Monday - 1st Year Focus Teachers
Most of the discussion from this day is from the early year's group. We spent the start of the day looking at what was tried since last time using the coding cards that were the focus of the lesson observation last time. They had time to speak in table groups and then provide feedback to group. The discussion started with the idea that the learning task can look very different depending on whether you are looking at a preschool, primary school or high school, however the learning intention that sits behind the task can be very similar in all of those sites. When you focus on the types of thinking you want children to be doing rather than focusing only on the content there are a lot more similarities than differences between the levels of schooling. Some interesting points came out across all sectors of schooling but only some of these are summarised below.
Next we discussed the tasks that would be delivered in the preschool. Rather than watching the whole group being worked with the focus teachers were asked to choose a task that they would take into the preschool and engage the children with. There were three tasks in total that the focus teachers could choose from.
One of these tasks is shown below, it involved placing 3 rectangular pieces of tissue paper inside a clear A3 document file. Tissue paper was used so that children could see through it to the layers below. The tissue paper was placed in such a way that it provided a range of interesting shapes. The intention of the activity was to build the understanding that the shape of an object is defined by it's border. When teachers had a go at the task themselves it was interesting to note that shapes like those in light and dark blue shown in the second image were much more comfortable shapes than the one in red. The thinking associated with this is that there are a number of factors that may make the red shape less comfortable when defining it as a shape. Unlike the others it contains a concave angle, one that points into the middle of the shape as shown by the purple star. It also has a number of sides that are very short when compared to the others. This is not the case with the blue shapes. We talked about the representations of shapes we see in most places whether that is on posters, in books, etc really only have the shapes displayed in the one way (e.g. triangles are normally equilateral and have a flat base and the point facing up) and therefore when we see a shape that is not consistent with the limited examples we have been exposed to through the resources we use then it creates some conflict as to whether it is a shape or not.
Tuesday - 2nd Year Focus Teachers
The Tuesday session was the first one for the year for the 2nd year focus teachers. A lot of the day was spent on reflection and planning, at least in the first section of the day. Teachers were asked to reflect on the following questions
Following the reflection and sharing of responses to these questions the focus teachers were asked to share their hopes for this year using the following questions as a guide.
In thinking about and sharing their responses to these questions the focus teachers were helping to inform some of the work that will occur over the course of the year as the training is tailored to suit the needs of the focus teachers. Their thinking on each of the questions is outlined below (click to zoom in).
During the course of the day we also spent some time looking at two separate but connected tasks. The first of these tasks was done in an observation lesson last year at SNPS. The lesson is from the NRICH website and a link to this lesson is here. The lesson is about taking a 1 to 100 square where each digit is written in code and the square has been cut up into jigsaw type pieces. The aim of the task is to use the clues on those jigsaw pieces to successfully reassemble it. It works on the idea of place value in a much more strategic way. By removing the numbers and substituting them with symbols students really need to stop and think about the number of digits and the place value parts. Giving them the same task but with the actual numbers on there would do little to build this understanding as they would think about number order instead, e.g what comes after or before, rather than looking at the place value parts.
It is a task that students initially find to be very difficult, They start trying to piece it together without looking at the symbols for a quantity of time and find that they are not able to do it, it is they that they stop and think and begin to notice the codes on the pieces and start to think more strategically how they may do it.
The second task that these teachers were given was also from NRICH, the task itself can be found at the following link. Like the last activity it strongly targets inhibitory control in relation to stopping and slowing down the thinking by thinking about what numbers it may be. However it uses a lot of working memory to keep the rule in mind as you search through the 100 grid for possible matches, many of the teachers supported their own working memory by determining ways to represent their thinking. The task also accesses working memory in relation to keeping the rules in mind so that they can be compared and contrasted, looking for hints in relation to the four rules that are useful and the four that are not. After these tasks the focus teachers were given some time to think about how they may use or adapt these tasks, or the intention behind them, in their own setting with the children that they work with.
In an interesting discussion that occurred with some of the kids at the school through the lunch break we looked at the idea of operations with positive and negative numbers. On a previous visit they were asking about why subtracting a negative number is the same as adding the non-negative. They new how to do it but were very curious about how and why it worked and it was a question raised with our visitors from Flinders University at the previous sessions. Having received a reply by email in the time between sessions they still had questions so came to talk to us again.
This story is a very strong example of the shift that is occuring in the thinking that kids are bringing to their mathematics learning. Operations with negative numbers is an abstract concept to think about, however they were not happy with just knowing how to do it, they wanted to know why it works, they wanted to know why it makes sense. These kids were able and willing to think about such an abstract concept for an extended period of time and were being strongly metacognitive by checking their understanding against the new learning they were doing. They were able to articulate whether this new perspective on the problem was one that convinced them or not. For the teachers in the room at the time this created a lot of great discussion about how we can represent abstract contexts in concrete ways and about how we carefully consider and craft the explanations we give to avoid creating more confusion.