Flailing About

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

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

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

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

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

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

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

Feedback is ALWAYS welcome.


One of My Faves

Just wanted to share, on a positive note, one of my favorite discovery activities on Compound Loci.  It’s accessible, fun (anything with markers is), and brings home the big idea clearly and visually.  Fun times in Geometry today.  Here’s a link to the pdf.photo 2
photo 1

Geometry Update

It’s been a while since I wrote about my problem child – the super multi-level Geometry class which I co-teach, and to which I am dedicated not only as a matter of course, but as a matter of principle as my principal (sorry!) seems to believe that ‘lower third’ students don’t need Geometry.  We completed a unit on Transformations successfully; the students not only performed well on a standard assessment (exam), but also created some lovely Coat of Arms projects.  photo 1 photo 2 photo 3 photo 4 photo 5





The class runs fairly smoothly on a daily basis, and there is a comfort level and mutual respect between the students, and between the class and me.  My co-teacher has not fared as well, unfortunately, despite our efforts to demonstrate to the students that we share leadership of the classroom; he has conducted lessons, circulates regularly, greets students at the door, and assists them during group work.  But when I am not in the room (as during a recent sick day), he is unable to keep them working.  Perhaps there needs to be two teachers in the room at all times.  I’m not sure.  I do know, however, that the classroom would not run as smoothly if he weren’t there.

Intro Similarity Guided NotesThe unit after Transformations is on Similarity, and it has been tough going. I have been using guided note sheets to facilitate the note-taking process.  But what started as a welcome support, I find, has become a rote activity which can replace actual participation in the classroom.  Most of the students follow along the lesson and fill in the sheets, but many don’t seem to be processing what they are writing, and/or misplace the sheets after the lesson.  The students who are using them as I intended, as a resource to which they can refer, would probably take thorough notes without them.  Yesterday, I was trying to finish reviewing the similarity shortcuts [thinking to myself how boring my delivery was], and ran out of time for any substantive practice.  I left the class dissatisfied with the direction the class has taken.

I need to interject here that the direct lessons are interspersed with groupwork and explorations, such as this volume/area/similarity exploration we completed the day before.  But I can’t seem to get a rhythm I am happy with in this unit (I didn’t feel this way during Transformations).  During my Common Planning meeting yesterday, I met with my mentor to discuss progress, or lack thereof, and to re-adjust the overall plan for this class.  She has conducted weekly observations, and her feedback has been supportive and invaluable; she always points out the ‘bright spots’ she sees, and her method of brainstorming is to elicit ideas from me and offer broad suggestions, which we then discuss and rehash until a clear direction emerges.

She also noticed that the notesheets, which had been so helpful a few weeks ago, seemed to be dragging the class down.  I decried the lack of practice time, during which I felt the students would be more engaged with each other and the content.  I realized, as we were talking, that walking through the Similarity shortcuts as theorems was not a fruitful exercise [I think]; we will spend very little time on formal proof of similar triangles, and a lot of time problem-solving, in both applied and abstract exercises.

What is the best way to deliver this content?  The explorations are engaging, but don’t necessarily lead to the specific conclusions that I want the students to be able to apply elsewhere.  And clearly many of them need a lot of scaffolding in order to complete the practice exercises.  My mentor suggested that I give the students the practice work and resources for the required content, and let them work in groups to complete them.  With two teachers in the room, and an introduction to the material, as long as they were cooperating with one another, she believes, they will make progress.  Work can be differentiated according to our observations and the individual learning goals of the students.  And we can debrief, share, recap – whatever – as a class to review any new ideas that are central to the work.

This idea was born out of the need for us to complete the curriculum for those students who were planning on taking the Regents exam, and a desire to give all of the students an appreciation for Geometry and more confidence in their ability to progress in a math classroom.

Finally, I want to create opportunities for those students who are not satisfied with their grades to demonstrate progress in a manner that they have more control over.  I thought of tossing the ball into their court, and telling them to figure out a way to show me this, but again, I know this will be a huge challenge for many of them (especially those that need this option).  One option is to create a choice board that will provide rigorous but approachable activities from which they can choose.

I know these are all good ideas, but here’s the thing, right now, at the end of March:  This is one prep of three that I have this term, including a class I have never taught before.  This class has taken all of my energy and resourcefulness, and to be honest, I am feeling somewhat burnt out.  So I am looking for suggestions, reflections (beyond these), any ideas related to how to keep this class vital, differentiated, rich in Geometry, while ensuring that I make it through the year.


#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 Imagelogo.)  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.  Image

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.  ImageThe 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.

ImageWhen 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. Image

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

Screen Shot 2014-03-03 at 7.57.33 PMThe 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.download

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!