Not going to jinx it but…

CafKo6RUkAAGETRThe fall term finished amidst a lot of anxiety – students anxious about their grades, me anxious about their reactions to their grades. Regents week was surprisingly restorative, and I was able to give a lot of thought and attention to what I wanted to change/try/implement in the spring term.  I am teaching, in addition to Algebra 2/Trig, two sections of the ‘non-Regents’ Geometry course.  This was a course I developed last year, but the pacing and units have been changed to be better aligned with the Common Core standards.  Thankfully, the composition of the class has changed as well.  Last year, the roster included a combination of sophomores who were perceived to be unlikely to succeed in the Regents class, off-track juniors and seniors who needed a math credit, as well as an over-compliance-limit number of students with IEPs and English Language Learners.    This mixture made for some very interesting times in class, but you can look in my blog archive if you want to read more about the past.  This year, the students programmed for the non-Regents Geometry class have come through a four term Algebra 1 class (don’t ask), and, for the most part, are on track for graduation.  Because of my Problem-Solving elective, I didn’t teach the first term of Geometry, but the reports on the fall classes from the two teachers who did were good.  I want to keep this momentum going, so I spent a lot of time visualizing lessons that were accessible and rigorous, with students doing the heavy lifting in class rather than me.  The first unit includes right triangles and trigonometry, and begins with a rather very dry topic – radical expressions.

Not only can radicals be a difficult topic to motivate, but the range of student experience and understanding can be very wide; this is a topic this is included in the Algebra I curriculum.  My lessons needed to be intriguing enough to keep those students who remember the content engaged, while opening the door for those who do not remember, or perhaps never understood it in the first place.  Thanks to the master of creating interesting activities out of even the driest of topics, Don Steward, my first two lessons were well-structured, well-scaffolded, and engaging.  And thanks to starting the term with the 100 number activity shared by Sara Vanderwerf and Megan Schmidt, and classroom seating using  Visibly Random Groupings every day, my students are already talking to each other mathematically, as well as beginning to work cooperatively and supportively.

UntitledBy opening with a warm-up which related square roots to area, I was able to give the topic a visual context, as well as introduce the idea of a cube root.  We reviewed perfect squares through 144, and I was impressed to see how seriously the students were taking this content that I am certain they have seen before – without being prodded or asking “do I need to copy this?”, they all created tables of the perfect squares in their notebooks.  [Side Note: I am going to do a modified INB in this class (I’ve been given notebooks and supplies thanks to  a Donorschoose grant which was funded Untitled2in record time!), easing up on page numbers and exactly copied content.] We then looked at determining between what integers some irrational square roots fell, which helped the students understand that not all numbers have perfect squares, but still have square roots.  The final activity on the Untitled3first day of the lesson was an exploration of the representations of square roots.   It was great to hear the students working together on each of these small activities.  I had some challenge worksheets in hand for a few students who knew the content fairly well, but needed both review and to be more deeply engaged so as not to hijack all class participation.  This intervention, too, was successful. (Dare I say ‘score!’?  I don’t want to tempt fate.)

Picture8Today we continued with simplifying non-perfect square roots.  Again, student understanding at the outset of the lesson ran from a truthful “I know how to do this already” to evident misconceptions.  Despite the fact that a lot of the content on this warm-up previews next week’s work, it got most of the students working – even if they didn’t remember exactly how to simplify radicals, they began messing around with the first example.  The increasing difficulty of the problems kept the students who were ready interested.  I wrote the perfect squares through 144 on the board for reference in looking for perfect square factors, although [and I’ve seen this before] most students resist using that support and instead use guess and check with a calculator.  When they worked on p204some practice examples, I gave them the worksheet in a page protector with a dry erase marker, and distributed only enough so that they needed to share.  Friday afternoon before a long weekend, after a very snowy morning – they worked all period.  I’ll take it.

An interesting note regarding the puzzle worksheet (I’m sure you’ve seen these or some like them; a successful solution to all problems rewards the student with a silly pun.  However, for my English Language Learners (13 of which were put in the same class without any kind of heads up to me), the puns are meaningless.  I think there’s a literacy lesson in here for me to develop.

A huge amount of thought went into these lessons on my part; I’ve taught radical expressions almost every year of my teaching career (now numbering 10!) but these lessons were more engaging, I think, for the students AND for me.  I like that I was able to improve on something I’ve done so many times before, even with borrowing all of those wonderful materials, and I’m pleased that I saw an appropriate result.  I’m looking forward to revamping more lessons for this group of students – their involvement and effort is a wonderful reward.


#MTBoS 2016 Blogging Initiative Week 2 – My Favorite


I’ve been watching the posts on this topic go up all week, and, as usual, have been taking notes on the wealth of resources my online community has been sharing.  It’s been a rough week, despite the Monday holiday; it’s been an end-of-term-grade-anxiety, getting-over-stomach-virus, finally-winter-has-hit kind of week, and to be honest, nothing was feeling too favorite to me except the weekend ahead (and delicious it is, I must admit, cozily watching the snow outside).  But I realize now that I have had a chance to breathe, that there are MANY things that are favorites of mine, so I’m going to highlight just a few of them.

My Favorite Strategy/Routine I love my weekly math maintenance routines.  Regardless of the group of students working on these, the engagement level is high.  I didn’t invent this202_answerstrategy – it was gleaned from at least one of my colleagues in the Blogosphere -most notably, Jessica over at Algebrainiac.  And my favorite part of this weekly routine?  My students inevitably ask me if I am making the solution videos over
at  These oh-so-cynical children became quite passionate this year over the legality of stirring down the marshmallows so that they melt a bit in order to fit more into this cup of hot chocolate.  Fun times.


‘Fata Morgana’ by Teresita Fernández at Madison Square Park

My Favorite Site for Last Minute Resources Hands down, this has to be Don Steward. Whenever I need something for a challenge,  a little differentiation, a different entry point, or another way to look at/practice a familiar topic, this is the place to go.  Where does he come up with these things?  Where do all those great banner images come from?  I don’t know the answer to either question, but I do know that this blog never disappoints.

IMG_7067Favorite Classroom Moment(s) Even though at times it has been the bane of the semester, my 6th period problem-solving class has also provided some of the term’s best times.  On several occasions, the solution paths to problems posed in this class have sparked huge debate.  The kids love to complain about the work, but when I distribute the problems for insertion into their notebooks (there is nothing like glue and scotch tape to unite a fragmented table of kids, even at age 17), they immediately begin cutting, pasting and arguing.   The conversation over City of Truth versus the City of Lies from Math is Fun (another great resource for challenges AND content) can only be described as passionate and delightfully cacaphonous. Screen Shot 2016-01-23 at 1.42.29 PM

Non-Math Class related Favorite Video of the Week I haven’t been watching Stephen Colbert since he made his move to late night network TV, but this video may have changed all of that.  Makes me laugh out loud every time I watch it, and I’m up to my fifth go round so far.  Cheers!

A Day in the Life

It’s 6:40 am and I’m waiting for the next bus, having missed the last one by seconds.  It’s been that kind of a week: a stomach bug combined with January blues/end of term apathy.  I’m hoping this day gets some zing to it – after all, it’s my blogging initiative img_7038kick-off! – but on a cold Friday when you’ve been sick, well, some teacher days are just like that. Best part of early morning commute:  quiet.


Today is staff college pride day; I don’t actually have garb from my own alma maters so I am sporting a Rutgers t-shirt, with a large red R emblazoned across the chest (ubiquitous on campus) for Marilyn,  layered with a modest grey sweatshirt with the artfully quiet MICA logo, for Geo.  In case you’ve never read my blog before, I’m pretty proud of both of those kids and their educational accomplishments.

IMG_7040Two relatively brief bus rides and I’m at school.  The sun is up (almost), and I’m looking forward to my first Algebra 2 class; they’ve been a great group to start my day with this term – hard-working and always willing to try.  Plus they get my jokes, such as they are. You can’t ask for much more than that at 8 am.  I’m going to try my best to spice up higher degree polynomials for them.  A puzzle? A game? Card sort?

Once I’m in my office, with 35 minutes to the first bell, I decide re-inventing today’s lesson is not the best use of my time; I’d rather take the opportunity to open the floor to some college-bound conversation.  I cue up a range of animations that Geo has producedIMG_6858 copyat MICA; I know on a Friday morning, the students will find watching them a treat (as will I).  I head down to the classroom with my trusty cart-o-supplies (bottom left of photo), looking forward to the cheery greeting I always get from the early crew.    I treat the early-comers to a brief animation – Geo’s work with scientists from NASA working on the Fermi Telescope.

As the kids pile into the room, they begin pulling out the tasks that are due today, and comparing work.   I’m excited to see what they’ve done with this assignment – I’ve named it “Jeopardy”; I supplied four answers with accompanying topics – they need to write the questions.  I’m looking forward to blogging about this after I’ve gotten a look at their work.

They settle down, and the lesson begins.  It’s not a favorite of mine – reviewing a lot of procedures for finding the roots of quadratic functions and applying them to functions of higher degree – but the kids need the review, and to be honest, I’m not up to a super creative discovery lesson after this week.  I’m pleased to see the students working together, going through their notes, and synthesizing the many bits and pieces relating to functions as we work through examples together.  They are, as I have said, a good-natured crew, and I make a mental note to do something nice for this class to thank them for starting my days well this term.

With a few minutes to spare in the period, I briefly share my educational resume – the school I most recently attended (Pace University) and those not so recently, SUNY Albany and Columbia.  I spend more time telling them about MICA and the Mason Gross School of the Arts at Rutgers; I think it’s as important for them to hear about creative fields in education as it is for them to think along specific career paths.  And I give them one more video.

The next class is pretty much a repeat of the first, although my third period students are a little bit more serious than the previous bunch.  I don’t know if it’s the hour, and they’re more ready to work, or the children themselves.  This class does benefit from my running through the lesson once already – even though I’ve taught these lessons before – we may, on occasion, dig into the content in greater depth because of this.  Predictably, perhaps, however, my relationship with the first class is warmer.

After the first 2 classes, my teaching day is 40% over.  And it’s only 9:40!  (Isn’t math grand?)  I have a double period free, which allows me to really dig into grading, work with students, read, plan – whatever the order of the day is.  Today,  some logarithm exams beckoned during the first half of my break .  I was pleasantly surprised at how well many of the students did on the extended response portions of the exam, and how efficiently the grading went.  Such will not be the case with the aforementioned task;  a creative assignment SHOULD MEAN widely different submissions, requiring a lot of individualized grading.  My rubric will hopefully stand me in good stead.  During the second portion of the break, my two monitors, Rachel and Tiffany joined me.  These girls are juniors in one of my Algebra 2 classes.  They are both transfers from another high school, and lovingly do whatever task needs done –  updating iPads, taking things out and putting other things in to page protectors, picking up photocopies, and cutting worksheets with the paper cutter (this is, interestingly, their favorite…)download.  They never take advantage of the fact that they are in my office and have access to – well, everything, and they are as reliable as the day is long.  I miss them when they have lab on Wednesdays.  Today, after the requisite errands, they asked me to look at their exams.  We went over them together, and while they were not 100% happy with their own performances, they characteristically did not try to exert undue influence.

The other 60% of my teaching load occurs in a long block after this break.  I teach two classes of Problem Solving, and finish the day with one more section of Algebra 2.  I’ve written mostly about the Problem Solving classes this term; my relationship with them is, sadly, frequently unpleasant.  With six days in the term to go, the students were working on a problem set utilizing the strategy “Identifying Sub Problems”.  In an effort to elicit original work from everyone, there were four versions of the worksheet (similar problems, different numbers).

Attendance has dwindled severely in these classes, but those students who are coming to class are working – many in an effort to keep their grades above 65.  Most of the students who are working require a lot of support, which I am happy to give.  I won’t reiterate my disappointment with the classroom culture that has evolved in both sections, although there is a perceptible difference between them.  In the earlier class, despite my frustration with the work ethic I have not been able to elicit from the students, I have a fairly open and honest rapport with many of the kids, and there is, ironically, mutual appreciation and affection.  The students know that my behavior in the classroom comes from a belief in their native intelligence and a refusal to let them off the hook regarding what they might claim is a lack of ability.  And even though they might wish I would give them a passing grade and leave them alone, they respect my appraisal of their intelligence; many, many teachers do not give them that benefit of the doubt.  However, this is not the case with the students in the later section of the class.   I have not been successful in getting many of these students to shut off their phones, do their own work, or accept my guidance.  I know many of them think I am unfair, and plainly, a pain in the ass.  I’m not going to belabor it any more.

My final class of the day – another section of Algebra 2 – has a different flavor than the morning sections, and affirms my belief that high school math classes can be most successful before 11 am.  They are an engaged group of students, and work well together, but the energy level in the room after lunch time is not always well suited to deep mathematical thinking, especially on a Friday.  We talked at the start of class about college options – this class actually questioned me about the sweatshirt I was wearing before I introduced the topic.  The kids were very interested in the creative paths my own children took – after all, they (my progeny) had a math teacher as a parent, went to well-respected public high schools in New York City, and were making their way with artistic rather than professionally oriented majors.  I loved the thoughtful looks on my students’ faces as they asked questions and digested the answers.  Afterwards, they worked their way steadily through the lesson described earlier in this post (oh too many words ago) in order to watch Geo’s JuniorThesis animation, definitely posted here before.

I finished my day at school bubbling in my attendance sheets, grading a few more exams, and checking in with my new colleague who is struggling with a tough program – a lot of slower track Algebra 1 (who thought four terms of Algebra 1 would be a GOOD idea for ANYONE??) and some off track seniors.  She came from a very rough high school, so this placement may be less stressful, but she’s definitely not been given any slack in her course load. Politics sucks.  I made sure my supplies were on hand for Tuesday’s classes, and closed up shop in the Bat Cave, as my office is affectionately called.

I actually made it out of the building at a reasonable hour, savoring the start of the three day weekend, and contemplating the long view of the last week of the fall term.  It’s been an intense one, personally and professionally, and to be honest, I can’t say I’m unhappy it’s almost over.  The good thing about teaching – we get do-overs every term, every week, every day.

If you’ve read this far, well, thanks for sticking through it with me – a day in the life of this teacher.  It’s a ridiculously long post, I agree – but it only reflects the nature of the work.  How does that saying go – you don’t have to be crazy to teach, but it helps?

And here’s a animation for YOU!


Proud Participant of the 2016 #MTBoS Blogging Initiative

I, Wendy Menard, resolve to blog in 2016 in order to open my classroom up and share my thoughts with other teachers. I hope to accomplish this goal by participating in the January Blogging Initiation hosted by Explore MTBoS.

You, too, could join in on this exciting adventure. All you have to do is dust off your blog and get ready for the first prompt to arrive January 10th!


Why I love logs

I have had two wonderful days of discovery and student-centered learning while introducing logarithms in my Algebra 2 classes, thanks to Julie Reulbach and Kate Nowak.

Last month, Julie asked me for my log word problems (which include zombie attacks and other infectious issues). I usually use these after I have introduced logs, but ever-wise Julie used the problems to create the NEED for logs. Brilliant. Using Julie’s idea, I modified my original lesson similarly.

Screen Shot 2015-12-19 at 9.04.00 AM

The students intuitively realized that they were using the inverse of an exponential function – several wrote the equation quickly (and then proceeded to use guess and check) or created a table. Those students who made tables saw that the answer was between 7 and 8 hours, but when I told them I needed a more specific answer, they, too, moved to guessing and checking. (This process led to a nice mini-lesson on the use of the TABLE and TBLSET functions on the graphing calculator.)

After reviewing the answer to the problem, I moved immediately to Kate Nowak’s Super Fun Log Puzzle.  Screen Shot 2015-12-19 at 9.05.36 AMThe kids worked through the ‘puzzle’ fairly quickly, and were able to articulate what they were doing. When I revealed that they could replace the word ‘power’ with ‘log’ – well, I love that moment – the moment that they realize that something they thought would be difficult wasn’t really that bad, or that their friends were wrong when they said logarithms were log10_tables_4_figureterrible and mysterious. [There is a moment in the lesson when I show them a log table from the back of a textbook – the kind I used back in the day. They are suitably horrified by life before epidemic calculator use. Another moment I love.] And the room was filled with math talk all day long – students helping students, students arguing with each other, students making sense of something new. A pretty easy day for me as well.

Today, I followed up with another of Kate’s activities (I owe you SO much, @k8nowak!) – discovering the properties of logs. The students began the work the moment they entered the room, and they were engaged in the process all period long. I steadfastly bounced all questions back to them, referring them to their tablemates as resources. I nipped calculator usage in the bud, except as a checking device.

Screen Shot 2015-12-19 at 8.56.30 AM

And, as I tweeted earlier, all I did was walk around the room listening for 30 minutes, occasionally redirecting if I saw a table going seriously off track, or asking some pointed questions to spark some recognition. Towards the end of class, we recapped their discovery as a whole class, and the relationship of the ‘laws of logs’ to those governing the use of exponents were universally clear. And the concept of inverse functions was reinforced once more, when viewing the relationship between logarithms and exponential functions.

After the difficulties I’ve been having in my problem solving classes, hitting a home run three times in a row in the Algebra 2 classes felt as good as you might imagine it would.

At the end of the day, I found myself in a conversation with an officemate who teachers Honors Pre-Calculus; he is finding that his students are weak in the skills that they should have mastered in Algebra 2, surprisingly so for that level of class. These are the students who will be going into AP Calculus next year, one third of them into BC Calc in fact, and this teacher is trying to strike a balance between making sure that their requisite skills are strong enough to handle the difficult conceptual work to come. He cited logarithms as a particular area of mystery and antipathy for his classes. I shared these lessons with him (the lessons are quite unusual in my school in their level of discovery), and I could see that, like the zombies, the idea might be infectious.




A Very Disturbing Week

   I was not in school on Monday when report cards were distributed.  I knew I would have some unhappy customers; several of the off-track seniors in my Problem-Solving class earned a grade of 60 in the second marking period.   A grade of 60 denotes that the student is not currently passing, but that there is an expectation that, with some effort, they can bring their grade up to passing by the end of term (January), as opposed to a grade of 55, which indicates that passing is not as likely.

When students are not quite on the cusp of passing, especially when they are seniors who need a particular credit for graduation, ’rounding up’ to a 65 is a dangerous thing to do in Marking Period 2.  Many of these students, given a passing grade, are confident that they have completed what needs to be done, and will exert minimal effort in Marking Period 3, which can cause their average to drop well below a passing percentage.  This not only creates a very unpleasant surprise for the student, parents, and guidance counselor, but also threatens the student’s graduation (there may not be enough math electives for them in the spring term), and quite frequently results in the teacher looking for some alternative assessment by which the student’s work can be deemed ‘passing’ without feeling like she gave away a grade.  Because I volunteer to teach math electives frequently, I am very familiar with this scenario, and usually have some ideas for alternatives in my back pocket for eleventh hour solutions.

In my Problem-Solving course this term, I have accepted [very] late work, and have created as many opportunities as I can think of for students to legitimately demonstrate that they are, indeed, trying to solve problems.  But as I have written about in prior posts, I have had serious classroom management issues this term – excessive and consistent lateness, minimal effort extended to complete work, cell phones, cell phones, cell phones, and socializing.  And I have encountered a lack of respect for the classroom and me that is disturbing in its depth and occasional animosity.  I pride myself on being respectful and caring towards my students, and have had that attitude reciprocated toward me.    I don’t take this behavior personally (most of the time); my students have many obstacles to deal with, and my math class is just another one on the list.  That said, it’s still pretty damn unpleasant.

The students who aren’t passing usually acknowledge their role in the low grade, and a number of them pointed out to me today how they are ‘doing their work now.’ So the first thing that’s disturbing to me this week is what they believe constitutes ‘doing their work.’  I model, I give them room to collaborate and discuss, I circulate, scaffold and differentiate in my approach, but for a whole group of kids, the standard of work I require is unacknowledged.  Has the bar been this low for them all along?  Is this acute senioritis?  How am I missing the mark?  The book An Ethic of Excellence haunts me;  I have what remains a fantasy of inspiring and leading my students to new levels of work, but the result eludes me.  And the gap between what they think is acceptable and what actually constitutes evidence of effort and understanding is too wide for me to be satisfied with the results of my teaching.

So this whole scenario weighs on me.  But what happened this week has unnerved me and left me thinking really hard about this communication gap.  One of the students who earned a 60 – a student with whom I had friction earlier in the term and with whom I thought I come to a detente – was enraged by his grade.  He came to class on Tuesday, when I returned, and accused me of lying; he told me (repeatedly) he would not let me teach the class until I explained why I was lying about his grade.  I offered to speak to him privately, but he continued loudly and threateningly in this vein, indeed preventing me from teaching, blocking me up at the front of the classroom.  I had no choice but to have him removed from the room.  This specifically directed unappeasable rage is a first in my ten years of teaching.

The student, as it turns out, has failed three classes this term (all with a 60), and created a similar scene in another class.  He was in the building all week, but did not return to class.  To be honest, I was concerned about his behavior if he did come back – the depth of his anger and his refusal to listen to anything I had to say left me wondering what I could possibly due to begin to fix this.  I reviewed his progress report, went through his notebook and classwork folder, and verified that his grade was accurate.  The dean’s office was able to reach his mother (this took a couple of days) and scheduled a meeting for this morning.  I came prepared with the progress report and copies of make-up work for him to complete which would certainly bring his grade back up to a passing level.

The student – who did not acknowledge my presence, referring to me as ‘she’ – repeatedly said that I was lying, that he wasn’t going to talk about it, that all his work had been done, and that I was lying, lying, lying.  He said he wouldn’t make up any work because I was a liar.  And the force of his anger was palpable, although it was unjustified.

I left after I told the dean and his mother that the student could make up the missing work; sitting there and being called a liar repeatedly – without being able to respond – felt awful in a way I’ve never felt before.  I wonder if my students (and perhaps this boy in particular) ever feel like that, or if they feel that way often.    I was unnerved, to say the least, by the meeting, and it is a feeling I have not been able to shake.  I believe that this student did not earn a passing grade in my class, and has not been doing a passable level of work since his grade of 70 in the first marking period, but clearly he sees things quite differently.

So putting aside this particular situation, I question whether my students have a misconception of what is required of them, or acceptable, regardless of what I believe to be my clarity, both written [course contract] and spoken.  [I’m using ‘I’ here because I don’t want to presume that my situation is broadly general, but I do wonder if it is.]  I know there is no magic pill, but I wonder what techniques or procedures I can use to reinforce these expectations, because I believe that beyond my classroom, the students need to be able to make sense of what is expected in them in college, on jobs, in life.  And I am looking in the mirror and trying to figure out what it is I am and am not communicating.

If I have any goal as a teacher, it is to show my students that they are capable of good solid work, of learning math and solving problems regardless of their experiences before they entered my classroom.  This term I am failing to meet that goal in the Problem Solving classes.  If I can fix things for some children now, that would be great, but at the very least, I want my failure to be a learning experience for me.

I welcome your thoughts.

Restorative Professional Development

by geosaurus

I don’t take any opportunities for granted, because not everyone gets them, and I’m feeling a little ‘Dayenu’ at the moment – or maybe a lot –

  • Getting to go to the Exeter Math Conference two summers in a row should have been enough –
  • Meeting a whole lot of awesome tweeps at TMC13 in Philadelphia should have been enough (well, not really…there’s the two I have missed since then) –
  • Going to PCMI last summer – truly, truly enough –

but then I had the opportunity to spend a lovely weekend getting another taste of the summer math teacher camp extravaganza at a boarding school which looked like a cross between Hogwarts and a whiteboard showroom.   The weekend was professionally and FullSizeRenderengagingly run by Tina Cardone, Brian Hopkins, Cal Armstrong and Jennifer Outz, and it was wonderful to reunite with not only PCMI folk I met last summer, but also some tweeps who I had met in Philadelphia in 2013, or never met in person at all.  I’m truly grateful for all of this. 

We spent approximately half of our time working a set of problems put together by Brian whiteboard hallwayHopkins, involving pennies, modular arithmetic, and combinatorics (or not), and a kinesthetic exploration called “Duck Duck Die” (I was the last one alive once!).  These problems pushed me out of my comfort zone, but I worked in two very collaborative groups, which helped me make some connections I don’t think I would have made on my own.  For a full description of the mathematical work of the weekend, I suggest you read Tracy Zager’s post here.

Reflecting on Practice comprised the other half of our work time; the topic was Worthwhile Tasks: what makes a task worthwhile and how to execute them in the classroom for deeper conceptual learning. Some of the work felt similar [but not identical] to what we did over the summer, but I found anything I had previously encountered appeared to have taken on a deeper dimension – a vote for spiraled curriculum.  The tasks we reviewed covered both middle high school topics, with a smattering of elementary school, and there was always much to glean, regardless of whether or not the topic was directly pertinent to my current teaching assignments.  For example, we looked at an activity including twelve cut-up systems of equations,  and sorted them according to any criteria we wanted before attempting to solve any of them.  When that task was compared with a worksheet which whiteboard tablehad the twelve systems and directions to solve them, a groan arose from some of us (myself included).  For me, I recognized work that I have given that missed the opportunity to engage students collaboratively and conceptually, and to provide an entry point for different readiness levels.  There is definitely a place, time and need for procedural practice, but that becomes meaningless without the deeper understanding that may come from a sorting activity.  And what a great way to uncover student thinking!

Cal and Jennifer also modeled the 5 Practices for Orchestrating Productive Mathematics Discussions for us by giving a simple open ended task, and allowing us to take it in a direction of our choosing.  After we had generated ideas, formalized the one we selected, made our posters and took a gallery walk, we discussed the sequence in which would have the ‘students’ present their work.  The beauty of this activity is that it felt rolly whiteboardlike the natural flow of a classroom.  So often when I read about a new technique/strategy/practice, I have trouble imagining how to use it in my classroom without logistical obstacles.  Our facilitators demonstrated that transformative practices are possible in your classroom by tweaking existing materials, or modifying how you use them (just like Kate Nowak apparently said in her NCTM Nashville talk).

12341414_10206268199877548_8849682681435848444_nThe weekend was professionally restorative for me in some very important ways.  I have been feeling philosophically isolated in my math department, and frustrated by the resistance to changing our practices.  I’ve had classroom management issues that I haven’t seen in five years, and unpleasant verbal exchanges with students that definitely have no place in my classroom.  I had begun making lists of options of my ‘next steps’.  But the weekend reminded me that I can change what goes on inside my own room, and that I have a professional learning community, and thanks to the Interwebs, most of them are always there, ready to communicate and share.


UntitledEnergized and emboldened by my experience, I adopted a ‘no more excused’ attitude and decided to modify my next Algebra 2 lesson on Function Inverses.  I turned my Do Now into an exploration of finding the inverse of a line.   (I’m glad I used this activity for more than its original objective; I now know that half of my students forgot how to write equations of lines from a graph.) IMG_6851 After the students shared their observations (and without giving complete resolution to the Do Now), I distributed iPads for the lesson.  I used, for the first time, Classkick  – no small feat since I made the decision at 4:00 on Monday for Tuesday’s lesson.  Classkick is an app which allows students to move through lesson screens at their own pace (unlike Nearpod), allows the teacher to see what her students are doing all at once, permits on the spot feedback (and stickers!), and if desired, students helping other students.  I took my lesson on Function Inverses, made a pdf of my

I had to add an audio tag saying , "Super Important!"

I had to add an audio tag saying , “Super Important!”

NoteBook, and dumped it into an activity.  Classkick refers to each screen as a ‘question’, but there were several screens that contained notes for students to copy.  I was even able to leave recorded notes and hints on the screens, and got to hear a mash-up of me saying “It’s not an exponent!” (regarding inverse function notation).  100% engagement, lots of collaboration and discussion.  I actually had NOTHING TO DO but walk around and eavesdrop.  The question remains whether this was an effective way to deliver the diffcontent; formative assessment and review will take place tomorrow.  On Thursday, we will begin exploring exponential functions hopefully with an activity I am going to borrow from Laurie B-Worthington over at The Angles Have the Phone Box.

Until this past weekend, the events I attended were held during the summer, as I was reflecting on the school year behind me and beginning to think about the one ahead. “Scaling the Teaching Curve,” as our weekend program was entitled, came at a point in the school year when the September honeymoon is definitely over and the winter holiday break is still a chunk of time away, and for this teacher it was perfect timing.  It recharged my batteries, reconnected me with my professional community, and reminded me of the teacher I want to be.