Grade Level

[caption id="" align="aligncenter" width="500"] Isn't this the point?[/caption]

I struggle with the concept of grade level.  I have tried and tried to understand this, but every definition ends with the circular argument of what is appropriate to the grade.  That is what I don't get, how can we say that this level of work is appropriate for this age of child?  What does a level 3 (or a B, or a three smiley face, or whatever quantitative assessment measure you are using) grade five student look like?

If it is based on the curricular benchmarks and standards, then how does that work?  Here is an example of a benchmark from a major curriculum provider;
Standard 1: Uses a variety of strategies in the problem-solving process

Level 3 - 1) Understands how to break a complex problem into simpler parts or use a similar problem type to solve a problem

Looking at this, I understand that the overarching standard is not something that is easily quantified.  It is like the big idea.  We are not assessing the big idea, but rather providing an opportunity for it to be explored.  I get that.  It is all the sub standards that confuse me.  For example, how do I assign a number to the process of breaking down problems into simpler parts (which seems a bit reductionist, shouldn't we be trying to help students see the whole problem and its context?  That is another blog post!)?  Is there a way to measure that?  Is it about consistency?  And then it gets further complicated (and I mean that in the mechanical context of the word, not complex) when I take into account that there are multiple standards for one subject, all of which are supposed to synthesized into a single grade in, I don't know, problem solving.  Do I assess each standard individually and then average them out to arrive at a final grade?  In this scenario, I would be reducing the big idea into smaller pieces to assess and then putting it back together to arrive at a score.  But it is not just a score or a grade I am arriving at after this process, it is a standard that is compared to other students.  Where does the concept of grade level come into this?  I get the standards, I just don't see how we say that each is appropriate to a certain age level.

I have met a lot of grade five students, and I would be hard pressed to lump them into leveled categories and say with authority that this is the level they are at right now.  Learning is so variable and dynamic (is it emergent and fractal?) that I continue to struggle with what this means.  I know what level my students are at if I compare them to themselves.  I know how to get them to the next level in their own learning journey.  I know how to motivate them to love learning and approach school with passion and curiosity.  I know how to measure their success based on where they were at the beginning of the year, and where they are going.  I do not know how to standardize and categorize them into levels of what a standard or big idea determines is important for a specific grade level.  Is it seems so, I don't know the word, artificial?  Something that teachers invented to make grading easier.  Somewhere along the line we felt that the teachers opinion was not good enough, and we invented a system to measure learning with numbers, letters, or smiley faces.  Can learning be measured with numbers?  My gut says, no. My gut also says, it is damaging to the long term goals of education to try.

I don't know, and I don't think I ever will.

But, I will keep trying to figure it out.



What if... Pt 8

**This is part 8 of a series of weekly questions that are meant to act as conversation starters, or thought experiments.  Discussion and debate are encouraged.  I am not taking a position, merely opening the space of possibilities through discussion.  This will be the last entry until next school year**

Part 1

Part 2

Part 3

Part 4

Part 5

Part 6

Part 7


A Dream

Wouldn't it be great if we had a space for kids to watch and explore bugs?
A simple idea.
We don't remember who suggested it.
It emerged out of curiosity.
The idea mattered.
Shovels procured.
Extra fencing utilized.
Rocks and sticks piled.
Objects were given names.
Imagination flourished.
Kids suggesting ideas.
Bringing in items from home.
Bananas for beetles.
Sugar water for ants.
A mayor was selected.
Monuments built.
It is alive.
It is not finished.
It is emerging.
It is learning.

Welcome to Bug City.



Inquiry Teapots

This is an absolutely wonderful project that is screaming out for international collaboration.  Think of it like a chain letter, but math related.

@Namastececi send out a call on Twitter to see if anybody would like to be the recipient of a teapot project.  I said Yes.  Over the next few weeks we exchanged a couple of emails about progress and addresses and such.  All the while, I had no idea what a teapot project was.  I was hoping that she would explain it to me, but I kept my mouth shut and played it cool, like I knew what was going on and I had done tons of teapot projects.  Truth, I had no idea what was coming in the mail, and I kind of liked it that way.  It made me very curious, and I shared it with my students, and they were curious.  Did they make their own teapot?  Was it like a time capsule, only inside a teapot?  Why teapots?  Maybe the teacher was English?  Maybe, there was actually tea inside of it?

It turns out, the teapot is irrelevant to the project.  The project was the box that the teapot was delivered in.  The kids planned it, designed it, created it out of raw materials, and then shipped it.  The teapot was merely an abstract object that was testing the durability of the box.  It could have been anything.  A plate.  A cup.  A figurine.  Anything made of glass that may have broken if the box was poorly constructed, or the packing was inadequate.  When I received the package and took off the bubble wrap, it all clicked.  I got it.  My first thought, without even opening the box and seeing the teapot which I know knew was inside, was 'what an awesome math lesson, I have to do this.'

Unfortunately, it is a little late in the year to start, so first thing next year we will do this.  This will be our big kick-off for our year of Inquiry Math.  I sent out word on twitter that I would be doing this, and already we have a home for the teapots.  @terSonya in Idaho is going to receive our box.  But, we have two.  So, I was thinking I would bifurcate them and send them to different places.  I need one more taker.  First come, first served.

NOTE: While writing this post, the second teapot was taken by @mkurashige in Hawaii!!

Inquiry Math Project

This project was done by @Namastececi.  It was an original project which came out of a workshop led by Chris Betcher and it was initiated by two teachers from the China school and @Namastececi and @aleaf .  The original post can be seen here with full explanation of the steps involved.  I will follow a very similar path, but there will be a few changes as my unique collective interprets evens in their own unique way.  I will blog about it when is complete, because I have no idea what it will look like.  All I can say, is that @Namastececi's original lesson progression was absolutely beautiful.  Here is a brief summary of what she did.

  • Trip to a local supermarket to investigate shapes and language of packages

  • Design an idea for a box on paper, and then Google Sketch

  • Sketch out ideas on 2D cardboard

  • Construct 3D model

  • Pack teapot in newly created box

  • Work out shipping options

  • Wait for reflection from friends

Looking over this project, which took her about 3 weeks, I am struck by a couple of things.  First, this is real mathematics.  Problem solving at its best.  There is a connection to the real world, there is a noticeable problem that has a solution that can be accomplished in a variety of ways.  It requires critical thinking, creativity, and thinking from different perspectives.

Second, this project is multidisciplinary.  Here are a couple of links I made, but I am sure there are many more!

Design, Aesthetics and Art - What is the functionality of packaging?  How do shapes help keep products safe?  Why do designers use so many colors and textures on their boxes?  Does how the box look make a difference to the person who receives it?

Technology - Google Sketchup is a great program, one that is difficult to get used to, but promotes resilience in technology and creative thinking.  It also lets them see their creation is real 3D, instead of just imagining it.

Teamwork - This kind of thing is best done in a group.  The filtering of ideas and compromising is essential.

Geography - Where is this package going?  What time of year is it there?  What season?  Will that impact our package and design?  How far will it go?  What route will it take?

Money vs Time - How much does it cost to send it?  What are the options?  How fast will it take for the different options?  Which one best suits our needs?  Which one will be safest for the product?  How do we decide based on these factors?  What is more important, money, time, or safety?

Democracy - The act of choosing one from the whole class is an excellent lesson in democracy and decision making.  Yes, students will be upset if theirs is not chosen, but it is a powerful look at how decisions are made.  How do we decide which one?  What is important to me?  What aspects of the package do I value?  Why am I deciding the way I am deciding?  What factors are influencing my decisions?

Connections and sharing - The global nature of sending the package to another classroom is setting up a relationship.  Ideally, we would Skype about it afterwards and have a conversation.  Friends are made, learning is shared, the world gets smaller, but it also gets larger.

Beautiful project.  So excited to try this next year!


Summer Plans

I have two weeks in Calgary coming up.  This is the middle hump of my M.Ed in Education, Mathematics for Teaching.  We have been focusing on Complexity Science and Education.

One year left to go.

It has been an unbelievable ride.

This is a fiery group and we mesh so well.

Looking forward to what we can come up with this summer.

I am sure it will be


and I am sure

it will continue

well beyond

the end

of this



Short and Sweet Reflection

This has been a great year in my life as a teacher.  I was at a new school with new challenges, and a new group of diverse kids.  I did some things well, and there are things I need to work on.  I feel I grew as a teacher, and at the end of the day, that is what I take away from this year.  I will continue to push myself to new heights, while remembering and reflecting on the mistakes and successes of the year that is almost done.  I will miss the kids that are leaving, am excited to keep the ones that are staying, and looking forward to meeting the ones who will join us next year.

Life is a journey.  It never stops.  Neither will I.

Art and Science; Connected Learning

Try something new.

In the past I have explored using abstract art as a way of expressing our understanding of scientific concepts.  Recently, I decided to take another dive into the world of interpretive dance.  I started my journey with a pal from #pypchat who is a performing arts teacher in Hong Kong.  She gave me some good pointers.  Still, I was nervous, I have no dance skills myself, and I needed more people to support me.  Sarah's advice was merely a kick in the right direction, which sent me down other roads and inspired me to keep going and seeking out more information.

This project was partly inspired by a wonderful TEDtalk and program entitled Dance your PhD.  The premise is simple; instead of doing a boring powerpoint (which the speaker describes as the single biggest drain on the Economy) do it with Dance.  The other half of the inspiration came from a colleague whom I worked with in Toronto while a teacher candidate.

A is a dancer.  She would talk about dance all the time, and how it can be used in the class.  I first saw her teach a math lesson with rotations, flips and symmetry using personal space, cartesian grids, and abstract movement.  It was astounding to see a group of grade 4 students dancing and moving and learning.  I found myself teaching black holes to a large group of grade 6 students, so I called her in.  She led them through a series of movements, put it to music, put it the science behind black holes in it, and then polished a wonderful little dance piece.  The awkwardness of grade 6 boys and girls disappeared when she was with them, and they danced together and problem solved and learned about space.  All in 50 minutes.

Fast forward to last month, and A is an ocean and most of a continent away.  I needed her, but the only way for her to help was over email.  She sent me a rough sketch of what I was supposed to do, and wished me luck.  Here is what she sent.  Feel free to use it, and if you try, let me know.  A is one of the true diamonds in a world of teachers who are trying to shine.
I'm happy to help with your idea though and I applaud you for venturing into the dance integration world!
Here's how to start no matter what topic you'll be working with:

1- You could play some classical music or space music (something without a distinctive beat because you want them working at their own rhythms). Have they begin walking around through the space. Ask them to remember not to talk or touch each other.
2- Ask them to avoid walking in a circle but to make an interesting pathway through the whole space as though leaving footprints in the sand/snow. Let them do this for a few minutes.
3-Continue instructing as they are walking. Say for example you are doing the layers of the earth's core, you could ask them to start to imagine they are at the very centre of the planet and begin to move with that quality. Solid core, stiff, solid movements, barely changing shape; Then liquid core moving with very slow but fluid movement.
4- Then they could make their bodies into the shape of stiff, flat plates that can only move laterally.
5- They could imagine feeling their bodies were in an enclosed space and under a great deal of pressure, moving against resistance with terrific force. Always remind them to explore with different body parts, at different levels in space.
6- Then you could ask them to continue moving but to hold still whenever they come in contact with another dancer, making connected shapes of two or three people.
This format of improvisation would work for whatever you are trying to explore. I did it the other day with the 3 Little Pigs: we danced like straw, like sticks and then like bricks.
7- Once you have had some fun improvising, you could build the dance with more structure, assigning a group of kids to each layer and giving them a few minutes to compose a dance that shows the quality of that layer.
8- They would then show their dance to the other groups who might make suggestions.
9- They edit and revise their dances.
10 - You could string them together to create a 5 minute piece of choreography, perfect for concert night!
Good luck and message me again with any questions. I'm happy to help.
Take care,

I took this and applied it to natural disasters.  The first dance we tried was about the movement of tectonic plates.  I had the students write a poem using the most vivid words from our studies.  Then, we tried to turn that poem into a dance.  The first draft was rough, and after some helpful feedback from a drama-expert friend in Calgary, we revised our dance for the next round. Earthquakes and Volcanos were much better done, but as we watched the video on the class TV, we realized we still needed to work on our fluidity.  Next week, we get one more shot; Hurricanes, Tornadoes, and Sandstorms.  As a group of people who have no prior experience with Dance, we are optimistic that we will see a massive improvement from the first round.

The kids have loved it.  They have taken on the challenge of trying something new with an impressive attitude.  They are aware that I am new to this, and understand that we all need to work together to make this successful.  They are also very appreciate of the help we have received from strangers around the world.  Whatever happens, we learned something new.  From the students perspective, they took a risk and tried a new way of expressing themselves.  They connected with experts and adults around the world (even if it was indirectly through me, I always told them where the ideas were coming from) and not least importantly, they had a great time.  Hong Kong to Toronto to Calgary, and us in Japan benefiting from the generosity of others.

From my teacher perspective, the process of writing the poem, planning the dance, and performing it, has helped them to understand the scientific concept.  Drawing diagrams is great.  Building models is wonderful.  Yet, we are trying to learn about something that is based on movement.  Plates collide.  Earthquakes send out waves.  Hurricanes build and then dissipate.  These concepts are all related to, and understood more deeply, through movement.

Personally as a teacher, it has added another tool to my box and shown me once again how powerful the arts are in a classroom.  I honestly believe that the dichotomy we create between Art and Science is entirely human-made.  I am now on the lookout for other ways to break that distinction down.  Learning to use dance in the classroom has given me a new lens on my own understanding of how children make sense of scientific concepts.

Try something new.


What if... pt 7

**This is part 7 of a series of weekly questions that are meant to act as conversation starters, or thought experiments.  Discussion and debate are encouraged.  I am not taking a position, merely opening the space of possibilities through discussion**

Part 1

Part 2

Part 3

Part 4

Part 5

Part 6



What if... pt 6



**This is part 6 of a series of weekly questions that are meant to act as conversation starters, or thought experiments.  Discussion and debate are encouraged.  I am not taking a position, merely opening the space of possibilities through discussion**

Part 1

Part 2

Part 3

Part 4

Part 5



Getting lost in the branches of the fractal tree


If knowing and learning are dynamic processes, then teaching should be too. Complexity science, Chaos theory and Emergence all have very powerful metaphors and implications for education. However, it is NOT a prescriptive method of teaching, and it is NOT a way to teach. Rather, it is about a mindful awareness of the environments that we inhabit, whether they be biological, cultural, or environmental. An understanding of how the characteristics of a complex collectives learning system operates could potentially help teachers to create occasions to allow the emergent nature of these activities to come to life. And in the end, that is what learning and teaching is all about to me.  Life.

Scanning the literature of complexity science across a broad spectrum of domains and disciplines, it is apparent that their is no simple definition of what a collective is, or what a complex adaptive system is, or how to define an emergent moment. There is no clear guide to complexity or emergence. It is an elusive thing to define, partly because it is not a thing, and partly because we are so embedded in it that is makes seeing it troublesome. Like Maturana and Varela said, a fish does not understand water because it spends it whole life in it. If a book arrives on your doorstep that claims to show you how to teach a collective, or how to control a complex system, I would be wary and skeptical of such a claim. It is about seeing, understanding, and being aware. It is NOT a standardized formula.

Even within the discipline of education and complexity, there is no clear consensus on what it means. If a joint definition of complexity in education emerged, I feel it would dampen the diversity of the system and take away from the robustness of education. My own ideas about this topic are formed by my own research and understanding. A different person who considers themselves to be a complexivist (I use this word not because I like it, but rather because I cannot think of a more appropriate noun) will have a different approach and definition. And, those approaches and definitions will change. They will evolve, and they will grow.  They may merge, they may bifurcate, they made collide, they may contrast.  Whatever the result, something new will come from the intersection of new ideas.  Different teaching styles need to bump into each other, they need to come into contact, and they need to grow together.  The diversity of teaching is its greatest strength.

So, what would be the common thread that exists between teachers and their interpretations of teaching, and what would be the similarities between teachers? I believe this has to do with a mindful awareness of complex learning environments. An acceptance of the adage, life is complex. It is a tuning in to the life of the classroom, and a desire to continue to hone and practice the ability to skillfully regulate and amplify that environment. Also, there is a shared understanding in the role of education as more than learning facts and skills, by helping kids to be aware on a conscious level of how the nested circles of co- implicated learning systems affect and influence their lives. This, to me, is one of the central aims of education; to be aware of the stories and narratives of life.

Complexity science is a lens for living in the world. All collectives are complex, and all classrooms are adaptive systems. Having a sense of where you are in the system, and what is happening around you is a skill that I will continue to practice mindfully throughout my teaching career. My definition of teaching; Teaching as orienting occasions for emergence, is one that will continue to evolve and change. I hope to continue to travel along the branches of the fractal tree and see what new possibilities arise and emerge. Most importantly, I hope that this self-reflection and attention to my environments translates into greater learning possibilities for my students, and expands the space of what is possible.

The point of the whole journey is not to arrive at a predetermined place, but rather to arrive at different interpretive possibilities. Education has too long been focused on the predetermined place, and not on the multitude of possibilities.  The creative fires of chaos, the amazing powers of self-organization, and the harmony of an emergent moment; to attempt to understand any of these factors in a dynamic learning environment require a teacher to be aware.

Mindful awareness.