A Vow of Silence

It seemed like such a simple idea.

No talking for an entire day.  The kindergarden teacher said that she did this with her kids for 45 minutes (or 1 hour, can't remember) and they loved it.  They rose to the occasion and thought really hard about how they could do this.

If they could do it for an hour, we could do it for an entire day, right?

The day before our Vow, we wrote a pre-reflection on our blogs (google sites).  I asked them to make a table and fill it in.  I also asked them to chose an image from FlickrCC that spoke to how they were feeling:

Some very interesting responses, but browsing over the entries I see a certain darkness.  I don't want to call it fear, but.... 

The previous day I had them blindfolded for 40 minutes, walking around the first floor of the school and doing tasks (put this book on the piano in the multi-purpose room, water the plants, get a drink of water from the fountain, etc).  They loved it.  Some of them went home and tried it there.  The reflections after that short 40 minutes was some of the best writing I have seen all year (I felt so lonely in the dark, It was like I was disconnected from the world).

Compared to that, this would be simple, non?  I mean, no talking for one day?  Easy.  9am to 3:30pm. Piece of cake. 


There were no rules.  No prizes.  No punishments if they failed or cheated.  They were allowed to use any other form of communication they wished.  Just no verbal communication.  This was a personal challenge, where the only judge of you would be you.  Could you do it?  

As one student so aptly put it, it is just you vs. you.  

Who will win?

I would also be doing it.  In a way, the challenge was even greater for me, since I had to plan an entire days worth of learning engagements and exhibit this self-control (it should be noted that self control has never been one of my stronger traits).  

But I never believed that for a second.  

Kids have incredible difficulty with impulse management.  It is part of growing up.  Their brains are wired this way.  This quote from one of the chapters in Taking the PYP Forward is glued in my head:
Kids cannot control their inhibition sensors due to the limited growth of the prefrontal lobes and thus cannot comprehend fully the consequences of their actions. 
For them, self control and an entire day focused on one thing (not talking) plus the added stress of having to participate in learning activities made for a much more difficult experience.

9:00 - 9:10
We gathered on the front steps of the school.  I stressed the following points:

- get used to listening to yourself think
- create your own bubble, and let your bubble bump into other bubbles
- this a challenge for yourself, just you vs you, if you cheat, you only cheat yourself
- constantly ask yourself; why am I doing this?  What am I learning?
- if you feel stressed, disconnect and go somewhere to be alone
- if you can't do it anymore, there is no shame in stopping
- before you walk through these doors, say one last word.  What is your word?  

My word was "imagination".  I didn't really hear what others said, the front foyer of a school first thing in the morning is not the best place was quiet reflective thought.  I did hear a "good-bye", a "love", and a "here we go".

9:10 - 9:50 
This was our designated library time.  Usually, they read with partners, with the librarian, and with me. However today, we used this as a tuning in session, a chance to just be alone and read a book, or think. It was a low stress time for them to get used to this whole crazy idea.  

There were still things they had to do.  They had to bring back their library books, sign new books out, and all that library stuff.  The librarian was not taking the vow, so she was able to speak with us.  

During this time I gave them a short guide I wrote on taking a Vow of Silence.  There was no activity to do here.  Just read it.  Think about it.  Wonder.  Prepare your mind.  Find your goals.

Get used to listening to yourself think.

I noticed that when asked questions by people, it is instinctive to answer.  Several of the kids were asked questions and started to answer before catching themselves and stopping.  It is hard to control.  I almost did it myself several times.

I was reading a good book and writing this blog post, so I had something to occupy my time.  I felt relaxed and comfortable.  I had a warm tea.  All was good.

A students iPhone cover.  Seriously.
How awesome is that...

9:50 - 10:10 
Snack and break time.  Every morning I give the kids 20 minutes for a break.  They hang out with friends, eat their snack, play mine-craft on their iPods, listen to music and dance, or just be silly.  

Today was different.  Kind of.

The room is usually incredibly noisy.  I like that noise.  The sound of children playing (yes, even grade 5 and 6 kids are still children, and still play) is one of my favorite sounds in the world.  Yet, today was silent.  But, looking around the room, it was the same old thing.  The iPod crew played minecraft, showing each other their screens, giving each other thumbs ups and smiles.  The dancers danced and played tag.  The readers read.  

Playing can exist without sound.

10:10 - 11:15 
I originally planned to continue our Vitruvian man measurements.  I was going to write a bunch of new proportions on the board and have them get to it.  But, right before we started I had a change of mind.  It was too easy for me.  I wanted to try and explain a complex idea and see if they could understand.

I drew a picture of myself on the board.  Then I wrote my height next to it.  I divided my height in half and got a new number.  Then I took a meter stick and measured my new number.  I found that it was a point directly below my navel.  This is my 1/2 point.  I wrote a bunch of other fractions on the board.  Some of them got what I was asking them to do, others needed me to write the instructions in words on the board.

I know I can't draw.  Doesn't bother me.
I really wanted to stress accurate drawings.  Change your drawing to make it as anatomically correct as possible.  I took a ruler and measured from the bottom part of the diagram to the 1/2 way point.  Then I measured from the 1/2 point up to the top.  If the two measurements were not the same, it was inaccurate.  

This was going really well, so I asked (haha) the ones who had finished to draw an anatomically correct picture of their faces.  This needed the help of a partner, so I got to see some really cool communication strategies.  

- Some were using white boards to write their thoughts, but this was too slow, so we tried to shorten our sentences to make it easier, but then the other person couldn't understand what we were trying to say
- lip-reading and mouthing words is hard, really hard
- artifacts around the room are great, and can easily represent words
- gestures are king and the majority of the gestures we used were embedded in our culture; head shaking, finger wagging, bowing, etc.
- facial expressions can understanding so easy; if the other person is getting it, they must let you know they are getting it, or it is frustrating (communication is a two way street)

11:15 - 11:30 
We took the last 15 minutes before lunch to clean up and organize our thoughts.  I asked a couple of leading questions on the board and asked to reflect on how they were communicating thus far.  

Do you feel frustrated?  
Is smiling important?  Why?  
How are you using gestures?  
Is lip reading and mouthing effective?  Is writing on the little whiteboards easy or hard?
Are you having fun? 
What are you learning about communication?  
What are you learning about yourself?

We had a class discussion.  This was probably the most fun I have ever had in a classroom (since the Tanuki ate our corn).  We noticed that different gestures are unique to different countries.  The American students thought no was a shaking of the head, but for the Japanese students it was a waving of the hand.   They mentioned that the whiteboards were not good for communicating because it took too long to write what you wanted to say.  Also, when you were writing and reading, you were not making eye-contact.  Eye-contact was the best way to communicate.  Smiling was also important, because it told the other person that you get what they are saying.  Our facial expressions are so important to determining if the other person is understanding.  Oh yeah, and lip reading is HARD!  It is okay for single words, but a waste of time for anything longer.  Different languages pronounce things differently, so the kids were getting confused with the mouth shapes while trying to read lips.

Most importantly to me, they told me that they were having fun, and they were enjoying the experience.

At least I think this is what we talked about.  It is how I was reading the situation.  Everybody will hear something different and read these conversations in their own way...

11:30 - 12:20 
This is lunch and recess.  I usually spend some time chatting with colleagues  eating my lunch, reading, blogging, or just relaxing.  Today though, I followed my kids.  Went to the cafeteria, ate lunch with them, went out for recess with them and played tag.  They probably thought that I was watching them and making sure they didn't speak, but the truth is, I wanted to be with them because I am loving the feelings I am experiencing today.  

So alive. 

12:20 - 1:05 
Usually this time every week I have a parent come in and read us a novel.  I considered canceling the class for today, but I decided to keep it in and I really glad I did.  It was a very different feeling.  Firstly, it was nice to hear a voice, especially the lovely Mrs B.  Secondly, it was interesting to see the difference between communication with two people, and listening.  The purpose here changed.  They went from trying to get their message across, to concentrating on somebody else's message.

I tried to orient attention to this fact, but I am pretty sure nobody understood what I was trying to say.  I just couldn't get my meaning across.  A couple of them might have got it, but I don't think so.  After a couple of minutes of this, I gave up.

It was hilarious to watch them react to the book.  Literature has such power over the human mind.  An exciting part of the book would come up and kids would just yell out their thoughts, completely forgetting about the vow.  It happened about 10 times during the 45 minutes of reading.  They couldn't control themselves, because they were no engaged and emotionally invested in the story.  Books have power.

1:05 - 1:45
Luckily, the only specialist class of the day was music.  And luckily again, the music teacher was excited to have a music class with no talking.  

Recorders, ok.  Singing, no.  This is what we agreed on.  

Even luckier, he took a vow as well for the 45 minute period!  And even luckierly (copyright me) he knows a bit of sign language!  He walked them through the alphabet and had them trying to sign their own names.  It was amazing to see how fast the kids picked it up.  Smiles all around.

Next, he led them through some rhythm activities, clapping to a beat.  Then onto recorder and finally onto glockenspiel and bells.  What was amazing though, is the whole time we went through his lesson, he explained all the instructions using the sign language from the first half of the class.  They remembered and were thinking hard about it.  It was amazing to watch.  The applause they gave each other after their glockenspiel solo's was filled with so much soul....

1:45 - 2:05 
Recess.  Beautiful weather today.  Bright blue skies, no clouds.  The snow is melting.  The weather is warm.  Only need a light coat.

Stunning.  Feels like spring is in the air.

2:05 - 2:45 
We are starting an art project next week.  Each team of students has already chosen their topic, or imaginative what if... question to explore (what if we only saw the world in 2D? or what if we could see radio waves?).  Today, they had to brainstorm ideas and feelings associated with that question (expect a long post in the coming weeks about this project).  This class has grown a lot this year in their ability to brainstorm.  Brainstorming silently was hard.  A couple fo groups got stuck.  I blame myself.  I should have given them a narrower topic to focus on.  I set it too wide open.  

I helped each group get started.  I wrote a couple of things down and then something clicked and they were off to the races.  We will take another stab at this next week while we can talk.

2:45 - 3:25 
To finish off the day, we went back to our gSites blog post and wrote about the day.  I sent an email with a brief overview of what I wanted, and let them go.  After our time of blindness the other day, I had such success with no structure I thought I would try it again.

1) Choose an interesting title for your article
2) Write about the day as and talk about your experience.  Imagine your article is going to be published in the Scoop (school newsletter).  What did you learn?  What was difficult?  Easy?  Fun?  Interesting?  Boring?  Stressful?  Etc.  Focus on feelings....
3) Choose an image that sums up your feelings for the day from FlickrCC

I left them along as much as possible.  It was important to me that this was a self reflective moment, and there is nothing worse than having somebody standing over your shoulder telling you what to do when you are trying to reflect.  As for me, I used this time to write this blog post.  

I will read their posts tonight.

At 3:30 we walked past the front door of the school, the same place where we started.  Buses were waiting.  The kids were excited.  I asked them to think about their first word out the door.  Again, it was noisy so I didn't hear much.

What I learned from my Vow of Silence

Too many to count, but I'll focus on two.

1) I talk too much
Way too much.  I need to explain less, talk less, help less.  They are very capable of understanding for themselves.  When set to their own devices, kids are amazingly imaginative.  I need to shift my role from:

v. manage, help, explain, guide, show, organize, facilitate, coach, train, teach, etc


v. inspire, engage, enliven, arouse, provoke, challenge, push, exhilarate, spark, inspirit, orient, empower, etc.

I am very confident that kids are able to take care of the first list of verbs.  The second list is what I want to be doing.

2) Blogging is a part of me
This blog is a safe place for me.  I wrote this post as it was happening during the day. Writing is a comfort.  A candle.  It is how I express myself and how I grow as a person.  Some people could spend the whole day alone with their thoughts, just thinking.  Not me.  I need to write.  I need to get the ideas out of my mind head, and onto something.  I can't tell you the amount of stories and blog posts I have written and never published.  I just write them because I need to process an idea, and this is how I do it.

I could care less if anybody reads it.  Getting it out is an impulse I need to satisfy.

This really was an inspiring day for me, and I hope for the kids.   I don't know if it was,  I haven't spoken to them about it yet!  Monday morning I might....

For now though, I have some blog posts to read.


The Vitruvian Man, or Thanks Bruce

I am always quite inspired by the posts made at Authentic Inquiry Maths (even though he puts an 's' at the end of math when there is clearly no need for one).  I read them whenever they popup in my google reader (Feedly for the iPhone is awesome) and bookmark many to do later.  It never happens that we are studying the same thing at the same time.


The other day a lovely post about Da Vinci and the Vitruvian Man.  Bruce made a wonderful list of Da Vinci's observations about the human body:

- a palm is four fingers
- a foot is four palms
- a cubit is six palms
- four cubits make a man
- a pace is four cubits
- a man is 24 palms
- the length of the outspread arms is equal to the height of a man
- from the hairline to the bottom of the chin is one-tenth of the height of a man
- from below the chin to the top of the head is one-eighth of the height of a man
- from above the chest to the top of the head is one-sixth of the height of a man
- from above the chest to the hairline is one-seventh of the height of a man.
- the maximum width of the shoulders is a quarter of the height of a man.
- from the breasts to the top of the head is a quarter of the height of a man.
- the distance from the elbow to the tip of the hand is a quarter of the height of a man.
- the distance from the elbow to the armpit is one-eighth of the height of a man.
- the length of the hand is one-tenth of the height of a man.
- the root of the penis is at half the height of a man.
- the foot is one-seventh of the height of a man.
- from below the foot to below the knee is a quarter of the height of a man.
- from below the knee to the root of the penis is a quarter of the height of a man.
- the distances from the below the chin to the nose and the eyebrows and the hairline are equal to the ears and to one-third of the face.
I noticed that fractions were all over this.  I also noticed that one of the difficult aspects my kids are having with fractions is that they get confused about what the whole is.  If I take 1/2 of N's pizza, and I take 1/2 of M's pizza, are they equal?  Well, that depends on what the whole was.  Who pizza was bigger?  1/2 of a square cm is not the same as 1/2 of a square meter, but both are half.

Bruce's post inspired me to use the thing that we can most relate to as our whole (1).  


Setting the Stage

I showed them a picture of the sketch and tried to evoke some discussion about its purpose.  A couple of the kids had seen it before, and knew it was drawn by Da Vinci, but nobody knew the purpose of it.  I asked them to brainstorm what they thought was the point of this diagram.  There were some silly answers and theories (this is what people will look like in the future, with four arms and legs) but eventually somebody asked what the square was for.

S1: What is there a square around the body?
S2: It must be to measure.
S1: Measure height.
S2: Yeah, and measuring how long the arms for.
S3: Then what is the circle?
S4: To measure the stretched body (I think he meant spread eagle).
T: So, what is the purpose of this diagram?
S1: Measurement.

I explained that Da Vinci used this diagram to make a whole list of proportions of the human body.  I told them that we were going to check his work and see if his work was accurate. 

But, we are going to take them one at a time.


The first one I presented was the observation above.  Before we started, we needed to know what we needed to know.  And why we needed to know it.  How could we find this out?

In groups they came up with a list of ideas and methods.  All the groups knew that we need the following measurements; from the chin to the top of the head, and height.  There was also more than one way to analyze this data.

1) Height ÷ 8 = the chin to the top of the head
If we take our height, and divide it by 8, we should get a number that is very close to the number we got for the ch

2) chin to the top of the head x 8 = Height  
If the chin to the top of the head is 1/8, then it would make sense that 8 of those pieces would equal the overall height.  Or thereabouts.

3) Height ÷ chin to the top of the head = 8
If we divided the chin to the top of the head measurement into the height, we should get 8, or near 8.  

After a short discussion, we decided that this is the method we would use to figure it out.  We need consistency if we wanted to compare all the answers.


I stressed the importance of accuracy.  I wanted them to be as precise as possible.  While they were measuring, I walked around and criticized their methods, pointing out flaws and asking them to try something else.  The height was easy.  Stand back straight against a flat surface, put something flat on the head at a 90 degree angle and mark the wall.  Now, measure from the floor to the line.  They have been doing this for years, at home and at school.

Measuring from the chin to the top of the head though, this was a new one, even for me.  The kids came up with some great strategies:

- Measure from the chin to the floor and then minus it off the overall height
- Lay your head flat down on a table and trace it and then measure from chin to top of head
- Put a book under your chin, and a book on your head (both at 90 degree angles), and measure the distance between books.


We collected all of our data on the table (I also started a google spreadsheet with class measurements in it, it could come in handy later and we should add a lot to it) and took a look at our findings.  It seems the average ratio was not 8, but 6.87.  It seems that

height ÷ chin to the top of the head = 8

was not accurate.  I posed the question, was Da Vinci wrong?  They let that sink in and thought for a long moment.

S: Maybe we did something wrong?
S: Our measurements weren't accurate.
S:  No, it is because we are kids are still growing!
S: Yeah!  We did this on adults right Mr D?
T:  Yes he did.
S: So because our bodies are still growing, we are not the same.
S: Yeah, look at Mr Dwyer's ratio.  He is an adult man and it is 7.8!  Almost 8.
S: Was Da Vinci just talking about men, or does this include women as well?

That last question is a great inquiry waiting to happen....

Thanks Bruce.


Animate it

I love RSA Animate.  My first experience with it was Ken Robinson's Changing Paradigms.  The combination of visual and audio was more comfortable than a Ted talk, and easier to understand than a podcast.  I've wanted to try it in the classroom since I first saw the video.  What better time than now?

The kids got into class this morning and found a letter waiting for them:

I didn't tell the kids that I wrote the letter, I used the mythology of the situation to make it appear real.  When they pushed me on it I kept deflecting it back to them and insisting that this was real.  Most of them knew that it was me, and happily played along with the drama...
My purpose here was to create a sense of urgency and stress.  Recently we have been going slow, taking our time, and trying to think deeply.  I still want deep thought, but I want them to feel the pressure of a deadline as well.  I want to compare the two feelings.  How did it feel to have someone breathing down your neck and demanding something from you (in this case, me)?  Did it make your work better?  What did you learn from this?

We will return to these questions later.

1) Introduce the context and choose a topic

After reading the letter, we took a look at an RSA animate video (Dan Pink Drive).  I think the language in the video and the complexity of the ideas presented was a bit high for them, but they were watching and studying the animation and not the content.  We brainstormed a list of ways that we could reproduce this technique with iPads, iMovie, and another medium.  I had a couple of ideas, but again, they came up with so many more.  Watching them talk in their group was very refreshing.  I just sat back and smiled.

2) Research

We have been working on taking notes and talking about what information is relevant.  Listening with a purpose is hard to do, and something that kids need to be explicitly aware of when they do.  It takes practice.  I have noticed over the last couple of weeks that they are getting much better.  They still tend to write more than necessary, but they are getting better at pictorial representations of ideas.  It was my hope that this project would really help them visual their thinking (and writing).

In order to transmit the content to them, I chose to do a lecture/demonstration.  Me, standing in front of them, telling them about these theories; with a globe, a paper cut out of the moon, and a really bright light.  In the dark.  Like a live TED talk.  I could have easily given them videos to search on Youtube, or readings to pull information from.  I chose this method because it was a chance to interact with the material and with the purveyor of the material.  To ask questions.  To ask for clarification.  Live and in the moment.  Plus, I love this material and I love this demonstration.  It was more of a two-way conversation than a one-way conversation.  Youtube and Khan Academy are one-way transmission styles of education.  Pausing, rewinidng and reviewing is nothing revolutionary, it is still one-way.  Asking questions, getting inside somebodies head, figuring out how they think, and interacting on a personal level with learners will always be a superior method of education, regardless of what edu-tech blowhards say.

Rant over.

3) Create the script

With our notes and our research in place, we got to writing the script.  I stressed the importance of entertaining your audience as well as telling them about your ideas.  Some groups chose to entertain in the script, while others thought they would entertain in the diagrams.  I had naively assumed that you must entertain with words, and I was refreshed when students decided to entertain with diagrams instead.  As one boy said, 'it will be funnier if the person talking is really boring and the diagrams are really funny'.

Group writing is always hard, and it something that I continually struggle with.  Do I have one half of the group writing and other half drawing?  Then the strong writers will write, and the strong drawers will draw, and nobody is working on their weaknesses.  Instead, I chose to do each step as a collective.  The entire piece was written by the group of four.  Four is a big number for group writing, especially with 11 year olds.  A couple of the pieces were disjointed and needed some reorganizing.  Others were pure and gleaming and perfect.  Depends on the dynamics of the group (which in my class are all randomized).

In hindsight, I regret separating the script from the drawings.  I should have let them self-organize and see what unfolded from their brainstorming.  I was afraid of the two going in different directions and not matching up, but I should have given up and let them figure that out for themselves.  I was being controlled by the clock, and I made this decision because I thought it would be better for our deadline.

4) Plan your Drawings and 5) Shoot and edit

I intended this to be a brief planning session, but it turned into the actual filming part.  Whereas in the last step I put to much control on the process, this time I redeemed myself and let them go.  The drawings moved with the editing, and ideas flowed with the realizations of the technical limitations.  iMovie for iPad is a great app, but it is very limiting in what you can do.  The trailers feature is awesome, but the actual editing of films is not great.  Turning off the Ken Burns effect should be a simple matter, but it takes skill and dexterity.

After some initial headaches, a few pioneers led the way and showed the rest of us the most efficient way to do it.  As I was working with one group, other groups were figuring out new things and racing ahead.  It seemed wherever I wasn't, was the place where the most innovation was going on.  It felt like a dog chasing its tail.

We realized that it is easier to take quick movie's instead of using the pictures strategy (thus eliminating the Ken Burns problem).  The kids came up with some pretty cool solutions to keep the iPads stationary to avoid shaky images.

Had I let them start earlier and not group write, we would have gotten the bugs out of the way with sooner and had more time.  As it stood, our deadline was fast approaching and we had a lot of work to do.  They were focused, but they struggled with the pressure.  A couple of fights among teams and some poor choices.  One team worked beautifully well and was finished at 3:00.  Another team had difficulty making key decisions and didn't finish on time.  Another team posted their video to Youtube at exactly 3:27!

The final products are rough.  They are shaky.  They are missing details.  The backgrounds are a mess. They are very raw.  They could have been so much better if we had given it the proper time and attention.

That was not the point.


The next school day we had a group discussion (because we were so rushed for time at the end of the previous day we almost missed the bus!).  I posed the questions and then typed down the responses below:

How did it feel to have someone breathing down your neck and demanding something from you (in this case, me)?
- I felt that if we didn't finish something bad was going to happen
- We had to move quickly, it was good because you can do it faser, but bad because the ideas are not good
- When you (me) told us to hurry and that we were wasting time,  we realized it was true and made a better plan
- I felt tired, when I got on te bus it felt good to turn my brain off
- I felt out of ideas
- It felt good to finish, really good
- My body was sore and I felt like taking a nap
- It felt good to refresh afterwards
- It was nice to have nobody telling me what to do after it finished, I got to relax

Did it make your work better or worse?
- better; work faster and generate ideas faster
- better; if there is no deadlines nothing would ever get done
- worse; the pictures were rushed and it was messy
- worse; ideas were not as good as they could have been
- worse; we could have rehearsed and practiced our speeches

What did you learn from this?
- I didn't know I could work that fast, I always thought I was slow
- Teamwork is so important, I couldn't have done it alone
- Everything needs time, you don't always have the time you want, so you have to use your time well
- I don't like pressure, it gives me a weird feeling

What a great day.  I had a great time, though my role seemed different.  I was less the supporter and more the demander.  I was concerned with time and trying to get everybody else to think about time.  It was a good experience, but I am grateful that on most normal days, we are free to go at our own pace.  Placing time constraints on learning makes for a stressful environment.  I don't care how rough the final products look, it was never the point.

I tried to create a stressful environment.  It worked.  At the end of the day I felt exhausted.  I was drained.  I had spent the whole day managing and ordering people about, and not assisting in learning.  It was an illuminating experience, but not one I plan on repeating again for quite some time.

Slow down.  Enjoy the ride.  Reflect.  These have always been a kind of mantra for me.

Now I know why.


Lessons from the ski slope

A parent, whose daughter was skiing for the first time provided my favorite quote of the day:

Feels like we wasted an entire morning on lessons and instructions. She learned so much more in the afternoon by being thrown onto a hill that was too hard and trying to cope.


Finding out is so much fun

We have been working through our Inquiry into Inquiry.

The first stage was Tuning In.  We looked into famous paradox's.  We got a sense for what we know what else we need to know.  We were ready to start digging and investigating.

Next, we started our Finding out stage.  We have been stuck here for about 3 weeks.  Not because we are failing to Find out anything, but because finding out it so much fun.  I guess stuck is a bad word.  We have been reveling in this stage.  The thrill of learning new things, of using our hands, of researching.  We can't stop asking questions and there is so much more we want to know.

We will eventually start sorting out, but for now, let's just enjoy this feeling while we can.

The thrill of the hunt.  The high of discovery.

Let's just hang out here for a little while longer.


Conjectures in the Math Class

We have been practicing mental math in grade 5/6.  We are working on ways to divide by one digit divisors in our heads.  A great place to start was dividing by two.  The kids realized, very early on, that when you divide a number with an odd number in the ones column, you will get a remainder (57, 31, 77).  Most of them were using a chunking or splitting strategy.

Forgot to double the remainder...

84 ÷ 2

is the same as

80 ÷ 2 = 40
÷ 2 = 2

40+2 = 42

Today, we moved onto dividing by four.  After an initial discussion on the differences, we were all the same page about how to do it.  Dividing by 4 was dividing by 2 and then dividing by 2 again.  I wrote a couple of problems on the board and asked them to try.

Something wasn't fitting with their previous knowledge this time.  One chlid noticed that when he did 54 ÷ 4 he got a remainder.  Why?  I thought that when we divide by an even number we get no remainder?

Note: My role during what proceeds was to capture what they were thinking on the whiteboard, and to ask for clarification.  The ideas presented came out of the group, though I had a very powerful position in that group. I am also doing my best to remember what was said, I am writing this a couple of hours after it happened.  None of this was planned.  I had originally thought that we would do games to practice mental math, dividing by 4.  However, when a student presents a conjecture, I cannot let it go.

Conjecture #1

Another child put forth a conjecture.  If the dividend has an odd number in the tens place and an even number in the ones place, there would be a remainder (when dividing by four).

They set to work to try and disprove this theory.  It wasn't long until somebody found a number that goes against this.

36 ÷ 4 = 9

3 in the tens place is odd, 6 in the ones place is even.  No remainder.  Conjecture busted.

(At this point I wanted to push them in the direction of why this disproved the conjecture.  I was hoping for them to see that because this was a factor of four, it had no remainder, and all numbers that were factors of four would follow this pattern.  However, another conjecture was presented, so we went in that direction instead)

Feb 15 dividing by 4

Conjecture #2

Once the previous conjecture was disproven, another child immediately put forth a new one.  If the dividend has an odd number in the tens place, and either 4 or 8 in the ones place, there will be a remainder (when dividing by 4).

Again we set out to disprove it.  Though this time it was a little more difficult.  Everybody was doing their own thing, selecting random numbers that followed this pattern and trying to disprove this conjecture.

Somebody took charge and made a list of all the numbers that fit in this set (due to the nature of the conjecture, it was confined to numbers between 1-100).

Now they had a frame of reference and they quickly went through all of them and found the conjecture to be true.  Each one of these numbers (when dividing by 4) had a remainder.

Now, I took over and played the teacher role asked them to think of why this was true.  How can we explain this?

Proving it

We started to think of why this was the case.  There was, literally, three minutes of silence while everybody stared at the white board, deep in thought (or not, how am I to know?).  Finally, I heard a little squeak from a rather quiet child.

S: "Because of the 5 in the ones column."
T: "Can you tell us more about that?"
S: If you have a number in the tens column that is odd, when you divide it by 2, you will get a number with a 5 in the ones column.

This kicked off some thinking.  

S:  "if you divide all the numbers in the ones in half, the biggest number you can get is 4 (from 8), or 4 and a remainder from 9."
S:  "these are added to the five we already have in the ones column (from the division of the odd tens column)."
S:  "So, if you add an even number from the ones column to the 5, you will get an odd number, but if you add an odd number you will get an even number. 

for example

5 + 1 = 6 
5 + 3 = 8
even numbers

5 + 2 = 7
5 + 4 = 9
odd numbers

S: "and when you divide 4 by 2, you will get 2, and when you divide 8 by 2 you will get 4.  They are both even numbers, which means you will get an odd number when added to 5, which means you will have a remainder."
S: "what about 2 and 6?  They are even numbers as well."
S: "No, because 2 divided by 2 is 1, which is odd.  And 6 divided by 2 is 3, which is also odd.  And anything divided by 1, 3, 5, 7, or 9 can't be divided evenly.  
S: "So, the only way we could get an odd number (because that will give us a remainder) is by adding 5 to an even number, and the only way you can get an even number is by dividing 4 or 8 by 2.

At this point they were pretty happy with what they had done.  They weren't quite sure what they had done, or why they had done it, but they knew they accomplished something.  I asked them to reflect on how they were feeling:

- I think I learned something a new about numbers
- I don't know if this will help me do division, but it was fun
- We had to think really hard
- It was interesting to listen and understand, even though I didn't say anything

Another Way with Patterns

During recess another student presented a different way to look at.  She said she didn't want to share it with the class because she was afraid of being wrong.  I respected her decision and let her explain her way to me.  She showed me a list of all the factors of four.  She noticed a pattern.  When the tens digit was even, the ones digit were either 0 or 4 or 8.  But, when the tens digit was odd (as per the conjecture) the ones digits were 2 and 6.  Therefore, all numbers with an odd numbers in the tens and 4 and 8 in the ones, could not be factors of 4.  That is why it works.

Inquiries into Spoofs - Scientific Literacy and the Media

A colleague shared a video with me recently that really made me think.

It got me thinking about Scientific Literacy and the Media.  I watch this video and I see spoof.  No questions.  When I showed it to my kids, 3/12 thought it might be fake, and the rest were entirely convinced that it was real.

Videos like this are a powerful way to delve into this topic.  And there are many more out there.  They van open up many roads of inquiry.  From this one here a couple that came to mind:

- Are these rides even scientifically possible?
- What is it about the scientist that makes you trust him as a person?
- Which was attracting your attention more; the quality of his science or the impressiveness of the visuals?
- What media conventions do these that make this so realistic?

I have started a gDoc to start collecting more of these types of inquiries.  Please email me if you would like to contribute to building up a database of science/media resources.


Spoofs and Mockumentaries make you think.

Here are a couple more:

A site dedicated to saving an endangered tree octopus.  Very thorough.

This one is actually trying to sell you a product.  Shoes.  Really waterproof shoes.  It uses the image of cool very successfully.  I deconstructed this with my kids last year.  Fascinating ideas about media embedded in this.

Science is like a candle in the dark, but it can also be like a dark tunnel if we aren't literate in its language and methods.


The Many Ways to Research

My class has been absorbed in the Finding Out phase of our inquiry into light and sound.  We began by asking some questions, sorting them into categories, and then each choosing a questions that we would research.


While we are doing our inquiry into light and sound, we are doing an inquiry into inquiry.  Part of this is discovering how we research.  We brainstormed a list of methods of research.  We put them into a googledoc, and we put our initial thoughts down about the pros and cons of each.  Then, we chose a question and a research method that we would use.  The only catch, we could only use one method.  If you decided to research with books, you were bound to only the books we had present.  If you chose wikipedia, you had to only use wikipedia.


The Research

Before we started, we agreed on some criteria for our notes:

- they had to be organized
- they had to be in our own words
- they had to have pictures and words
- they had to focus on the main point
- they had to be easy to understand so anybody could read it

I set them off with their questions, headphones, piles of books, and iPads.  They struggled and soared.  Some of them had chosen a perfect method for their question and could easily find the answer.  Others really struggled with finding any information.  I spoke with students who were struggling and they mentioned that the method they had chosen was ineffective and inefficient.  I asked them to share their thoughts on this with the class.  We took a short break from research to orient attention to how we were researching.  Quick, simple, and collective.  I have been doing this a lot recently, part of trying to create a culture of reflection and self-awareness.

**There are some kids in my class who get really annoyed when I do this.  They are absorbed in their work, and then I keep calling them away to talk about matters of meta-cognition.  Some of them love it, others cringe.**

While the ideas were fresh in our heads, I had them go back into the gDoc and update the information for their method.  We got really authentic reflections, as the ideas were relevant and real.  After we reflected on the researching with one method, we opened it up and they were allowed to us multiple methods (often at the same time).  I have a great picture of a student sitting at a desktop computer with an open book on her lap and an iPad next to her.  

What amazed me the most during this was the sharing that was going on.  One student would tell another of a great site they found, or a page they saw in a book, or a video they watched.  They knew what everyone else was doing, and they were listening in the background of their work.  For an individual research project, it was surprisingly noisy.

After an hour or so, I had them make one more trip to the gDoc to make some more notes about what they thought.  Finally, I collected all of their work.  That night I looked through the notes and gave guidance on what to do.  Looking through the notes, I was able to see what students were struggling with what aspects of note-taking.  

For some, it was organization issues.  I suggested some frameworks to re-organize their ideas.  

For others, they were focusing on the wrong main idea.  I found a good website and emailed it to them.

For a few, the information was very text heavy.  I gave some search terms and told them to look on Google Images for something to draw.

The next day, they had an hour or so to look into the changes I suggested and clean up their page of notes.  In the end, I was very pleased with how much information they found, and the quality of that information.  Some pages were overwhelming.  They were filled with tons of facts and diagrams that won't be necessary, but that is okay!  The process of sorting and organizing is next.....  

We also had one more crack at the gDoc, just to add in any last minute thoughts before the big surprise....

The Big Surprise

After we finished up our one page (or maybe two) summary of our research notes, we got started with how to present it.  For this, the kids needed to determine what was the most important information, and what was less important.  They were told they had to design a one page answer to their question in a joint google presentation.


They would have to use somebody else's notes, and design a page for somebody else's question.

You could hear the groans from upstairs I imagine.  I listened as closely as I could to their concerns, all of which were valid and true.

"But we worked so hard on these notes and now we give it away."
"Why did I spend so much time if somebody else is going to use it?"
"They won't understand what I meant."
"They might not get our pictures, or the words we used."

I explained that the reason we were doing this was multi-faceted:
  • when working with other people, sometimes you have to try and translate their words into yours
  • this is the same process you were doing where you took information out of books and websites
  • it is going to assess how well you made notes that followed our agreed on criteria
  • it will tell you how well you focused on the main idea
  • this will challenge you to think
They accepted the challenge, reluctantly, with hesitation and a little bit of resentment.  I was not swayed by their protest.  I understood their point of view, but I told them that I think this is a great learning opportunity.  Some of my students, the ones who have really jumped on the Growth Mindset idea, saw it as a great opportunity.  Others, did not.  It made me think of my role as a teacher.  Am I their friend?  Or am I here to challenge them to think?  Certainly, the latter.  I honestly felt bad that it upset them, but at the same time I hoped they would see it from my side as well.  I believe in a democratic classroom, where the kids have voices and control over their learning.  However, at the same time it is not always that easy, and sometimes the top-down voice of the teacher takes precedent.... but even still, it made me feel uneasy to go ahead when so many of them were against it. 

After an initial 15 minutes of fiddling about with the look of their page, they started to get into a rhythm. 

(I think this is an important point that often gets ignored.  I can't tell you how many times that teachers have told kids to ignore the formatting until the end.  I am guilty of it all the time.  Yet.....)

They began to communicate with each other, ask each other for clarification, and engage in conversation.  Some were defensive of their work, not open to criticism from others, while others were able to see how it might not have been clear.  Clarity of ideas was one of the skills we were focusing on, so this was a place where I could give instant feedback and ask for instant reflection.  My role during this process was simply to get kids to think about how they took notes, and what they could have done to improve.  I must say, it felt really nice to be freed from the content, and only focus on the thinking skills.....

How this helped me with our Finding Out

This whole project acted as a way to inquire into inquiry and research, but it also let me do some more Tuning in.  By reading all of the pages, they were able to get a bigger picture understanding of Light and Sound.  At the same time (from a content/concepts perspective), I could see that they needed comprehension on vocabulary terms, and we needed to understand concepts like refracting, bending, transparent, etc.  They have the basic shell of these ideas, but we need more direct focus.  This project has led me to plan a learning centers day, where the kids will rotate through a series of very simple experiments, in the hope that they can pull it all together and find the connections..... the Finding Out will continue for a couple more days.


Slow Blogging, or Blogging Slow

I am thoroughly enjoying blogging recently.
I am writing more but I have


Instead of having an idea and
a post,

watching as the learning
my eyes.

It feels like an inquiry into how I teach inquiry.

Our inquiries are more
more skill driven,
more conceptual, and

Blogging has always been a part of my practice.

And always

But blogging slow, or
slow blogging,
has afforded me a
way of
looking at my practice

slow down
look harder
be more critical
and make new connections
new and exciting
ideas and spaces