Radical Art – A Story of Photocopies

So any of you who know me personally or follow my blog, know that I am the extremely proud parent of some very creative children, one of whom is an Animation/Illustration student at MICA in Baltimore.  Many of Geo’s illustrations have graced these very posts, and if you want some awesome entertainment, you should watch the video below.

Hand animation takes a lot of paper; each and every movement needs to be individually drawn.  Geo did several rough projects last year, and while cleaning up before returning to school [under the threat of having to take public transportation back to Baltimore], they decided to recycle several huge stacks of drawings.  Always trying to do my part in saving trees and the environment, I rescued all this paper (which still had one side blank) for printing; many of the pages had minimal drawing on them and were perfect for my planning purposes.

We are fortunate at my school to have a Copy Center, where you can submit work, and 24 (sometimes 48) hours later, have everything printed, stapled, and neatly stacked.  For those who plan ahead, it’s a wonderful resource (anyone who has ever worked in a small public school with 2 [repeatedly breaking] machines for 20 teachers will know just how fabulous this is).  The Copy Center, however, is only as good as its staff, and although I have been getting my copies reliably in terms of timing, I have had numerous orders messed up – things printed double-sided that needed to be single-sided (because they were being cut up) and vice versa – despite what I try to make ever clearer instructions.  Aggravation and wasted paper.

Last week, I decided I was going to submit everything exactly as it needed to be photocopied, so that written instructions were superfluous (although I did leave those as well).  If things needed to be single-sided, I submitted them on separate orders, and if copies needed to be double-sided, I made sure my original was printed double-sided.

But several worksheets (graphic organizers for Adding/Subtracting Radicals Expressions, for example) I submitted had been printed on the back of Geo’s animation sketches.face  It didn’t occur to me that the gentleman in the Copy Center wouldn’t realize that a sketch of an angry man didn’t need to be printed on the back of a math worksheet (but then again, who knows what his high school math experience was like?).

My ENTIRE copy order this week had animation sketches on the back.  It made for a great diversion in Algebra 2.  Some of the worksheets were cut in half, and the students compared and traded halves of  pictures.  We talked about animation and art school, and my kid’s talent. : )


But how do you really feel about radical expressions?

And some of my students added their own spin to the art – or did the art add a spin to the math?

Cheers!  (And watch the video!!)


When Things Go Right

IMG_4050Just a brief post, but after yesterday’s lament, I feel that I must share that today’s Geometry classes all went awesomely well!  It was a day of practicing angle addition – which can be fairly mechanical – but I had the students work in pairs using worksheets inside plastic sleeves, which allowed them to mark up the sketches and better visualize the combinations of angles.  A lot of the kids jumped right in due to the wonderful M.E.F. (Marker Engagement Factor), giving me the freedom to circulate, refocus those students who needed some assistance, question the students and have them defend their work, and correct misconceptions.  It was beautiful -the more the engaged students worked, the more their initially apathetic colleagues wanted to join in.   The classroom was happily noisy – with math talk!  And there were wonderful moments – Mideline, the girl who emigrated from Haiti three years ago with no English and little formal education, working successfully through problem after problem, the ‘brain trust’ in the back corner challenging me on every problem until they all made sense, and Sitara, another English Language Learner, who persevered on her own – correcting and self-correcting without flagging (after meeting with me at 7:30 this morning to redo some homework).  I can’t overstate my respect for the students who struggle daily, often without success, but continue in their efforts for days, weeks, months, years.  I’m fairly certain I would not be able to sustain that level of commitment in the face of frustration and failure.

Here is one of the worksheets I used; I created another [which I don't have digitally] which repeated the more basic problems several times before introducing a new twist.  I am also including the templates for this worksheet for which I do not have an accurate source; they were passed along to me on a CD with other resources at least five years ago.  Whoever created these templates – a big thank you from me.

So I’m feeling much heartened by today’s energy and active learning.  Tomorrow is test day – so less on my feet time, but mega-grading time ahead.  It should be very interesting – in the inclusion class, 11 students require a ‘separate location’ and 15 are allowed time and a half to double time.   My co-teacher is taking all of the separate location students to a small classroom – where they can distract each other? Hmmm….

A logic poster by Joseph G.

A logic poster by Joseph G.

A Comment on My Own 180 Blog

This was today’s 180 post: 

hamster-wheel-oAnd this was last Wednesday’s:


Clearly, something is awry.  And I don’t like feeling like this – complaining about everything that’s going wrong, when the simple truth is I feel like a crummy teacher these days.   I seem to be way more reactive than proactive, particularly in my Geometry classes.  I most recently found out that in addition to the must-be-out-of-compliance 44% IEP students and the 35% ELLs, I have 7 students who were in our “PushStart” program last year – a self-contained class for ‘hall-walkers.’  (In an effort to keep students in class, the teachers rotated through the room rather than the students moving throughout the school.)   And of the 34 students on the roster in that class, I have only one student cutting – which is GREAT – and crowded.  So I’m reflecting here tonight – to try and objectively look at what is going well, and what I can realistically improve.

This week I took a big step towards more efficient use of the INBs; I can’t leave supplies around because I share the room with 2 other teachers, but I can PRETEND it’s my classroom for 3 periods a day.  So each morning, I offload baskets of supplies from my trusty cart (now featured in at least 3 posts!) and jumbo bags of notebooks.  Having the notebooks and supplies readily available has immediately promoted maintenance and updating of the INBs, not to mention a veritable explosion of scotch tape art around the room.  As a matter of fact, one student raced over to another who claimed she had ‘an open wound on her finger’ to bandage it with that polyfunctional supply.

However, I found myself entangled in a Notebook Planning Oversight (hereinafter referred to as an NPO), and neglected to leave pages for a lesson we had done last week.   But even that has a positive side, because it was the students who brought this oversight to my attention (“Miss, we need a page for the Famous Theorems!”).  Their desire to keep the notebooks complete is a very good sign.  I think what I need to do is plan the notebook when I refresh/write my unit plan.  For

We spent a lot of time getting used to being geometers in September – exploring vocabulary, folding paper, doing constructions.   I am focusing now on basic content that this crew needs to receive as direct instruction.  Those Famous Theorems – the Pythagorean Theorem and the Triangle Sum Theorem – which are middle school standards, re-visited in Algebra I, needed not only to be re-taught, but the algebraic procedures required for solving problems with them also needed serious reinforcing for many students.  The range of ability in the three sections of this class goes from budding geometry nerd [I am VERY proud of how many angles Raquan found to name in each sketch at 7:45 a.m.!] to a lack of basic arithmetic skills.  Thus, the big ideas of Segment and Angle Addition (including the foundational skills of naming those segments, angles, and rays) struck some students as completely intuitive, and others as foreign concept.  Differentiation and flexible grouping are the next big  priority.  And that I know how to do.  (I also know that it makes class time an aerobic activity for me!) This will require a shift in thinking for the students, and thus will require a very well-thought out plan from me for each class – the grouping, the learning process,  and the practice of new content.

In one of my Algebra 2 classes today, I made the mistake of distributing Thursday’s exam instead of the intended review sheet – a giggle started to ripple through the room as the papers moved around.  My students had the pleasure (and I do think they enjoyed it) of seeing their teacher lose it for a moment as I let slip a few choice words about my goof.  But the reality is that an error by the school copy center resulted in the students not getting hard copy of the review sheet today for their exam on Thursday.  The stigma of last year’s Regents exam results still smarts, despite the fact that I know I am not a number (I guess I just don’t want anyone else to think I am – I am human, after all.)

We are finishing up operations with rational expressions, a fairly dry topic which can be treacherous for a student who struggles with fractions.  I’ve addressed common misconceptions as we went through each topic, had the students work together (Row Games – thank you, Kate!), share and explain their work, and used formative assessment to intervene as frequently as I could.  I’d like to find an alternative way to summatively assess them on this topic, although I am ever in search of a way to make this highly procedural unit more lively and relevant.

So upon reflection, I feel a bit less like that hamster and more like the teacher-y me – not quite Her Mathness, but ready to go back tomorrow and tweak things a little more.

(Just the latest piece of brilliance from geosaurus.tumblr.com)


#mtboschallenge Week 8: You call this organized?


Thanks to a nod from the always lively Jemma PDuck (pit pat paddle pat), I am dipping my toes into this weekly challenge again, just as I was about to add ‘write blog post’ to my to-do list.  But organization tips?  I feel pretty organized, I am perceived as organized, but when I look around my workspace(s) for systems, I’m not sure I see any share-worthy tips.  One of the nice benefits of blogging, however, is that you reflect as you write, so maybe something new and helpful will come out of this piece.


My trusty cart loaded with supplies, ready to go.

My trusty cart loaded with supplies, ready to go.

I am peripatetic at school (damn – I’ve FINALLY used that GRE word in real life!) although I have a desk and three or four drawers in ancient file cabinets in an office space we affectionately call the Bat Cave (it has also been referred to as the Clubhouse and the Hovel).  Those drawers mostly hold hard copy back-up of past term grades, miscellaneous office and classroom supplies (patty paper, index cards, extra glue, tape, staples, etc.).  Under my desk (a term I use loosely; it’s a moderately wobbly table with a cracked formica top), I store extra markers, colored pencils, game supplies – things that don’t fit in or on top of the file cabinets.  I’m not sure you would call it organized, but I do know where everything is, and am known for having a Mary Poppins-like ability for reaching into my various storage spaces and finding anything anyone asks for.  When I am on the go, my trusty cart – purchased with a DonorsChoose grant – is my rolling classroom – holding my document camera, the famous Converse sneaker box of whiteboard markers, scissors, glue, extra worksheets, paper imagestowels, tools of geometry, and anything else I may need for class.  I wouldn’t call it the height of organization, but it’s a system that works for my life as a teacher right now.  When pushing this puppy down the hall, I have been referred to as Ms. Frizzle – one of the highest compliments as a nerdy teacher I have received!

At home, I have gone through several systems of organization – for hard and digital materials, and to be honest, I wish I had a better way.  I worked in offices for many years, creating and maintaining records, so I know what a good filing system looks like, and it isn’t like these milk crates.  milk cratesTo be fair to myself, however, that is how I started out 9 years ago, having no clue of the resource deluge that would be the result of my quest for better teaching.  Four years ago, I moved from a school that struggled from term to term to a more established place, and began to teach courses with established curricula.  Thus were born my binders: I created one per term per class, but as I refine my approach in the classroom, I am moving towards one binder per course which is updated each time I teach it. bindersIn retrospect, I suppose that would have made sense from the outset, but hindsight – well, you know.  I try to keep my books organized as well – textbooks on one shelf, resources the next, and then a mix of content and enrichment – but you can see the lines blur here as well.  bookshelves

Digitally, I started out saving all my work on Dropbox, but moved to Copy when I ran out of room – my files are now divided between both of them (probably not the best situation).  Thanks to a talk by Anna Blinstein, at TMC13, I have been using Evernote to clip and organize resources as I come across them on line, and that has saved me a lot of time, storage space, and paper.    And one of the great bonuses about Twitter and the MTBoS is its collective memory – I may remember that I read something great on someone’s blog, but can’t place it; a tweet will usually find someone who does remember it, and a link.  I know I should be using my blog reader to better effect in this case, but this is a skill I haven’t yet had the time to master.

As I write this post, I wonder if I am actually justified in thinking I am organized.  Like most people, I have an organizational system that works for me – most of the time.  I always endeavor to put things away in the same place every time, and my children and husband refer to me as The Finder – I can inevitably locate objects which they desperately need and cannot find.  I am very grateful for my good memory, because I think that compensates for the lack of filing system which is flexible enough to handle new types of input, and can easily grow.   It works with my fabric stash – I just purchase another plastic bin!  As long as I have room for the bins in the closet, I know I don’t have too much fabric!! ; )


A New Year

I have not observed the Jewish New Year in synagogue in many years.  When my mother was still alive [as hard as that is to type], we always had a special dinner, complete with apples, honey and matzoh ball soup,  even though she had long since abandoned her efforts to have us join her at services.  And in the last few years, my acknowledgment of the holidays has dwindled to some annual phone calls and deeply encoded wishes exchanged with my sister.

But this year, I used the days off from school to attend a workshop on Undoing Racism, and for the first time since I can remember, I have a sense of renewal and purpose as the year begins.

IMG_3995Sitting for two days in a room with 30 other people covering a range of ages, ethnicities, and professions, I found myself completely humbled by my dawning awareness of the systems which  perpetuate the status quo.  The workshop was facilitated with inclusive kindness, humor, and unflinching honesty by two trainers – Ron Chisom and Joe Barndt – who have organized and worked to dismantle racism for years.   They led us through a discussion of the history of the concept of race, a power analysis of poor communities of color, and finally to a definition of racism, which, perhaps, many of us in the room had not used.   The first day finished with an examination of how internalized racial oppression enslaves and destroys all of us [in different ways].  We also spent a long time discussing our roles – all of us – as gatekeepers of some sort, and how we could be more accountable as gatekeepers if that was a part we needed to play. IMG_3980

The second day involved more intimate conversations – venting of frustration, cries of emotional pain, sharing of warmth and acknowledgment.  Each person had the opportunity to reflect, question, and receive feedback on the experience of the first day.  Each person also had the opportunity to share what they liked about their race identification.  The contrast between the people of color and the white people was painful and startling – because what the people of color in the room liked – loved – about themselves was much richer, more personal, and way more connected than anything any of the white people said.   The white attributes, while definitely accompanied by privilege, were cold and disconnected.  Somehow this paucity, this loneliness hit me harder than many other things I had heard.  All of a sudden I saw our cultural appropriations as cheap ways to piggyback on someone else’s heritage, a sad echo of something lost long ago.

We finished the workshop with an analysis of the institutions each of us worked in, and where they stood on the Anti-Racist spectrum – from “Club House” to “Multicultural” to “A Changing Institution”.   Not surprisingly, upon a close look, most organizations, while multicultural, still exhibit signs of paternalism and privilege, despite their ‘diversity’ programs.

[NOTE: This is a very superficial and over-simplified description - for the sake of brevity and privacy - of a personally (and hopefully professionally) transformative experience.  I encourage anyone who is truly interested in change in this world to attend a workshop like this.]

This morning, during our circle of feedback, I expressed the discomfort that I was isolated at school in my viewpoint.  Unlike the others at the training, I attended on my own – most others were sent by their organizations.   And as a teacher, and particularly one of high school math, I am by definition a gatekeeper.   I am not sure how to use my experience to transform anything, other than my own consciousness, but I am aware of my responsibility to try to do so.  While I wasn’t given any easy answers, my concerns were acknowledged, addressed, and some suggestions were made.  Other participants reached out to me in support, and offers of future connection, and we even found some commonalities that were not at all apparent.

I am afraid this post sounds very vague, and maybe even jargon-y.  But I can tell you as I am sitting here typing this that I have been profoundly changed by this experience.  I do not yet know how this will manifest itself in my life, in my relationships at home and at work, or in my classroom.  But I am grateful for the enrichment and the pain that this new awareness brings.

L'shanah tovah.

L’shanah tovah.


Two out of three ain’t bad

I have three sections of my ‘Regents-optional’ Geometry class. Over the last 9 years, I’ve taught all levels of students in geometry, I’ve differentiated, accelerated, re-taught (if you can actually re-teach something that wasn’t learned the first time around), and rewritten lessons. In this course, however, I am re-designing from scratch; my objective is to engage these students with more discovery and hands-on activities, thus hopefully giving them a connection to the content that they might not get in a more traditional [read focused on two column proof] class. My success in this endeavor is important – critically to me – for another reason: my students are the children who are being directed away from the most rigorous math classes; some members of my school’s administration think these children don’t even need to study geometry.

So if you read my blog regularly, you know I have been planning for this class since last June, and even wrote a successfully funded Donorschoose proposal for supplies.  I am implementing Interactive Student Notebooks in all three classes, and have been given a newly renovated classroom with tables (a rarity) for the planned cooperative nature of the learning process.  Each section of the class has developed its own personality – what works well in 3rd period may lag during 2nd period, due to its early morning sleepy [and less well attended] nature, and may flop in my 5th period class – the one in which 44% of the students have IEPs, and 35% are current or former English Language Learners (5 students fit into both categories).  Clearly this last class presents the biggest challenge, despite the two teachers in the room (we are both math teachers, by the way, neither with Special Ed certification), and has prompted this post.  They are a creative and funny bunch, but transitioning from classwork at tables to whole class discussion or teacher-led work has become increasingly difficult – and today was close to impossible.    Friday was our first quiz (4 different versions to accommodate the table arrangement); I’m wondering if a ‘grade’ will have a sobering effect on their chattiness.  But I’m pretty sure it won’t; it will only reflect back to these students what they have been (and are still being) told – by past teachers, standardized test scores, and the powers that program their schedules.

So as I enter the third week of school (a short week due to the Jewish New Year), I know that I need to implement more structure in these classes.  I need to (a) keep the students accountable to me, themselves, and their tables, (b) have differentiated work for the multiple levels in the room, (c) most importantly, engage, intrigue and perplex them,  hopefully giving them in the process an appreciation for geometry, and some satisfaction in a math classroom.  No small order, but it is for challenges such as these that I carry around such a large mathematical toolkit.  I’m sure if I can put my mind to it, I’ll come up with a system with which to successfully teach this course, and win the minds, if not the hearts, of my students.

The problem?  It isn’t even October, and I am exhausted.  I have spent an entire weekend in a cold-induced haze, with pieces of great lessons floating in and out of my unproductive mind, like puzzles I can’t solve.  I keep remembering wonderful ideas that have been generously shared on Twitter and through blogs that I was sure had a place in my classroom, and have already, halfway through the first marking period, fallen by the wayside.  This was the year that I was going to maintain balance – I avowed that publicly in this blog barely three weeks ago.  Three weeks in which I haven’t been the gym or done any calculus.   And I am wondering how I find myself in this school year situation again, so quickly.

Every time I dip my toe into Twitter, I am drawn in by the energy, generosity and creativity by the MTBoS – so I have actually stayed away.  The unread number in my blog reader climbs up as I avoid combing through all the ideas that present themselves so delectably.  There are days when I wish I had the means to walk away from teaching altogether because this is the annual struggle.

But what else would I do?  I’ve been in the non- and for profit worlds, and neither of them gave me any lasting satisfaction.  My work never felt nearly as important – to me or anyone else – before I was a teacher.   I know that education (and math education in particular) is what lights my professional fire.

Wow – this blog post started in a completely different place from where it has landed – and I apologize for the self-pity.


Tomorrow is Monday.  We will finish the different forms of conditional statements, and begin our Logic Poster project.

Then we will move on to constructions – first traditionally (by hand) and then dynamically with GeoGebra and Euclid the Game.  Next week, we will begin talking about Direct and Indirect Proof using the models of Rube Goldberg machines and Logic Puzzles (tip of the hat to Harold Jacobs), and I know there is a great activity in me to bring home those big ideas.

Thanks for reading.


geosaurus.tumblr.com aka Child of a Math Teacher




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.