We can harvest ideas, assets and strengths.

We harvest ideas through our professional learning networks, social media, workshops, online learning opportunities, books, blogs, magazines and in conversation with each other.  This type of harvest can be accomplished alone, but feels more powerful when learning experiences are shared with others.

In Learner-Centered Innovation, Katie Martin (@KatieMartinEdu) writes “Creating a culture of effective collaboration, which includes professional learning, means that schools must leverage the collective genius of all teachers and ensure that everyone is equipped and aware of the what, why, and how of any new initiative.” (Martin, 2018, p. 234)

I firmly believe that everyone has their own special gifts, talents and strategies to share, and it’s important to shine a light on each individual’s particular strengths in order to grow a professional learning community within a school, and within a district.  Teachers can be very hard on themselves, and often don’t recognize the important knowledge they hold, or perhaps they feel that others fail to value their contributions to the team.  This is where it is critical that leaders and/or facilitators deliberately surface these strengths and make them visible to everyone.  There are many strategies that might be useful to achieve this outcome.  

The easiest and most accessible strategy is discourse. We need to spend time talking to one another.  Using an asset stance and providing precise descriptive feedback connected to the things we value helps educators to see themselves as part of a solution.  They become agents of change and influence - a highly empowering stance.

Every time I work with a teacher, I learn something from them.  I make sure to tell them what I learned, before leaving their classroom.  It also helps to tell someone else in the school - another teacher, an administrator - in order to spread this learning just a little bit further. 

When we collaborate and share ideas with one another in service of a common goal, we are supporting the development of Collective Teacher Efficacy (CTE).  John Hattie [@John_Hattie] describes CTE as “the collective belief of the staff of the school/faculty in their ability to positively affect students.  CTE has been found to be strongly, positively correlated with student achievement.  A school staff that believes it can collectively accomplish great things is vital for the health of a school and if they believe they can make a positive difference then they very likely will.”  https://visible-learning.org/2018/03/collective-teacher-efficacy-hattie/ 

In a recent article in Educational Leadership, Hattie, Donohoo and Eells build on Martin's statement and urge us to see CTE as a critical aspect of successful schools.  This year, I had the privilege of working alongside Jenni Donohoo in one of our secondary schools.  The effect of the work with teams of educators on their collaborative stance and the increased confidence of participants are clear evidence to me of the following statement:
“Team members' confidence in each other's abilities and their belief in the impact of the team's work are key elements that set successful school teams apart.” http://www.ascd.org/publications/educational-leadership/mar18/vol75/num06/The-Power-of-Collective-Efficacy.aspx 
(Jenni Donohoo, John Hattie and Rachel Eells. Educational Leadership, March 2018)

Are you interested in learning more about Collective Teacher Efficacy?
Jenni Donohoo’s [@Jenni_Donohoo] blog post on the Learning Exchange provides further information about the key conditions which enable Collective Teacher Efficacy.  https://thelearningexchange.ca/collective-teacher-efficacy/ 

This Tuesday and Wednesday, John Hattie and Jenni Donohoo will be facilitating an institute in Toronto.  Follow @VisibleLearning on Twitter - you can be certain there will be a # to follow for the event.  If you’re interested, here’s the registration information link: http://www.cvent.com/events/toronto-visible-learning-institute/event-summary-75ea0b2897b04b4eb2932834a2910cf2.aspx

To view free videos and webinars, follow this link:  https://us.corwin.com/en-us/nam/resources/hattie 

We can harvest strategies.
In a blog post entitled “Harvesting Strategies for Learning”, Sandra Herbst [@Sandra_Herbst], explains “The Strategy Harvest is a list of strategies that are “collected” by the facilitator and the learners throughout the session. These are the strategies that the learners have used – the ones that have invited them into processing, whether externally or internally.  They can be listed on chart paper that is hung around the room or can be electronically posted on a shared document. Essentially, it shines the flashlight clearly on the learning approaches that have been employed.”  

When we curate a list of powerful strategies, we are also noticing quality instructional moves.  Just as we want students to be able to understand what quality and proficiency are, we can help all educators as well.  Sandra says that students who struggle can’t name quality.  They assume that smart kids have a secret they don’t have.  We need to notice and name the learning for and with them.  This can also be a problem for educators.  Identifying indicators of quality instructional strategies with confidence can be  intimidating.
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Learning alongside Sandra over the past several years, I’ve experienced the power of Strategy Harvest in action many times and have come to make it a standard practice in any learning session I facilitate.  As she points out in her post, we want to provide educators with strategies that might be helpful to use in their classrooms.  By experiencing the inherent value in a particular strategy as a learner themselves, educators are far more likely to try it in their classrooms.  

You can read the full blog post here: 
http://sandraherbst.blogspot.com/2013/06/harvesting-strategies-for-learning-it.html 
In celebration of 25 years, the connect2learning team is sharing their top 25 strategies here https://www.connect2learning.com/resources/celebrating-25-years/  
Bookmark this site and check out the resources page for books, pdfs and more!

We can harvest resources and materials.

Harvesting resources and materials involves more than just googling or getting new things.  It’s about opening up cupboards and assessing what you already have.  It’s about getting into the book room and the math room and the spaces for which no one wishes to claim responsibility.  It’s about pooling what you have as a school community and figuring out what makes sense for sharing and distribution, together.

Two years ago, our learning focus with principals was representations and models in mathematics.  We spent time using different tools and representing our mathematical conversations using different models.  In my role as a system math facilitator, I also spent time in key schools, working directly with teachers and students to explore representations and tools.  We looked at the power of a "10 stick" (10 linking cubes organized in two sets of 5 cubes of different colours).  One school was very excited by the activities.  They wanted to all have a 10 stick per child, but their linking cubes were just tubs of mixed colours.  Their solution?  Everyone brought their cubes to the library and they worked together to sort them.  Each teacher then took enough of two colours of cubes to make the sticks they needed.  Harvesting the resources available in the school and redistributing them to meet their current need was a win-win.  Cubes were in classrooms, and in regular use.  The principal and I enthusiastically shared this idea with other schools, with similar outcomes.
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When harvesting professional learning materials, it’s helpful to think about how to curate them in order to encourage their use.  One thing we did in my previous school was to create a display in the photocopy room of professional reading materials connected to our School Improvement Plan goals.  A limited number of titles was on display at any given time, with a brief descriptor card, and a place to sign out the book.  Recently, on Twitter, I saw another great way to share resources with each other:  

One other important thing to do is to make time to debrief with a colleague after attending any learning session.  This might take the form of a coffee break and conversation, it may involve sharing notes and discussing.  It may involve the use of a protocol.  The main idea here is to take time to look back through your notes and materials and to extract the big ideas and key takeaways, and to ensure that you share them with others.  We need to share the harvest!

Processing the Harvest
Once the harvest has begun, we also need to do something with everything we’ve gathered.  With food, we eat some immediately, savouring the rich fresh flavours.  We might make a colourful salad, blend a soup, put things on the grill, or even bake a pie.  The think you might notice is that when you are cooking, the very best flavours come from a blend.

In education, there’s a similar paradigm.  Powerful schools and systems value diversity in schools and classrooms: divergent thinking, divergent experiences and divergent skillsets.  A school’s education team will thrive based on the range of skillsets and experience among staff.  Imagine that the staff each bring their respective gifts to the table, providing a wonderful blend of complementary flavours.  The meal that results is way beyond stone soup!

My very best teaching years were spent working collaboratively with two other teachers.  Between us, we taught Grades 3-6 French Immersion.  With a common long-range plan, we co-taught weekly and constantly reflected on our daily practice together.  We were very different, weaving our wide range of experiences together.  What we appreciated is that when we  team taught our three classes, the outcomes were unfailingly positive.  We worked in concert, balancing energy levels, observing students, facilitating their learning.  By harvesting our strengths and working as a team, we had a far greater impact on our students than we might have had alone.  We also built common norms, routines and structures which the students could rely on from year to year, as they moved from one class to the next.  

Our collaboration influenced our students and they also worked in concert.  We helped our students to notice their respective strengths and watched them leverage the skill sets around them, when working on projects or grappling with problems.  We shared materials between our classes and the students knew how to move fluidly between spaces, without disrupting learning.  Valuing divergence empowered our learning community.  

Katie Martin references three questions from Brandon Wiley in her chapter entitled “Meet Learners Where They Are”.  In this chapter, she talks about effective coaching strategies that focus on growth, not compliance.  These three questions apply to any learner:

Do you see me?
              Do you know me?
                             Will you grow me?

When we can answer these questions about any learner in our care, then we will be able to help them to harvest their own strengths and bring them to our community's learning banquet.  Because in the end, we want self-sufficient, powerful learners of all ages.  Note that not everything we harvest will be fully ripe (see my end of season tomatoes in the photo, above, for example).  That's ok.  With encouragement and care, everyone will be ready to share the full flavour of their talents in time.  A caring, supportive professional learning community, providing pressure and support towards a common understanding of quality learning and teaching will provide the environment that nudges even the most reluctant learner forward.

  I Over the past few weeks, I have spent a lot of time cycling.  As I pedal, the wheels turn around and around and I propel myself forward.  The harder I work, the faster and farther  I go.  The gears, also round, work together to make the bike easier or more difficult to pedal.  Lower gears allow me to climb challenging hills.  Higher gears allow me to speed along the flats and capitalize on a downhill slope to gain momentum for the next hill.

There's a predictability in the work.  I know I need to maintain a certain level of effort, particularly on a slow uphill climb. Sometimes, I allow myself to coast for a bit.  At the halfway point in my ride, I stop for a break and hydrate.  Then, I turn around and challenge myself to ride home just a little bit faster.

In education, we are always working in cycles.  Teaching and learning is an iterative process that requires our energy - pedaling - to move forward.  Students, teachers and instructional leaders are all expected to engage in some form of inquiry process, identifying a problem, making a plan, acting on the plan, observing, tweaking and reflecting, refining our thinking  and beginning again.  In her book Learner Centered Innovation, Katie Martin (@KatieMartinEdu,   https://katielmartin.com) states:

"Learners have to experience something. We all learn and change our behaviour through cycles that include action reflection and revision that go beyond thinking, analyzing, and reading." (Martin, 2018, p. 191)

This section of the book got me thinking.  Just as our students require time and space to pursue learning opportunities that matter to them, to inquire, test, reflect and share, so do educators.  The experience we attach to a learning opportunity is what enables us to shift gears and refine our practice.  We know that collaborative inquiry is a more effective professional learning model than a workshop session, but how might we blend learning opportunities to provide even greater power?  One key idea that resonates is that the learning must be meaningful to - and driven by - the learner.  When the learners are educators, this means that the learning must be centred on their identified area of need or problem of practice.  One size doesn't fit all.  However, when a school team identifies a common concern, the learning is bound to be more powerful.  And when they engage the consultants, coaches and knowledgeable others in the process, their framework for related professional learning is supported.  Aligning professional learning  to address specific school-identified needs will personalize the learning for teams and reduce the perception that professional learning is an add-on.  Instead, it might just feel like a great fit.

​In Ontario, we are familiar with this professional learning cycle model:

Click on the link to read Katie's blog post and learn more.  Training vs Learning: Changing the Paradigm of Educator Development

When we embark on a learning cycle, we ride with a destination (outcome) in mind and have criteria for success.  We are prepared for hard work, sweat and bumps in the road.  We know that sometimes we will have to stop, look, listen, monitor traffic, perhaps even rest and then proceed. Sometimes, there’s a barrier or detour which changes our path, but not our destination.  We know that learning isn't a race.  There are speed limits for a reason.  Learning takes time.  All we need to do is start pedalling...together.
​

Further information about learning cycles for students, teachers & instructional leaders are available at the following links:


http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_SystemLeaders.pdf
System Leaders and Collaborative Inquiry (Capacity Building K-12)
Join us in this Capacity Building monograph as we explore how collaborative inquiry fosters
a spirit of innovation while enhancing a problem-solving disposition and embracing a commitment to learning. Reading online provides hyperlinks!
http://www.edugains.ca/resourcesPLC/PLF/2015_Module/HO3_SpiralOfInquiry.pdf
A framework for transforming learning in schools: Innovation and the spiral of inquiry 
Helen Timperley, Linda Kaser and Judy Halbert 
http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_CollaborativeInquiry.pdf
Collaborative Inquiry in Ontario:  What We Have Learned and Where We Are Now
(Capacity Building Series #39)
https://thelearningexchange.ca/cascading-challenges-choreographed-approach-sustained-student-inquiry/
Cascading Challenges: A Choreographed Approach to Sustained Student Inquiry 
By Garfield Gini-Newman | May 15, 2017
https://rms.thelearningexchange.ca/virtuallearningseries/
Facilitating Mathematics Professional Learning
This series of sessions explores the visible and invisible actions of facilitators of mathematics inquiry. Discussion of the unique challenges and strategies for noticing and reflecting upon one’s own practices allows participants to implement research-informed strategies into their practice. As the use of inquiry-based professional learning increases, the demand for nuanced and effective facilitation is expanding. However, this is a complex role which is difficult to articulate as the work is often invisible and the mathematics content knowledge is embedded and central to the inquiry. Furthermore, there has been limited information and learning opportunities for facilitation of mathematics inquiry. When facilitators can name the actions they use it allows them to expand and refine their understanding of the work. Participants will be asked to engage in an on-going examination of their practice throughout the four sessions and contribute insights and artefacts of their learning to the group conversation.
http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_StudentInquiry.pdf
Getting Started with Student Inquiry  (Capacity Building Series #24)
http://www.edugains.ca/newsite/plc/index.html
Teacher Inquiry resources

http://www.edu.gov.on.ca/eng/general/elemsec/job/passport/experiential.html
​The Education and Career Life planning framework, a 4-step inquiry process

We often refer to the flow of language.  As a secondary English teacher, elementary teacher and later as a parent, I often provided feedback on writing pieces that described the quality of  flow.  Flow is a word that evokes movement, it's visceral.  You can feel it.  Close your eyes for a moment.  Imagine you are standing in shallow water (let's be safe, here!).  The water is flowing. What does it feel like?  Is it gently lapping around your knees? Is the current so strong that it's dragging you under?  Do you feel calm and relaxed, or stressed and anxious?  This range of potential experience is dictated by the strength of the current or flow of the water.  Somewhere in the middle is the experience that I seek.

How does "flow" connect to learning and teaching?  Here are three ways we might think about flow in our classroom practice.

1. Water seeks to flow toward oceans; it has a destination & purpose.

​As educators, we plan for learning to flow in our classrooms.  Our long range plans are literally flow charts, noting how we plan to drive learning forward throughout the year.   Click on the button below to see my Grade 3 long range plan from a couple of years ago.  You'll notice that I posted it at the top of our class news page, as this visual graphic helped our classroom community (including parents) map out our learning.

As we design specific learning opportunities, we consider how the learning will flow towards the end goal, which reflects the achievement of specific curriculum expectations or standards. Teaching resources are structured to help us to focus on specific curriculum expectations or big ideas. As an example, check out the TIPS4Math Scope and Sequence, available for Grade 1 -10 Applied Mathematics. These free Grade/Course Overviews, available on EduGAINS, are organized into grade bands, so the flow of learning can be seen in two directions: over a series of weeks in one school year (vertical) and over multiple years (horizontal).  
​
​You can access these materials, complete with lesson plans, by clicking on the button below.

2. Droplets of water connect and flow farther together.
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We engage in discourse in the classroom, and it's the flow of conversation that gives students the opportunity to process new ideas, connect them to schema and engage in critical thinking.  Lucy West and Antonia Cameron describe turn & talk as a powerful strategy that supports learning in their article, "Turn and Talk:  One Powerful Practice So Many Uses" (metamorphosistlc.com/free-resources/articles.html). The article explains why student conversations matter:

"In the USA and Canada educators agree that robust student academic discourse is vital for deep learning. It is also a practice we see far too little of in many classrooms. Standards for all academic areas emphasize the ability to communicate ideas; articulate reasoning, and listen respectfully to other perspectives as critical life skills no matter what the domain. Research from around the world validates the importance of dialogue as a key avenue for learning content with understanding and developing reasoning, social skills, and intelligence (Alexander). Whether students are learning a second language, have language processing issues, come from impoverished backgrounds, or are highly verbal upon entering school, all are expected to be able to engage in discussions using academic language and eventually write in the content areas using appropriate terminology and sentence structure. Various researchers (e.g. Reeves, Allington, Vygotsky, Alexander, Resnick) have linked academic success with the capacity to engage in conversation and to ask and answer questions in full sentences."


If you'd like to read the full article, please click on the button below.  The website link (metamorphosistlc.com/free-resources/articles.html) will provide you with further articles, ideas and strategies to use to build more powerful discourse in your classroom, professional learning sessions, or in your school community. 

3. The flow of water can be channeled and managed.

​Peter Liljedahl [@pgliljedahl, www.peterliljedahl.com] is working tirelessly to help educators build thinking classrooms.  In his research, he is negotiating the non-negotiables in education and raising the level of rigour and discourse in math classrooms to a whole new standard.  One of the key concepts he is exploring is the idea of managing flow in a lesson. 

His work is grounded in Mihály Csíkszentmihályi's concept of flow, which he refers to  as the optimal experience."The optimal experience is something we are all familiar with. It is that moment where we are so focused and so absorbed in an activity that we lose all track of time, we are un-distractible, and we are consumed by the enjoyment of the activity. As educators we have glimpses of this in our teaching and value it when we see it." [Liljedahl, 2016, "Flow: A Framework for Discussing Teaching"]

​ In my household, an optimal experience is often achieved when working to solve or complete a  a puzzle or game.  My kids get into "the zone" and work together to come up with a solution or get to the finish.  When this happens in the classroom, when kids are fully invested in solving a problem, a teacher feels that indescribable feeling that everything is finally working.  We want to replicate this experience the next day, but we're not entirely sure how it happened in the first place, so....

This is where the notion of managing flow comes into play.  In a workshop with our secondary math teachers and administrators in June 2018, Peter explained how we can manage flow through our use of questions, prompts, nudges and other strategies that hold the students accountable for thinking and problem solving just at the edge of frustration.  

As illustrated in the graph above, in order to keep students in flow, the teacher executes moves that channel the learners in the sweet spot between frustration and boredom, increasing the challenge as ability increases.  This is truly about ongoing growth, as any student, regardless of ability, can be challenged to stay in flow.  

This week, I've been thinking a lot about water.  I ride along the Ottawa River each day.  In some places the water pools and sits calmly, while geese paddle by.  In others, it rushes past rocks, in a hurry to get somewhere.  It's difficult not to conjure up an image of water when you read the word DRIP.  But, why have I chosen this as my second word for the #5Days#Words challenge?
​
​In her book, Messy Maths, Juliet Robertson [@creativeSTAR, creativestarlearning.co.uk ] suggests “rather than overwhelm parents with suggestions, it can work well to drip-feed mathematical opportunities into the ongoing activities in your setting”.  When you think about it, drip-feeding feels like a good option for educators and leaders, too.  

Why drip-feed?  Why not turn the tap on full?
Let's face it.  We all move forward one step at a time. Educators often tell me that we (coaches/consultants) give too much information at once.  Think about how you feel at the en of a full day workshop.  Through the course of the day, you take in idea after idea, making notes, engaging in conversation, gathering handouts, links and book recommendations.  As the day progresses, your brain begins to feel full.  Often, we describe the feeling as "overwhelming", and we walk away unsure of where to begin.  In the end, a common reaction is to place all of the new ideas in a pile - literal or figurative - and return to the safety of familiarity.  
What if we were to offer just a drip of information at a time, with the opportunity to ingest, process and connect the idea to our practice? Might we continue to thirst for new learning? Information would sink in slowly.  We would fill up over time,  rather than overflowing in a rush.  
As a facilitator/coach/instructional leader, the tough part is managing the drip. I must admit my tap is happiest when flowing full. I get on a roll, spewing out ideas that even I (the speaker) can't retain.  Drip-feeding requires patience, intentionality and active listening to determine what drip might resonate with a particular audience.  It’s responsive. Differentiated. Proactive. That’s a tricky blend.

What constitutes a drip?
Perhaps a drip is an idea. 
Perhaps a drip is a question.
Perhaps a drip is a link.
Perhaps a drip is a quote or excerpt from an article, book, or knowledgeable other.
Perhaps a drip is an activity or game we engage in together.
Perhaps a drip is a tool, app, routine or strategy.

On the receiving end...
Do you remember standing outside with your head tilted back, trying to catch a raindrop or a snowflake in your mouth?  Did you wait calmly for the rain to come to you, tongue outstretched?  Or did you shift impatiently from foot to foot, trying to capture each drip as it fell from the sky?  Did your strategy vary, depending on the rainfall?  Did you ever just duck your head and try to stay dry?  If you did catch something, did you savour it or just try to get the next drip as quickly as you could?  We are all different.  We process differently.  

So that's my challenge this year, to slow the flood of information to a drip.  Picture a system where educators are collecting drips and pooling them together to create a lake of learning.  Hmmm...sounds like building collective efficacy, doesn't it?

For those of us who blog...sometimes...there's a summer challenge to get back in the groove.   Five days.  Five words.  Nothing fancy.  Just a mini-blog post. See Kristi Keery Bishop's blog for the backstory -  https://kkeerybishop.commons.hwdsb.on.ca/2018/08/08/5days5words/ 

 Challenge accepted.  

#1  Simplify.
My 85 year-old mother lives independently in Ottawa.  I live in Sudbury, with my husband, dog and a varying quantity of our 4 grown children.   This summer, she needed to have knee replacement surgery.  I offered to spend the summer living with her while she adjusted to her new knee.  In the end, it turns out I have been caregiving both of us.

​I arrived in Ottawa mid-July with a carload of books and magazines, a laptop, iPad and iPhone, my recent notes, calendar and some assorted files.  I had my bike, a yoga mat and enough clothes to keep me going for the season (and more).  I had big plans about how I would spend my time balancing caregiving, crafts, fitness, reading and professional learning.  I had an agenda.  It was full.

Goal # 1:  Fitness
In my plan, I was going to join a yoga studio and/or a gym.  I would ride my bike there, take a class and ride home.

Goal #2:  Professional Reading and Writing
​In my plan, I was going to read all of the 20ish books and magazines I brought, take notes and thing about an outline for my own.  I would curate all of the notes and documents on my laptop.  I would blog all summer.

Goal #3:  Learn to weave.
In my plan, my mom would teach me to warp her looms and she and I would weave, using her treasure trove of wools and cottons and leaving her with something to tinker with in the fall.

Goal #4:  Reading for pleasure.
In my plan, I would read all 10 of the novels I had brought.

​I am an "all and everything" kind of girl, always curious, always aching to learn.  I say "yes", take risks and jump in with both feet in my work life.  I am forever coming up with another "crazy idea".  I juggle the many balls that life brings me - as an educator and a parent - with tireless (reckless?) abandon.  But, honestly?  I was pretty tired.  Perhaps my plan was a little too ambitious.

A wise colleague once told me..."Pick one thing.  Do it well."
So I focused on Goal #1 and got on my bike.
Every day, I got a bit stronger.  My muscles ached less.  
Just riding was enough.

It turned out that riding gave me the energy to blog a bit.
I read bits of the books on my shelf.  And tweeted about them.
I took in as many sessions as I could in #buildmathminds18 and tweeted.  A lot.
Riding gave me space and time to think.  Time to write in my head.  Time to breathe.

But what does the word SIMPLIFY have to do with teaching?  Why is it my #1?
As I focused on this one thing - riding my bike - everything else began to make sense.  I allowed myself to slow down and make connections. 

As educators, we feel compelled to do everything at once.  We plan lessons, inquiries, assessments and more in a variety of subject areas for a broad range of learners.  Every day is a new adventure and we must be prepared for everything!  As enthusiastic lifelong learners, we are inspired by new ideas, want to try cool things and jump on bandwagons.  However, this frenzied multi-tasking is taxing.  By June, we are exhausted, drained and often disappointed in ourselves for the things we didn't achieve.

The Oxford Dictionary defines "simplify" as "make something easier to do or understand".
www.mathwords.com defines "simplify" as "To use the rules of arithmetic and algebra to rewrite an expression as simply as possible."

Both of these definitions make me think of "reframing" an idea, bringing it into focus by removing clutter.

As educators, when we focus on good pedagogy, make connections and leverage them with students, we are simplifying the classroom experience for everyone.  I was blessed to have phenomenal collaborative partners.  As we created and refined our shared Grade 3-6 long range plans, we began to realize how much easier planning became when we leveraged key ideas, strategies and skills across subject areas.  

For example, we began our year focusing on visualizing. We practiced visualizing with our students in language, math and the arts.  We talked about how visualizing helped us to learn and why we might want to use this strategy to makes sense of any text, including a math problem.  Students started to make connections out loud, noticing that visualizing is something they can use for anything.

Well....that led us to focus on making connections.  In math, we talked about connections across strands, between representations, between problems.  At one point, a student noted "Wow!  It's like everything we do is connected!" Mic drop.  That was a great day.

How did this happen?  We sat back, took space and time to think, and brought our planning into focus by removing clutter.

​In their book "Coherence", Michael Fullan and Joanne Quinn state "coherence consists of the shared depth of understanding about the purpose and the nature of the work in the minds and actions individually and especially collectively." (pg 16).  This book, written for system thinkers and leaders parallels the experience we had in the classroom.

What we discovered is that students became agents of learning and carried their schema forward with more confidence and purpose, when they had core strategies as a focus, rather than content.  In fact, the content became a tool for exercising their strategies.  Our classroom cultures weren't focused on who knew the most or least, instead we were all building our capacity as learners.  

So, what has this summer taught me?

1.  Brainstorm/make a wish list of goals.
2.  Pick something that's important (to me).
3.  Do it well.
4.  Everything else will begin to fall into place.

I gave myself permission to SIMPLIFY, in order to navigate the complex world that lies beneath.

This summer, I am actively looking to see how people use mathematics intuitively and intentionally in their creative pursuits.  

A couple of weeks ago, I had the privilege of meeting some very dedicated artists, whose attention to detail and precision with proportion has resulted in a magical miniature.  We visited the St Jacobs and Aberfoyle Model Railway, begun as a labour of love by 6 railway enthusiasts over 40 years ago.

The railway ties were also all hand-cut individually. Fun fact:  CP and CN used different-sized railway ties. And yes, you can see what the difference looks like in miniature!

This visit got me thinking about the mathematical reasoning required  in art, hobbies and crafts.  

Consider the math thinking  and problem solving involved in the planning and construction of this miniature world. 

The artists paid attention to proportional reasoning:
These artists measured out the actual buildings and trains. They then calculated the 1:48 scale in order to build the models with precise details. 

Why this matters:
“The ability to think and reason proportionally is one essential factor in the development of an  individual’s ability to understand and apply mathematics. Susan Lamon estimates that over 90%  of students who enter high school cannot reason well enough to learn mathematics and science with understanding and are unprepared for real applications in statistics, biology, geography  or physics (Lamon, 2005, p. 10). While students may be able to solve a proportion problem  with a memorized procedure, this does not mean that they can think proportionally.” (Paying Attention to Proportional Reasoning). click on the document cover to read more

The artists paid attention to spatial reasoning:
The models sit in a landscape, housed around one large room. Within this landscape are rural and urban spaces and reams of track. Envisioning this landscape was no small feat, but it was even more astonishing to hear how they had moved the installation to its current home from its former one by cutting it into 35 pieces and carefully reconstructing it. Now,  that brings a jigsaw to a whole new level!

Spatial skills are also practiced by the operators, as they work in concert to move a plethora of trains around the miniature world. Weaving around one another, connecting and dropping cars, all from their booth high above the exhibit, these operators demonstrated their excellent sense of location and movement.

Why this matters:
“In general, people with strong spatial skills also tend to perform well in mathematics. Moreover, the strength of this connection does not appear to be limited to any one strand of mathematics. Researchers have found evidence to suggest that spatial thinking plays an important role in arithmetic, word problems, measurement, geometry, algebra and calculus.” (Paying Attention to Spatial Reasoning) click on the document cover below to read more

There's a lot of conversation lately about creativity in education...and about creativity in general.  My kids, my colleagues, great books, and the twitter sphere have all inspired me to do some thinking.  Today, I was cycling in Ottawa and spent a bit of time capturing some photos of an amazing art space along the river at Remic Rapids.  Please check out the artist's website ​using the button below:
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Looking at these structures, a big idea clicked for me.  Creative thinking is built and strengthened by a set of attributes:  flexibility, intentionality, patience, vision and faith.  If we, as educators, spend time fostering them, then we are creating the conditions where creativity can thrive.  So how can we achieve this?  Let's think about each attribute.

A creative thinker is flexible, able to work with the materials/equipment/resources/people at hand and transform them into something new.  Some of us like to call this a "MacGyver", a reference that might date me a bit, but you get the gist.  The artist whose work is featured in the photo above is working with found materials - rocks - and a rugged shoreline.  Despite these challenges, the sculptures stand proudly because the artist spent time analyzing the landscape and the materials, enabling them to work in harmony.

A creative thinker is intentional, taking the time required to envision the possibilities and determine a range of strategies to achieve them.  In this case, perhaps the artist spent time looking at each rock, thinking about what it might be able to represent as a result of its shape and girth.  Perhaps the artist envisioned an image and then sought out the rocks that would bring it to life.  Both approaches require intentionality, reflection and revision.

A creative thinker is patient with herself/himself, knowing that the first attempt at a solution will likely not work, or be considered the best possible outcome.  Setting out to take a risk, try something, knowing that multiple attempts will be required before a final product is achieved...this is growth mindset in action.  In the case of these sculptures, the artist must also be patient with the materials and the environment, moving slowly in order to ensure that the rocks are placed with precision, in order to find balance.

A creative thinker has vision, seeing what's possible, rather than just what's there in the moment. In 1986, John Ceprano began his rock art installation at Remic Rapids.  Imagine what he saw in his mind in the beginning, and where the journey has taken him, as this landscape unfolded.

  

Finally, a creative thinker has faith, knowing that the vision is achievable, given enough time, energy, patience and perseverance.  This artist began this work 32 years ago.  This body of work has evolved over time.  Now, every day, there are people sitting on Adirondack chairs, installed on the grass so that people can spend time with the sculptures.  In the evenings, a crowd gathers, and alongside the installation children carefully construct their own rock art, with feedback from their siblings, the seagulls, geese and a few ducks. Creative thinking inspires others to think creatively.  ​

As an educator, I'm thinking about how these attributes impact the learners in my circle of influence.  

I need to be flexible in my approach and interactions with others, working with people where they are, in their situations.  Hmm...sounds like differentiated instruction.

I need to be intentional, walking into learning situations with a clear plan and desired outcomes.  Hmm...sounds like learning goals and success criteria.

I need to be patient with myself, the process and the people.  Hmm...sounds like growth mindset and assessment as learning/metacognition.

I need to have a clear vision of the amazing possibilities that can unfold in our learning spaces.  Hmm...sounds like the inquiry process and Habit 2:  Begin with the End in Mind.  (Thanks Stephen Covey!)

I need to have faith in myself and others.  Together, we can change the story.  All we need to do is look at a blank canvas together and really talk about what we see.  And then...well, we just roll up our sleeves and make it happen.

My colleague Denise and I have been working in Grade 3 classrooms in two of our schools for the past few weeks, engaging students in problem solving using concrete materials.  Our focus has been on concepts where our board has generally struggled , based on EQAO data over time.  What's really interesting to us is that the data we used has led us to uncover a common thread.  We realized that students are often asked to build and compare when problem solving.  At the same time, we notice that many students don't build, which means they can't compare.  Hmmm...I think we are on to something, here.  We decided to use this common thread to help students to build a stronger understanding of equality.  These photos document some of the learning we observed during lessons around equations and equal amounts of money.

What amazed us was the simplicity of the game that we used to help students to build their own equations.  Each of us started with a stick of 30 cubes in two colours, with 5 cubes per colour in a repeating pattern (as described by the students).  The students readily described our two lines as equal, and we were able to prove this by placing one line on top of the other.  This creates a pretty cool visual.  The cube lines became the equals sign.  This led students to use the cube lines to solve for missing values in equations, by describing the actions they took to make their two cube lines equal lengths.  

In the next lesson, we explored equal money amounts.  At the beginning of this lesson, students made connections between the cubes lesson and equal amounts, which made it much easier to launch the idea of equal amounts of money.  Pairs of students were given a paper bag with an amount of money between $5 and $7, which they needed to represent using different combinations of coins and bills.  Using the mathies money app on a screen, we were able to model the different ways to represent equal amounts of money, in order to consolidate our understanding of the problem as a large group (see the image above for an example).  

The power of connections across different models, strands and problem types really stood out to us as a result of these two lessons.  The idea of equality resonates everywhere in mathematics, and yet it's an idea that seems to stump many students.  That leaves me wondering why?  How might we make more explicit connections between big ideas (like equivalence) in order to help all students see the idea more clearly?

Sitting here, listening to Cathy Fosnot talk about young mathematicians is creating quite the conversation in my kitchen.  Conversation with whom, you ask?  My 17-year old daughter.  This year, all manner of opinions about education have surfaced at our supper table, and I've really enjoyed listening to the impact of learning and teaching on my own kids.  As the last of my children prepares to graduate, I am happy to say that our kids have strong opinions on what makes the difference in education. 
The conversation seems to revolve around the educator's learning stance.  If the educator takes on the stance of learner, alongside the students, then my kids are much happier.
"Teachers don't know everything and they haven't run across all of the different types of learners.  They never will."  This is a powerful statement from a student.  
Cathy Fosnot and Stephen Hurley start a great conversation, not just about ensuring that students have equitable access to math learning, but they also propose that it's not enough to just engage kids in having fun with math, but that we are compelled to help them to recognize themselves as mathematicians and powerful thinkers.  
Cathy has many key ideas in this podcast, with a particular focus on what mathematicians do, and how mathematizing isn't just a process, but it's also content. She says that mathematicians are constructing meaning within the medium of mathematics. They are mathematizing the world around them, using mathematical models and mathematical lenses.  This is how they construct mathematics and see relationships between ideas, proving conjectures.  This is the process of building meaning.    

Let's think about supporting the unfolding of mathematical ideas in the classroom, rather than transmitting our ideas to others.  This stance really underlines the importance of educators engaging in the classroom as learners and observers, rather than just assuming they know how all of their students will see mathematical ideas.  

If you haven't had the opportunity to listen in to Cathy Fosnot facilitating discussion about the first chapter of her book Young Mathematicians at Work, Constructing Multiplication and Division, click on the button below.

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