My leap into regular blogging took place a year ago, when I had the opportunity to attend the Anja S. Greer Conference on Math, Science and Technology at Phillips Exeter Academy.  The experience of the conference was personally and professionally enriching, so much so that I was overflowing each night with ideas and reflections, and managed a detailed daily post.  So affected was I by the opportunity provided by the conference to learn, collaborate and connect that I spent a lot of time and energy trying to get back there this year.  Last week that happened, and it was as wonderful an experience as the anticipation warranted.

I attended the conference this year with a friend and former colleague, which added another dimension to the experience – sharing something wonderful with a friend.  You don’t really know how well you get along with someone until you travel together, and I learned how compatible we actually are – our conversation flowed continually, tangentially, and effortlessly, making the road trips there and back easy, and we shared both ideas and new acquaintances as we experienced the conference separately but in tandem. Another big plus  this year was being reunited with a kindred spirit on the Left Coast  – someone who I met last year but felt as if I had known for a very long time.  So, before even thinking about the rich professional and mathematical experience that the week provided, my soul was personally soothed and enriched.

At the Exeter conference, participants take 2 week-long courses, sit in (voluntarily) on 45 minute stand-alone sessions which run throughout the day, and attend evening programs with speakers.  This year, Geometry was the ticket for me – my 2 classes were ‘The Geometry of Origami’ with Philip Mallinson, an Exeter instructor, and ‘Geometry Labs’ with Dan Butler, a public school teacher from Minnesota.   I came away from both of these hands-on classes bursting with ideas and energy to push the geometric envelope a little further in my classroom.

In the origami course, we began by doing some proof regarding folded paper, and I learned an amazing fact about A-size papers – which may be common knowledge, but not to me – that the ratio of the sides in all of them is 1:√2!  Think of all of the math problems we could do with PAPER ALONE if we used these sizes!  But I digress…we explored patterns created by ‘flattening’ folded figures, the ratio/relationship of the number of mountain versus valley folds, and finally, did some origami.    The conversation in the class, expertly and humorously facilitated by the teacher, flowed easily – participants posed questions and made conjectures which the rest of the class immediately explored.   I have since purchased Project Origami by Thomas Hull, some origami paper, and will be engaging in some folding on my own very shortly.   As a result of the infectious enthusiasm of my instructor, I went to see the Surface to Structure exhibit at the Cooper Union, which was nothing short of awe-inspiring and mind-blowing (images at conclusion of post).

Last year, I became friendly with someone in the Geometry Labs course, and was completely envious; my experience this year confirmed exactly what I had imagined the class would be, and it was, from start to finish, a delightful and enlightening experience.  First and foremost, the instructor, Dan Butler, has an open, warm, and engaging teaching style.  He very rarely gives answers (someone after my own heart), but rather prods students into working through their wonderings.  He is continually good humored and generous with both time and supplies, and has a way of making every student feel acknowledged and heard.

Our activities during the week included hypothesizing why a snail ball won’t roll down a ramp, calculating the distance required to have a marble sent down a chute land in a cup, problem-solving with Taxicab Geometry,  discussing the implementation of Gateway Exams to ensure basic skill competency, identifying changing patterns and shapes created by the shadow of a stellated icosahedron, and modeling with Geogebra.   And in between activities, or waiting for class to start, we attempted to solve cube puzzles made out of tetrominoes.  We spent one full class period working on the multi-level Goat Problem – how to determine the grazing area of Billie the Goat as her tether was repositioned relative to barns of various shapes.

 

 

 

 

 

 

Dan offered an extra-curricular activity as well – creating our own stellated icosahedra.  Using string and straws from the 99¢ store, he opened his classroom for three afternoons between class and dinner, and coached us through their construction.  [I do not have written instructions for this project, unfortunately, but there are a number of examples out there on the Interwebs.]  There were always other participants in the room –  discussing problems from class, working on other experiments, or just hanging around.  It was easy to envision Dan’s classroom at school filled with students all day long; he creates that kind of welcoming space in which everyone feels comfortable and wants to participate on some level.    At the end of the week, Dan held a lottery for his samples which were created with FANCY hard plastic straws (from Party City), and which he did not want to fly home with.  Lucky me!   Lots of geometry swag for my car.

Another highlight of the conference (I really should have written some interim posts; I see that clearly now..) included a lecture on The Future of Learning by Alan November – a thoroughly engaging speaker who explored increasing students’ abilities to self-assess and teachers’ skills in providing meaningful feedback.  Alan is one of those people who spout ideas as quickly as you can write them down (for me, anyway) – including resources like kaizena.com, clubacademia.org, and mathtrain.tv.  He reminded us of that which most math teachers have – The Curse of Knowledge – and probed the eternal questions of how to (a) motivate students and (b) get them to do more than you actually ask.    This RSA video by Dan Pink reflects a lot of his thinking.

I also attended a CwiC session (Conference within a Conference) offered by Frank Griffin of the Cate School which was chock full of tips on ‘Animations, Simulations, and Visualizations.’  While many of the resources Frank presented were ones with which I was familiar, he showed specific applications of particular features which enabled me to actively envision using them in my classroom.  A partial list of these resources includes SmartBoard algebra tiles, Proof of the Pythagorean Theorem on hotmath.com, the Wolfram Demonstration Project, and some spiffy uses of TI Smartview.  This was another workshop which had be writing as fast as I could.

If you’ve managed to slog all the way through the content, now I’ll tell you about the magic of the conference.  Phillips Exeter Academy is in a picture perfect New England town and we were blessed this year with lovely cool weather.   The school itself is beautifully maintained; the dorms are basic and clean, the academic facilities are state of the art, and filled with visual and academic surprises (see my posts from last year for some of these).  There were 5 different education conferences running simultaneously: the math conference, a biology conference, a writers’ workshop, a humanities conference, and a diversity conference.  We wore nametags all week, and each conference was identified with a different color lanyard.  This year, the main dining hall was under construction, and meals were relocated to a smaller facility, which was a bonus in disguise – there was much more inter-conference mixing and discussion than before.  I loved hearing about how the writing teachers had to awkwardly share their own work, or sharing concerns about identity with the diversity conference participants.   On the last two evenings, we ate dinner out on the lawn in the quad – and it was a sight to behold.:  400 teachers, all engaged in intensive professional development, having the time of their lives.   We all deserve – and need – opportunities like this.  We can most effectively help our students learn when we are better prepared and engaged as teachers.  And being sent to conferences like this gives teachers the message that they are worthwhile, that their ongoing professional development is critical and that their role as educators is as highly esteemed as it should be.  Children are the future – how the ongoing education of their teachers can this be any less important? 

Attending the conference this year was not easy – I had to search for funding, and fight for the days to attend.  When I first arrived, things had a bittersweet feel, because attendance a third year in a row seemed impossible.  I left with the conviction that it is mandatory.

 

IMAGES FROM SURFACE TO STRUCTURE EXHIBIT

 

 

 

 

In the long 6 weeks since my last post, a lot has happened, both in my Geometry class and outside of it.*   The last time I wrote we were in the throes of similarity, struggling with the most difficult of theorems.   Out of the frying pan and into the fire, we moved on to circles after spring break.  I knew Circles would be no picnic either; students who have had difficulty pulling apart sketches of triangles and parallelograms can become overwhelmed by the complexity of the circle problems.  We worked our way through the unit slowly – one day of concepts, two days of practice; I felt like I was keeping the students moving through sheer force of my will (to their credit, they continued to persevere), until we reached the more difficult angle and segment problems.    With the end of the term in sight, I knew it was time to begin a final assessment.

The course terminates in a Regents exam, but the class is split 50/50 along the line of will or won’t take.  For many of my students, the exam they have already passed (Algebra 1) fulfills the graduation requirement, and they have no intention of sitting for another test.   But the other half of the class wants to take the exam (or, in my opinion, should challenge themselves to prepare and take it), and needs a lot of preparation.   I need to somehow measure the growth the students have made over the term, as well as the first 2 terms of the course; the traditional assessments done in class have not yielded great results, but I know that they have been learning.   Conferring and brainstorming with my colleague, I reached into my pedagogical carpetbag (a la Mary Poppins) and decided to put together what was dubbed at a former school of mine the HOTS and LOTS chart.

 

This acronym (referring to Higher Order and Lower Order Thinking Skills) is a huge choice board.   It has 8 columns, one for each major unit, and 5 levels of complexity, very roughly aligned with Bloom’s Taxonomy.  The students need to complete one activity for each unit, including only one at the lowest level and at least one at the highest level.    I’ve spend an inordinate amount of time over the last 8 years searching and saving resources, and had a nice selection of activities from which to choose.  I created a rubric and a log with specific instructions,  put samples of each activity in color coded plastic sleeves, created new work groups, and prepared to launch the project.  For those students who were going to prepare for the Regents exam, I have 8 Review sheets comprised of past Regents questions.  They will work through the sheets one at a time, and each will be graded.   They will have the benefit of cooperative groups and classroom resources (which includes teacher assistance).  And they get a log, too.
So we launched the final project last week.  We spent one day discussing the whole idea of the final assessment, and the students had a chance to review the choice board and look at the sample activities.   They asked good questions, like whether this project could save them from failing (the answer being yes, if their work substantiated growth), and could they do the project and take the Regents exam as well (of course!).  As the students were milling around looking at the activities, I observed them, a little nervously, but with excitement.   I knew that everything I have been doing for the last 8 years has prepared me for this – crafting an activity that meets a wide range of needs, involves student choice (and thus higher engagement) and accountability, and sets the stage for what will hopefully a great learning experience for everyone.  I looked back on all the noble failures (a.k.a. learning opportunities) I had over the years, and all the nuggets I squirreled away from blogs, TED talks, twitter chats, and articles, and knew that I was bringing my best game to this class.

Next: what actually happened.

*I made this quilt.

Today 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.  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.

I 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.

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.

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.

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.  

 

 

 

 

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.

The 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.