below par, I know I could have done a better job (a) with student mastery of the content (or as Rick Wormeli so accurately describes, automaticity) in the fall and (b) deep understanding of trigonometry in the spring.  I’m convinced I can improve in including appropriate conceptual activities while maintaining the pace required by our curriculum.  This morning I am especially excited to borrow an activity from Glenn Waddell; my students will learn about Desmos by playing with it, like I did here.
  3. My newly crafted classroom! – Because I am considered the only math teacher in my school who would be happy to have tables rather than [old, graffiti-drenched, right-handed only, hard-to-group] desks, I have been placed in a brand new classroom, complete with tables whiteboards, and bulletin boards (all a rarity in my school).  I will be sharing the    IMG_3803classroom, and it doesn’t have a locking supply closet [yet], so I will still be using my beloved cart (Donorschoose proposal #5).  Luckily, the classroom is on the same floor as my office, so I will be spared the long wait for the ancient and only elevator.  I am looking forward to being able to decorate my room, and….
  4. Bulletin Boards – I have been put in charge of the math department bulletin boards, and although I may have thought of this as a chore in the past, I can’t wait to remove the Jeopardy board with Pre-Calc questions that was on the wall when I started working at this school three years ago.  I have wonderful monitors who love a creative challenge (they did my MathMunch display last spring); cheery elves to help with the work always make it better!
  5. Mathletes – I can’t wait to see my math club – again, their enthusiasm, their desire to tackle problems  – discuss and argue different solutions – make staying late a pleasure.  One of the students attended the NY Math Circle’s Summer Program and I am looking forward to hearing about his experience; this is a child who loves a challenge, to learn -or teach himself – something completely new.

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  6. A New Co-Teacher – There are two new teachers in our department this year, one of whom will be my co-teacher in the inclusion section of the Geometry class.  Last year, my cooperating teacher and I were not so cooperative (read any of my blog post’s from last spring), but he was only temporarily placed at our school, which probably undermined his commitment.  I’ve had wonderful relationships with cooperating teachers in the past, and I’m determined this one will be added to that list.
  7. Talk Like A Pirate Day – Just because we need to have a little fun, and I’ve never done this before.
  8. My New Attitude – I am DETERMINED to achieve greater balance in my life – both personal and professional this year.  I have set goals for myself (see Conundrum), and am envisioning how I will meet them and stick to them.  I’ve tackled and survived a lot worse.

I want to thank all of you in MTBoS who have already gone back to school and have been blogging about it; your energy, insight, and honesty have all helped me get ready.



I spent the day sifting through piles of papers, rediscovering lost gems (my favorite Onion math teacher article), tossing things I’ve never used (though I once was certain I would), just generally weeding things out, recycling old folders and binders.  After the positive meeting at school yesterday, I thought for sure I would be able to focus on the imminent start of school, envision and map out the first days in my classes.  But the hours slipped away this afternoon – amazing how time passes when your goals are unclear.  By dinner time, all the loose papers had either been sorted into binders or recycled, my files had been thinned and streamlined, and my planner for the fall organized.  I was troubled, though; I knew that this time last year, I was enthused and excited with my plans for the start of school, and that even with the good work I’ve done this summer, I’m not there yet – I can’t specifically conceive of how it’s going to go, in just one short week.  photo (7)

After dinner, I took a walk; the evening was lovely – breezy and cool.  I found a quiet place to have a coffee and try to establish clear goals for myself – the foundation of any successful plan.  I started with the same goal I have had for the last three years:

    • Time for the gym 2 evenings/week and once on the weekend;
    • Time to quilt at least 2 full weekend days per month, and evenings;
    • Time to relax in the evening 3-4 hours/week;
    • At least 7.5 hours sleep each night.


It all sounds reasonable, doesn’t it?  Yet I haven’t been able to do this yet in the last 8 years.

I moved on to my goals for Geometry, which came pretty easily – after all, that is the class I’ve been thinking about all summer, the course I’ve already mapped out.  But Algebra 2 is the problematic course for me this term.

Following the Regents Passing Rate saga last June, I need to better ensure that my students master the content according to my department’s goals (this was made quite clear to me yesterday by my Assistant Principal), but the volume of content required to be covered in the fall term is formidable. 

A list of the daily "Aims" from our curriculum

A list of the daily “Aims” from our curriculum

  The only way I can see completing the required curriculum successfully is by abandoning many of the conceptual activities which make so much more sense to me for creating deep understanding, in favor of procedural teaching and practice.  This goes against a lot of how I believe math should be taught, and the work I have done to transform my practice in the last few years.  But ignoring what’s been asked of me by my administrator is not in my best interest (nor necessarily in my students’ best interests, either).  

It is actually easier to teach this way than to craft [even when borrowed] engaging inquiry and problem-solving activities that elicit productive conversations and deeper understanding, isn’t it?  But not nearly as interesting, for sure, and not why I teach. Following this train of thought, however, I was able to map out the semester, and sadly was able to see myself barreling through the content with lots and lots of worksheets, driving my students to continually practice those problems which will appear on departmental exams and the Regents in June.  Maybe this is what I need to do for a year to improve my ‘results.’

Or do I?  Sigh.  I welcome and seek your feedback.

On your mark….

I met with my Assistant Principal today to discuss my plans for the Geometry class this fall, and to clear the air over the Algebra 2 Regents passing rates – it was a wonderful meeting.  First of all, I found out that this lovely classroom will be mine for at least 60% of the day: IMG_3803

What you can’t see is the SmartBoard in the front of the room, and the whiteboards which wrap around the other walls with bulletin boards at either end.  Now this might not seem so earth-shattering to many of you, but I teach in a building that is 75 years old, and the only improvement to the classrooms (besides layers and layers of paint) is a SmartBoard smack in the middle of the original blackboards (which are not magnetized because they are so old).  One wall in each classroom is also dedicated to unused student lockers (well, they are used for trash now and then), and all of the math rooms have desks.  My AP knew that I was probably the only teacher in the department who would be HAPPY with tables.

I’ve been jealously reading blog posts about classroom decor from Sarah at mathequalslove, Miss Calcul8 and JemmaPDuck and even printed out the Jedi Mindset Posters from TeacherPaulP, knowing that I had not had any opportunity to decorate a room since I came to my current school three years ago.  But now the sky is the limit – I even have a place to hang my icosahedra!10572112_10203125744598130_8974409172441000582_o

The other good news is that I will be teaching three sections of my hands-on Geometry course (updated curriculum map below) and two sections of Algebra 2/Trigonometry.   There are big focuses (foci?) this year at school on quality feedback and formative assessment, so the weekly math maintenance worksheets I created (borrowed) were a big hit as well.  I decided to create two different sheets for each of the classes: in Geometry, we will doing the Estimation180/Visual Patterns/Would You Rather dance, whereas in Algebra 2, I will be focusing more on skills and current content.  Once again, I owe a lot to the generosity of Jessica (@algebrainiac1), Lisa Bejarano, and Kathryn Belmonte.

The final positive note in this meeting was the reception of my offer of running a professional development session, based on the workshops I attended at Exeter in June.  It turns out that our district is planning shared professional development on Election Day with four other schools; each school will be dedicated to a particular content area, with representatives from each school offering classes.  I’m excited that we will be doing something so relevant and productive this year, and that I’ve already planned out several activities to choose from.

So even though I am clinging desperately to these last few days of vacation, I’m pumped.  Now if only I can get myself out of slo-mo.

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