# #DITLife 4 and 5 – Finishing the Week

My hat’s off to @justinaion - I don’t know how you manage to write every day for a week, never mind an entire school year!  I have enjoyed the process of examining one class under a microscope for the week, but the blogging takes more time and mental space than I have to spare each day.

Day 4 – Thursday

Thursday was a day of direct instruction following our Patty Paper Fun Time on Wednesday.  The students worked on a brief warm-up from this book; they had to draw a 45˚ and 180˚ rotation of a figure. The activity was very accessible, and I saw results from very casual sketches to carefully rotated figures drawn with straight edges.

I created another guided notesheet for today’s lesson on Rotations.  After going through the terms and definitions the students needed for this topic, we discussed rotational symmetry, and the students brainstormed different logos that have rotational symmetry. ( I unwittingly amused the class by playing hopelessly ignorant teacher, confusing the BMW logo with the Mercedes Benz logo.)  Before we went over the ‘rules’ for rotating coordinates counterclockwise on the coordinate plane, we explored using patty paper, and the students made observations about the pattern of the changing coordinates.   My co-teacher also demonstrated how you can hold the origin fixed with your pencil point and rotate the paper in order to record the new points.  The class had a quiet buzz during the lesson, most of which was students assisting each other while they tried out each technique.  It was gratifying to see not only that everyone was attempting the rotations [not always the most willing crowd], but that the students have been somewhat won over by the structure of the class – different groupings, including one group they have chosen themselves, hands-on activities alternating with direct instruction, and tiered practice.

The lesson finished with a discussion of clockwise versus counter-clockwise rotation, in which I learned something new (forgive me, o science teacher colleagues for my ignorance) – that water always goes down a drain in a counter-clockwise direction.  Why this is the case is a mystery to me – but I have been staring at my drains ever since.

Day 5 – TGIF!

The day began with a meeting between my co-teacher, my mentor and me to discuss the planning and administration of the class.  My mentor, as I have mentioned, is the ESL coordinator (and principal intern) who I have known for 7 years; we taught together at the high-need ‘trial by fire’ school I came from before my current placement.  My co-teacher has his own relationship with her; he is Indian (English is his second language), speaks Urdu and has been a much-needed resource for her department.  He also, as it happens, has experience teaching new immigrants and SIFE students (Students with Interrupted Formal Education), so despite his lack of formal special education training, he has spent a lot of time developing strategies for demonstrating abstract concepts in concrete and visual ways.

We agreed on a planning strategy – I would develop the overall unit plan based on the departmental curriculum, and we would each cover several topics within each unit in whatever manner we felt most appropriate given our students.  We will alternate lead teacher/support teacher based on whose lesson is being delivered, and we will include one hands-on/group activity each week.   Preparing for the Regents exam in June is a challenge we still need to address; not all students will have enough content coverage to sit successfully for the test.  How to determine which students should prepare for the test and how to prepare them is an unanswered question.  But I am glad we have a strategy of moving forward together.

In class we began a MARS formative task – I love their materials.  They are thoroughly and thoughtfully written; very rarely can you find something on line and use it ‘right out of the package.’  The lesson we are using this week is a conceptual activity on transformations.  The activity begins with each student completing a deceptively simple formative task which was actually quite a challenge for many – they were asked to describe a translation, sketch a pre-image, and rotate a figure clockwise.  Each piece of these activities was done on an adjacent but separate grid, thus requiring an additional level of abstraction.

Before we proceeded, we had a class-wide discussion on grades.  The only grades they students have thus far are from an initial diagnostic (not a grade, really), homework assignments, and our 2 Quadrantal Quizzes.  Many of them are not satisfied with their averages at present (nor should they be).  In a week’s time, however, we will have a traditional exam on transformations and a creative project – one of my favorites – the Coat of Arms project, originally shared with me by one of my pre-service professors, Sam Jovell.   These will be the major contributors to their first marking period grades, and we hopefully allayed a lot of anxiety by discussing this.

The MARS task is a two day activity, which will be completed on Monday.  After we collected the formative assessment (which will be reviewed, given comments, and returned for revision after Monday’s activity), we had some individual WhiteBoard Fun Time – perfect for a Friday.  Each student had their own whiteboard, and this screen was displayed on the board.  The students needed to determine which terms on the right were associated with each term on the left.  The Teachers Guide gives very specific ‘correct’ responses; for example, the correct term associated with Reflection is (1) A line.  But the students came up with much broader associations, which I asked them to articulate. One student pointed out that a reflection was quite often done in an axis, and that if it was in the y-axis or any other vertical line, it was reflected some horizontal distance.  Having the students justify their assertions was an empowering exercise in using mathematical vocabulary and reasoning.  So the week finished on a positive (and colorful) note.  The students were given homework to complete on Rotations on two levels of difficulty, and I appreciated the fact that the students carefully looked at which assignment they were given; some asked for the more introductory work if they felt they would be more successful with it, and others said, “I can do something harder than this.”

This class has me working harder than ever, but I really feel as if I am bringing my best game here – synthesizing a lot of what I have learned over the last eight years, and putting the differentiation, engagement, formative assessment and planning strategies into practice.  I am fortunate to have a co-teacher; logistically, I don’t think it would be possible to manage this size class with this range of ability alone.  Hey – wait a minute – that’s what I’ve tried to do before….

Thanks, Tina, for the challenge!  Reflecting on one class for the whole week has been a powerful tool for me; I may even try doing it with a different class…next month.

# Day in the Life – Day 3

I am exhausted and it is getting late, but I have to write this post tonight.  I wish I had been able to write it immediately after class, because I was having quite an adrenaline rush after our patty paper exploration.  I prepped the materials for class early this morning, knowing that every second spent in dealing with logistics would geometrically cost minutes of refocusing in class. As I was counting out sheets of patty paper and clipping them into stacks for each group, I remembered the wonderful document camera I was given by iPevo last fall.  I don’t use it often because of my peripatetic schedule, but I knew that it would be a huge support for this lesson, making it much easier for the students to create the transformations if they could actually see what I was doing with the patty paper because they have never worked with this material before.  I had enough time before classes began to install the drivers and test the document camera, so the stage was appropriately set.

When the students walked into the room, I had this wonderful photograph displayed on the board, courtesy of a tweet yesterday by Dan Meyer.   The bulb in our SmartBoard is getting a little dim, so the lights were out.  Following @ddmeyer’s instructions, I said nothing while the students began to question, argue, and debate.   We took a vote before we began to discuss which calculator was displaying the correct answer – the class was evenly split.   First we retraced the path of calculation of each calculator, and the corresponding order of operations that was being observed.  And here was the most worthwhile part of the activity – just as Tina (@crstn85) decries in Nix the Tricks, the majority of the students swore that multiplication had higher priority as an operation than division.  When I explained to them that the operations were evenly matched, and were to be performed in the order they appeared in any expression, they were skeptical.  (I think they believed me in the end.)  And then Jerrin, a rough and tough senior who secretly enjoys math, asked, “So if you were using that calculator on a test, and it gave you the wrong answer, you would lose points?”, which led to a conversation about when and how we should be using calculators.  Truth be told, I don’t know why the calculator on the left is displaying the wrong answer, and how something like that could be prevented.  I’d love to know.

We moved on to the transformations exploration.  The students were intrigued and impressed by the document camera, and even more by my ability to write upside down.  We talked about why patty paper was such a wonderful tool for exploring, how it enabled copying, tracing and measuring distance and right angles.  Caroline, completely pre-empting part of the activity, pointed out that we could fold the paper and trace a figure, and create a reflection.  She grinned every time I referred to her ‘instruction’ during class.

I walked through translations and rotations using the patty paper, demonstrating with the document camera and giving the students time to practice them in their groups (they had written instructions from Michael Serra’s Patty Paper Geometry as well).  There was a lot of quiet talking during the activity, but I also heard a lot of patty paper rustling – a sure sign that they were working their way through the exercises, and helping each other to do it.

As I’ve said before, it is a large class with surprisingly good attendance (if not punctuality).  Keeping a distractable group of kids focused while sitting in a corner in the dark with only a document camera and some tracing paper felt like a huge feat; I felt as if I had taken an aerobic class when the bell rang.   But here’s my pre-assessment evidence that the activity was meaningful to the students:  as we were winding down, I gave them some instructions for re-assembling the room at the end of the period.  I told them that the patty paper they had used was theirs to keep, and in the event that they didn’t want it, I asked them to make sure it ended up in the trash by the door.

Guess what?  When the class left, the wastebasket was empty.  I hope there is some patty paper up on some refrigerator doors tonight!

# Day in the Life – Days 1 and 2 of 5

The inimitable Tina C (@crstn85) of Nix the Tricks fame threw out a challenge on Sunday to blog the life of a single class every day this week.  I like the idea of being externally motivated to blog, because my internal inspirations come sporadically.  I also tend to wax poetic about my emotional process rather than the classroom action, so this challenge is a good one for me to refocus my writing.  Thanks, Tina!

I’m going to be brave here and write about the class where I have my greatest struggles – the inclusion Geometry class that I am co-teaching with a teacher new to our school as of February 1.  This class,  which I have written about before, is a slower track class filled with juniors and seniors whose mathematical abilities span a wide range.  I am trying to address their many needs, challenge those students who are ready for it and support those students who need more success, all while learning how to work with another teacher with a different style than mine.  A challenge for me as well as them.

Day 1

We are two days into a unit on Transformations.   I have created guided notesheets to accompany the SmartBoard files which are a big help to those students whose note-taking skills are not well developed.   I do this with trepidation, because I know that these can lead to a slippery co-dependent slope.  But given what I know about these students and the classroom dynamic, I have decided the notesheet will help them focus on the content rather than each other, and create a written product to which they can refer later.   Some students prefer to take their own notes, which is wonderful.   As the students entered the room on Monday, my co-teacher greeted them at the door with the guided notesheet (which has their Do Now pre-printed on it) in an effort to get them to work quickly.   The class was only about 5/8 full when the bell rang; getting them into the room on time and settled requires a lot of corraling.  But finally everyone was looking at their worksheet, and we began to review it on the board.

My co-teacher and I have not had a lot of time to plan together; in fact, I have done all the planning thus far, and have shared the work with him at the beginning of each week.  Being moved to our school midyear, and assigned a full Special Ed program (he is a math teacher), he was quite overwhelmed when the term began.   The plan for Monday was a fairly direct lesson on translations on the coordinate plane (we covered reflections on Friday).   He took the lead on the lesson on Friday while I ‘worked the room’, so on Monday I began the lesson.  We had not explicitly discussed how we would share direct teaching (for the most part, I had been leading the room while he provided support for the first few weeks), but so far we had worked fairly well together.  So I was a little surprised when he interrupted me while I was teaching and re-introduced the material differently.  This happened a few times; I tried to keep things smooth (even though the control freak in me was jumping up and down and screaming, “My flow, my flow, you’re interrupting my flow!”) because he needs to establish more authority in the room.  Unfortunately he leaves class a few minutes early in order to get to his next class in the basement, so we had no time to check in.   The students were focused on the lesson throughout the class, however, so I am glad that my gut reaction was well managed, knowing that it came from a place in me that needs to do some constructive communicating.

The lesson took most of the period, leaving next to no time for practice; I assigned the classwork problems for homework.  I realized that we had run out of practice time on Friday as well, after the lesson on reflections so I decided that today (Tuesday) would be a day of practicing what we had covered so far.

Day 2

My co-teacher popped in to visit me this morning before classes began; I shared with him my idea of spending class today with the students practicing in their homogeneous groups. (We have ‘A’ groups (homogeneous) and ‘B’ groups (heterogeneous, and created with student preferences accounted for.)   He thought it would be helpful for some of the students to have a cut-out shape to use in practicing their transformations – a good idea for concrete learners – but seemed reluctant to prepare the materials for this.  Mental note #2 regarding constructive communication requirement (more on this later).

When the students came in today, they were given Quadrantal Quiz #2.   These quizzes, which will be given weekly, assess mastery at 4 different levels.    I have several goals with these quizzes – the first to assess more frequently in order to gather relevant data and adapt instruction, the second to give the students more ownership over their own progress (we will be tracking the standards they have mastered in individual folders kept in the classroom), and finally help students overcome quiz and test anxiety by making it more routine.  The brevity of the quizzes keeps them accessible to everyone, and I really like having  fresh information on how they are processing the lessons.

After the quiz, I directed the students to move into their A groups to begin practicing transformations.   I had prepared two different packets – one which contained straightforward exercises in translations and reflections, and a second packet comprised completely of Regents questions – both multiple choice and open-ended.  The students got right to work.  We circulated among the groups checking and correcting homework, and providing support for the classwork.  I was very proud of how diligently everyone worked, and also that several students working on Regents packets felt safe enough to ask for the more introductory work.   While this wasn’t the most exciting work, it was time well-invested in creating a uniform level of competency with which we can move forward to more conceptual material.  And tomorrow we will spend the period doing some Patty Paper explorations of transformations – I can’t wait! – it’s my favorite manipulative.

A final note for the day regarding my co-teaching situation:  I realize that this is an area in which I need to open more clear and explicit channels of communication for the good of the students, my co-teacher and myself.  I think of myself as someone who collaborates well with others, but I may [definitely] suffer from the ‘don’t worry – I’ll take care of it’ syndrome that many competent people have.  I have been working with a mentor at my school on the overall plan for this class, and asked her for some guidance here; she offered to sit down with the two of us later this week to establish some planning, preparation and teaching routines.  I am looking forward to this; my mentor is similar to me in temperament, but has been observing the class and has a good feel for my co-teacher’s balancing strengths.

Whew!  And it’s only Day 2 of #DITLife!

One final lovely thing that happened – my younger child who is a student at MICA, created a logo for our math team t-shirts, based on requests from the team members.  Ze emailed it to me Monday night – and I can’t WAIT to wear this hoodie!

# Them or Me (working title)

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.

# A Geometry Class is Born (Part II)

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.

# Feels Like Spring (Not)

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.

# Tricks in New York

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  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.