On Friday afternoon, my instructional coach and I shared the work  we'd been doing in my classroom around using centers to teach some of our math units this year in the intermediate grades.

Since we wanted to ensure that participants would get a chance to both experience a centers-based classroom and work in groups to network and learn from one another, we spent a few hours in the room on Thursday night, rearranging furniture and going over our ppt.

On Friday afternoon, we welcomed approximately 40 participants to our session, and shared our vision, concerns, successes and challenges with this teaching model.

Participants also had the opportunity to work through some of the centers from our most recent unit, on Fractions, Ratios, Decimals and Percents.

It was neat to see people working in different configurations, alone, with partners or in small groups, getting what they needed, when they needed it, just like an "ideal" day in my classroom back at school!

And, just like in my classroom, it was good to have two presenters/facilitators, as we were both able to chat with different groups of people throughout the session, to respond to specific needs of different participants.

I like facilitating sessions like this, where I don't have all the answers.  It generates excellent discussion amongst participants, and forces me to think about the pedagogical decisions I make, and why I make them.  I always walk away with many affirmations and ideas for improvement!

Hopefully the participants felt equally enthusiastic about our session.

We were interested to find out more, and were lucky enough to catch up with them for 40 minutes before Friday morning's Keynote.

A challenge I have found this year while providing descriptive feedback in the absence of letter or number grades is the amount of time I am spending convincing both students and their families in some of my classes that feedback rather than marks is a good thing.  

The last time I was in a classroom, I taught Grade 3.  By Grades 7 & 8, students and their families have had a lot more time to become marks-dependent!  And -- in fairness -- the provincial report card, with its emphasis on marks-based assessment, encourages this marks obsession.  I feel like while these conversations are critical, they consume so much of my time, that my actual feedback ends up being less than stellar, as I am constantly racing against the clock to plan lessons and assessments and provide feedback to all my students effectively. 

I asked our new colleagues how they handled the learned dependency on marks in the older grades.

Their response was that they were partnering with families so that parents who were on board could act as bridges to the community, and help communicate philosophy and research to other parents.  They admitted that "unlearning" the marks dance was a challenge for some students, however they had found teachers who were on board so that students could experience a more feedback-centered classroom for more than a year at a time, and that this was making a positive difference.  

They also agreed that the report card as it currently stands can act as a barrier to effective pedagogy and assessment practices.  In fact, their team was working on creating a form with a check box for families to fill out if they did not wish to receive a report card. So many parents were happy with the descriptive feedback model now, and felt that they had a better grasp of what their children knew and could do and still needed to work on, that they no longer felt that a letter grade report card was necessary.  

Having families document this more formally would help the team move forward in expanding the research next year, and having data on hand vis-a-vis the number of families for whom effective feedback had made the report card redundant will hopefully help them convince the powers that be to modify or eliminate the provincial report card in the future.

Personally, I am struggling with the chicken and egg conundrum:  Would more effective teachers using effective instructional and assessment techniques make the report card redundant, or would a revised reporting model encourage more effective teaching and assessment/feedback?! I'm not sure what needs to come first, but I am sure that something needs to change!  

I look forward to hearing more about this group's progress.

Professional Development as Bridge Building 

At lunch on Friday, I attended a session where a team from Rainy River shared their story of how a project to deepen teacher understanding of how young children learn math lead to developing strong ties between the school (where, we learned, 98% of the students were FN and 100% of the teachers were not) and the communities they served.

Reaching out to the community education counselor (apparently every FN community has one) ensured that the local families were on board for things like the math night the school put on, and ensured that the activities on that math night were culturally grounded (i.e. tangram clan animal quilt, locally prepared "feast" vs catered meal) to ensure community buy-in.

Partnering with FN educators also helped others on the team (and in the schools) move away from a deficit model in their perspective of the students who struggled, and instead begin to truly comprehend the richness to be found in the local culture.  

We learned, for example, that the Ojibway language is a verb based language (whereas in the western world, we tend to take a rather static, or noun-based approach to teaching math), and that the number system itself helps learners develop a sense of number (their number system runs 1-10, then builds on to 1000).  Also that many of the words for key math vocabulary actually have the concept already built into the language, for example, the word for rectangle is "elongated square".  


Understanding this prompted the team to develop partnerships between math and FN language teachers, and we were intrigued with the video footage of kindergarten math-language lessons being co-taught by two educators from different "silos"!

It was interesting to see a team of highly trained, western, professional educators model humility as they demonstrated so many of their assumptions and celebrated their learning.  It was clear that their mathematical project, which had set out to use their knowledge of cognitive science and spatial reasoning to develop a rich math program, had in addition led them to an understanding that bridge building with the community was a necessary and vital part of improving student learning.  It was also clear that the Kindergarten students with whom they worked were not the only beneficiaries of this rich project!

Community Conversations

As I reflect on the success of the colleagues from whom I learned this past week, and consider the current challenges in the community right now with regards to things like the revised health curriculum, I realize that -- as much as ever -- communicating effectively with families and other community stakeholders is absolutely fundamental to everything we do in schools and classrooms.

While I continue to grow as a mathematician, I resolve to refocus on building community connections as well in the year ahead.

This week, I had the opportunity to attend OAME, the provincial math educators' conference, held at Humber College's North Campus.  As Ontario's biggest math education event of the year, the buzz on campus was huge, as teachers, coordinators, ministry people and other math champions shared their take on the latest and greatest, and learned from one another.

A major contribution to the hype was the fact that Dan Meyer was keynoting Friday morning.  Having only ever seen head shots of the guy, I didn't have a full appreciation of how TALL he was!!  Since my people and I had arrived early and managed to score third row seats, one of the most fun parts of the morning for me was taking photos of Dan taking selfies of, well, himself, with various configurations of adoring fans...

He'd genuinely smile and shake hands with his people, then obligingly take their smart phones, put one long arm around the teacher (or group of teachers) and lift up the phone with the other, look engagingly into the camera and smile for the selfie.

I can't even begin to imagine how many "Dan Meyer and Me at OAME" selfies were tweeted out yesterday, lol!

In any case, despite his somewhat limited experience as a classroom teacher (after a few years teaching high school math, he is now a PhD candidate at Standford)  I must say that Dan Meyer is an engaging and thought-provoking speaker.  He used humour to encourage us to examine the myths of student engagement in a way that made his audience more comfortable untangling the misconceptions that many of us had been holding onto, and helped us to consider a more accessible approach for all learners.

Myths of Mathematical Engagement

1. The Math has to be "real world" 
   Dan helped us see how the triangles superimposed on a "real life" photo of the tail of an Orca whale might not convince students to engage with the implied math!
   
   
2. Students must see how the math is relevant to their job in later life 
   Jose the translator -- who owns a translation business, and whose plea to keep up with math is printed on a page in the middle of a unit in a Grade 9 math textbook -- might be more likely to provoke students to wonder "who the heck is this Jose guy, and why is he in my textbook?" rather than convince the average Grade 9 student to stick with the math!!
   
   
3.  We have to make the math "relevant" to students' lives
   Dan invited us to consider whether replacing meatballs with spherical ice cubes and a cylindrical spaghetti pot with an ice cap cup from Starbucks was really any more likely to ignite and excite middle school or high school learners to engage with volume and capacity...

Dial it Back Instead

Dan instead suggested "dialing back" the math class vibe, in order to make our lessons more accessible to a wider variety of learners. This could be done with something as simple as an image, or a short video, to draw students in and make them wonder.

Rather than giving students the question, Dan encouraged us to invite questions from the students.  Using rich visual provocations could help facilitate such questions.  (These can come from textbook questions or pictures, where some information has been removed, for example, covering up the title or headings on a graph.)

Once students have generated questions, said Dan, choose one question to focus on, and ask more questions:  Have students share a guess they know is too high, or too low, and invite them to consider how/why they know those are not reasonable estimates. 

From there, students can begin to build on their knowledge and understanding to arrive at more reasonable estimates.

Ideally, says Dan, we want to provoke intellectual debate, "start a fight" in our classes, where students want to argue and explain their thinking to prove that their answer is the correct or more reasonable one!

Managing the Dial

While Dan spoke I thought how our job as teachers often centered around managing the dial, so to speak. 

Offering multiple entry points and encouraging intellectual debate are both important facets of building an engaging math class, it's true.  Equally critical, I would argue, is setting the tone in class and offering specific opportunities to practice disagreeing respectfully, so that -- as the teacher moves the dial forward --  all learners feel comfortable contributing and sharing ideas as they explore their world with math eyes.

As part of an OTF Teacher- Learning Co-op I have been involved in this year, we wanted to collect some feedback from students about how they have experienced the units taught through a centers-based approach (about 40-50% of my math units this year). 

We had, of course, collected assessment data to ensure achievement of ministry curriculum expectations, but as this was my first attempt at using this approach, we did not really have a "control" group to compare results to.  We also wanted to capture some "student voice" qualitative data that would -- we hoped -- speak to the value beyond purely math concept acquisition.

My instructional coach and I prepared a survey using survey monkey, and invited three of my classes (two Grade 7s and one Grade 8) to complete the survey anonymously.

A Mixed Response

As we suspected would be the case, based on our in-class observations, the responses from the first two classes differed significantly from the third's, both in terms of "select from a menu" type questions, and more open ended responses.

Whereas the first two classes selected many things they liked about centers, the third class chose one or none (we allowed students to select more than one option, or the skip the question, if they wanted to).

Also, although the first two classes were not unanimous in their appreciation of the centers based model for math instruction, their responses tended to be far more articulate in their breadth and depth -- despite the fact that those classes comprised largely students who were English Language Learners or who had Special Education needs -- than the more negative slant taken by their peers in Class 3.

said a student from Class 2, versus the following comment, from a student in Class 3:

I celebrated students' insights into their learning style; as evidenced from the first comment above, as well as several others from all three classes, students recognized that while they enjoyed working with peers on some learning activities, this freedom to choose with whom they would work could also be a pitfall, as peers could become a distraction while working.

Learning: A Shared Responsibility

The comments from the third class also suggested that these students differed from those in the other two classes in terms of who was responsible for their learning.

In particular, while the first two classes wrestled a bit with having to make their own learning choices and balancing the distraction of working with friends with the benefits of having a peer group to consult when they got stuck, the third class's responses frequently included comments about the teacher "not teaching them anything". 

It was clear that the vast majority of the students in this class were desperate for "spoon-feeding", and wanted to be told exactly what to do.  Definitely something to consider when planning for future years... I would for sure engage in more communication up front and throughout each centers unit, both with students and their families, about why we are adopting this approach for some of the math units.

Given that I had recently taught younger students and was moving into Grade 7 and 8, I think I had made assumptions about both the students' previous exposure to a more choice-based model of instruction, and the degree to which their learning skills and work habits were developed.  In the future, I would spend considerably more time modeling and practising self-regulation skills with students prior to launching a centers-based unit.

Learning Skills & Work Habits

Interestingly, despite Class 3's general complaints about the teaching and learning model, many agreed that when they encountered a problem they weren't sure what to do with, they found multiple ways to solve tough problems, including asking peers or teachers and consulting other resources, all skills that will serve them well later in life as they become decision makers, both in post-secondary education and in their chosen professions after their formal schooling ends.

So, although they had less developed foundational skills than I had assumed in terms of established learning skills and work habits, the students' skills in these areas inevitably grew when faced with the challenges presented through math centers.

Reflecting on Diversity

It was interesting for me as a teacher to reflect on the differences in attitudes towards math centers between the first two classes and the third.  What were some of the influences for that class that were different from the first two, and were they things I could modify or change in future years, or were they factors -- like timetabling, behaviour make-up of the class and prejudicial attitudes of the students' families -- that were largely beyond my control?

I was also intrigued by the range in responsiveness within the first two classes as well.  For example, from the same class, the following two responses:

And students differed in their opinion about the role of the text book as well:

(Interestingly, many of the problems presented at the centers were taken directly out of the text book for both grades!)

In Summary

Overall, I would say that while teaching through a centers-based model frequently freed me up to work one on one or in small groups with students who needed a little extra support which is what I had hoped it would do, I did miss teaching full class, 3-part lessons during some of my centers units.  

I was pleased to find that the centers model did help many students become more independent thinkers and develop habits of mind such as perseverance.  

As one student noted, 

Nevertheless, I believe there are times when more directed instruction and facilitation of parallel or open problem solving in small groups, with a teacher-directed consolidation, can be as effective a method for promoting thinking and perseverance.

A balanced approach is -- as one of the more "open" students in Class 3 suggested -- perhaps the best line of attack:

While my initial goal in adopting a centers-based model was 90-100% of my math units taught this way, I managed this first year to deliver about half of my units through centers.  In future years, I would take a modified approach to centers, and continue to deliver about 50-60% of my math units this way, while continuing with 3-part, problem-based lessons for the vast remainder of the units.

After hearing about grossly misinformed and sometimes homo- or trans-phobic opposition to our updated health curriculum, I have been wondering where the voices of reason are.  Finally, it seems they are making themselves heard, and are gaining momentum!

FINALLY!!!  After far too long, I was up in the air again... so nice to be crossing the gap on the ferry to head over to CYTZ for a short but delightful spin in a 150.

We flew HaZeL, the bird who carried me through my first solo some years ago.  After fueling up, we took off on 26 and spent .5 hours in the circuit, flying some rather challenging approaches; I'd forgotten the sometimes-crazy sink factor over the water just before the threshold!

I'm really getting a bit done with people who raise concern about "the gay lifestyle", and how they want to protect their children from homosexuality and gender creativity because it's "just against their religion".  

In particular, I'm curious what exactly it is about my alleged "lifestyle" as a queer woman, that is so upsetting to them...

Is it that we sometimes mix our colours and our whites when we do our laundry in a hurry?  Is it that I shop at the wrong grocery store?  Is it that I'm sometimes late picking my kids up from Saturday morning Language School?

Maybe it's that we watch independent movies rather than bathing ourselves in the hetero-normative, misogynist, materialistic Hollywood crap that seem to dominate the mainstream?  Or perhaps it's that we volunteer with refugees and new immigrants?  (Oh, wait, Jesus was a refugee, wasn't he?)  Maybe it's that the families my partner, children and I attend the post-Pride picnic at the park with when on PEI in the summer are mostly comprised of two women or two men at the helm rather than one of each, or just one parent, period?

Quite possibly it's the fact that I am a vegetarian.  That must be it! Refusing to eat creatures who have been raised in the most inhumane, torturous conditions imaginable, only to be slaughtered for human consumption... that must be what is so offensive to some that they feel compelled to comment on my lifestyle and raise it as a concern when considering updates to a 17-year-old curriculum that our government has FINALLY decided to haul into the 21 century so that we teachers can finally have some current, official documentation to support the work we so desperately need and valiantly try to do with the students in our classrooms who must navigate the ever-increasing mess that is our society today.

On the one hand, we claim to believe in equality.  On the other hand, women continue to earn less than men (yes, even in Canada).  On the one hand, we say "dress appropriately" at school, on the other hand, students walk past billboards and bus ads on the way to school, that model anything but "appropriate" clothing!!!  On the one hand, we tell them violence is bad, and that we use our words to solve problems, on the other hand, they go home and watch the news that tells them all about how many bombs have been dropped on whom and by whom, or we take them to a movie where the main characters spend most of their screen time hurting, maiming or killing others.  On the one hand, we tell them not to lie, on the other hand, the adults they see lie all the time to preserve their self image.  Only when they are "busted" do those adults finally fess up.

It is within this hypocritical context that our young people have to try and figure out who they are, and where they fit in.

The rampant hormones of adolescence make this figuring-out process even more complicated.  Students who come from households where modesty and respect are modeled in certain ways intermingle with students who come from households where these characteristics are modeled differently or not at all.  

And then they have to figure it all out without irreparably damaging their reputation online or in person.  

This year alone, a student at my school was caught texting a photo of his penis to his "girlfriend", a group of students decided to allot one day a week to "ass-slapping", and another student sent naked pictures of herself to others students.

Teachers need to be comfortable addressing these issues in ways that name and invite authentic exploration of the problem without shaming those who are still learning to make good choices.

What's particularly troubling to me as a teacher is that without an updated health curriculum and clear guidelines about who can be exempt from what, we risk disenfranchising our most vulnerable youth.

Last week, I got a note from one of my students's parents indicating that they would not be attending school this week "in protest" of the new sex ed curriculum.  Curious, I asked the student if they knew why they were missing school.  "Not really", was the response.

This scene played itself out four more times in my classroom with either a note or a student letting me know that s/he would not be attending school the following week.  Each time I gently inquired further, the students' responses were nebulous at best.  And each time, I encouraged these students to have a respectful conversation with their families, to find out why they were missing school, and to learn more about their parents' concerns and how their family would be addressing these sorts of things.

As a parent, I have always valued authentic dialogue with my children.  We talked openly about death when they were as young as 3 years old, and they knew from early on that their maternal grandmother had died before they were born.  As far back as they can remember, my children have known where they came from (both spiritually/philosophically and biologically!), and they speak articulately about the wonder of birth and the connectedness of mother and babies.  While I feel strongly about a woman's right to choose what happens to her body, I encourage my children to explore their own feelings and combine it with facts to make their own decisions about what they value most, and one of my boys in particular is extremely pro-life.  My children have known and been able to use the proper names for their various body parts since they were about four years old (they are now 11), and soon, their father and I will be having conversations with our kids about healthy body boundaries, supplementing the "good touch/bad touch" conversations we've had earlier on with more age-appropriate information and advice.

I believe in arming children with facts and information along with unconditional love, so that in situations both pleasurable and challenging, they are equipped with the tools needed to make the best choices they can.  Perhaps it is this aspect of my lifestyle that is so problematic for those who prefer to keep their children in the dark.

We live in a world where people define love in different ways, and where people have diverse interpretations of what's acceptable.  As a society we've agreed that this diverse world is "okay", and therefore, I believe we have to support our schools in providing an understanding that either extends or invites the initiation of the foundation built at home.

That some of those teachers will be members of groups who practise lifestyles different from those practised by students' families can only enrich the conversation.  Ultimately, surely, we all want what's best for our kids.