Is articulation of thinking overemphasized?

The Case for Communication in Numeracy
Currently, one my school's goals is to improve our student's numeracy by having them develop their communication skills.  I have been a big proponent of this drive for communication.  My reasons are: my students are not very good at communicating their thought processes, their strategies, or even their attempts at thinking.  Why do I think this kind of mathematical communication is important?  My students are pretty good at calculation, they can solve problems, they are not bad conceptually, and they do have strategies for tackling mathematical thinking. They are NOT good though, at explaining their thinking.  And I think this kind of articulation is important because I think it will help them to solve similar or different problems in the future.

The case against?  Blink
During Spring Break, I get a chance to read for pleasure but I also listen to a lot of audio books. So while I am catching up on spring cleaning, I listen.  Right now, I am re-reading (actually re-listening to) Malcolm Gladwell's Blink.  It is about how people can make fairly accurate and discriminating decisions in the blink of an eye.  Though Blink is not an education book per se, it is making me rethink my stance on having my students communicate their mathematical thinking. 

Jam and Math
In one story, Gladwell describes how researchers gave a focus group a number of different jams and had them rank the jams in order of preference.  When the group ranked the jams in these circumstances, they ranked them in almost the same order as a field of jam experts.  But when a focus group was first asked to key on different qualities of each jam (such as colour, texture, taste, etc.), there was almost no correlation with the expert rankings.  It is as if getting people to focus on these qualities inhibited them from being discerning jam tasters because they were distracted by a number of factors. 

How does this relate to articulating mathematical thinking for elementary students?  Sometimes we ask students to do things that work counter to the end goal, in this case for example, the ability to be numerate or to solve mathematical problems.  Maybe getting students to overthink communication is getting in the way of being strategic in math the same way preloading the focus group with parameters distracted their jam judgement. 

I just know.
Over the years when I ask some of my best math students to explain their thinking, they will say, "I just knew."  I thought it was a cop out when they would say that, and when I would press them on it, they would get frustrated, not being able to articulate their thought processes.  I took that as evidence for increased emphasis on communication because I thought such emphasis would increase their ability to explain their thinking. 

Now, I am not so sure this is logical.  I think back to my own youth.  I used to love puzzles and logic problems.  I'd like to think that my thinking was ordered and strategic, but even now as an adult, I can say my thinking is never linear or organized.  Usually, when I am confronted with a problem or I am creating something, I think and I think and I think.  Then I sleep.  Then  I think and I think and I think.  Then I eat.  I think and I think and I think.  You get the idea.  I load myself with a whole lot of thoughts, and then during a random moment of clarity (usually in the shower, when my brain unclenches), I reach through the maelstrom of thought and get an idea or a solution or a weird glimpse that will lead to a solution.  (I am thinking of keeping a set of markers in the tub or at least some more absorbent towels handy).   But like my poor math students, how are you supposed to articulate this thought process?

A shift
So what do I do about my students' ability to communicate numeracy?  Abandon communication entirely?  No, but then, what?  I've never been a fan of word walls, especially because in my classroom design journey I've come to realise that they can become visual noise.  No, I think the integration of math and communication has to be more organic than that: lots of reflection and discussion during the thinking process, and lots of sharing after the problem solving process.  I still hope to expand my students' toolkits of strategies through sharing among each other, but also reinforce students internal metacognition strategies.

Teaching is Autobiographical

Last night, I had a dream that I was teaching high school Math (yeah, it was close to being a nightmare), and I was trying to help a student understand trigonometry in a way that was accessible to her and her mom, (her mom was in my tutorial too).  

After I awoke from the dream, my mind started to wander in my semi-conscious state.  First, it started with how teaching is about engaging students to increase their accessibility to learning.  Then I started to think about this workshop I have coming up, explaining about how classroom design helps SEL or Social and Emotional Learning.  Meshing these two ideas together (in the middle of the night, in the bathroom, typing on my phone), I came up with this:

Everything you do as a teacher is autobiographical.  Over a lesson, a term,  or a year, you are telling your story of yourself. The bits you reveal tell a very specific story.  The room is no different. It is part of the same story. Your story has to allow places for your students to come along for the ride. The kids have to be able to see or fit themselves in your story, your setting. 

You are trying to help kids create their own lives, their own stories by showing them yours. 

Adele is not an innovator. But who cares?

I've been listening to Adele's latest, 25, and I'm loving it.  It is everything one might expect from an Adele release: big, emotional songs.  Lots of adjectives come to mind  while I listen to the songs: genuine, cathartic, heart-felt.

But the word that does not come to mind is innovative.  When I think of innovation in popular music, I think of Jimi Hendrix, Madonna, David Bowie, or Moby.  Each of them is an innovator because they found ways to create new sounds or almost new genres of music.  Adele hasn't really created an avant-garde sound or a different way of making music.  If anything, her style hearkens back to someone like Edith Piaf who used soaring vocals to tug at people's heart strings.

Adele's gimmick is just pure talent.  She "gets by" by pairing songs that speak to people's innermost feelings and powerful vocals.

Similarly, good teachers do not have to innovative.  I know I write and think about innovation all the time.  I have read dozens of books about innovation (with respect to teaching and not at all related to teaching).  I have been in lots of schools and hundreds of classrooms.  I like innovation and I seek innovation, but I also realize that innovation is not the Holy Grail of teaching.

I have seen very workman-like teachers who are very effective.  They do not create much in the way of new material or strategies, but their students still learn a lot.  These teachers, like good singers, find ways to interpret other people's content or methods that really reach learners.  Conversely, I have seen very innovative teachers whose students did not seem to be getting much learning done. Sometimes, these innovative teachers had so much going on that it was hard to focus in on what students were supposed to be learning.

For me, I will still continue to seek new ways of reaching my students minds.  I try to be forward thinking while still using some tried and true methods from the past, and I try not to be judgemental of teachers who spend a lot of time in either of those camps.  

If I did have to pick one trait that I have witnessed increase the efficacy of teachers, it would have to be engagement.  Effective teachers seem to be able to engage the hearts and minds of their students. Just like Adele.

Teaching is Prototyping

The other day, I was reading about 3D printers, and how they are getting so good and so fast that they are not just being used for prototypes but actually for production. 

I remember first getting the concept of prototyping from reading Tom Kelley's excellent book The Art of Innovation.  He talks about the starting with a basic model for a concept (like the Macintosh mouse or a shopping cart), knowing that the model will be changed, adjusted and adapted with each successive attempt to get at the final product.   The basic model might go through countless iterations as testing informs each modification. 

I also talked with Lisa Mulzet about the idea of protoyping when she gave me my first look at a 3D printer, and how she used it with her design students.  Her students would design, make a 3D model adjust, redesign, and make another model, repeating the process until they achieved the desired end.


Reading this article last week about prototyping, I started to think about how I use prototypes, but I don't always do so intentionally.  The risers I created in my class for an alternative to traditional desks and workspaces were meant to be a prototype, but I didn't change them that much, though I did alter the original design after using the risers with kids in a class. 

The original plain, bare plywood and 2x4 prototype.

 

The tall riser, if you tip it on its side, is the same height as the short riser.  The original design I envisioned was closed at the back, capped with plywood so that when you tipped it on its side, you would have a massive flat surface like a stage, especially slid it up against the short riser.  We would have used it as a platform for drama, playing, or display.

 

Why didn't I stick with the closed-back design?  I wanted to get the risers in class as soon as possible so I slapped them together with the materials I had (remember the Ikea cabinet door for the top?), and a minimum of bought materials (mainly 2x4s).  Then when the kids started using them, the open back worked way better than the envisioned closed-back design. The students put chairs behind the tall risers so they could go face to face with students sitting on the short risers, picnic bench-style.  Students were able to crawl under the risers from both sides, creating some "cave" space that kids like.  The lack of a back kept some of the weight down too. 

 

Okay, okay.  Here is the real reason, maybe not the real reason, but the initial reason I didn't start closed-back: I couldn't get a piece of plywood that width to fit in the back of my car!  But all of the other good reasons for keeping it open-back came out of this initial accident and then testing the prototype in the classroom.  This is why prototyping and an open-minded approach to design is important because you get to work out the bugs and explore the possibilities without being constrained to a set design.

 

The current prototype (the design hasn't changed in 5 years) is stained, stabilized with cross beams,
and is covered with laminate flooring because it is durable, cleans nicely, and I had some left over!

 

 

The evolution of the lapdesks, from plastic doc holders to the current wooden "J" design has definitely been a (slow, multiyear) journey of prototyping.  Each model had advantages and disadvantages, and even with the current model, there are things I will change. 

 

 

The idea of prototyping really appeals to me, especially in terms of teaching.  I don't believe there is any one way to do anything, and I cringe when presenters or teachers say, "The WAY to do  ________ is ...."  Different things work for different teachers.  Different things work for different kids.  Yes, you need to have a goal and a plan, but that plan should be open and flexible to meet the needs and nuances of different students and teachers. 

 

Teaching is a series of prototypes.  We start with a basic model, and then adjust and modify to shape our learning.  We are going to make mistakes, but those mistakes are like chipping away unneeded stone to create the sculpture of learning.  As much as possible, I try to stick with this open model of teaching and create a workshop-like atmosphere: a little bit of instruction, a whole lot of trial and error, then we share and reflect, then we try again.  Repeat.  Just like prototyping. 

 

 

Prototyping goes beyond teaching for me.  I am a lifelong tinkerer.  I used to take stuff apart when I was a kid (and on the rare occasion I could get them back together).  I liked seeing how things worked and how I could change or improve them. Even now, I tend to buy cheaper things, thinking that I will change or improve them at some later date.  Maybe it is why I like old, anachronisms like safety razors, winding watches and fountain pens.  I wrote a post on another blog about how I like to mod guitars on the post: "Why Buy Cheap Guitars?"

 

The only things I don't prototype are people.  My family and my friends are perfect; they don't need change, modding, or improvement.    But our relationships?  Those are definitely works in progress. 

The Last Lapdesk? The J.

If you have been one of the 7 faithful followers of this journey, you would know that I have been looking for the ultimate portable desk.  In fact, the name of this blog came from the idea of portable learning anywhere.   Having the risers in my class where students work in different places all over the room and in different body positions, regular desks were not going to suffice.  So I started trying different kinds of portable desks.  

First, were the $2 plastic document holders.  They were light, gave a nice flat surface for writing and had a little storage, but they did not last more than a year.

Next, I tried dollar store clipboards.  They were okay, but because of the lack of storage, students lost a lot of pencils.  They were good for hanging up on the wall out of the way when not in use.

So I started making my own desks inspired by a wine box I saw.  They were gorgeous and had some storage.  Putting a clip on the long sliding lid made for a good clipboard and built in stand up easel. Unfortunately, these boxes were bulky, heavy, and used all of my woodworking skills, so they took a long time to build.  

So back to the clipboards for a while.

Then I came across some shower board and played with an easel idea.

But I wanted to have some storage, and came up with this idea based on a boutique shopping bag. Between the great surface that could be used as a whiteboard and the shopping bag appeal in the design, this was a very popular lapdesk.  After cutting the wood, it was a snap to build by using duct tape which gave a little pencil storage at the bottom.  But that was the downside: the tape could not hold up to the rigors of being a lapdesk.  Plus, the shower board is no longer available.

I started thinking about something sturdy and that had some storage.  I was looking at what students had in their pencil boxes that they needed all of the time.  I played with the idea of a zippered pouch velcroed to a clipboard, but my sewing skills are worse than my woodworking skills.  I kept going back to the students' ubiquitous pencil boxes to figure out how I could replace them.  That is when I had my eureka moment: Instead of replacing the pencil boxes, why not incorporate them into my design?

Enter my latest lapdesk incarnation:

The J.

(Yeah, I know.  Ooh.)

Made from my labour-friendly factory (where I normally park my car), skilled craftsman (with grade 8 woodworking skills) can whip one of these babies up in minutes (once all the parts are cut and prepared) for less than $1 CAD per unit.

 

The wood is cut from one large sheet of 3/8 plywood.  It is light and sturdy.

The lapdesk stands up for compact storage, but can also be hung from the handle.  

The solid wood bottom gives bottom ballast so the surface does not tip easily.  

  

The clip is allows the lapdesk to be used like an easel.  The lip, (the J) allows the pencil box to be nestled under the writing surface when in use or when stored.  

When the lapdesk is flipped over, the "hook" part gives a raised part 

so the user has a good writing angle.  

The screwed-in solid wood bottom is strong enough to hold the angle in place 

when written on (unlike the duct-taped model).

The writing surface is slightly larger than a letter-sized piece of paper, 

but unlike other incarnations, the surface is not so big that grade 2 arms can't reach the top.  

The clip can be moved to the side to keep the paper in place. 

Below is a chart that outlines the qualities that I wanted in my lapdesk (on left) with the different incarnations of lapdesks (top).  

	traditional desk	plastic transparent document holder	clipboard	box with sliding lid	shopping bag style	The J
portable	no, unless you are really strong	very	yes	somewhat	yes	yes
robust	very	fragile	somewhat	somewhat	NOT	hopefully
eco-friendly	no, but long lasting	not	somewhat	yes	somewhat	yes
economical (cheap!)	no	somewhat	yes	somewhat	yes	yes
buildable with grade 8 woodworking skills	nope	nope.  I don’t extrude plastic.	easier to buy	sort of, but time consuming	yes	very easy
storage	lots	yes	none	yes	yes	yes
good-looking	can be	somewhat	boring	yes	very	yes

While The J does not win in all categories, it does well enough in all the categories that are important to me.