Where do ideas come from?

I was over at Authentic Inquiry Maths (one of the best math teacher blogs on the internet), reading a post about ideas for inquiring into 3D shapes.  Great stuff.  As I was reading, a new idea struck me so I left a comment:
Imagine you live in a 3D shape.  Design the interior.  Perform a mime for the rest of the class describing what life is like inside this shape.  The rest of the class guesses what shape you are living in.

I have no idea where that came from, but I want to try it!

Where do your ideas come from?  Do you know?  Do you care?


Visible Thinking; Growing Definitions

This is a strategy that is not in the book or on the website (note: it might be, but I haven't come across it yet).  I first heard of this from a poetry workshop with Larry Swartz about three years ago.  We did it for the word Poem, but it can be done with any word.  I am calling it Growing Definitions for now.  Also, I am still wondering about what thinking moves (word in blue on the poster0 would be best for this routine.  Obviously, defining must stay.  Not sold on the other two.  Any ideas?

Context: Studying bias in the collection of data; for example surveys

1. Show the word (we were Bias) and have each student write a personal definition for this word.  This was tough for my kids.  They kept wanting to use the word bias in the definition of the word.  I let them look at a dictionary to get help with how definitions are worded.

2. With a partner, write a new definition.  This was fun.  At first they tried to cram them both together, but we stopped and reflected that that might not be the best strategy.  We eventually admitted that sometimes, another person said it better and you should go with what they said.  In the future, we are going to focus on different wording and phrases, which one sounds better or makes more sense.

3.  With a group, write a new definition.  Again, they did a good job of choosing the phrases and words that they needed.  Teamwork was the biggest issue at this phase, and in the future I wil orient attention to how we are working together, rather than what we are working on.  Some people were quite enthralled with their own definitions and had trouble dis-enthralling themselves and admitting that others might have done it better.  Still, there is a sense of value judgement in this step that I really like.  This would be supported well by providing evidence for your reasons.

4.  As a class, write a new definition.  I led this phase so it went rather smoothly.  I collected all the ideas in a central place (our whiteboard) and then we picked through them and took the parts we liked.  The final definition was much better than anyone could have possibly written in the first stage.  A wonderful example of collective knowledge building and teamwork in action.  In the future, I will have the ids led this session.  Maybe start with a moderator and then slowly take that support away until we working in an egalitarian way....


Let the Bag decide... random groupings in the classroom

A while ago my wife (who is quite the seamstress and crafter) was experimenting with a new type of canvas she bought and she made this bag as a test prototype for something larger.

[caption id="attachment_1340" align="alignleft" width="240"] The Bag[/caption]

She was unimpressed with this design but it sparked ideas for something else.  I have always been a garbage hunter my whole life, so I took this bag into my class to find a new use for it.  At the beginning of the year I found it in the bottom of my desk and decided to use it for our random groupings bag.  On a math hexagon, I wrote each students name and places it in the bad.  I had originally planned on using it every once and a while to assign random groups for projects and possible seating arrangements.  I had no idea it would evolve into what it has become in our classroom.  The bag has become a supernatural being.  It decides arguments.  It makes groups.  It assigns seats.  It chooses what to do on free time.  Whenever the decision process comes to a standstill, we let the bag decide....

Random Groupings

This summer, I was listening to a speech given by mathematics super educator/researcher Peter Liljedahl from Simon Fraser University.  He stated that completely random groupings were more efficient than assigned groups.  I had been using quasi-random groups until this point, with the occasional spattering of a completely random group.  I wanted to know the research behind it so I shot him off an email asking for a bit more information.  He responded with a chapter of a book that he was writing on the subject.  Unfortunately, I cannot link to it since it is not yet published, but here is the quote at the beginning that basically sums up the findings.
Results indicate that the use of visibly random grouping strategies, along with ubiquitous group work, can lead to: (1) students becoming agreeable to work in any group they are placed in, (2) the elimination of social barriers within the classroom, (3) an increase in the mobility of knowledge between students, (4)a decrease in reliance on the teacher for answers, (5) an increase in the reliance on co-constructed intra- and inter-group answers, and (6) an increase in both enthusiasm for mathematics class and engagement in mathematics tasks.

Who wouldn't want that?  I think to important take aways from this are; visibly random grouping strategies (the kids have to know it is random) and ubiquitous group work (group work has to be a major part of life in the classroom).

Reflecting on this before the year started, I was having difficulties giving up that control.  In my head, I still wanted to keep certain students apart, or put certain students together, because I thought it would be best.  I constructed a model of how we could use random groupings but interjections from me.  I was ready for the school year to start.  Then, I found the Bag.

I don't know what it is about this bag, the pattern, the fact that my wife made it, the imperfections in the seams?  I just like it.  It is beautiful.  I decided that I would put all the chips I use for deciding groups into this bag and keep it on my desk.  Before the first dy of school I made a bold promise to myself.  I would use this bag to select groups all the time for projects.  Sticking to it was easier than I anticipated.  Perhaps it was how well this groups works together, or the atmosphere of the class, but I found that I did not have the issues that I thought I would have with random groups.  The engagement was there.

So, I decided to push it further.  The bag started to be used to decide seats.  Before the kids enter the class every morning I chose a name out of the bag and place it on the table and that is the seat for the day.  Even this evolved, it has turned into a once a day thing, into a three or four times a day thing.  After recess the seats are changed.  After lunch they change.  Sometimes, in the middle of class they change.  Sometimes, we are working with the same group (that the Bag chose of course) for the entire day.  The kids ask for the Bag to decide games at recess, or what to do during free time, or who likes who games (grade 5 and 6, what can I say?).  If there is a dispute and the Bag is used to moderate, the decision of the Bagis like the law.  One does not argue with the Bag.

[caption id="attachment_1342" align="alignright" width="225"]Hanging proudly on our tree, in the center of class Hanging proudly on our tree, in the center of class[/caption]

Here are some things I have noticed since I started this idea at the beginning of the year.  These, at least to my group, have been the main benefits of randomized groups:

Any group needs a great deal of redundancy to work well together.  A shared language, culture, and interests.  However, the same groups also need diversity to be creative.  Back when I chose the groups, I was deciding the diversity of a group.  The bag, doesn't care.  It forces the diversity.  It brings it to the front.  It forces you to think critically of how we differ from each other and how those differences will lead to new and creative ideas.  This has led to a meta-awareness in our class of how we are in a group; what is my learning style?  What am I like to work with?  How do I gel and blend with other people?  How do I work with those those do not gel and blend with me?  The self reflection that that bag has provided the atmosphere for has been amazing.  The kids understand themselves better, and they understand how they operate with others.  They are adjusting their temperaments and behaviors to fit those new members of their group (not all the time, but gradually this class is becoming much more collective than fragmented).  Some of the rivalries that existed amongst students are disappearing slowly.

If I take it back to Liljedahl's findings from his research, I see that it in indeed happening in my class as well.

(1) students becoming agreeable to work in any group they are placed in (Defiantly!  Not just that, meta-aware of how they work with others and able to speak about that awareness)

(2) the elimination of social barriers within the classroom (I see friendships forming and an openness with others, and I know the Bag is not responsible for all of it, but it certainly plays a role.  How big of a role..... not sure that can ever be measured, but I have a instinct that it is important..)

(3) an increase in the mobility of knowledge between students (defiantly, working with everybody and the chaotic nature of switching places and groups has led to an understanding of who knows what, what everybody's strengths are, and if I need help with something I know how to go to to get it)

(4) a decrease in reliance on the teacher for answers (not sure about this one, because it is just my style not to be too helpful in the first place!  The kids in my class are getting better at not asking, but not sure if there is anything to do with the Bag.  My instinct says no...)

(5) an increase in the reliance on co-constructed intra- and inter-group answers (for sure, even thought they are in groups, they are constantly bouncing back and forth to help each other, and using ideas that others groups form.  I believe this is directly related to the understanding of their different styles of learning that the bag has forced on them)

(6) an increase in both enthusiasm for mathematics class and engagement in mathematics tasks (not sure what the role the groupings play in this since group work is ubiquitous in my class to begin with)

All in all, I feel that the bag has really shaped our environment.  It has been a powerful force and has created opportunities for us to learn from each other, and most importantly, about each other and ourselves.

The random groupings are here to stay...



Visible Thinking; Looking Ten Times Two

This one is not in the book, but was recommended by a good friend from the Visible Thinking website.  The flexibility of this routine allowed a very interesting conversation to emerge, one which I had not planned for.  This is what I love about VT, it allows a space for emergence to take place, and expands the scope of what you are doing to new and exciting places.  Also, anyone who knows me well enough or reads this blog could predict that I would eventually use the VT routines in a Math class. Took me a little longer than I thought it would, but here it is....


Context: Starting a new math unit on Data Management

Quietly Look - this is an important step for tuning into the diagram.  I had 30s on the template above, but it was more like a minute.  I have no idea what they are thinking about, but I tell them to try and look at the whole picture and just feel it.  We meditate daily in my class, so I think they are getting a sense of this feeling that I talk about, which is impossible to put into words.  More than feeling, a sense of mindfulness....

List 10 Words - Here the groups worked together on their page and wrote down ten different things that they saw.  I didn't really interject here, but I saw something interesting emerging in what they were writing.  At this point it was a feeling that I couldn't explain.  The picture itself was just a simple graph, with bars and lines and titles and a scale.  It could have been any type of graph really, I wanted them to thinking less about the details of the graph and more about the concept of Data and how it is visualized.

List 10 more Words - This is where something interesting happened.  A student in the class made a comment to a classmate that she was reading that wrong.  At this point, people were struggling (which was my hope) with listing what they see.  They started to read the graphs instead of just listing what they saw.  I noticed that there were two distinct types of comments being written down; those that were about what is there, and those that required an act of reading.  For example, the observation that in the year 2010, Cats are more popular than Dogs, is reading.  It does not say that on the graph, but by understanding the data and the context of the picture, they read that information from the graph.  They are taking out of the graph.  I stopped the class and introduced this theory I had between Seeing and Reading.

We then moved into a discussion about the difference between the two.  What is the difference?  What are we doing that makes these different?  Together as a group we created a mind-map.

This led to them having a discussion with their groups about which of their 20 points were seeing, and which were reading.  At this point I had completely abandoned my original plan and was in adaptation mode, bouncing among the groups and observing where they were taking the learning.  They were shading in the observations in different colors and trying to differentiate the two different ways of observing.

I thought that we needed a way to pull all this together and finish this off, so I jumped right into the main topic at hand, Data.  As a group, we made a huge mind-map, and they copied it down into their books.  I hadn't planned to actually introduce the main idea until tomorrow, but the great thinking that was happening made we want to keep going.  That is one of the things I love about Elementary School, we don't have fixed blocks where a subject is a subject.  We are able to go with the flow.

Again, a VT routine sparked great thinking, which sent us in an interesting direction that I had not planned.  That is the true power of this book.  It's expansiveness.


Visible Thinking - Generate-Sort-Connect-Elaborate: Concept Maps

Another really great day with a VT strategy.  Despite having the worst possible name for a classroom routine (who is going to remember that?) it provided for some real critical thinking opportunities, and dovetailed nicely into our topic of the day.

Context: we are starting a new Unit of Inquiry into healthy living and the choices we make

What is a concept map? - This was their first introduction to the specific term concept map.  We came to a basic understanding that it was like a mind-map, but a bit more organized.  One of my key focuses of this unit is developing scientific models, so I am comfortable with a little fuzzy thinking around the idea of a concept map.  It will come.

Generate - This step is easy, list words, phrases or ideas that relate to the main topic (in our case the main topic was simply the words Healthy Living).  Still, it is amazing how off topic they can get in just a few steps.  One child says healthy foods, another says bananas, and then another says palm trees (I have no idea, don't ask) and suddenly they are discussing aspects of living on a tropical island, not the more broad topic of healthy living.  A good point of orientation for the teacher is pointing out when something like that happens, and for the students to eventually notice themselves and self correct when they have gotten off topic (I use the term loosely, because often these off topic moments have a way of producing some magical moments if they are allowed to blossom).

Sort - In this step, you can sort the ideas generated into a number of different variations.  I chose to go with a cluster effect around the middle topic, where the cards nearest the middle are the most relevant, and the ones farther out are less relevant.  I could have easily chosen a list, or a ranking, or any number of ways to visualize information.  This is what I love about Making Visible Thinking, it is not prescriptive, it is easily adapted to new situations and changed and made better.  This lead to some great discussions about the details; is diet more important than exercise?  Are they the same?  Big questions with no answers, but tons of learning potential.  Lots of talking and thinking.

Connect - This step is making connections between the different ideas.  Making connections was a great way for them to expand their discussions in the Sort stage.  They had trouble deciding on which was more relevant, so in this stage they got to further visualize those difficulties by seeing what is similar among the parts.  If the sort step was the zooming in, this was certainly zooming back out.  Reminds me of one of the elements of sustainability from Fritjof Capra, from parts to whole.  Understanding how the parts work within the whole is central to a complexivist approach to education.

PS - Writing on desks is a great way to build a collective spirit.  Also, engagement is not an issue!  It takes the idea of a concept map and makes it more collective and collaborative.

Elaborate - Here we took one aspect that we were most interested in and further expanded it to see what else we could come up with.  This is such a great step because it makes this messy diagram even messier, and I hope the kids realize that this messiness is inherent in all things in life.  The world is messy.  It is non-linear.  It is complex.  Sometimes, simplifying that messiness is the worst thing we can do to children.  Sometimes, they need to swim in the swamp and feel it themselves.  It leads to more ideas, and more possibilities.  By only elaborating one card, they get the sense that the map would go on forever and the connections would be endless.  One of these days, I want to make the biggest, messiest, most non-linear concept map ever.  On the table, with markers, everybody together, branching off until the whole table is filled. Hmmmmm.....

By the time we finished this step, we had a nice little start to our unit underway.  I Concept Maps and put them up our learning wall.  Next job, take the key concepts we decided as a group and turn them into a scientific model.  This routine set the stage perfectly for that task, which should occupy our time for the next couple of days.  Wonderful set up.  Now, we have to do something with it....


Teapots sent

Finally, the teapots are done and sent. This has been a wonderful project. We covered the entire geometry curriculum in a single project, and more. We took our time, we zoomed in and out of the project, working on it for a bit and then taking a break to practice other skills. Engagement was never a problem, everybody was eager to learn because they wanted the box to arrive safely. Now, we wait. The recipients in Hawaii, Bandung (Indonesia), and Idaho will soon receive their boxes. Where will they go next?

GoogleMap Showing the Teapots Tracking


Visible Thinking; The 4 C's

I like this one.  This led to an amazing class discussion and caused some real cognitive dissonance with the kids.  I think that text I chose was perfect, and that really pushed the conversation forward.  It was deep, with lots of room for different ideas and interpretations.

Henry Climbs a Mountain is a book about the one night that Henry Thoreau was put in prison for refusing to pay taxes to a government that recognizes slavery.  I needed to fill a couple of content holes before we started to make that everybody knew what government, taxes, illegal, and prison meant.  After some explaining, I felt that we were all on the same page and we continued on with the routine.

Connections - I found that during this stage the kids needed support to make deep connections to the topics.  Most of them were comparing some aspect of their lives to Henry.  We both like drawing.  We both like to walk or hike.  We both get in trouble.  Yes, well why?  Do you both to like to draw for the same reason?  What is the motivation for your and Henry's drawing?  Finally, we started to see connections like we both like drawing to express ourselves, or to imagine a new world, we go for hikes to think or to be free, we love our freedom.

Challenges - This was the most interesting section.  A spontaneous debate arose about whether it was okay to break the law when you see something unfair.  Some thought it was, others said it wasn't.  We tried to change the context to our school, and decide if it was ever okay to break rules that you thought were unfair.  This brought us to Thoreau's concept of Civil Disobedience  which I explained to them during the discussion and how he applied it in his life.  I tried to sit back and let them discuss it amongst themselves.  I interjected a couple of times, only when there was a misunderstanding of the meaning.  I love this topic, and I am very glad that my kids were thinking about it.  It pushed a lot of them beyond the zones they were comfortable with, and it certainly ended with no clear answers or conclusions.  Just more to think about.

It is my personal opinion (and not that of my employer, institutions of education that I attend, or organizations that I am affiliated with) that kids nowadays need a little more of the idea of civil disobedience.   A healthy distrust and skeptical eye trained on the people and organizations that hold power in our world, and an ability to organize against them in a peaceful and non-violent way are essential skills for a globally connected world.

Concepts - After the discussion we had on the challenges, this part was easy.  It was still fascinating to see how the responses varied.  This book is about fighting the government, changing un-fair laws, doing what you think is right, helping everybody to be free.  Each of these are vastly different if you break them down, but each kid had a different angle to which they thought was the most important.

Changes - This was hard, and this one something that I think will get easier as we delve deeper into Visible Thinking.  The step is asking for a meta-analysis of how your thinking is changing.  Essentially, it is asking for you to use the thinking skills to reflect on the thinking skills.  Some kids just are not ready for this step yet, more scaffolding will be needed.  They wrote things like I didn't know that people (insert fact from the story), or I am going to (something that Henry did).  Only one child in the class got the idea and wrote I am going to keep an eye out for people who use their power for bad things.

This step is hard, and will come with time.

Our visible thinking wall is starting to grow.  I have been referring to the thinking routines and the thinking moves during our lessons as I see them in action.  I hope that by orienting attention to this board, that the kids will soon start to do the same.  I realize that I will have to start repeating these activities as well, and doing them multiple times so that they get ingrained in the collective memory.