Blogging with Ruby on my Wrist

Yesterday I had an epiphany of sorts – I realized that the more of ‘me’ I pour into my teaching, the fewer reserves I have for myself.  I think I have known this for a while, but in the past year – between my ‘regular’ teaching responsibilities, Twitter, blogging, working with the Common Core Fellows, and private tutoring (college tuition, you know), the me time – the private mental space time – has really shrunk.

It’s not that my choice of activities isn’t in many ways conscious, and it’s not that these activities don’t have their substantial rewards – emotional, intellectual, even financial.  Rather, it’s that I go along, trying to bring my best self to everything I do (trying to be awesome?), and then suddenly, the recognition that time is finite – for us as individuals, anyway – hits me and literally stops me in my tracks (I actually stopped in the hallway for a moment yesterday as I thought about this).  Maybe this is because I am of a certain age, maybe because I am dealing with scary health issues.  Or maybe my subconscious is just issuing a cry for help (Danger, Will Robinson!) that I need to pull back a little.  Unfortunately whatever it is that I am – overachiever, controlfreak, perfectionist [not really; come see my house] – eggs me on.

Whenever those teachable moments about honesty and integrity arise in the classroom, I always ask my students, “Who do you want to see when you look in the mirror?”  And I think about that a lot in relation to myself – because I wasn’t always proud of who I was, and I have worked hard to become satisfied with my reflection.  But of course, we’re never really satisfied – or at least, I’m not.  I never imagined that I would save the world by becoming a teacher, or that I would be THAT person who made a difference in so many lives.  But after 8 years of working harder than I knew I was capable of, I have come to be very proud of what I do, and of the efforts I make to reach as many of my students as I can.  I know (and admire) many hard-working and dedicated teachers, but I also know more than a few teachers who are satisfied ‘enough’ with what they do, and rarely feel compelled to extend their practice.  I also know which camp I prefer to find myself in.

I used to identify myself as a ‘quilter, mom and teacher – not necessarily in that order’.  Well, my children are not entirely grown, and definitely still need me, but not in the immediate ways they used to (this is actually occasionally debatable, but I digress).  My quilting mojo has been one of the major casualties of my development as an educator, and this frustrates and saddens me terribly.   When I began quilting in earnest, about 15 years ago, I felt like I had finally found my creative outlet, something that I enjoyed and was good at.  I taught workshops in my children’s school, wrote articles about my quilting, and I actually had a very small quilt featured in Quilters’ Newsletter magazine.  Ironically, this was a mini-quilt I made to honor the start of my teaching career.  These days it’s very hard for me to finish a project, and I long for the ability or motivation to put everything else aside and work with my hands and with color.  But even as I think about that loss, I am sitting here typing.

This post strikes me as somewhat whiney, and I apologize for that.  But as a blogger I know that this space is as much a place for my personal reflection as it is for public commentary.   Every day I find myself weighing the priorities of my ever-present to-do list (only during the summer does everything get crossed off –  for a short while), and trying to carve out a little time to fit everything in; there are always a few floating tasks that MUST get done but I cannot schedule; my Pi Day bulletin board and MathMunch display case are currently in that category.    And all day long I am formatively assessing how my classes are doing, what needs to be tweaked, reviewed, clarified, livened up.

My New Year’s resolution for the last 5 years has been to have greater balance in my life – I guess I haven’t done so well with that.  Last August, Nathan Kraft wrote a blog post which I re-read periodically, in which he addressed this particular issue.  I think I need to take this post truly to heart – to be less awesome in school, but more awesome in life.  As a parent, I know that your children learn more from what you do than what you say; I imagine the same holds somewhat true for students, even though as a teacher, we have specific responsibilities to say certain things (like mathematical content).    So I guess it’s not ‘them or me’, but rather ‘me for them’.

I think I can face tomorrow now.

The Sign-In Sheet from Math Club today, on which students needed to number themselves. Keeps me going back.

So what actually happened in The Class that Nobody Wanted?

Encouraged by how intrigued the students were by the Illustrative Mathematics composite figures task on the first day, I decided to continue with the activity the following day, allowing the students to self-select groups.  I created a worksheet to give them more workspace, and brought in the group whiteboards – always a hit.  I also invited my colleague and mentor into the room for suggestions and feedback.   When the students came in, I distributed the worksheets, went over the formulas for area, perimeter and circumference that they would need, and instructed them to select one of the shapes to work on as a group.

The level of engagement in the room was complete and palpable.  Because the composites were squares and circles, because the length of each square was a friendly unit of one, and probably because there were no variables or exponents, the task was not intimidating to the students.  Many of them went right for the blue shape, which, to me, was one of the more challenging figures.    They began to debate the correct method for finding the area.  The whiteboards were a great tool for visualizing how the shapes overlapped, and even students who were uncomfortable contributing mathematically could participate in the sketching.  (Markers always  make it better. ALWAYS.)  There were also 3 adults in the room, which was enormously helpful – gently guiding the work, answering and asking questions, and observing the interactions.   The students worked steadily until the bell rang – everyone (myself included) was so absorbed that we ran out of time for sharing.

I met with my mentor later, and through our discussion realized that the challenge for me was to keep these students motivated with accessible, engaging and respectful tasks.  But I also knew that there was a wide range of ability, as well as a range of goals among the students.  There were seniors who needed one final math credit, and  juniors who were on track and wanted to take the Geometry Regents exam.  There were also students who might have previously been in a more quickly paced class, but failed a semester for a number of reasons – attendance, teenage distraction – and were moved into this slower track.  And finally, there were students who were very weak mathematically, who had been pushed through many classes without retaining much.

So I am faced with the task of managing this class effectively, with the end goal of imparting some mathematical learning and appreciation to these students, while simultaneously demonstrating to the administration that this cohort could and should learn geometry.  I need to show my principal that the assumption that these students were not capable of (or would ever need) the abstraction required by the content was not only an erroneous, but also an objectionable assumption by so-called educators.

The following day I brought the iPads into the classroom, having designed (or so I thought) an interactive review on angle pairs based on this blog post by Amy Zimmer.  The app I intended to use (Educreations) didn’t work out quite as planned, so we used the iPads as digital whiteboards as I quizzed the class on sketching angle pairs.  The students were working in pairs (we don’t have a full class set of iPads), which kept things lively.  Again, high engagement, instantaneous assessment and feedback, and some fun.

On Friday, I knew I needed some hard data on the ability of each student.  So I planned a ‘Quickie Assessment’ such as the one I read about in Steve Leinwand’s Accessible Mathematics.  I planned on beginning the class with a six question quiz, beginning with a friendly occasion and working up to a problem involving parallelograms, and then spending the balance of the class exploring the Taco Cart problem.  As my mother would have said, “WRONG!”  After the first equation, many students needed guidance and encouragement.   Some students could barely work through the two-step equation, while others zipped through all the problems, and began working on a more course-appropriate review worksheet.  It took 25 minutes for the whole class to go through the six questions.  We collected the papers, but the students wanted to review the problems immediately.  My co-teacher took the lead while I moved around the room, checking in with some of the kids.

I reviewed the results of our assessment, and they painted a daunting picture.  The class is split into 4 levels, as I see it.  There are students who are on track conceptually, who have landed in this class because of a personal screw-up in a previous course, who need to be not only challenged, but prepared for the Geometry Regents on which they can clearly do well.  Next in readiness level is a group of students who, with preparation and hard work on both of our parts, can also complete the course at a Regents level, and hopefully move on to Algebra 2 next year.   The less accomplished students fall into two categories – a group which can do a modicum of geometry, and a group which was, to be honest, lost on Friday from almost the get-go.  Most of the class falls somewhere in the middle (naturally) – a real bell curve of a situation.  But the difference in current mathematical ability between the high and low ends is huge.  This weekend, as I tried to wrap my brain around what I could do to address everyone’s needs, I imagined myself stretching (literally, across the classroom) so I could work with several different students at once.

So after a weekend of thinking, pacing, asking for advice, and consuming mass quantities of Ritz crackers, I have come up with the following plan:  The class will be split into 4 groups which reflect the aforementioned stages of ability.  On three days a week, my co-teacher and I will teach two lessons on the same topic, but at levels which are appropriate for the higher and lower ends of understanding.  Luckily, the classroom is a long one, with a SmartBoard at the front and blackboards across the back wall.  Everyone will be working on the same topic, but practicing the skills at a level from which they can reasonably improve.  Two days a week we will work heterogeneously – one day on a group task, and the other – well, I am still trying to envision that fifth day each week.

I am going to introduce this re-organization of the class tomorrow, and I will be explicit about the rationale behind this plan.  We will do an exercise on Mindset, and I will explain to the students that the goal is that each student gets what they NEED right now, and that each will be assessed and evaluated on the progress they make from where they are RIGHT NOW.   The intention is that everyone moves forward mathematically, and that each student has individual learning goals.  My hope is that they will appreciate the assumption that they can all learn math (I do not believe they have always been treated that way), and that they will be taught in a way that addresses their specific needs.  My co-teacher is on board, and we have set up a schedule of weekly meetings with each other in order to execute what feels like a very ambitious plan to me.

At the end of class on Friday, I took one student aside – a senior who started out being very social, but by the end of the week, was focused [successfully] on tackling the geometry problems.  I told him I was impressed with his work, and that he should definitely take the Regents exam in June.  He looked puzzled and said, “Really, Miss? But I don’t need it.” (Students only need one math Regents – usually Algebra 1 – to get a NYS High School Diploma.)   I said to him, “You are intelligent, and you can do this work, and you should challenge yourself academically.”  He just looked at me for a minute, and then said thoughtfully, “Thank you, Miss.  I’ll think about that.”

I have to make this plan succeed, because I am fairly certain this hasn’t been said to this boy before, and that thought makes me want to cry.  But instead, I will teach.

While this first week of the spring term didn’t feel especially long, it definitely was a journey.   This may be a long post; I apologize for my lack of brevity, but, well, there’s a lot to say.

On Monday, I arrived for staff development day – in a snowstorm – a bit late, and joined the plenary session (our staff is so large that we use this lofty term for a full staff meeting) run by our principal in time to hear him ask for new courses to meet the needs of our students.

[I need to take a brief moment to explain that the large urban school in which I work has a population comprised of students who enter through both screened admissions and through the local zone.  The split is fairly even, and this mix creates a diverse atmosphere which does not fully integrate the two groups of students, nor does it completely segregate them.  While it’s not quite a Tale of Two Cities,  there are definitely distinctions drawn along academic, and in part, but not completely, racial lines between the two groups of students.]

“We need to adjust our expectations to meet our students where they are at,” the principal announced.  “Take Geometry for example – a lot of these kids – they’re never going to need Geometry.  Why are we setting them up for failure?”  While his exact verbiage may be slightly off, these words – or very, very close to them – were uttered by the instructional leader of our 3800 student building.  My mind went blank, or perhaps I saw red, but some switch, some alarm went off in me when I heard this.  I was incredulous – was the principal of one of the most sought after high schools in New York City telling us to lower our expectations?  Was he saying this right after he told us that while our ‘gifted’ students loved our high school, those who were ‘lower achieving’ left without the same warm fuzzy feeling after we had somehow managed to help them graduate?

I wrote in my last post about my on-going efforts to educate myself in order to be a better ally, or to begin to become an ally to those who were oppressed by or excluded from mainstream systems.   And I decried the attitudes of my colleagues who look at some students and only see failure; those teachers refuse to modify their own output in order to achieve a different outcome in their classrooms.    But I never anticipated hearing such explicit  condemnation of an entire class of people from someone who was supposed to be acting in their best interests, the  alleged guardian of their education.

This exhortation cast a pall over the rest of the day.  In our math departmental meeting, we debated long and painfully about what type of courses we should be offering to students who failed repeatedly, and whether we should be encouraging or ‘inviting’ them to take Regents exams (which they are by law entitled to take once they have completed a Regents-based course).  Thankfully, several teachers besides me spoke up against telling adolescents that they didn’t need any higher levels of math because they weren’t college material and never would be.  But the lowering of expectations had begun; the principal’s priorities were already causing their downward effect.

Tuesday was the first day of classes.  Four of my five classes are ‘regular’ and ‘gifted’ track students, but I have one team-taught inclusion section of Term 3 of 3 Geometry  (the slower track of Algebra 1 and Geometry are broken down into three terms each).  There are currently thirty five students on the roster, with a huge range of ability, as well as a range of class year and credit accumulation.   On our first day – we had a very brief period – I gave them an activity from Illustrative Mathematics, in which the students were asked to find the area and perimeter of each composite figure.  Ever overplanned, I had created a worksheet I thought we would complete.

The students were intrigued by the process of finding the area of the purple figure, and began sketching, calculating, and arguing with one another.  A lot of them.  We just had time to finish the area portion of the problem when class was over.

I was thrilled (and a bit surprised) by the level of engagement – of perplexity! – of the students.  And I loved what I saw – this desire to solve a problem, to look at something they had never seen before and tackle it.  I realized in that moment – my own personal Aha! – that this is THE class for me this term.  This is the class to defy those lowered expectations.  I know I must rise to this occasion and bring everything I have to [try to] transform the mathematical experience many of these students have had into something positive and affirming.

I consulted with my mentor, inspiration and dear friend – the ELL Coordinator for our school who is currently an intern for a supervisory license.    Lucky for me, her office is just down the hall from mine, and even luckier, she was equally cognizant of the high level of need of these students,  and the opportunity presented not only to create a uniquely student-centered and differentiated classroom, but also to demonstrate to the nay-sayers, purveyors of low expectations and thinly veiled racism that which can accomplished when we acknowledge that it is our responsibility as educators to be thoughtful, intentional and work as hard as we can to – yes –  meet our students at their level, and then bring them beyond it.

Realizing how intriguing the composite shapes were, I decided to postpone my lesson plan for the next day in order to continue this exercise; the students would work in self-selected groups (I was still getting to know them and wanted to observe their choices) with the large whiteboards.  My colleague offered to observe the class and share feedback and insights, as well as support me as I undertook the task (which was beginning to loom as I looked forward) of creating a classroom in which there were high expectations of every student: that each student would honestly acknowledge where they needed help and where they could grow, and do their best, in cooperation with their teachers (my co-teacher and me), to move in that directions.

It has taken all evening just to set this thought process down; another post will follow (hopefully tomorrow) about what we actually did in class this week, what my plans are going forward, and a plea from the #MTBoS for help and ideas.

Several things converged today – in my life as a math teacher, as a reader, as a person who wishes the world was a better place for those who are being left behind by educational and societal systems.  The seed for this convergence was a twitter conversation I participated in (or maybe just lurked around) on racism and privilege, in which @sophgermain recommended the book Why Are All the Black Kids Sitting Together in the Cafeteria by Dr. Beverly Daniel Tatum.  I purchased the book and have begun reading it, stopping frequently to copy down quotes on post-its and reflect on uncomfortably resonant truths.

Similarly, last night I attended “How I am Working to Learn to Suck Less” at the Global Math Department with @sophgermain.  I listened to the presentation with my daughter, trying to think about ways in which I might be contributing to racism, committing micro-aggressions, and engaging in culturally insensitive behavior, loathe as I am to imagine that I am doing any one of these things.  I take Soph’s first suggestion deeply to heart – Educate Yourself – and have a long reading list already.  (I keep hearing my child Geo telling me “Just google it, Mom,” when I asked for enlightenment on non-binary gender identity.)

Then today, I was sent from my school to a central grading site to participate in the scoring of the open ended questions on the NYS Geometry Regents exam.  I was assigned to grade two questions, one of which was the last question on the exam – the big 6-pointer, which was, as it often is, a proof.  What was unusual – and mind-boggling to this math teacher – was that the proof was a FILL IN THE BLANK question.  That’s right – a 9-step proof on similar triangles in which all of the statements were provided for the students, and three of the nine reasons.  I won’t go into my lowering of expectations rant right now, but know that it exists in my mind.

Before we began grading, we had to ‘norm’ as a group; we reviewed the state rubric, the provided student work, and discussed what answers we would additionally accept that might not be included with the materials from the State Ed Department.  The final step in the proof involved the equality of the cross products of the proportion of corresponding sides from the similar triangles, and a lengthy debate took place over whether ‘cross multiplication’ was a legitimate reason for that step.  I led off the more ‘conservative’ side of the conversation, and pointed out that Cross Multiplication was merely a procedure – and a trick (right out of Nix the Tricks) rather than a bona fide justification for taking a logical step.  I was surprised (naively, perhaps) to hear a good portion of the teachers in the room disagree with me, the rationale being that students were taught for so many years that Cross Multiplication was a mathematical ‘idea’ that it might not be reasonable to expect them to be able to state “In a proportion, the product of the means is equal to the product of the extremes.”   The debate went on for almost 30 minutes.  I am a firm believer in the idea that there is always more than one way to approach a problem in math, and that students should be encouraged to express their mathematical thinking in all of its diversity.  But I also have strong feelings (clearly) about what constitutes actual mathematical reasoning, and the net downward effect of lowering expectations so far that real critical thought is no longer required. In short, the conversation left me surprised, and well, shaking my head.

As we began to grade, the long debate became moot in many cases; very few students were able to complete the proof, and even fewer wrote anything which resembled an appropriate reason for that last step.   As anyone who has graded these exams knows, you can become downright awed by the breadth of misunderstanding and the chasm between what we think we are teaching and what evidence is actually provided by students in their answers.   But right after that ‘awe’ follows the sadness that this huge disparity exists, and what it implies about our classrooms now, and the students’ futures.  We think – or I think, rather – that there is real teaching and learning, of some sort, going on in my classes, even if my students aren’t articulating the mathematical brilliance which I am certain I am imparting.  I think there is something of value that I am passing on to them, a means to make sense of things, that they can use somehow in the future.  But there – in those [sometimes unbelievably  and creatively irrelevant] answers on the tests is the hard cold truth – I really am the teacher in the Charlie Brown cartoons.

So where is the convergence?  It exists in [my mind, clearly] the space between the need for us to be intentional in our behavior and in our teaching, in the idea that I have to acknowledge and learn about the system of which I am a part, the system which maintains advantage and privilege through oppression, and I somehow have to turn that awareness into meaningful teaching of mathematics for my students.  This thought struck me so forcefully today – how critical it is that I try to provide them with some type of tool in the form of math to help them make their way and rise up against the odds.  I don’t know how to do  that – it’s the question I have been trying to answer for eight years now – but every time I allow myself to fully look around, its exigency hits home again.   The future belongs to all of us, and to ignore this pressing need condemns not only our students, but all of us, to a dangerous world.

I didn’t write a New Year’s resolution blog post.  I read those of my colleagues and tweeps with admiration and occasional envy.  I wish I had the boundless enthusiasm of Sarah Hagan at Math = Love, or the diligence of @JustinAion at Re-Learning to Teach.  Sarah writes blog posts in which her dedication and creativity are tangible, and she’s got the foldables to prove it!  Justin provides his followers and students with original artwork EVERY DAY, as well as a reflective entry complete with humor, humility, and ultimately truth.

But January has been a huge struggle for me this year, personally and professionally.  As I look back on the fall term, which is ending in 4 short days, I see some changes (improvements?) that I incorporated in my classroom as intended – estimation, better questioning (or rather NOT answering questions directly), more exploration in Algebra 2 – but I also cringe at the list of things that still didn’t happen the way I want them to, the way I conceived of them, the way I knew they SHOULD have gone.

And I wonder for how many years will I continue to feel this way?  I am SO jazzed by my interactions with teachers at conferences (Exeter/TMC), on Twitter (#alg2chat, #msmathchat), or working with my colleagues at the NYC Department of Education Common Core Fellows.  Through these rich conversations, I develop (borrow/steal) a million ideas, narrow them down to an allegedly manageable few each year (I’ve learned to do that, at least), envision and document their execution as clearly as I can – complete with plans, graphic organizers and rubrics – and forge ahead.    Regardless of my effort and enthusiasm, however, I frequently find myself disappointed with the results:  Were my expectations not clear enough to the students? Was the lack of follow-through on my end? Is this just part of the endless process of teaching and learning and learning to teach?

There have been successes this term, to be sure – and I am glad that my blogging efforts provide that documentation.  But I would really like to get to that place – professionally – where I know that I can consistently take an idea, plan for it, make it happen in my classroom, and have evidence that learning has taken place.  I am not being facetious, or dissembling.   Like I said, this January is tough, and I have been questioning everything about my professional choices.

I had the pleasure of having both of my children home at the same time this month – something that doesn’t happen all that often anymore – and when Geo went back to school for the spring term, my descent into the doldrums was pretty complete.  I usually keep myself too busy (and am still in too much debt) to let Empty Nest Syndrome sink in, but the house became very quiet over the long weekend.

At the end of the afternoon, however, I had three private tutoring students, which lifted my spirits enormously, and I remembered that I love doing math with kids.  When I reminded one of my students that we would have a two week hiatus because of the end of the term, she said, “Oh, no – I HAVE to see you.  You are my FAVORITE math grown-up person.”

I’ll take it.  February is just around the corner.

I’m not sure when I first became aware of the MathMunch website; I’m pretty certain I happened upon it before my attendance at TMC13 last summer.  Wonderful resource that it is, I know I spent a fair number of hours perusing the collection of articles, games, art ideas and links.   Last summer in Philadelphia, I not only attended a presentation on MathMunch, but had the opportunity to spend a few hours chatting with one of the founders, Justin Lanier (@j_lanier), as we drove back to Brooklyn after the conference.  It was clear to me after this conversation that the spirit of MathMunch was in part underpinned by Justin’s deep belief in the uniqueness of each child’s educational requirements and rights (which led to his changing positions from already liberal St. Ann’s School in Brooklyn Heights to the even more open Princeton Learning Cooperative).  So I knew HOW great a resource MathMunch was for students; the question now was how to enlighten them as to this web-based gold mine of mathematical enrichment.

While this question was still percolating in my mind, one of the MathTwitterBlogoSphere luminaries, Fawn Nguyen, came up with a simple and actionable plan: just make them do it!  She designed a simple log form which required each student to visit the MathMunch website 15 times over the course of a marking period and sample 5 different types of activities: three each of games, articles, videos, art projects and puzzles.  I decided to sincerely flatter Fawn yet again with imitation, and borrowed her log form with [very] minor revisions.   My honors track Algebra 2 students were the target of this experiment; I learned the hard way that the attempt at something new and challenging would most likely be successful with your most motivated students.  Sometime in early October, I showed them the TEDx video in which the MathMunch founders described the origin of the project, distributed the log form, and gave them a long window for completion (Winter Break).   The assignment was not extra-credit, but I promised to include the grade in such a way that it would help their test averages.

A few students dipped their toes in the water by playing some games right away (how did I know that would be the immediate draw?).  I cautioned them that only three games were allowed on their logs, and that their efforts needed to be spread among the five activities.  We got caught up in the swing of radical equations, absolute value inequalities, quadratic functions, and November slipped by.

Weekly reminders were issued that 15 activities over 9 weeks was a minor assignment, whereas that same requirement in a few days would be highly stressful.   Still, by Thanksgiving, I had only received a smattering of submissions.   The log form I had created for myself to keep track of their work was depressingly empty.

On November 6, I received my first piece of MathMunch-inspired art – a hexaflexagon from Kimi.  I was so touched and excited I demonstrated the uber-coolness of it to the class, and featured it on my 180 photo blog.  Kimi was the first – but certainly not the last – of my students to encounter the brilliance of Vi Hart’s videos.    As a matter of fact, if you visit her Thanksgiving Turduckenen-duckenen video, you will find a host of comments authored by my Algebra 2 kiddies.   And then, over Thanksgiving weekend, I received this message from Anson, a student who, lucky for me, has been in my class for two semesters now.

 On fire!  Anson was ON FIRE  with MathMunch.  You know that feeling when you assign a project and you aren’t quite sure that your students will get out of it that which you had hoped?  Well, Anson dispelled that feeling for me with that one line.  There was still a modicum of doubt because his comments were all about games, until I received this note from him, a couple of weeks later.   The best thing about this message was that he left MathMunch to look for similar resources, and felt compelled to share them with me.

Still, things did not begin to pick up steam until the second week of December, when I began to receive snowflakes and origami daily.  I treated each submission as the treasure that it was, pausing in class to thank the students for their lovely work.  But it wasn’t just snowflakes and origami  that I received.   Many students became fascinated with the Fascinating Wooden Puzzle video, but Stephanie recreated it for me.  Nicholas, whose math was spot on but whose handwriting is illegible, created computer art.   Diana, whose work is impeccable and rolls her eyes every time I tell her to stop texting [does she REALLY think I don’t know why she has her book standing up on her desk?] ran into class one day, and was practically stammering when she told me how the video How to Create Chocolate Out of Nothing blew her away.  By the time I left school on December 20, my log looked like this.

I brought home a shopping bag full of student MathMunch art, which made my dining room table look very cheery.   I am overwhelmed with the effort and excellence in some of their work, and am going to ask my principal for a small display case in which to showcase their work – a nice contrast and complement to athletic trophies, in my opinion.   I want to find a way to leave the students not only with pride in their efforts, but with the curiosity and impetus to continue their readership of MathMunch.    I am sure that some of them just slogged through the checklist and were relieved when they were finished.  But I know that there were some, like Kimi, Anson, Stephanie and Diana, whose mathematical curiosity was piqued and challenged.  And then there is Michelle, who never says a word but does exemplary math.   She gave me these beautiful works of art.  I know I touched something in her.

(This post was begun on Wednesday, December 18) Today was the kind of day you want to bottle, or put in a little box that you can open and peek into for a shot of confidence, adrenaline, efficacy.  I exhausted myself meeting the edicts issued by our administration in anticipation of the biennial Quality Review; even though I consider myself to be a well-planned and relatively intentional teacher, the degree of documentation required to be at my fingertips at any point during the 48 hour school-wide assessment was ridiculous.   All teachers had to carry folders with them which included two copies of their lesson plans, curriculum maps, student work with rubrics, student action plans (for failing students) and a description of our administrative duties.  All students had to carry folders which contained examples of their best work; these could be handed in to the teacher of their choice for extra-credit at the end of the QR, per the principal.  And ALL classes were to be engaged in ‘project-based groupwork’ – the whole school!  (The number of times the thought ‘Are you kidding me?’ ran through my head during this process is countless.)  But good girl that I am, I dotted all my i’s and crossed my t’s; my completed folder was on my person at all times.  I have been on the hit list during this dog-and-pony-show twice before, so I fully expected [erroneously, as it turns out] to be observed.

The day began with one of the few classes in the school that actually has been engaged in project-based learning for the last month, my Geometry class.   Sadly there was no chance of this class being visited, because the Reviewer did not arrive at the school until 8:45 a.m., three minutes before 2nd period ends.  I’ve written about the struggles I’ve had with this class and this project in other blog posts, and had invited a colleague and mentor to observe me that day, looking for constructive feedback.   I had this uneasy sense that the students were floundering and that the iPad presentations on which they had been working for 2 weeks  were amorphous and directionless.   The students had a deadline on this date to share drafts of their projects; I purchased a VGA adapter so we could connect their Pads to the Smartboard.    As we began the Share, I informed the class that they were groundbreakers at Midwood High School (clearly, since I needed to purchase the technology which allowed them to project their iPad screens).  I thought I detected a hint of surprised pride on their sleepy faces (it was after all, 8 a.m.).

To my delight and surprise, the students (a) had cohesive ideas of where their presentations were going, and (b) were articulate about sharing them.  I didn’t have to cajole anyone to present, and I didn’t need to remind anyone to respect their fellow students while they were presenting.    We discovered a few kinks together in the use of the adapter, and I also learned how well some of my students had done in adapting their ideas to the available apps.   My colleague had several suggestions – a specific checklist for completion rather than the open-ended log I had provided, and better monitoring of the location of the work given the attendance issues in that class.  But she was positively impressed as well.  I am very proud of the progress that this class has made.

In my Discrete Math classes, we began @approx_normal‘s terrific Intro to Statistics lesson on Kristen Gilbert.   The murder mystery was an immediate attention-grabber.  Some students wanted to declare the Angel of Death guilty before we had even begun our investigation (teenagers can be SO judgy!).   But they also were clearly engaged in the activity, and in working through the data to build their case.    Making sense of a simple chart of nine numbers (deaths that occurred during shifts Gilbert did and did not work) proved to be a huge challenge for many of them, which nicely reflected the opening Big Idea, “Data is Messy”.  We ran out of time during the second day of the lesson, and the students asked me to return to it after vacation.  Not bad for a group of disenchanted seniors, a third of whom are graduating in January!

Having thus far escaped the Reviewing Team, I knew that my Algebra 2 classes in the afternoon could also be on their itinerary.  I had planned an exploration from the Mathematics Assessment Project on using quadratic equations to solve word problems which involved a tricky application – using a quadratic function to determine how far a bus wheel would cut into a bicycle lane when making a right turn.   The equation itself was simple, but visualizing the problem, I knew, would be a challenge for many of the students.  (It took me a few minutes to grab a hold of it, which did not bode well for those in the class who gave up easily.)  I had assigned a first pass at the problem for the previous night’s homework, which many of the students declined to complete, so class began with a mini-lecture [I chose not to resist the impulse this time] on perseverance, challenging oneself, and the value in finding solutions that are not readily apparent.  The students moved into assigned groups, were given big whiteboards, and I circulated, refusing to answer questions (My responses to almost all of them were limited to  “what shape do you see in the sketch?” [a right triangle] and “have you asked the very smart people with whom you are sitting?”).  Lo and behold, there was enough collective initiative in the room that magic began to happen.

As I walked past one group, I noticed the crumpled homework sheet, and asked Sam, its owner, what happened.  He told me he needed to go to the depths of despair with the given situation before the solution began to take shape in his mind.  The group whiteboards are so effective, because everyone can get in on the work, even if only to draw a picture of the problem.  I heard lots of great math chat – students talking about tangents to circles, the Pythagorean theorem, and the two roots always created by the quadratic formula.  There were discussions about whether or not an answer was reasonable and even required a ‘check.’  In the second part of the lesson, students were given work  completed by other ‘students’; each example had an error ranging from a sign switch to a clear lack of understanding.   Amid the rich discussion I heard coming from every group, there was also speculation as to the identities of the students whose work they were trashing. (“They must be from the OTHER class.”  “Donna should definitely NOT pursue a career in mathematics.”)  Two days of great math.   

One of my Algebra 2 students, Carrie, participated in the student meeting with the Quality Reviewer.  She ran into the classroom, late and breathless, and described the intense conversation to the class.   She was mystified regarding the purpose of the interview, a disparate group of students brought together to be asked loaded questions by a former superintendent.  Carrie pointed out that she mentioned the post-PSAT score report class we had, in which I coached the students on the following issues: (a) how they can use their disappointing PSAT scores as a learning and action tool, (b) why the PSATs do and do not matter, and (c) that they can still have good, fulfilling lives regardless of the outcome of any standardized test.    In my view, this should a required conversation in at least one high school class, but sadly, my classroom is apparently one of the few in which it takes place.  Hopefully, Carrie raising the issue will have some ramifications.

The day finished gloriously with the Math Club meeting – the largest yet: 36 mathletes attending!  Many students brought festive snacks, and I piloted the Pirate Game I recently downloaded from tes.co.uk.  It is a great way to spend a pre-holiday class – a combination of strategy, the coordinate plane, and competition.  It can become quite boisterous, so use it, for sure, but with care.

So here’s the thing – clearly a wonderful day, clearly my Herculean planning efforts paid off.  I am proud of the fact that each of the classroom activities were lessons I would have used at some point, regardless of the Quality Review (not the case for many of my colleagues).  Would I have attempted ambitious group activities in 5 classes over two days?  Hardly – the effort was exhausting, or was the exhaustion a result of the external pressure?  My goal is to be able to teach at this level on a regular basis without feeling like I am using every bit of my energy reserves, and then some (note that I became ill as soon as holiday break began two days later).  How do I get to that place where this type of teaching is the norm and not the exception?   The engagement, level of discussion, and concomitant learning all speak to the value of what I accomplished in my classes.    I want this to always be the watermark of my classroom – and another New Year’s resolution is born.

Week 2 of our PBL unit was not quite as promising as Week 1.  We alternated between some straight geometry lessons (reflections and translations) and beginning to formalize the presentations.  My challenges as a teacher are two-fold:  first, to make sure that these students are actually learning some geometry (3 of them – high school juniors – asked me where the y-axis was this morning), and that they are making progress on the final product.  The class includes a spectrum of learners – there are students who understand the material as it is presented to them, can work independently, and even keep a project moving in a group.  At the other end of the range, besides my students who don’t know where the y-axis is (I did not think I needed to check on that prior knowledge, but the more you teach, the more you learn you can’t assume ANYTHING), I have students who want to check every bit of progress, every image they find, every decision on their presentation with me.  I have been having success, happily, at redirecting the students to their groups.

There is one group in the class (self titled the “Yokels”) that was operating (or not) very dysfunctionally last week.   They have a strong female anchor – a young woman who, while not the best academician, is very motivated to do well, and willing to do the work.  The three boys she is grouped with are all quiet, but all workers with good attendance (a big plus in this early morning class).  When I created that group, I thought they would be the Dream Team.  Not so.  Every time I walked by, one of them would be looking only at his notebook, another would be writing down notes from Wikipedia, and the girl lead would be angrily trying to produce a draft of SOMETHING on paper.  I gave them several nudges last week, and finally sat down with them this morning.  Again, no one wanted to talk except Dora (name changed).  “They won’t talk,” she said, “they won’t do anything.”  And no one answered, sort of supporting her claim.  We went over the list on the board of what should currently be included in their presentation, and luckily, there were exactly 4 items on the list.  I asked them who would take on each task, and they each volunteered for one, and then began working.  Dora is collating all the work into one app.  So a plus for PBL and groupwork.

The drafts I saw today are in various stages of completion, but every group had something to show me.  Attendance is a big issue – two of the groups had members absent who were responsible for major chunks of work.  I intended to share some progress work on the SmartBoard – even purchased my own VGA adapter for that purpose – but checking in with each group and the intervention with the Yokels left about 4 minutes in the period.  So I am worried that I will not be able to bring this project to completion in a reasonable amount of time – I need to leave at least 2 weeks at the end of the term to go over some new content.

The task of moving things forward feels Sisyphean, even on a good day like today.   I would like to do this with a higher track class, just to see how extra student motivation impacts the process in terms of depth of learning, meeting deadlines, and quality of product.  Sadly, I can do this project in this particular class, because no one in administration is paying attention or expects these students to actually succeed in math beyond earning a 65.  I am hoping that sharing their work and celebrating it will give them the feeling of efficacy they deserve,, and that the process of the project will deepen their understanding and appreciation of transformations.

More to come – sorry no pix.

Four days in to my first Project-Based Learning unit in my Geometry 1 class.  So far I am pleased and I think the students are on board.   Here’s a rundown of what has happened so far this week:

Day 1: I introduced the project, showing them a brief video about PBL and how it relates to the type of work they will encounter outside of school – teams, problem-solving – and how the learning can be more meaningful because they are taking charge of it.  I gave them each a packet, and they perused them thoughtfully, pleasantly surprising me.  Then I introduced the actual assignment, “Selling Geometry” – developing a presentation directed at teenagers, convincing them of the relevance of Geometry.  (As I did this, I thought ‘Welcome to my world, kiddies!’)  The students didn’t ask a lot of questions, but I think they were trying to process the big idea of what was in front of them, so different was it from anything else they had done before.  We looked at the different rubrics, and although we didn’t go through them point by point, I highlighted the different ways in which they would be assessed – whether they were working mathematically (the practices are posted on sentence strips around the room), exhibiting knowledge and understanding of their content, functioning well in their teams, and creating/delivering effective presentations which evidenced mastery, creativity, and effort.

Once I had laid out the scenario of what our classroom would become for the next 4-5 weeks, I addressed the larger issues (in my mind, anyway) – what they hope to get out of this class (a credit, for most of them), what my expectations are of them in this class (that they actively participate in the learning process and demonstrate mastery of the material), and what type of classroom culture we need in for both of those things to happen.  I let them know that responsibility for their learning lay with them as well as with me, and that I had confidence that this project was a way for us all to achieve our goals, while working on some additional real-world skills in the process.

As an exit ticket, they had to write down who they wanted to work with and why, as well as anyone they DIDN’T want to work with, and why.   They took this very seriously (I was glad to see); I received some detailed rationales for their choices, and some amusingly frivolous ones (“He has good hair” was my favorite).  Day 1 – a success.

Day 2 was team-building.  I was able to create teams that gave each student at least one person they requested, and no one they rejected.  Of course, 50% of the students in the class have attendance and punctuality problems; there was no avoiding that creeping into the groups.  But I made sure that each team had at least 2 reliable attendees.  The students then completed some Silent Puzzles in their groups – lots of engagement and focus! – brainstormed some team names (still in progress) and discussed possible formats for their presentation.  I wanted to have a gallery walk to share their work, but we ran out of time.  I think I need to bring a case of Red Bull to each class – getting teenagers moving at 8 a.m. is no small feat!

Days 3 and 5 were dedicated to technology.  I loaded up our iPads with productivity and presentation apps like Educreations, VoiceThread, Doceri, Evernote,  Prezi, Kidblogs and Haiku Deck.  The first part of the period was spent exploring these apps; next week I am going to have the students make very brief presentations using the app of their choice; we will share these presentations to introduce the teams.  I have also decided to use Khan Academy as a tool for differentiation and formative assessment – despite some of my issues with the website and the underlying implied philosophy of education, it might possibly be a no-brainer for individualized practice that I can monitor.  I tested both the website and  iPad app at home ( so I thought), and was somewhat confident I could implement it as a tool – even though documentation on certain activities (like creating a teacher playlist and assigning work to specific students) was hard to pull out of Khan Academy’s many resources (at least for me).

Well, the students had a lot of difficulty in class on two fronts – creating an account through the iPad app, and selecting me as a ‘coach.’  We had to bounce back and forth between the app and the website in order to accomplish this.  Once we got everyone signed up and logged in, the students began working on the exercises (in Safari) I had assigned (geometric translations).  But on some of the iPads, the questions, which involved dragging graphs around, became distorted, and the figures wouldn’t drag properly.  In fact, those rigid motions were definitetly NOT rigid in some cases.  And when a student is working on exercises, they can click on a video to watch if they are stuck on a question.  But – oh, shoot – iPads don’t support Flash!  Back out of Safari to the app.

The kids, to their huge credit, persevered (MP-1!!) through this technological quagmire all period, and I was able to check to check their progress with reports like these:

I still have a lot of troubleshooting to do so that this tool reaches becomes as meaningful as I hope it can be.   But the engagement was high, and I only encountered once instance of a student using the iPad in a manner in which he had not been directed to use it, and that student was easily redirected to his work.

Day 4 was a direct instruction day – we are going to approach congruence Common Core-style – through rigid motions, and began this process by learning about translations on the coordinate plane.   Teaching up at the board for a good portion of the period felt odd after all the groupwork – easier for me in some ways (just talk about what I love), but more difficult as I looked out at a silent classroom, students taking notes, but waiting for ME to do the work – the Ms. Menard Geometry Show.  I am hoping that as we get further into the unit, the days when we are engaged in whole class work will be livelier, the students more involved and confident as a result of the mathematical empowerment this project gives them.

I feel like I have set the stage for the student work I hope is to come, and that my job now is to effectively orchestrate the transition from all this groundwork to authentic learning and the production of project artifacts, which will of course include the appropriate grade-level geometry.  I’m nervous that I can’t make it happen, that the kids will require so much scaffolding and direction that the learning I intend to take place might not occur, or that what they produce will fall far short of my hopes and expectations.  And like my good friend @JustinAion, I feel that this is my responsibility – to bring my best game to this classroom of struggling and somewhat forgotten students.

So my work this weekend is cut out for me – I need to envision the path we will take as a class to move into the next phase of this project, model the process for my students, and somehow create the learning environment in which the work will happen.

Feedback/suggestions requested and appreciated.