It is a scary thing to let go as teachers. To let go of control and decision making. To step back and let a natural learning process take place. This year our grade 4 teaching team have grappled with the question of when to intervene and when not to. I have discovered that it is one of the hardest things to do as a teacher. We are wired to sort, to organize, to order kids and resources and to ensure that all learning moves forward as it should. Our first foray into handing organizational control to the students was during our unit under the theme of "How We Organize Ourselves". We realized that the more we as teachers organize kids the less hands on experience they have of organizing themselves. 

First, the students decided to organize a flash mob in the school cafeteria. Our 55 grade 4 students are all very opinionated!  The biggest difficulty was that everyone wanted to lead, they all thought their own ideas were best. They easily spent the first two planning sessions talking themselves around in circles, while we, their teachers, bit our lips and sat on our hands. After school meetings as a team centered around questions of parameters. Should we set any? How long were we willing to wait for action? Is there a time in which we will need to step in and at which point might we need to pull the plug? After the first agonizing week, where they went nowhere, we finally delivered an ultimatum. By the end of the next lesson, they had to agree on how they would organize themselves, who would be responsible for what, and they had to deliver a schedule of rehearsal times so that they could being making bookings for facilities and equipment. Suddenly they were off and away. Rehearsals went well and corporate  decisions were made, although not always the ones we teachers would have chosen. The final flash mob was a success - in our small world at least.  

We were ready to step up the ante. We floated the idea of a Maker Faire with the students. A Maker Faire would give them the opportunity to participate in the organization of another whole grade event, but also each student would need to be responsible for the organization of their own exhibit. The scariest part was that none of us teachers had ever even been to a Maker Faire before. The projects were all their own choices and in many cases they needed to source their own materials. We worked closely with our Design teacher who supported the students through the design cycle and the development of various prototypes. Some students chose to work alone while others grouped together. Again, it was excruciating at times to see kids spinning in circles achieving nothing but then at other times there were huge gains in product development taking place. The same questions of intervention and timing arose. I was hesitant to step in too quickly, wanting to give them the chance to find their own way back to the task. One group decided to design a product display box to market the headphones they had made. I watched them muck around with this ugly naked box for about a week, basically achieving nothing. Finally, I stepped in to demonstrate action and to get them moving forward. Within 10 minutes, 1/2 the box was painted and their mylar window had been installed. Suddenly they caught the vision and I stepped back again. Over the next two lessons that box was fully kit out with a persuasive paragraph, instructions for use, a photograph showing it in use and the product logo. In class, we had moved onto our new unit about persuasion and influencing others, so the students were also asked to develop an advertising campaign both for the Maker Faire itself and for their own stall.  

The final Faire was a huge success. There was a range of items on show from stomp rockets, to recycled can cars, a fishing game, a model airboat and even a cool hovercraft. One of my favorite was a very addictive squishy ball. Some products definitely had the WoW factor, while others were frankly weak and didn't reflect a productive engagement over 6 weeks. It was very evident in the final event who had shown good organizational skills. I hope the school repeats the Maker Faire, opening it up to the wider community in future years. I think this is an event where the quality of the exhibits can only get better each year, as they learn from each other and the experience of being a maker. The biggest indication of success for me was the very high level of engagement from our visitors. Many students had sourced sufficient materials to encourage visitors to get involved and make too. As I moved through the throngs calling for pack up time, there was a chorus of disappointment from the visitors and grateful relief from the presenters. They were exhausted, having spent 90 minutes teaching, demonstrating and helping others become makers too. 

How innovative can one be when introducing students to long multiplication? I wasn't sure, but I definitely wanted towards more of an inquiry process. A pre-assessment had shown only 3 students knew any procedure, so I was starting from the very beginning with most. I hadn't intentionally tried to bring design thinking into the lesson plan, so was surprised when mid-lesson my colleague reflected, "This is design thinking in Maths." I was quite delighted. We had just come off an inset workshop on building design thinking into all curriculum areas, and I had subconsciously done this in my Maths plan. Here is what I tried and how it worked. 

Rather than direct teach the steps of long multiplication, I wanted the students to inquire and uncover the steps. Although there are many procedures, I decided to stick with a standard long multiplication algorithm for this first lesson. Below are the stages of the lesson broken into the parts of the design thinking cycle we used. 

Analytical Thinking (Defining the problem to be solved)
I decided to first model through think aloud and shared responses what analysis thinking looks and sounds like. I did this with a 4-digit subtraction problem by writing one on the board and having a student solve it. Then I asked the class to analyze what they could see, starting with the obvious and going deeper. I modeled a few starting observations and then invited responses from the class. I scribed these responses all over the board, around the problem. I used 3 guiding questions

• What is happening?
  
• Why is it happening?
  
• What if ....I didn't do that? etc..
  

The sorts of thinking the students came up with ranged from 
- It is subtraction
- It is borrowing
- Numbers are being changed
- The working numbers are smaller than the numbers of the original problem  
- The working numbers are going down, from 9 to 8, or from 10 to 9
- You are crossing off borrowed numbers

I then had students work in pairs to analyze a long multiplication problem. They were a mixture of 3 or 4 digit numbers multiplied by a 2 digit number. Each pair had only one problem written and worked out, including the answer, in the middle of an A3 sheet. I asked them to use the 3 guiding questions to analyze what was happening and to write their observations and understandings around the problem. 

Here is some of the thinking that came out of this time
- There is multiplication of big numbers to make even bigger numbers
- There is a multiplication sign
- There are two puzzles
- First there is multiplication and then second there is addition to get the answer
- Here is multiplication, here is addition and here is the answer (arrows)
- This is a 50 (digit 5 in ten column circled)
- This 1 looks like a 1, but it really means 100 (digit 1 carried over into the 100's column)
- Small working out
- Cross out the working after it is used
-  First we do 306x6, then 2nd we do 306x10 and then we add it together. (306x16)
- 7x6=42, so the 40 goes to the tens place and the 2 goes to the ones place.
- There and two lines (answer bars)
- This means = (pointing to an answer bar)

They discovered a lot of truths about how this algorithm works.

• No one in the class identified or defined the role of the placeholder zero, although several followed the procedure)  so I know that will definitely be part of my follow up. 
  

Trial & Error (Prototyping)
Once students started to form an idea about how the algorithm worked they were told they needed to test this idea on the mini-white boards. I encouraged the students to prototype early, even if they only had a partial idea. They did not need to understand the whole problem before starting. If they were correct they could add that observation to their sheet and continue, otherwise they needed to revise their ideas and go back to further analysis thinking. 

Practice and Teaching (Refining)
Once the algorithm was fully understood, students needed to be sure that their partners understanding was equal to theirs. For the few students that had already learned long multiplication this meant that they couldn't skip analysis or trail and error as their partners needed to see these stages to fully understand as well. In the last few minutes of class, I placed a few extra unsolved problems on the board so that they could have further practice. I encourage them to take turns with only one solving a problem each time and the other acting as a mathematics coach. They could also create their own problems to further challenge themselves.  

Adaptation (Modification & Enhancement)
Only about 1/2 of the class made it all the way through to confident understanding of the algorithm, and all of them need further practice to gain computational fluency. This is where I will focus in the immediate lessons. However, my teaching partner multiplies by a slightly different algorithm and I am sure 1 or 2 students will come up alternative algorithms too. I will therefore plan some lessons that let all students replicate this same investigative approach to the other algorithms. We will probably finish by doing a very personal comparative investigation. In this they will write their own problem and then solve it using all the algorithms they know. Under each they will need to write a reflection of pros and cons, and make a personal choice for their preferred method.