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.

Digital art by geosaurus.tumblr.com

Digital art by geosaurus.tumblr.com

Watercolor by geosaurus.tumblr.com

Watercolor by geosaurus.tumblr.com

#mtboschallenge Week 2: Professional Books

sunset at lake Coming back from Vermont is always a shock to my system, and even though I spent some time online while I was there – thanks to the Encompass Summer Institute – I somehow missed the #mtboschallenge start.    As I caught up on my blog reading, and listened to everyone’s start of school stories (mine is still 9 days away), the urge to participate has won out [for the moment] over my escapist fantasy of living in the mountains on my beloved lakeshore.  And talking about books is always a joy – I mean, I do have a degree in English Language and Literature….but that’s a long story.

Microsoft Word - Document1 copy

Let me admit, right off the bat, that I am addicted to books.  These are the  bookcases in my office at home.  I try these days to limit my purchases to books that I cannot read online, from the library, or borrow, but the recommendations from the many people I respect in the online community make it difficult to control the impulse to own these treatises of pedagogical wisdom.

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This first set of books were seminal texts in my development as an urban educator.  When I joined the NYC Teaching Fellows, I ‘talked the talk’  – I said that I became a teacher because I thought that was one of the few ways in which an individual could actually effect change in the world, even if on a small and personal scale, and that I wanted to help provide quality education to all children.  I don’t think I knew what that meant until I started reading about the importance of language (Lisa Delpit, Other People’s Children), discourse analysis (James Paul Gee, Social Linguistics and Literacies), and the limits of urban school reform (Jean Anyon, Radical Possibilities).  I can truly say that these books changed my outlook in a fundamental way – or maybe they just gave me the words for the inchoate ideas that motivated my career change.  I read Rafe Esquith’s Teach Like Your Hair’s on Fire at the end of my first incredibly difficult (who’s isn’t?) year of teaching, and his creativity in creating a classroom culture of achievement and community gave me fuel and ideas to return for a second one.  Of course, trying to implement all his ideas at once wasn’t a recipe for success (so I learned by mid-October), but I remain inspired to this day.


These two books by Paul Lockhart – especially A Mathematician’s Lament - have hugely impacted my philosophy of teaching math, and especially Geometry.   Geometry was my first love in high school, and I was thrilled to be teaching it.  I was certain, when I started out, that I would be able to enlighten my students, help them progress upwards on the Van Hiele levels, and convert them all to the religion of geometry.  Guess again.  So when I came to the chapter entitled “High School Geometry: Instrument of the Devil”, I took a hard look in the mirror, and began to rethink my approach.   And Lockhart made sure that I suffered no delusions about the benefits of my ‘traditional’ approach to the curriculum: “All metaphor aside, geometry class is by far the most mentally and emotionally destructive component of the entire K-12 mathematics curriculum.  Other math courses may hide the beautiful bird, or put it in a cage, but in geometry class it is openly and cruelly tortured.”   Measurement is a delight; Lockhart explores the beauty of math in an accessible, challenging and engaging way. 

5 invisible vilson

These are my most recent favorite reads, although truth be told, I am working my way through 5 Practices (I know, I know – it’s such a slim book!), but every page has something worthwhile for me to think about, and I have approximately 20 pages unread in both Invisible Children and This is Not A Test.  Vilson’s book – part memoir, part policy narrative, was engaging, familiar [as a fellow Teaching Fellow] and very accessible, and then it hit me right between the eyes – the chapter “Where The Hustle Comes From” held up yet another harsh mirror to my classroom, and my impatience with any student not paying attention, or trying to leave the room.  You can’t read this book and come away unchanged.   I found the book Invisible Children while perusing Don Steward’s excellent blog; he mentioned this book as a highly influential text in his teaching, and based on my respect for his work, I sought out a copy (it was published in 1989 and is no longer in print, I believe).  Pye describes the ‘bottle shape’ in the classroom which captures the teacher’s attention when they are in the front of the room – the center rows and the back of the class.  The sides of the room, even at the front, are where the ‘invisible children’ reside.   His descriptions of how remarkable children, only needing acknowledgment, are hidden and looked over (by their own design at times) ring true for any teacher of large classes.  I will be looking at my classroom very carefully this fall, with new eyes. 

I also have to mention Embedded Formative Assessment; its research-based analysis of formative assessment and practical strategies were enormously helpful in developing my practice in this area.  I don’t have a picture of this book because I have lent it to a friend.

On the reading list for this year are the following goodies:

There are many other books on other lists I have (tucked away in lots of nooks and crannies, both virtual and real) of book references made by people I respect, and I know that these lists will continue to grow.   And I’m sure I’ve forgotten some faves here.  But like I said, I studied Literature, and I can keep going….ad infinitum….

I don’t know how to finish off this post, for some reason, so I’ll conclude with this photo from the Lake Champlain Dragon Boat Festival in Burlington on August 3.  It’s a moving and exciting annual event to raise funds and awareness for breast cancer.  The boats are lovely, and there’s something very mathematical about the rowing team, don’t you think?

Dragon Boat Races in Burlington, Vermont

Dragon Boat Races in Burlington, Vermont





Before I head to the lake…

My view for the next 2 weeks

My view for the next 2 weeks

I’m about to embark on my annual pilgrimage to Lake Dunmore in Vermont.  It’s a little piece of heaven on earth which I have visited almost every summer for 20 years.  It’s the place where I truly relax and restore, where my family’s collective vacation memories live.  And while I will spend a little time contemplating the coming school year (and hopefully having a Burlington tweet-up with @jaz_math and @SmithTeach), writing curriculum is not on the itinerary.    Thus, my feverish work on the geometry curriculum – revised here:

It’s not finished by a long shot, but I’ve combed through the clippings I’ve been making in Evernote all year (thanks to the presentation by @borschtwithanna at #TMC13), the blog posts I have bookmarked, and the hyperlinks therein, annotating the map with ideas for activities and lessons.  I’m still wrestling with the Geogebra iPad app, but I’ve had personal assistance from the Geogebra Queen, @jensilvermath, and offers of help from others like @a_mcsquared, so I’m hopeful I will be able to incorporate this interactive tool in a way that will enhance geometric reasoning.    So again, I welcome feedback and suggestions.

I’ve also drafted a sheet to use each week for recording daily warm-up activities.  I owe this document to @algebraniac’s Weekly Warm-Up sheet, Lisa Bejarano’s spin-off, and finally Kathryn Belmonte’s shared presentation on Math Maintenance from #TMC14.

Here is my version of the weekly warm-up sheet:

Again, everything is a work in progress, but having completed reasonable drafts of both of these documents, I am ready to relax.  And maybe play with designing my own Interactive Notebook….

I have to conclude by thanking everyone in the #MTBoS who shares their hard work so generously.  Looking at all the links in my curriculum map, I am incredibly grateful to this community of people – some of whom I know, many who I don’t – that thrives in mutually beneficial interpersonal professional development.  I regret that I missed #TMC14, but honestly, I feel everyone’s presence as strongly as ever.  Lucky, lucky me.

Chippy seems to rotate just a few degrees each year.

Chippy seems to rotate just a few degrees each year.


The stuff of memories

Getting ready for Fall

I am teaching (I think) a revised geometry course this fall, one in which taking the Regents will be an option for students.  This gives me the freedom to do some more inquiry-based and exploratory activities, which are usually eliminated in the rush to cover every topic by the June exam.  I am also planning on using Interactive Notebooks in this class.

My first step has been to draft a curriculum map http://hermathness.wikispaces.com/Geometry, which as you can see is not complete – it needs, at the very least CCSS alignment posted, as well as assessments for each unit – but having a complete grid will give me an organized structure with which to fill things in, as well as an outline for creating my INB templates.

I welcome comments, suggestions, thoughts, and and will update the map as I go along.

Sounds of July

Postage-stamp Yards

Postage-stamp Yards

Sitting here at my dining room table, it’s pretty quiet – and sounds like a summer afternoon. Occasional shouts of children filter in through the window, the fan whirrs [sort of] quietly overhead, and there is an occasional gardening machine (lawn mover, edger?) briefly creating some dissonance. Thank goodness the backyards in Brooklyn are postage-stamp size; mowing the lawn only takes about 5 minutes, for anyone on my block.



I am relaxed – which is no small feat – but there’s a little bit of a nagging feeling, which I easily ignore much of the time, that I am not ‘getting enough done’ in this wonderful expanse of free time. The summer is when I can do grand planning, self-study, pleasure reading, and quilting. I have a list which I tried to keep manageable, but it’s always longer than any one person could accomplish in a summer. I’ve been reading on line and on Twitter other teachers’ preparatory work, and I’m wondering whether I’ve gotten anything done. So, to put my mind to rest for the moment, I thought I would make a list of what I want to do and what I have done to get some perspective.


(1) Write curriculum outline for new Geometry “Regents-optional” class including:

- hands-on activities using patty paper, manipulatives, tools of construction, iPads

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To-do Central

- cooperative problem-solving

- interactive notebooks [which need to be separately planned];

(2) Review Calculus through Schaum’s Outline in preparation for online Calc III class;

(3) Finish reading Lockhart’s Measurement finally! (I can’t resist stopping to solve every problem which makes it slow (but fun) going;

(4) Learn to use Geogebra;

(5) Finish 3 quilts of varying sizes and complexity, one which I have been working on for 10 years (not steadily), and two for current occasions with DEADLINES;

(6) Read/peruse at least 3 other books for school/math: Invisible Children by James Pye, Taxicab Geometry by Eugene Krause, and at least one of the 6 or 7 other books on my desk!

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The Desk of Which We Do Not Speak

That’s a crazy list, I see that now.


(1) Begin writing curriculum outline (through Unit 3) after energizing meet-up with @samjshah;

(2) Begin learning Geogebra after equally energizing online session with @jensilvermath;

(3) Work through 4 units in Schaum’s, although I haven’t gotten to the hard stuff yet;

(4) Read half of Invisible Children;

(5) Worked through a whole bunch of hands-on activities collected through the year and at conferences and explored their inclusion in geometry class;

(6) Make slow progress on all three quilts;

(7) Get back into the MTBoS and my tweeps, which thankfully, wonderfully is always available, which includes not only chatting but actively reading blogs (which means linking to more blogs with more ideas and on and on) ;

(8) Gone to the gym every other day – consistently!

(9) Caught up on a LOT of Netflix binging!

I guess I’m on the right track; it’s just when I hear those sounds of July, I feel SO lazy, and wait – there’s another series on Netflix I haven’t watched yet?

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The 10 Year Quilt (maybe a little more)



Passed Out

thumb203_content_335_ITIL_v3_Examinations_Average_Pass_RatesAfter all the hard work, the enthusiasm, the reflecting, the HOURS and HOURS spent researching, networking, sharing, thinking – my year has been summarized by an overall passing rate on the Algebra 2 Regents exam that is lower than my colleagues.  And after a year of my best work as an educator, not only did I find this out in a rather unpleasant manner (via text message while away at Exeter), but it seems as if the support and encouragement given to me by my supervisor has vanished because of this number. (It is thus highly ironic that I was awarded an extremely high number under the new teacher evaluation system prior to this.)

This was my first year teaching this course, and I am not happy with my numbers.  But I am also looking at this situation objectively and recognizing that this is what it feels like to be defined wholly by a number.   I shudder to think what teachers whose test scores were published in newspapers went through.

I had a great deal of difficulty writing my glowing post about Exeter earlier today because this issue was lurking just below the surface.  I put it aside while I was away, but am now confronting what it may mean for me next year programmatically and as part of the school community.  I have been filled with anxiety about a ‘loss in stature’ within my department, without seeing the larger issue – that my quest for excellence and engagement for my students and myself only matters if standardized test scores are high enough.  And that is an ugly truth.

I’ve survived far worse in my life than this, and refuse to allow my cherished summer to be ruined.  But the black storm clouds this evening definitely mirrored my mood.  Thankfully, the thunderstorm brought cooling rain and a lovely breeze.  We’ll sleep well tonight.

Watercolor by Geo geosaurus.tumblr.com

Watercolor by Geo







My Return to Exeter

NEW11_Math_Conf_logoMy leap into regular blogging took place a year ago, when I had the opportunity to attend the Anja S. Greer Conference on Math, Science and Technology at Phillips Exeter Academy.  The experience of the conference was personally and professionally enriching, so much so that I was overflowing each night with ideas and reflections, and managed a detailed daily post.  So affected was I by the opportunity provided by the conference to learn, collaborate and connect that I spent a lot of time and energy trying to get back there this year.  Last week that happened, and it was as wonderful an experience as the anticipation warranted.

IMG_3374 copyI attended the conference this year with a friend and former colleague, which added another dimension to the experience – sharing something wonderful with a friend.  You don’t really know how well you get along with someone until you travel together, and I learned how compatible we actually are – our conversation flowed continually, tangentially, and effortlessly, making the road trips there and back easy, and we shared both ideas and new acquaintances as we experienced the conference separately but in tandem. Another big plus  this year was being reunited with a kindred spirit on the Left Coast  – someone who I met last year but felt as if I had known for a very long time.  So, before even thinking about the rich professional and mathematical experience that the week provided, my soul was personally soothed and enriched.IMG_3321 copy

At the Exeter conference, participants take 2 week-long courses, sit in (voluntarily) on 45 minute stand-alone sessions which run throughout the day, and attend evening programs with speakers.  This year, Geometry was the ticket for me – my 2 classes were ‘The Geometry of Origami’ with Philip Mallinson, an Exeter instructor, and ‘Geometry Labs’ with Dan Butler, a public school teacher from Minnesota.   I came away from both of these hands-on classes bursting with ideas and energy to push the geometric envelope a little further in my classroom.

IMG_3286 copyIn the origami course, we began by doing some proof regarding folded paper, and I learned an amazing fact about A-size papers – which may be common knowledge, but not to me – that the ratio of the sides in all of them is 1:√2!  Think of all of the math problems we could do with PAPER ALONE if we used these sizes!  But I digress…we explored patterns created by ‘flattening’ folded figures, the ratio/relationship of the number of mountain versus valley folds, and finally, did some origami.  IMG_3390 copy  The conversation in the class, expertly and humorously facilitated by the teacher, flowed easily – participants posed questions and made conjectures which the rest of the class immediately explored.   I have since purchased Project Origami by Thomas Hull, some origami paper, and will be engaging in some folding on my own very shortly.   As a result of the infectious enthusiasm of my instructor, I went to see the Surface to Structure exhibit at the Cooper Union, which was nothing short of awe-inspiring and mind-blowing (images at conclusion of post).

lge-snailballLast year, I became friendly with someone in the Geometry Labs course, and was completely envious; my experience this year confirmed exactly what I had imagined the class would be, and it was, from start to finish, a delightful and enlightening experience.  First and foremost, the instructor, Dan Butler, has an open, warm, and engaging teaching style.  He very rarely gives answers (someone after my own heart), but rather prods students into working through their wonderings.  He is continually good humored and generous with both time and supplies, and has a way of making every student feel acknowledged and heard.

Our activities during the week included hypothesizing why a snail ball won’t roll down a ramp, calculating the distance required to have a marble sent down a chute land in a cup, problem-solving with Taxicab Geometry,  discussing the implementation of Gateway Exams to ensure basic skill competency, IMG_3310 copyidentifying changing patterns and shapes created by the shadow of a stellated icosahedron, and modeling with Geogebra.   And in between activities, or waiting for class to start, we attempted to solve cube puzzles made out of tetrominoes.  IMG_3289 copyWe spent one full class period working on the multi-level Goat Problem – how to determine the grazing area of Billie the Goat as her tether was repositioned relative to barns of various shapes.


goat p1 goat p1-1goat p3 IMG_3348 copy






IMG_3371 copyDan offered an extra-curricular activity as well – creating our own stellated icosahedra.  Using string and straws from the 99¢ store, he opened his classroom for three afternoons between class and dinner, and coached us through their construction.  [I do not have written instructions for this project, unfortunately, but there are a number of examples out there on the Interwebs.]  There were always other participants in the room –  discussing problems from class, working on other experiments, or just hanging around.  It was easy to envision Dan’s classroom at school filled with students all day long; he creates that kind of welcoming space in which everyone feels comfortable and wants to participate on some level.    At the end of the week, Dan held a lottery for his samples which were created with FANCY hard plastic straws (from Party City), and which he did not want to fly home with.  Lucky me!   Lots of geometry swag for my car.IMG_3395 copy

Another highlight of the conference (I really should have written some interim posts; I see that clearly now..) included a lecture on The Future of Learning by Alan November – a thoroughly engaging speaker who explored increasing students’ abilities to self-assess and teachers’ skills in providing meaningful feedback.  Alan is one of those people who spout ideas as quickly as you can write them down (for me, anyway) – including resources like kaizena.com, clubacademia.org, and mathtrain.tv.  He reminded us of that which most math teachers have – The Curse of Knowledge – and probed the eternal questions of how to (a) motivate students and (b) get them to do more than you actually ask.    This RSA video by Dan Pink reflects a lot of his thinking.

I also attended a CwiC session (Conference within a Conference) offered by Frank Griffin of the Cate School which was chock full of tips on ‘Animations, Simulations, and Visualizations.’  While many of the resources Frank presented were ones with which I was familiar, he showed specific applications of particular features which enabled me to actively envision using them in my classroom.  A partial list of these resources includes SmartBoard algebra tiles, Proof of the Pythagorean Theorem on hotmath.com, the Wolfram Demonstration Project, and some spiffy uses of TI Smartview.  This was another workshop which had be writing as fast as I could.

IMG_3291 copyIf you’ve managed to slog all the way through the content, now I’ll tell you about the magic of the conference.  Phillips Exeter Academy is in a picture perfect New England town and we were blessed this year with lovely cool weather.   IMG_3270 copyThe school itself is beautifully maintained; the dorms are basic and clean, the academic facilities are state of the art, and filled with visual and academic surprises (see my posts from last year for some of these).  There were 5 different education conferences running simultaneously: the math conference, a biology conference, a writers’ workshop, a humanities conference, and a diversity conference.  We wore nametags all week, and each conference was identified with a different color lanyard.  This year, the main dining hall was under construction, and meals were relocated to a smaller facility, which was a bonus in disguise – there was much more inter-conference mixing and discussion than before.  I loved hearing about how the writing teachers had to awkwardly share their own work, or sharing concerns about identity with the diversity conference participants.   On the last two evenings, we ate dinner out on the lawn in the quad – and it was a sight to behold.:  400 teachers, all engaged in intensive professional development, having the time of their lives.   We all deserve – and need – opportunities like this.  We can most effectively help our students learn when we are better prepared and engaged as teachers.  And being sent to conferences like this gives teachers the message that they are worthwhile, that their ongoing professional development is critical and that their role as educators is as highly esteemed as it should be.  Children are the future – how the ongoing education of their teachers can this be any less important?  IMG_3343 copy

Attending the conference this year was not easy – I had to search for funding, and fight for the days to attend.  When I first arrived, things had a bittersweet feel, because attendance a third year in a row seemed impossible.  I left with the conviction that it is mandatory.



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