My reality?  Is not nearly so pretty or amazing.  It’s actually just barely passable for organized chaos.  My process looks a bit like this:

Plan pretty decent lessons that let students play with the ideas (thanks to awesome real-life and internet colleagues).  Have chaotic, but really interesting discussions about math rules & conventions.  Continually be impressed by the things students notice and observe and conclude about math. Be not so impressed with the general hormonal behaviour of 14 year old young people.  Arrive at desired conclusions eventually; sometimes painfully, sometimes brilliantly.  Transition into applying the rules we’ve discovered.  Realize that many students need more time with the idea, but that curricular demands say there is no more time.  Default to giving struggling students procedures to “get questions done correctly.”  Feel horrible.  Repeat.

Folks, I know what the research says.  I know in the long run these conversations, inquiries and struggles are far more important for students than if they can find a common denominator and remember to reduce.  But I’m asked to evaluate students on their ability to find that denominator.  That and many many other things.  I just don’t have faith that if I don’t tell them how that they will eventually get there on their own.  Especially when they bring all sorts of crazy math baggage with them and are defeated before we even begin. (Seriously, I asked students to tell me the most fun they’ve had in math and 80% of kids couldn’t think of ANYTHING. 9 years.  Nothing. Oy.)  Showing them step by step procedures doesn’t feel right either though.

What do you do for these kids?  How do we afford them more time but not lose them in the class?  My units are less sequential/dependant on previous stuff than most, but still, some stuff is just plain ol’ important in a “curriculum” kind of way.

It is brought up often that this “new math” is challenging for you. That you’re not really huge fans of the new resources. That in general, teaching math is intimidating for most of you. That, in short, you hate it and feel like you’re “doing it wrong.”

While I haven’t been teaching for 30 years, so I can’t give you a real historical overview of the general mathematical competence of ninth graders over any significant amount of time, I have been teaching long enough to be able to see a shift in how students are thinking about math.

5 years ago, my grade 9s would have been able to recite all the rules of how to add, subtract, multiply and divide fractions to me. They would have applied these rules somewhat correctly, often making weird mistakes. They would have been champions of finding common denominators. They would have answered “BEDMAS” questions. But, if I would have asked these former students “Yeah, but what is a fraction?” or “Can you tell me why that’s a larger fraction?” they would have looked at me with what my co-teacher refers to as “dead fish eyes,” randomly choosing rules to spit at me until I was happy.

This year, my students panicked at our gr 9 pre-assessment. The notations of integers and order of operations just sort of zoomed right over their heads. However, even the weakest among them has a really wonderful understanding of what fractions are. They can compare them, describe them, draw them and talk about them. They say things like “well obviously that one is larger because – insert brilliance here-” and then sort of look at me like I’m the dumb one. They spontaneously break out into arguments about whether 0.999999 is actually equal to 1 or not.

Procedurally speaking, my students are weak (and I’m not really too sure what I’m going to do about it yet.) But, conceptually, they really get it. And while this throws some interesting challenges my way, I’m pretty sure it’s a win for numeracy in general.

So thanks elementary teachers, I think you’re doing it right.

Case in point, my “fabulous” concept attainment lesson on rational numbers.  I love concept attainment a lot, because I love watching the kids get excited when they think they have it figured out, and the continued cycles of this as I add more complicated examples that smash their ideas so they continue to refine their definitions.  The kids really did a bang up job, and as a class did a really good job of defining rational numbers, so good that the formal definition just fell right out into our laps.  They were also able to generate lots of examples of things that were not rational numbers, which is just as important.  High fives all around right?

Sigh, wrong.  Two days later I had them fill out an exit slip that had their own definition of “rational number” as well as two examples of rational numbers and two examples of non-rational numbers.  Somewhere around two-thirds of the class gave me a bang up definition of irrational numbers instead…  and the examples/counter examples were all over the place.

So it would appear we have some work to do!

Well, it’s not even the end of week 2 yet and I’m already not doing so hot with said goal. Oops. One of my students’ first assignments was to make a timeline of their mathematical history. While we discussed the integrated nature of our courses on the first day, I didn’t specifically put the purpose of the assignment on the handout. I should have known that anything we did in those first few days just sort of added one more piece of information to the huge pile of overwhelming information and experiences that are the beginning of grade 9. Good thing it’s early in the year and there’s lots of room for improvement. Extra good thing I had several boys think they were funny by posting their grade 9 mathematical event as “Made this timeline. Not sure why, but it was pretty fun.”

Before I handed back their timelines for improvements, I revisited our integrated model and the purpose of the assignment and got a huge chorus of “OOOOOOOhhhhhhhhhs.” The idea that work they do in math “counts” in the social studies class they take across the hall is still a little confusing for them, which I think is likely a much larger commentary on our school system than I’d like to get into for this post.

In the future, to keep myself really focused on the purpose of what we’re doing I’m planning on:

1. Writing which outcome we are working towards on the board in a visible location. (This shouldn’t be difficult but I always forget.)
2. Using unit outlines for the students. On the front is the outline, and on the back is what I have them self-assess with during the unit. I wish this one was prettier, but I was running short on time and I just couldn’t bring myself to put clip art of a calculator on it.
3. Including a purpose statement on all assignment sheets. I hope this will be helpful for students not only as they’re doing their assignments, but as they go to curate their portfolios.

Anything else I’m missing?

So, our first real “math” problem was a slight adaptation of the garlic problem from nrich.  I chose this problem because it has a really low floor – all students can count! – and can be extended quite nicely if needed.  Being “high tech” in my school is often quite a bit of effort, so instead of using the applet I simply gave each group of 4 a bag of 100 linking cubes.  My first class needed a little bit of prompting “Who is the facilitator?  Have you read the question? Who is the process recorder? Did you write that down? that was really interesting!” but was mostly off to the races.  After about 15 mins I did check in with all the skeptics to help groups that were having trouble moving past using brute force and to stir up some controversy but that was about it.

My second class is clearly the weaker of the two.  They needed way more prompting/scaffolding to get going.  After one day I’m not sure if this is because their ELA skills are really weak as well because just understanding what the question was a real challenge for many groups.  Or maybe they just didn’t find the question as engaging.  After some heavier lifting on my end, all groups managed to at least get to the brute force part.  Everyone except one student.

This student was SHUT DOWN.  I kept revisiting their group, trying to get him on task and involved with the group.  Every time I returned to check in and ask him what was going on, I receive the same responses.  ”I don’t understand” or “I can’t do math” I asked the facilitator to reexplain the question, I asked a group member to model their reasoning for a number, I asked a student to demo how they could use the cubes for him.  The student was so shut down, that he was refusing to even listen to his peers.  I won’t lie, I was starting to get really annoyed – I mean, this student was refusing to count blocks.  However, it’s only the third day so I’ve got extra teacher patience up my sleeve.  I came over and tried to get the student to work a few numbers with me.  ”I CAN’T DO MATH.” I handed him 31 blocks and asked him to plant them in rows of two to see what would happen.  ”I CAN’T DO MATH.” (deep teacher breath here) Just group them in twos, what happens?  Finally.  I got him to work two different numbers with me.  Semi-success.  I still don’t think he really understood what we were doing though, or why, but we had to quit because class was ending and I needed to wrap up the groups.  Now, had I paid more attention to an email received from admin, I would have done a better job at internalizing which students had flagged themselves for “modified” math and my response to this students lack of engagement/effort might have started with even more patience but hindsight and all that jazz.

I have worked with a lot of reluctant/modified/etc. math learners in the last 9 years, but I can’t say I’ve ever encountered a student so paralyzed he couldn’t count.  I was pretty much at a loss for what to do.  I did pull him aside after class and said that I understood he doesn’t like math and that he thinks he can’t do it but to just give it a shot.  Also, no more negative talking about himself.  He’s a hockey kid, so I’m working the “just keep practicing” angle.  Now I’m left wondering how I can best support this student in overcoming his total mathematical paralysis.  It’s clear he’s going to need a ton of support, but how to achieve that without calling attention to him in a way that embarrasses him?  Grade 9 is such a tough year to begin with, and I’m going to guess he’s been playing the “I’m bad at math” card as an avoidance tactic/defense mechanism for a long time now.  There are several other students who have flagged themselves as “modified” but within the groups they weren’t immediately obvious.

This certainly takes my differentiation planning to a whole other level.

You see, in the fall I’m part of a really exciting grade 9 program that we will be piloting at my school. Those of you who work in middle schools, or school with a middle school philosophy for your grade 9s will find this as old hat as imaginable, but trust me that’s for my school this is HUGE progress. We will be moving to an integrated morning for our grade 9s with their electives & Phys Ed in the afternoon. I’m so excited!

There are a few different logistical nightmares in my building, so there are a few variations of the plan. For me this means that myself and my co-teacher will be responsible for a 2 hour block with 52 students every morning that needs to meet the objectives for ELA, Social Studies, Math and PAA. Obviously I’m officially in charge of the Math & PAA.  However, the division of the minutes doesn’t work out quite as nicely as “you teach half the kids ELA for an hour while I teach Math and then we’ll switch.”  Officially, our subjects should be split a whole lot closer to 2/3 for ELA & Soc and 1/3 for Math & PAA.  Which, is fabulous.  It’s going to force me to learn all sorts of cool things, like how to edit. Something, that if you read this blog, you know I desperately need to learn.

I’m extra excited about the pilot because my co-teacher is just so fabulous.  We agree on assessment and evaluation (no marks, lots of feedback, co-constructed criteria when it makes sense), on how we treat students, and that being accountable to another teacher will be a huge plus for both of us.  We’ve had a couple days to plan together and our vision for how our classrooms will work is slowly coming into focus.  Part of this is how exactly we’re going to integrate all our subjects.  Not wanting to kill ourselves in our first year, we’re going to try the following:

1. A large integrated project to be the final project for each semester.  These projects are community based, require knowledge from all subjects, and will reinforce skills learned through the semesters.  I’ll talk more about them when they’re a bit more finalized, but what we’ve got so far is pretty great (at least I think it is anyway).
2. Integrated themes.  While integrating math with ELA and Social is sometimes challenging, there are instances where the themes are similar even if the content isn’t.  For example, circles are used all throughout First Nations culture.  Circle geometry is a large piece of the grade 9 math curriculum.  While the content isn’t similar, we will try to coordinate our teaching of the circle theme so we can look at different perspectives simultaneously.
3. All students will keep a portfolio of their work for all four subjects that focuses on them skills that are important for all learning.  More on this later also.

Teaching is an interesting profession.  EVERYONE has an opinion about education.  I guess it’s fairly hard not to, since the majority of the population spent at very minimum 12 years in school.  Everyone seems to have a story about their favorite teacher, their favorite coach/supervisor, and a handful of stories about the worst teacher ever.  The subject matter addressed from K-12, for the most part, is accessible to the general public as well.  These years of experience plus a seemingly accessible level of content makes everyone an expert.  Experts, as it would seem, love to judge.  More on this later.

Saskatchewan teacher have been trying to negotiate with our government since May 2010.  We have been without a contract since August of 2010.  There has been much focus in the media about how this dispute is strictly over money.  The media has neglected to mention one of the very important reasons for this – Saskatchewan teachers have a bi-leveled bargaining system.  We bargain at both the provincial and the local level.  It is at the provincial level where we bargain for money, our benefits package, and our working conditions.  At the local level we bargain for our preparation time, leaves (maternity, parental, educational, sabbatical), how we get paid, and other general support issues.  I think this is important to mention because the “only” thing we’re bargaining for is money.  If the election that was just held is any indication, our conservative province (and country) should support our teachers in saying we’d like the money please, we will deal with additional health expenses on our own if they arise.  We can’t bargain for other things related to our profession that we value at this time, as they are out of the control of the province and in the control of our local associations.

From my personal experiences, I think there are two huge reasons teachers have been and are being devalued by our government.

1)  Teachers are really nice people.  Have you met us?  In general, we all really like our jobs.  So much so that we continue to do it long after the school day is over.  Historically, the cost of living in Saskatchewan has been quite low.  While we were in a provincial state of financial distress, I would hazard a guess that the majority of teachers didn’t want to seem greedy.  We accepted lame duck contract after lame duck contract, happy to have jobs we love.  However, during these same times we watched other government employees bargain for huge raises.  Fiscal distress for the province seemed to translate mostly into “no money for teachers” instead of “no money for anyone.”  With the housing boom in Saskatoon, Regina and many other smaller centers, new teacher families can no longer afford to purchase a house on their salaries unless they get a second job.  Our government has done nothing but brag about how well our province is doing financially.  These people, creating this fantastic economy?  They are our students.  They are the products of our education system.  In this time of strong economy, we would like to be acknowledged for our hard work at helping create it, for our patience in recognizing that we understand that the government needs to be financially responsible.  We also would to maintain our profession and we can’t do this when becoming a teacher simply isn’t financially viable or appealing for young people.

2)  Back to that whole everyone is an expert thing.  After the birth of my son we had the experience of needing to stay in the pediatric unit of our hospital for 5 days.  It became very obvious, very quickly that there were a handful of not so good nurses mixed in with all the excellent nurses.  However, the general public does not feel that tomorrow they could leave their jobs and just be a nurse.  I don’t think this is the same for teaching.  Those 12 years spent as a student give the public the impression that the could step into a classroom tomorrow and be a teacher.  Sure, many will say they would never want to do this, but they could.  Folks, the majority of you could not, without being that horrible teacher you love to reminisce about so much.  If you would like proof of this, please look at our neighbours to the south (Hi America! I have some seriously fantastic American teacher friends, but your system is a bit of a train wreck right now, I still love you!) and the top achieving countries in the world (Finland, Singapore and Japan are great examples).  The differences between these educational landscapes are largely because of their teacher training, and following that, the recognition and compensation teachers are given.  I’m sure you all went to school with education students who at some time were “making a collage” while you were busy writing an essay but you can trust me when I say getting a B.Ed is not 4 years of making collages.  I understand that you all have a story about a bad teacher, or your kid’s bad teacher.  This, paired with the impression that anyone could do our job, somehow equates into teachers being lazy schmucks who get summers off.  Perception is a funny thing.  That one bad experience tends to trump all the good ones combined. (Also, for the millionth time, WE DON’T GET PAID DURING THE SUMMER!)

In the last week I have watched my government take out attack ads on my profession.  I have watched my tax dollars hurt myself, my colleagues and our reputation as teachers.  I have watched the government use scare tactic after scare tactic to turn the public against me.  Me, who is currently pursuing a master’s in mathematics education on my own dime, so I can be a better teacher.  Me, who regularly spends my own money to attend professional development since our current government continues to cut educational funding.  Me, who for large portions of the year spends more time with other people’s kids than I do with my own family.  Me and all the teachers in Saskatchewan who tell their own stories of teaching that will look remarkably similar to mine .

I am ashamed for our government.  While I understand that negotiations are difficult things, I cannot believe the very same premier who claims in his online political bio that it was a teacher who inspired him to become a politician, would stoop so low.  The government is not simply skewing the facts for their own benefit, they are flat-out lying and hurting the teaching profession in the process.  Yet, I have never been prouder to be a teacher in Saskatchewan.  The solidarity shown by my colleagues in these hard times has been phenomenal.  We do not always agree on teaching practices, on emphasis of curriculum content, on schedules, but more often than not we are better off because of our differences and the professional dialogue we have because of them.  In this, we can all agree – we are the professionals in this messy situation, and we have acted as such.  Our value to this province is far greater than the salary increase we are asking for, and we need not feel greedy for asking to remunerated fairly.

In relationship to what’s starting to come together for my thesis, I’m wondering if being from SK has an effect of teachers’ relationships to their professional lives.  I’m sure everyone can relate to being slightly different people in different scenarios, and part of this is how great it is when you can reinvent yourself occasionally when moving on to something new.  It gives you an opportunity to grow without the majority of people you’re interacting with having a reference back to “the old you.”

Since it is so small here, this really doesn’t happen for many of my colleagues.  It is entirely possible that you wind up working with people you went to school with all the way from elementary school.  More likely these connections are from university and maybe high school, but my point is they exist.  Do some of the unprofessional attitudes and posturing I see all the time come from this strange identity constructed from people known in a different context?  A desire to preserve the perception people have of you of being laid back?  always the one having a good time?  ”cool”?  If there weren’t as many other life connections would people have an easier time doing the right thing in hard situations?

A thesis idea/direction is starting to take shape so I’d like to pilot something here if you’ve got a spare few minutes.  If you’re game I’d love it if you could write about a particularly vivid memory you have of professional development, good or bad, as you remember it.  If you’re not really wanting to post it in the comments, you can always email it directly to me at chelle.naidu at gmail.com.  Thanks, you folks are all awesome.  (and I will of course continue to share this little journey as it unfolds)

1.  Keep the houseplants alive.

This might seem like a silly goal, but I can’t for the life of me ever remember to water our plants.  We have a couple upstairs that are still alive since I walk by them on a daily basis and notice when they start to turn yellow/look sad, but the ones is the basement are dead.  Real dead.  I’m going to replace them, and hopefully the plan is they will be alive to ring in 2012 with us.

2.  Submit articles to be published in the vinculum.

Since I’ve started my masters I’ve had the pleasure of taking two courses with a pretty innovative prof.  He also happens to be the new editor of our provincial mathematics journal.  In a win-win situation, assignments for both courses have involved writing articles for the vinculum.  Win for those in the class since we get published (and write something more meaningful than a paper), win for those involved with the journal as then they don’t have to go hunting down people for articles (it is SK after all, it’s a pretty small place).  This has been really good for me since I’m pretty sure it’s the first time ever I’ve bothered to properly edit anything.  I’m a write from start to finish person and when I edit things myself it’s very superficial things that get changed.  While I’m pretty comfortable with my academic writing in a it’s slightly better than average kind of way, I had (still have really) no idea how to edit so I could keep improving.  Continuing to prepare and submit articles for publication (without having to!) is a bit of a commitment to continue to improve my writing.

*Aside.  If you’re thinking you’d like to publish something in a journal you should submit things too.  It’s still small enough that you’re almost guaranteed to be published and the editors are all very nice people so it’s a fun experience.*

3.  Sew a bag.

I’ve been looking for a new hobby for a while and have been trying to decide whether I wanted to take up knitting or sewing.  A friend has recently taken up quilting and her stuff is amazing so it sealed the deal.  Sewing for the win. My most wonderful husband has enabled my decision by buying me a machine for Christmas.  Even though there are many things I’d like to sew this year, the bag will be my goal.  This is because whenever I fall into an etsy black hole I always find great bags I really like and think they don’t look like they’d be too hard to make.  I’m sure they are actually much harder, but that’s why I’ve got a year!

4.  Read at least one journal article a week that’s not required by a course.

While I read a lot of blogs, I don’t often seek out journal articles to read.  I need to get better at actually making time to read articles I’m interested in instead of just making notes that I’d like to go back and read it someday.  This is likely the most challenging of my goals since the little man isn’t always very supportive of me reading and I have a hard time reading journal articles in multiple sittings.  Going to guess that’s something I’ll need to get better at also.  I’d like to be really lofty and summarize any articles I do read into my citations manager, but let’s not get too carried away just yet.

4 seems like a manageable number of goals for the year so I’m going to stop there.  Happy New Year everyone!