I only spent a few days getting to know @sophgermain at #TMC13, but finding a kindred spirit who worked at Hogwarts-in-Troy prompted me to join her #shutupandduckface Instagram event last March and this, my discomfort with selfies notwithstanding.  So when I read her blog post Things that scare me, I somehow began typing this, even though it is Sunday evening and my work is not finished.  I used to be afraid – truly anxious – of so many things.  I still am, but I have faced a lot of scary stuff, and realize the fear is a construct that I have some control over.  But there’s still a list, for sure.  So here I go.

  1. I am afraid I’ll never be a really good teacher.  No matter how hard I work, how many resources I hunt down, how many blogs I read and ideas I try to incorporate into my practice, I frequently feel like I am not doing enough, reaching enough students, eliciting enough critical thinking, or raising student achievement.
  2. I am afraid I will run out of time and have worked too hard. I love my job, and I love math.  But I also love quilting, and spending time with friends, and reading, and movies, and exercising (well, I love its effects, anyway).  But I spend way too much time on those first two – work and math – and I know very well that our time is not infinite.
  3. I am afraid of the world my children are inheriting. This world is a scary place.  Nothing gives me greater joy than their talent and success; the flip side of that is a fear of the problems they will face.
  4. I am afraid of severe weather.  I think this is a result of watching This Wizard of Oz as a small child.  No shit.
  5. Speaking of running out of time…I am afraid my cancer will recur.  I have wonderful health care, and an oncologist I might run away with some day.  But anyone who has ever had cancer lives with this fear, and some of us have more regular reminders of it than others.  The good news is that the fear keeps me honest, and forces me to confront things I might otherwise avoid if I was under the illusion that I had time to spare.

Thanks, Annie – love your posts, and love that you get me to try things.

March Madness

[You may notice from the title of this post that is was written, for the most part, last month.  I’ve had a lot of trouble finding the mental space to blog this spring, as explained below, and have been only barely involved in my usual online activities of tweeting and chatting.  I’m returning to school tomorrow after a restful week off, and am thus posting this delayed entry.] This is not about basketball, not in the slightest way.  But it definitely describes my life right now, one of the reasons why I have been averaging one blog post per month. I have a tendency to metaphorically overload my plate, which is why teaching is such a perfect career for me – it feeds right into one of my best and worst qualities.  This month, in addition to teaching 165 students, 100 of whom are in a course I am putting together for academically high need students, I have a full private tutoring load, and am participating in Common Core curriculum reviews for the NYC Department of Education twice each week.  I applied for this last opportunity in mid-January, and didn’t hear back until February 26, 5 days before the reviews were set to begin.  Initially pleased, I took a look at my calendar, and took a mental gulp.  Something doing EVERY day for the entire month of March. I’m three weeks into the month, tired, but in a good place.  I’ve had some great moments in my classrooms (which I will get to in just a moment), I’ve almost hit the 2/3 mark in my online Calculus III class (which occasionally makes me understand exactly how my students feel when they say “I don’t get it – any of it”), and, just this week, found out I was accepted to the Park City Math Institute Teacher Leadership Program for this summer, with a funding package generous enough to allow me to attend.  So even though I’ve got 2 weeks of this madness yet to go, and even though the term ‘spring’ is a joke with 4 inches of snow on the ground here in Brooklyn, I’m feeling [just a little] engerized. But my classroom: IMG_4807Algebra 2/Trig has been a series of lows and highs.  The first big exam on Radians and Trig Functions was a disaster, truly, sending me into a deep and unhappy reflective mode – unhappy because I was so surprised by the results.  I thought I had given the students a lot of time to question, discuss, clarify and practice, along with review materials which addressed all the content on the exam.  We spent a day of going over the exam, examining common errors, and then I re-quizzed them on key ideas, with much better results.  The upside of the experience for me was insight into those spots in which my familiarity with the material was still blinding me to what my students needed, things that I hadn’t realized I needed to say explicitly (and repeatedly) in the classroom, as well as a tap on the shoulder to remind me that I should be ‘backwards planning’ more effectively.   The upside for the students was that they received (a) a second chance to demonstrate that they had actually learned the content, finally, with appropriate studying and (b) a bit of a wake-up call, which they needed. We moved on to another favorite topic of mine – graphs of trig functions – and with the traumatic experience of the first exam still echoing in the classroom – much better preparedness each day by the students, and more focused formative assessment on my part.  I am very pleased with how I planned the unit (this is my second year teaching the course) – not only did I have the final assessment in mind when I began, but I was able to incorporate a wide range of technology and strategies to keep the classroom a vital environment of discovery.  We began by plotting curves by hand, then examined them in Desmos, used iPads and Nearpod to practice writing equations of graphs, and even watched some videos which some wonderful teachers have generously shared with the Internet.  I haven’t finished grading the final assessment, but the results already look enormously improved. The final two topics in the unit  – graphs of reciprocal and inverse functions – always give me a bit of trouble.   I decided to do a “Notice and Wonder” a la Mad Max of the Math Forum with the graphs of the cosecant and secant, with wonderful results – the observations of some of the students thrilled my teacher’s heart, such as these:FullSizeRender Danielle: The graph of the cosecant is everywhere the sine isn’t. Kizelle: The graphs can’t be between -1 and 1 because the hypotenuse of a right triangle is always longer than the legs. Sawaniya: Every time the sine [or cosine] is zero, the reciprocal graph has an asymptote. It was a great day in this teacher’s life, and I am finishing this blog post 3 weeks later so I don’t forget it.

INB Resources

Just want to share the love!  I’ve created/revised/massaged/borrowed resources for my geometry students’ interactive notebooks and wanted to share some of them.  If you would like a Word file to tweak for your own use, just send me a message.

Flash Cards I created on Slopes of Lines for our Coordinate Geometry Unit.  The original idea came from Sarah Rubin and her wonderful blog, Everybody is a Genius.

More flashcards inspired by Sarah Rubin on Congruence Shortcuts:

This graphic organizer on slopes of lines accompanied our lesson on the fabulous Slope Dude.  My co-teacher, Mr. Peterson and I created it together.

Finally, a foldable I created for our Special Quadrilateral unit.

I hope some of these resources are as useful to others as all of the shared resources out there were to me.


Auspicious Beginnings

On a break just 8  days into the Spring term (ironic as that denotation may be), I’m feeling more energized than my 7 a.m. start time would suggest. It’s a great relief after an angst-ridden fall term, and while I am not looking this gift horse too closely in the mouth, I am reflecting on how I managed to scale the wall that felt insurmountable just a few weeks ago.

IMG_4654In Algebra 2, the term begins with an introduction to Trigonometry, which makes me unspeakably happy. We started out by discovering radians with paper plates, exploring arc length and special right triangles (I am not sure why they are so special, Dan Meyer, but the universality of those ratios resonating throughout math and design is, in some literal way, awesome. Call me crazy, or nerdy, or both.)

Screen Shot 2015-02-17 at 11.03.06 AM

IMG_4670Proving the Pythagorean Identities was also a wondrous exercise, even eliciting applause from a student who clearly has a future as a math teacher.  I’ve got a better understanding of how to sequence the content this year while keeping pace with my department’s calendar, and I’m finding time to infuse class with discovery.  Thanks to the generous assistance of Audrey McLaren and the thoroughly spot on webinar by Crystal Kirch, I’ve begun some forays into the flipped classroom.  I started with a VoiceThread on reviewing the basic trigonometric functions, which met with a lot of student approval and enthusiasm.  I wish there were a few more hours in the day to incorporate all the ideas I’ve got, but I’m committed to starting to build my own library of flipping resources.  More to come.IMG_4671

1238962_10100612775140764_910897993_nWe’ve also gotten off to a great start in Geometry, due to several factors.  The programming office shuffled the students between the sections of the course, and the resulting rosters are more balanced, with some of the more toxic behavioral combinations disassembled. There has been a 4th section of the class created – I was teaching three of them in the fall –  and as a result, my BFF at work and I are planning together; he has been given one of the sections to teach solo, and we are co-teaching the ICT class (never mind that neither of us is a special educator – that’s a long story, and another blog post).   This is the first time in a long while that I have had the opportunity to engage in true common planning with a like-minded colleague, and it has made a huge difference in alleviating the stress and isolation involved in creating a new course single-handedly.  Mr. P and I have always shared ideas and experiences, but as c0-teachers, there is a true collaboration happening, which fosters more thoughtful planning.  In trying to be always on the same page in a busy classroom (aka the 3-ringed circus of math), we have debated classroom decisions, pushing back on each other’s thinking, and in the process, crafting more authentically reflective policies and procedures.

IMG_4674It was gratifying to see that the students who had been in the class last term, fell quickly back into the established routines of the Daily Quiz*, the Interactive Notebooks, and collaborative work at the tables.   Bringing the new students up to speed on the Interactive Notebooks has been more of a challenge; we spent a lot of time setting them up and working on the intent of the notebooks in the fall.  Again, the group at each table provides a support for the newbies.
We spent the first two weeks reviewing special quadrilaterals, completing a graphic organizer (link below), a chart in which the properties of the polygons were compared and sorted in a Venn diagram, and Lisa Bejarano’s Always, Sometimes, Never activity.  When we return from break, we will begin working on equations of lines as a lead-in to Coordinate Geometry.

When I go so long between posts, there’s always too much to say – some very, very dear friends of mine are relocating – one to California for graduate school, another to Shanghai for an amazing career opportunity.  This has, inevitably, got me reflecting and rethinking choices I’ve made, and continue to make.  But my own children continue to pursue their own unique interests and education with passion and talent, reminding me that every child deserves that chance – and brings me back, once again, to why I teach.

Speaking of my amazing children, which I can’t help myself from doing, my younger one is involved in a project to produce animated films in collaboration with NASA scientists working on the Fermi telescope – how completely cool is that?  Read about it here, on the Tumblr run by Geo.


*The Daily Quiz is a low stakes formative assessment used as a warm-up for class which sparked an interesting twitter conversation last night, and which I may write a separate post about later this week.

What’s Working/What’s Not

I need to know her secret!

I need to know her secret!

I started this post last Sunday, and haven’t finished it yet.  Last night I asked Justin Aion how he manages to write so prolifically and so frequently – he told me he keeps his post open all day long and writes a bit at a time.  So it’s 7 am, it’s the last day of the fall term, and I am re-opening this post, determining to post it by the day’s end.

From Sunday: It’s 4 days from the end of the term.  I’ve been informally reflecting in my mind since we returned to school on January 5.  I am trying to be constructive with myself, and to silence those demons that Mattie B wrote about earlier in the week at Pythagoras Was a Nerd (although Vi Hart says Pythagoras was actually a crazy cult leader in this epic video) – the demons that continually point out everything that is going wrong in my classes or lacking in my practice.   Mattie says his kids are lazy, selfish and possibly stupid – well, mine are ungrateful, inattentive and rude.  And, for the most part, eminently lovable. (Last aside: recommended reading on this topic – Matt Vaudrey’s post on Stupidity and Adolescence – one of my all time faves.)

So I started a page in my planner called “What’s Not Working/How to Fix It”, with a positive section entitled “What’s Going Well/Modifications” – because nothing is ever going well ENOUGH.  I want to write some of this publicly; it will help me process, and hopefully garner a few suggestions from the Math InterBlag.

Here’s a picture of my list so far:IMG_4583 It’s not much, yet.  But it’s a start at hitting the reset button for the Spring term.

My students, particularly in my Geometry classes, lack independence.  I provide as many cues for them as I can to help them execute their jobs as students each day.  We do have a routine (Daily Quiz, notes, practice or Daily Quiz, exploration/group work/tiered practice), but for a reason which mystifies me, beyond that Daily Quiz opener, my students do not avail themselves of the tools at their disposal, i.e. agendas on the tables, directions on the board, spoken word by teacher.  I know they are checked out [until they are ready to check in], and I want to engage them more quickly, having motivated them to participate in the learning that is going on in the classroom.  (As I typed the word ‘engage’, an image of Dan Meyer popped into my head, exhorting me to PERPLEX THEM, BE LESS HELPFUL – stop boring them! [last bit was mine, not Dan’s]).  Concomitant with the mental absence from class, naturally, is the lack of deep understanding of the content.  So while I am closing out the term today, I am trying to glean some insight into my students’ perception of what’s going on, and hopefully get some constructive feedback from them.

Yesterday was a fairly terrible day – I discovered a plethora of methods students were using to copy work on a final packet – from plain old copying from the original to sharing photos of a completed packet by text, and actually transferring the information during in class in front of me.  This incensed me on so many levels, particularly in light of my school administration’s utter lack of an electronics policy.



But mostly it made me sad – very sad – because I haven’t managed to create the culture I want in my classroom, a culture in which students take pride in what they have learned, and are willing to exert some effort to practice with this newly acquired knowledge and demonstrate their geometric understanding. (Sorry – it’s been a long week – maybe geometric prowess is going a bit far.)  I can – and will – reflect on whether the assignment was appropriate for this purpose, and what its place in the course is, but the dishonesty is on the part of the children, and I saw enough of it in more than one class to know that it’s not just a couple of kids.



I’m finishing out the day and term by grading some notebooks.  I’ve got a monstrous stack of papers to go through this weekend, and I am having an internal debate on how to grade the work that I know was completed dishonestly by some percentage of the students.  At the same time, I am working on (a) ways to prevent this while still maintaining a workload that I can handle (110 individual assignments is just not feasible) and (b) assigning meaningful work (online homework is useful for some purposes, but not all).  Meanwhile, I am looking forward to reading some of their comments on the end of term course evaluation as further fuel for reflection.

Who says triangle shortcuts can't be pretty?

Who says triangle shortcuts can’t be pretty?

{I would like to note here that my participation in the#ElemMathChat and #LGBTeach chats last night, two chats in which the power of the online education community to share and support its members was fully demonstrated, restored me and my faith in why I teach.}


Ruby and her Sun Lamp

Ruby and her Sun Lamp

Congruence Check-In

IMG_4434After the investigation I discussed in my last post, we spent the rest of this week learning about triangle congruence in my 3 geometry classes.   The students took notes, identified congruent parts, wrote congruence statements, and made flashcards.  [All files linked below.] An assignment in which they had to identify the appropriate shortcut from a marked-up sketch was fairly successful.  On Thursday, I introduced the idea of drawing secondary conclusions from given information, and actually writing down those conclusions and why they were justified (a.k.a. proof) using this great exercise from the Oswego City School District Regents Exam Prep Center: http://www.regentsprep.org/Regents/math/geometry/GP3/preproof.htm   IMG_4435

IMG_4437And then we began to talk about proving triangles congruent.  Many of these students have already taken (and failed) a term of geometry, and if they haven’t, they have heard from friends the perceived horrors of two-column proof.  I have thus deliberately avoided introducing that type of rigid structure, and I believe that it has kept many of the students who might have checked out in despair in the geometry game, willing to go further with this new subject.  But I could see from the one exercise we did that making this leap is a huge stretch for so many of them, and I am wondering this evening how to proceed.  Do I ‘super-structure’ it – create fill-in-the-blanks examples?  Do I switch to a more accessible activity?  Can I handle differentiating this topic?  The students are at such mixed levels to begin with, and with the added disparities in their Van Hiele levels of geometric reasoning, I am not sure how to create a meaningful activity which will bring them a little closer to understanding the nature of proof.  My dining room table is currently piled with the resources I have culled in my hours of researching.  The ideas are buzzing around my head  – both outside and in – and with 2 days to go before the holiday break, and less than three weeks when we return on January 5, I want to get the biggest bang for my lessons possible.

Too-Many-IDeasI’d love to do the MARS Analyzing Triangle Proofs formative assessment lesson, but I’m afraid I really, really don’t have time if I am going to cover the content that I need to by January 26 (and for those of you who say better to cover this topic in depth and leave out another topic, well, the Geometry Regents waits for no teacher, so to speak, and I need to hedge my bets).   But I’m also laughing at myself, because I am spending a weekend evening wringing my hands over Monday’s lesson, which will be taking place on December 22.

IMG_4437Writing this post has helped me realize one great thing – that my students, who do not generally like or succeed in math, don’t dislike geometry, don’t think it’s some Rosetta Stone of which only their math teacher can make sense.  They are willing to try the work presented to them every day, and believe they can learn it.  And that’s not nothing, believe me.

On an unrelated, but critically important topic, I want to share images of 2 quilts which the president of my quilting guild, Sylvia Hernandez made in response to recent events.  She is an inspiring woman, and her quilts about the deaths of Trayvon Martin, Michael Brown and Eric Garner and the disappearance of students in Mexico moved a room of 150 quilters to tears.  I envy her ability to put her feelings into fabric art so eloquently and efficiently.


Quilt by Sylvia Hernandez http://www.brooklynquiltgirl.com/


Quilt by Sylvia Hernandez http://www.brooklynquiltgirl.com/

I’m not convinced

When I was planning the unit on congruence for my Geometry classes, I wanted some new activities to introduce the triangle congruence shortcuts to go along with the hands-on discovery approach I am using in this course.  We are not doing formal (2-column) proofs, so I am working on eliciting verbal justification from the students.  I combed through the notes I had saved in Evernote (thank you, Anna!) and came across this post by the ever-inspiring (and challenging) Fawn. Her discovery activity for the congruence shortcuts was exactly the approach I wanted to use, especially the part about avoiding lecturing.

IMG_4422The straws which were originally earmarked for stellated icosahedra seemed perfect for our triangle sides ( Fawn used barbecue skewers but they had pirate sword fights as the least objectionable activity in my classroom written all over them), and since my students are not adept at copying angles, I created some angle templates for them to use.  I attempted to debug and envision the activity as thoroughly as I could, using in-house counsel – my 23 year old daughter, who, although in graduate school, remembers her high school days very well.  In truth, I was not confident that the activity would succeed this IMG_4423morning, but I was determined to go ahead and see what my students would make of it; I wanted them to engage in this very open-ended process.

IMG_4429The first class is always a little sleepy; many students have a punctuality disorder.  That said, they are good-natured about trying new things.  They did agree on the SSS shortcut, but didn’t come up with enough evidence to support their claim.  My third period class, after a slow start, dug into constructing triangles with the straws, and we had a lively discussion about the minimum congruence requirements put forward by the different groups:  2 sides, 3 sides, 2 sides and 1 included angle, 2 sides and 2 angles.  However, I was still not able to push the students towards providing solid evidence.

IMG_4430The big disappointment came in my fifth period class.  This class – my hugely mixed bag of emotional, language and learning issues – is capable of great enthusiasm and conversation; my challenge is channeling it towards the content rather than everything else they would rather talk about.  But the week before the holiday break is a tough one – emotions are high and distraction is everywhere.  My co-teacher and I could have 2 clones each and the room would still need more adult presence (basically, each of the 8 tables could use a teacher).  Of late, I am detecting undercurrents of tension, bromance, and harassment, and phone use is rampant.  I confront unacceptable behavior and language decisively and publicly whenever it appears, but there’s too much going on simultaneously in that room.  I know the students are learning geometry, and I know many of them want to learn more.   But teaching them, many days, is an uphill and exhausting exercise.  Today was one of those, although to their credit, the straws were mostly used appropriately.  After a chaotic attempt at discussing the results of their exploration, I put the notes for the S.S.S. and S.A.S. congruence shortcuts up on the SmartBoard and stopped talking.   At least they were writing while socializing.IMG_4428


Looking at these pictures, it appears that discovery is happening.  But I was disappointed in the results that my efforts produced.  I want to try this activity again next year – I am convinced it is worthwhile – but I’m unsure of how to modify it for greater success without giving too heavily-handed direction.  And I’m unhappy about the scene in the 5th period class, although a week ago, I remember being pleased at how well many of the students were working together.  It seems that the specific attendance on any given day greatly affects the classroom dynamic.   And, honestly, I think by the time I figure it out, the term will be over.

Good thing that every day at school is a do-over.