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

photo 2

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!

photo (5)

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?

photo 1

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

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,, and  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, 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.



IMG_3486 copy IMG_3457 copy IMG_3450 copy IMG_3425 copy IMG_3423 copy





Hots N Lots Recap

ImageThe dust has truly settled, and I have finished up my 8th school year.   I escaped from NYC, and am ensconced in a cozy room at Exeter, where the Anja S. Greer Conference for Math, Science and Technology.  So far, the experience has been everything I hoped for – a great road trip with a wonderful buddy, in which our stories seamlessly and tangentially flowed from one to the other for 6 hours straight, and a delicious locally sourced dinner at Blue Food Evolution, complete with a waiter who made math puns every time he visited our table. The weather is cool, dry and sunny. Perfect!

But this morning, before my head gets filled with the enrichment this conference will surely provide, I want to talk about the end of term project in my Geometry class – highlights and lessons learned.  I am very proud of what happened in this class, the work many of the students did, and the opportunity it provided for them to demonstrate what they had learned in the three terms of Geometry they took.  What needs to be improved stands out as well, glaringly so (to me).

ImageMost days the class was truly abuzz with math.   The hard planning was finished once the students began working, but each day in class was an aerobic activity for me.  Whatever math these children had learned was not accompanied by independence.    Many of the students needed (demanded) reassurance and guidance and checking every step of the way. I provided them with as many resources besides myself that I could – I had three different textbooks they could use, made the iPads available every few days, and sat them in strategically chosen groups which I hoped would give them the opportunity to support – but not distract – one another. This worked for some but not nearly all. Basketball was discussed frequently across the room, at a volume which made it impossible to ignore. And phones – PHONES! The very bane of my existence during 4th period each day. Class time for me was filled with answering questions, checking in with those who weren’t asking for help, policing, and helping students choose new activities.

After a couple of weeks, I noticed that some students were engaged in creative assignments which permitted them to talk about other things (read NOT math) while working, whereas others required greater focus to complete content-heavy work. The resulting pockets of distraction grew less manageable, and I noticed a drop in the progress students were making in completing their assignments. The groups which were working on straight Regents prep seemed to be making more consistent progress. Keeping my eye on the desired outcome of this whole process – a portfolio of work which substantiated learning and growth over the entire Geometry course, I subdivided the room – one more time – so that the students working on individual assignments were working in rows at the front while the Regents prep groups were moved to the back of the room, where my co-teacher took over their supervision and instruction on the back blackboard. I also asked the Regents prep groups to take a Imagestep back from their work to come up with a list of topics they were all having trouble with so we could specifically target some mini-lessons. Each morning I would prioritize which folders would be checked; giving regular feedback to each student was one of my biggest challenges.Image

At the start of the last week, I asked each student to self-assess their progress. Most of them were honest in their need to be more focused, and many said they needed more help. Getting them to work independently, and with more confidence, needs to be a priority next time around.



I debriefed the project with my collaborator and mentor, in which she focused on the overall success of the project (thank you, Veronica!) while I dissected the problems. The big issues with which I am not satisfied – mostly surrounding quality of work and feedback – are as follows:


Possible Solution

Keeping up with feedback was a huge issue. The students did not receive it often enough.

Have the students select one item of work to be reviewed each day for a check-in; at least one assignment should receive a grade/formal feedback each week. Figure out exactly what logistics will make the process manageable for the teacher in advance.

Quality of work wasn’t satisfactory in too many cases.

Expectation needs to be explicit and specific. Students need to know what level of work is acceptable for final submission. Have students engage in on-going self-reflection after receiving feedback.

How can I move students towards greater independence?

On-going process throughout the term.

How much feedback from teacher is fair in order for students to meet level of expectation?

Again explicit examples of quality work as well as regular check-ins are required, particularly at outset of project.

Copying of work

Have final versions of work collected and removed from folders.

But even with these bumps, I was very proud of how the classroom ran, how everyone was working through the last bell of the last day of school, and how each student had an individualized assignment in which they had significant input. As I graded the final submissions, I was impressed with how much work the students had actually completed, well aware that these were not normally high achieving students with impressive portfolios. And all but three students demonstrated a sufficient level of mastery of the course content to earn a passing grade, a result which was not at all predictable based on their performance in the first two marking periods. A lot of bumps in the road to be sure, but a huge learning process for everyone in the room. And a great way to finish my 23 year of teaching.





Progress Report

photo (7)In the long 6 weeks since my last post, a lot has happened, both in my Geometry class and outside of it.*   The last time I wrote we were in the throes of similarity, struggling with the most difficult of theorems.   Out of the frying pan and into the fire, we moved on to circles after spring break.  I knew Circles would be no picnic either; students who have had difficulty pulling apart sketches of triangles and parallelograms can become overwhelmed by the complexity of the circle problems.  We worked our way through the unit slowly – one day of concepts, two days of practice; I felt like I was keeping the students moving through sheer force of my will (to their credit, they continued to persevere), until we reached the more difficult angle and segment problems.    With the end of the term in sight, I knew it was time to begin a final assessment.

The course terminates in a Regents exam, but the class is split 50/50 along the line of will or won’t take.  For many of my students, the exam they have already passed (Algebra 1) fulfills the graduation requirement, and they have no intention of sitting for another test.   But the other half of the class wants to take the exam (or, in my opinion, should challenge themselves to prepare and take it), and needs a lot of preparation.   I need to somehow measure the growth the students have made over the term, as well as the first 2 terms of the course; the traditional assessments done in class have not yielded great results, but I know that they have been learning.   Conferring and brainstorming with my colleague, I reached into my pedagogical carpetbag (a la Mary Poppins) and decided to put together what was dubbed at a former school of mine the HOTS and LOTS chart.


Hots and Lots Final

choiceThis acronym (referring to Higher Order and Lower Order Thinking Skills) is a huge choice board.   It has 8 columns, one for each major unit, and 5 levels of complexity, very roughly aligned with Bloom’s Taxonomy.  The students need to complete one activity for each unit, including only one at the lowest level and at least one at the highest level.    I’ve spend an inordinate amount of time over the last 8 years searching and saving resources, and had a nice selection of activities from which to choose.  I created a rubric and a log with specific instructions,  put samples of each activity in color coded plastic sleeves, created new work groups, and prepared to launch the project.  For those students who were going to prepare for the Regents exam, I have 8 Review sheets comprised of past Regents questions.  They will work through the sheets one at a time, and each will be graded.   They will have the benefit of cooperative groups and classroom resources (which includes teacher assistance).  And they get a log, too.
121984DDSo we launched the final project last week.  We spent one day discussing the whole idea of the final assessment, and the students had a chance to review the choice board and look at the sample activities.   They asked good questions, like whether this project could save them from failing (the answer being yes, if their work substantiated growth), and could they do the project and take the Regents exam as well (of course!).  As the students were milling around looking at the activities, I observed them, a little nervously, but with excitement.   I knew that everything I have been doing for the last 8 years has prepared me for this – crafting an activity that meets a wide range of needs, involves student choice (and thus higher engagement) and accountability, and sets the stage for what will hopefully a great learning experience for everyone.  I looked back on all the noble failures (a.k.a. learning opportunities) I had over the years, and all the nuggets I squirreled away from blogs, TED talks, twitter chats, and articles, and knew that I was bringing my best game to this class.

Next: what actually nbk

*I made this quilt.

Flailing About

ImageToday was a day which left me feeling frustrated on several fronts, not the least of which was the Geometry class I have been writing about all term.  We are finishing up a unit on similarity, immersed at the moment in the final and difficult topic of right triangle/altitude similarity.  The students have completed a hands-on exploration which went well albeit boisterously, and watched a video on iPads which explained the theorems clearly and visually.  Today, it was my intention to make sure they had the theorems written down in their notes, and to go over some sample problems before launching independent practice.  We have a unit exam coming up at the end of the week (right before spring break), and it is important to everyone that the students do well – important to me because I am hoping for some validation that my Herculean (at least they feel that way) efforts to differentiate and engage in this class are effective, and important to the kids because they want to improve their grades.

The Do Now was a midsegment problem. Image Because punctuality is an issue in this class, it took a while to get everyone (well, mostly everyone) settled and working.  As we reviewed  the problem, there was a lot of conversation across the room about the problem.  I would prefer the discourse a little more organized, but many students were contributing to the conversation, offering responses and corrections, and asking questions.  I saw that we needed to get quickly down to business or chaos might reign.

ImageI quickly recapped what they had been working on the past few days, and then put the theorems up on the SmartBoard for them.  I know that these theorems are confusing and hoped that practice solving problems would solidify their understanding; I distributed a worksheet, demonstrated the first problem, and set them to work.   We were working as a whole class, rather than in groups.

I’m not sure I would say it was an unqualified disaster.  Many of the students were working away and trying to make sense of the different types of problems.  But not an unsignificant number of them were talking loudly – not about math – and only refocusing on their work when I was nearby.  Phones are also an issue in this class, and there are two or three students who not only have them out regularly, but who deny that they are using them. (Really??  Really???)  I am not even sure how to counter the lying and denial.  But it is clear that I am losing these students – or may have already lost them – and they are committed to using subterfuge and dishonesty to maintain passing grades.Image

When the bell rang, I collected their work, which I will review before class tomorrow.  But I felt for the first time today that the class was almost out of control.  I realize that they have been doing a lot of work in groups, and that in working as a whole class, perhaps they were transferring their group work behaviors to the entire room.  I also realize that this change in routine may have contributed to the chaotic environment.  But what really upsets me is that I have tried, as I have written in this blog before, to bring my best game to this class, and I am not sure the investment in resources, creativity and energy is going to give me the results I had hoped for.

[You will also note that I did not mention my co-teacher in this post, because that is a subject which requires its own post, unfortunately.]

In the meantime, my plan for tomorrow is to put the students back into their groups – the groups that I selected – and have two levels of practice problems for them to work on.   The students who work more independently need problems that are appropriately challenging but also ones that can be done independently; the weaker students need simpler problems to start and more one-on-one attention.  I’m trying to envision the entire class before we meet tomorrow; this has always been my best strategy for executing a lesson.  But I am nervous, and hope that the seeds I have planted have taken enough root to get things back on course.

Feedback is ALWAYS welcome.