For the second year in a row the Empowering Local Learners Project is a finalist in the Innovation category in the SA public education awards. a link to all the finalists can be found here
Monday - 1st Year Teachers (Middle Years Group)
In order kick off the morning the quote below was put up on the screen for people to think about.
"Good mathematics is not about how many answers you know... it's about how you behave when you don't know" - Author Unknown
Kristin then handed out an executive function summary and were ask to reflect on the quote in relation to that summary.
The discussion continued in relation to ELL not just aimed at improving subject knowledge or executive functions, it is aimed at improving both, using one to build the other.
From here we started talking about about the lesson that would be presented, it was a lesson that would introduce fractions with the class, they had done fractions in previous years but this was the first time that had done it this year.
The lesson started by asking students to fill out a post it note using the following prompt
"When I hear the word fractions I feel ____________________ because _____________________________________"
This was to help them start thinking about their past experience with fractions but also was an opportunity to write those feelings down. Writing down your feelings about an activity or bit of content is particularly effective in helping to reduce the effects of maths anxiety. The post it notes were separated into postive feelings and negative feelings and it was noted that there were more positve than negative responses, mainly because they felt confident as they had done it before.
In the next task the students were asked to make up a diamond diagram. This diagram is a way in which students can represent the different ways of thinking about a mathematics problem. How to make one of these is shown in the video below and a copy of one a little closer up is shown in the image.
In this activity students were asked to pick a card out of a pile, the card had two fractions on it, they were asked to write these two fractions in the centre diamond as that represents the problem to be solved. Their task was to determine which of the two fractions were bigger. Some of the strategies used by them to do this are as follows
From here the rest of the day was spent on some further discussions and some planning for what they will try before the next session
Thursday - ELL Site Based Leaders
In the morning the teachers worked on a problem called the "fold and cut theorem" which essentially states that any shape with straight sides can be cut out with just 1 straight cut if you are willing to fold the paper first, a video on this theorem is below. Teachers were first asked to cut a square out of the centre of a peice of paper using only one straight cut and were then asked to look at the other shapes and rank them from easiest to hardest to cut out. They then had a go at a few from different levels to see if they could do them. The shapes given are available from the file below.
anticipating likely student responses to challenging mathematical tasks
Monday - 1st Year Focus Teachers (Early Years Group)
In the morning session the early years group looked at why our partnership has the focus on executive function. The conversation was around how the ELL project is using maths is the vehicle for building executive functions, but improved maths outcomes is not the only destination.
We looked at some of the charts and tables from the Dunedin Study which followed a group of about 1000 people born in the same year from the year of their birth, right through to their mid-thirties, and looked at all the different aspects of their life such as health, wealth, relationships, careers, incarceration, etc and found a strong relationship between strong inhibitory control and stronger life outcomes. We also looked at an article from Adele Diamond regarding the impact of executive functions on all aspect of our lives. So although we are looking at how to improve mathematics learning, we are probably more accurately looking and developing their dispositions towards learning in every subject area and looking at how we can develop problem solving and reasoning skills both in school and beyond it.
We then had a conversation in small groups reflecting on their growth as a result of the ELL project. They were asked to reflect on three questions which were
People shared a lot about their journey with the project to this point but there were a few key threads that came out of it.
These responses really spoke to the need of the focus teachers to develop their on executive function as they are implementing a greater focus on developing them with their class.
We then moved into a discussion of what would happen in the lesson, as an introduction to this they were shown the video below that comes from the Adventures of You series of videos. This is a video that was going to also be shared with the children during the lesson.
After watching the video there was some discussion as to whether the development of executive function follows the same process in the video where different executive functions are at different levels. The executive functions are not in different levels as stated in this video, they are a set of intertwined skills that all impact on each other, however it was also mentioned that inhibitory control is normally the first step. It is very difficult to focus on your working memory or on thinking flexibly if your are not yet focused enough on the task by using good inhibitory control, it is also hard to think flexibly if you cannot keep enough in your working memory. So by developing one executive function we are also impacting on the other two. It was explained that the lesson would start with children thinking about how their brain works then then working on a small maths task at the end of the lesson. During the lesson the teacher were asked to look for evidence of:
In the lesson with the children we showed them the video and then asked them to think about all of the different things in their head that their brain controls. They were asked to use a post it note to write down all of the things that is stored in their brains, with one thing per post it note. They then put these on a piece of brown paper to see how how "full" their brains are. The images below show some of their work on this.
They were then ask to think to try and think about something that is not there yet and there were a number of children who went and checked the paper to see if they could come up with something that was not there.
We sat around the paper and they were asked "How does all of that fit into your brain?" Some children said that when you talk about an idea or write it down, it lets an idea out of your brain so you have space for new ideas. This stems from their believe that your brain only has a finite capacity to store information, they feel once your head is full you cannot learn anything new. One girl in particular had a particularly insightful idea on this and said that all the little parts or ideas join together to make bigger ideas. This was a very strong articulation of how learning works and was used to build on the task they would be doing next.
The next task was to give the children an appreciation of the extent of the connections occurring in the brain. Deb scrunched a piece of paper into a ball that would fit in their head, acting like it is a substitute brain she then unscrunched it and we took lines with a texta following the creases left in the paper, with each line representing an idea or thing we have learned, we showed how the ideas cross over or connect to each other and also showed, as per the images below, just how many connections there are between ideas. They used this as an idea to think about what they do when they learn new things
Following this Deb unveiled a brain shaped jelly she had made out of coconut milk and talk to children about how the creases in the paper look like the creases in the brain. Children had an opportunity to taste the jelly if they wanted too.
Tuesday - 2nd Year Focus Teachers
In the morning session the 2nd year group looked the video on maths anxiety blow and then had a deeper look at maths anxiety which was defined to be;
We looked at the difference between stress and anxiety. Stress being defined as being caused by an existing stress causing factor or stressor whereas anxiety is stress that continues even after the stressor is gone. For example if someone was scared of spiders, then while they see a spider, it is likely to cause them stress, but once the spider is gone, so would be the stress. Anxiety is different in that the person would still feel the same when the spider is gone, it continues to play on their mind.
In the 5 years that the ELL project has been operating across the Port Augusta / Quorn Partnership there have been clear gains in achievement and engagement in relation to numeracy learning. However over those 5 years the impact of the project has also extended beyond the partnership. The information below comes from Professor Martin Westwell and is about the ripples of the project, the how and where this project is spreading it's influence.
The Science of Learning Research Centre (SLRC) chose to highlight our work as the first case study in their annual report. The case study for the partnership is below as is the entire report.
The Australian Research Council has also picked up this story and will feature it in a publication highlighting the impact the research they have funded has had in every discipline.
The SLRC will be holding an International Conference in Brisbane in September with academics and education leaders from around the world. Flinders University in conjunction with the Port Augusta / Quorn Partnership have been invited to give a workshop specifically about the Pt Augusta work and write a chapter for a book that will come out of the conference. Below is a link to the conference website.
The model that the Flinders Centre for Science Education in the 21st Century has developed with the partnership has been the basis for their work various schools and a successful large grant application to the Myer Foundation. This grant will allow Flinders to work with three other partnerships across South Australia. The Myer Foundation see this as a proof of concept at a larger scale so that education systems around Australia might be encouraged to adopt the approach.
Professor Westwell also notes that he talks about the work with the partnership at almost every one of tne numerous keynote presentations he gives. Some of the audiences for these include partnership pupil free days or interstate and international events. Earlier this Year he was the IB Schools Australasia visiting speaker and talked about the project to teachers and leaders from IB schools in Melbourne, Brisbane, Auckland and Adelaide.
Monday - 1st Year Focus Teachers (Middle Years Group)
In the middle years group one of the first tasks for the day was for the focus teachers to work with a partner to play naughts and crosses. After several games they were then stopped and the rules changed. This time they had to play again, but they had to try to deliberately lose. Playing this game was a reminder from the sessions last term where it was discussed that in order to develop tasks that target the development of kids executive function skills, often all it takes is to tweak an existing task, rather than designing a whole new one. In working with this task the focus teachers talked about how this task really focused on their impulse control, they had to consistently resist the urge to try and win and to think flexibly about how to lose. One talked about having to try and trap the other person into winning.
Next the focus teachers were asked how their thinking has changed over the course of term 1 until now. Some of the responses given were
In looking at how children engaged with this task it was clear that they found it very difficult to place the first number. Many commented on how they were used to using a 1 to 100 grid and therefore the numbers on this grid were not where they are used to them being. Often it was they case that they didn't realise the first, or first few numbers, were in the wrong place until they came across one that was a contradiction to the ones that were already there. It was also interesting to see how the strategy changed as they went through. With the first number they mostly addressed it in relation to place value. by counting down the number of tens and across the number of ones. However once a few numbers had been place in the table they switched to a strategy of counting on or counting back by tens and/or ones from numbers they had already placed.
The second task that they did was the coded 100 square activity from NRICH. This is a task they had done previously so this time the task was changed to more strongly target children's understanding of place value and also target their impulse control. Previously with this activity children try to complete this activity by fitting the pieces together like a jigsaw, they don't focus on the symbols on the pieces which tell them exactly what to do. Even when their attention is drawn to they symbols and where they may place them, they resort back to trying to put it together like a jigsaw. To help overcome this they were given this problem again but with two pieces of the jigsaw missing. The pieces that were missing are shown by the red crosses in the image on the left and in the gaps in the image on the right. These pieces were chose as they remove some clues, these clues are shown by the green circles in the image on the left. in the bottom piece in the right hand image contained the number 100 and was removed, that is the only three digit number and therefore would be placed very easily providing a lot of information for what goes next to it. The piece at the top removes the number 2 and therefore more strongly relies on having to use the piece with the 1 on it to be able to successfully notice the place value pattern.
This was a task that the student's found more difficult than last time however they were able to successfully complete it. To extend the task they were then asked to draw in the symbols for each box that would correspond to the pieces missing.
Tuesday - 2nd Year Focus Teachers
The morning with the second year teachers focused on developing a stronger understanding of working memory.
This was used to help explain the psychology of Powerpoint. When you have a slide full of text you are activating the verbal short term memory, and when you talk about what is on the slide you are also activating that verbal short term memory, therefore you can't attend to both, you can read and not listen or you can listen and not read. However if you have a strong visual on the slide with limited text whilst you are talking then you are activating two different types of short term memory and therefore processing this is easier. The central executive is what controls your attention, does the higher level processing and interacts with the short term memory systems
In the second session we looked at a task that was brought up by Deb and Kristin. The task involved a large map of some London streets. We were given a range of data for the area including the location of pubs, schools, hospitals, water pumps and factories (shown by the paper cut outs in the images below. We were also given data one how many deaths there were in each square of this map as a result of a particular event in history.
With this task we had to try and hypothesise what happened to these people, to cause all the deaths. The initial part of this was to talk about what we noticed and what we wondered before starting to bring those noticings and wonderings together to form a cohesive argument for what happened.
On Thursday of term 2 week 4 the site based ELL leaders again met for their second training session for the year. A copy of the presentation for the day is below.
The first half of the day was a follow up on some tasks that these teachers were asked to work on over the course of last term. The work we looked at in this session can be found in the previous post.
We started by looking at progress with the #observeme process. Essentially the process provides a way to make the intentions of our teaching clear to others, to open up our classes for others to observe and to get regular ongoing feedback on our teaching. At the end of the last session the focus teacher has thought deeply about their signs and what they could put on them. We spent some time thinking about how the process of implementation has gone.
The ELL Project has been operating across the partnership for 4 full years and is now in it's 5th year of implementation, with a commitment of this year plus another 2 years from the partnership it is an ideal time to think about the further work that needs to be done across the partnership to build the sustainability of this work. Focus teachers were asked to perform site level audits to look at the current progress of the work in their site. Audits were conducted on three different levels, whole site, teacher/educator, and individual children.
We sat down and took the time to unpack what we have learnt from these audits in relation to
Beyond Relevance and Real World - Dan Meyer
At the NCTM conference last year Dan Meyer presented a session entitled "Beyond Relevance and Real World: Stronger Strategies for Student Engagement". The talk itself talks about the traditional views of how we make mathematics engaging to students, these strategies include
The talk examines why these methods of building engagement are unreliable and looks at some strategies that work better in relation to building engagement in mathematics. Central to the discussion is the concept of a "maths dial" that sits behind every class, this dial describes the formality of the mathematics that is occurring at the time, rather then the complexity of the work. At the higher end of the dial you have mathematics that is highly procedural, formal, abstract and precise, using a lot of exact mathematical language. The lower end of the dial is informal and imprecise, intuition plays an important part in the learning.
The premise is that if you start your learning towards the high end of the dial then it becomes overwhelming and hence engagement drops of significantly, whereas if you start the dial much lower and then turn the dial up slowly over time then this is a lot less daunting students have time to develop that conceptual understanding and then the more formal and abstract end is a lot less intimidating.
In building engagement he believes we need to redefine the nature of the "real world". Rather than trying to make it fit the world they live in, he seems to be advocating making it real in their mind, therefore it becomes about the cognitive buy-in.
Each successive level asks students to develop an increasingly sophisticated understanding of the problem. First of all it is at the 'notice and wonder' stage where they need to be able to look at the question closely enough to be able to notice something and ask a question, at the next level they need to think about how they they might answer that question given some additional information, they then need to think about applying some mathematics to the situation, and finally they need to be able to justify their answer if they are going to argue effectively for their answer.
The full video can be found in the links below but for the purposes of this session the video was broken up and discussed. We then went on to discuss a the idea that 3-act maths tasks can be used as a framework to help sequentially build these ideas. Links to some websites with numerous 3 act tasks are below. The focus teachers were also given the opportunity to design their own question or adapt a NAPLAN question along the lines of this framework. What follows below is a summary of the discussions that took place.
Beyond Relevance and Real World by Dan Meyer - Video Link
Introduction to 3-act maths tasks - Website
Dan Meyer's 3-act maths tasks - Website
Andrew Stadel's 3-act maths tasks - Website
Elizabeth Brandenburg's 3-act maths tasks (primary focus) - Website
Kyle Pearce's 3-act maths tasks - Website
Dane Ehlert's 3-act maths tasks - Website
False Growth Mindset Article - Website
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.
The first ELL sessions for the year with Flinders University were for 1st year focus teachers and for leaders. Both of the days ran with a very similar structure. The days were split in to an early years group (preschool to year 3 approximately), and a middle years group (year 4 and above). In both groups there was an initial discussion about the three core executive functions. To help further that discussion the video was shown below on the marshmellow test.
The discussion about this video focused around the ideas of impulse control, and to a point cognitive flexibility. We talked about the strategies that the kids were using to avoid eating the marshmallow such as
The discussion then moved to the lesson that would be presented in both the early years and in the middle years observations. The teachers were shown the cards that would be used in the observation session, the only difference between the cards for the early years and middle years groups was that the text was removed, leaving only the arrows on the card. Links to a more detailed run down of the intent behind the lessons presented and how it was implemented are in the two links below
After the lesson was conducted the groups again split into their early years and middle years groups for a discussion about what was seen in the lesson, the early years group also had a discussion about different types of play that came out of the article 'Pedagogical Play Types: What Do They Suggest for Learning About Sustainability in Early Childhood Education?' by Susan Edwards and Amy Cutter-Mackenzie, in which it outlines three different types of play in an early years setting these descriptions below were taken directly from the article.
1. Open-ended play: is located towards the left of the continuum and involves play experiences where the teacher provides children with materials suggestive of a sustainability concept, and with minimal engagement and interaction allows them to examine and explore the materials as a basis for learning about the concept.
The ideas being examined from this article is that play can take on more than just one form and is characterised by different levels of educator involvement. The article also talk about there being an important role for each of the three types of play in developing a concept.
The middle years group talked about how the presentation of task can influence the thinking that comes out of it. and how the questions asked can help to drive the thinking with a task forward. Some of the questions examined in looking at problems in the primary and secondary years are as follows
In week 3 of term 1, 2017, sessions for site based leaders of the ELL project kicked off at Flinders View Primary School. The presentation for this session is below. All links used in the session preparation and links for further information, can be found at the bottom of this post.
In the morning session we looked at the ELL results video for 2016 and gave the teachers an opportunity to provide any feedback. We also looked at the purpose of the sessions for the year in relation to their role in assisting their site to spread the work further than the focus teachers. We spoke about ways of approaching this through coaching, resource development and training for staff.
Next we looked at the announcement at the partnership staff meeting that the ELL project will continue in the region for an additional 3 years (including this year). Therefore as a collective group we have until the end of 2019 to have the project implemented in a sustainable manner across all sites in the Port Augusta/Quorn Partnership.
The bulk of time in this session was however spent on looking at an audit of the project across the PAQ partnership. Audits were done in sites a number of years ago near the beginning of this work. However 2017 is a good year to look at auditing again as it will be an indication of how far we have come, and also where we need to focus our attention both this year and into future years. We discussed the need to look at different levels off auditing which includes a site level, educator level and student level to get a full picture of the effect of current ELL activity on each of those stakeholder groups. We also talked about the need for diversity in who we are collecting information from. The views and opinions of those staff and students not directly involved with the ELL project is just as important as the opinions of those who are involved as it signals how well the message is getting out to others. However the diversity we are seeking is also in relation to gender, Aboriginality, schooling levels and previous achievement.
We spent time looking through different audit tools that came out of the Leading Numeracy Improvement Course that leaders attended a few years ago, As a collective group we decided on an appropriate audit tool that could be used at a site level, one that could be done with individual teachers and one that would focus on individual students. The aim would be to gather the views and opinions, as well of achievement data, of a diverse sample of these groups early in the year and again late in the year to look for any movement.
The remainder of this session was spent looking at the 'Quarter the Cross' activity that was on tables at the partnership staff meeting.
This session focused on the coaching aspect of their role. Initially this session looked at deciding who to work with in this capacity. We talked about the factors that will maximise the success of the coaching process in that very early stage. Next we looked at the concept of what a coach is and what a coach does in an attempt to unpack and understand what they need to know, do and be in that role. Finally in this session we looked at the notion of coaching heavy and coaching light and my reflection on this as a framework for looking at how we support staff as we work with them, but also ensuring that we maximise the growth out of the time we spend with them.
Session 3 looked at how we can begin to make the pedagogy we are in examining in ELL more visible across the sites. In 2016 it was proposed that people entering a focus teacher's class to look at a lesson may come with their own ideas about what quality maths instruction looks like, but may have limited understanding of how we are approaching maths instruction through ELL. However we want these staff members visiting the maths lessons of focus teachers the classroom observation section of ELL has been an important factor in getting people on board early.
The #observeme framework is a useful one in making visible to others what we are trying to achieve through our teaching, but also provides a good way to get informal feedback on how others believe we are progressing towards those goals. We went though the #observeme process to look at what it entails and also looked at some of the issues that have emerged, and have been rectified with the process as it has spread across the globe. Such fixes have included the careful structure of observation and feedback prompts, the use of pineapple charts and the promotion of the #observeme process across the site.
They were then given time to design their own #observeme sign and feedback sheet, or observation tool with a particular focus on ELL so that anyone visiting their class will know what to look for, especially in maths instruction. They are aiming to have their sign up as well as working with experienced ELL focus teachers to also have their sign up to help promote this work in their sites.