Tools for sharing thinking

Teachers and students have access to an impressive set of tools for sharing ideas and making thinking visible. The old model of calling out answers to questions has certain limitations and while it remains the mainstay of many classrooms new options allow for a mix of options. Some of our goals are to provide our students with appropriate wait time or think time and to ensure the voice of even our most introverted students is heard. It would also be nice to have a record of our students thinking and a way to easily see patterns of thinking across a group of students.

Fortunately there are a number of free tools that do these things and they are available for use on any technology platform as they require nothing more than access to the internet. Recently Eric Sheninger used a set of these tools to give his audience at the Hawker Brownlow Conference on Thinking and Learning in Melbourne a voice.

One of the simplest to use and set up is “Answer Garden”. This allows you to quickly pose a question online and it provides an easy to share web address that respondents use to enter their answers. Results are pooled and the result is a tag cloud or answers where the size of the answer reflects the frequency of the response. Answer garden works well with open ended questions and can be used to quickly identify issues, understandings and thought patterns of a group. It is so quick and easy to set up that it can be done on the fly and on demand.
 

Padlet is a well known tool for gathering responses to a question or issue together. It is a virtual inboard that allows users to post and share notes through an easy to use website. In many respects it is similar to the practice of using Post-It notes to record ideas and share them by sticking them onto a wall. Padlet is easy to set up and can be customised with coloured backgrounds, coloured notes and can handle images. Post-Its on Padlet can be randomly placed allowing similar ideas to be grouped together or it can be sorted in various ways automatically to create a neat grid.
 

Lino is in many respects similar to Padlet and could be used in exactly the same way. It adds the ability to comment on or reply to posts, a feature that encourages dialogue and could prove useful when more contentious issues are shared in this format. It allows multiple questions to be posted to a board with users replying to each, it would allow users to ask questions of each other and to post replies to ideas in a way that ensures relevant pieces stay together.
 

For linear conversations or back-channeling with media resources “Today’s Meet” remains an excellent choice. In some respects, it is like a temporary and task specific version of Twitter. A meet is created and link shared that allows users to post responses of up to 140 characters. Each post is added to the flow of ideas and the discussion evolves. It can become chaotic and it is at times difficult to link ideas together as multiple conversations emerge but it does provide a record of the thinking and conversation occurring within a group.
 

A tool with a definite wow factor is Plickers. This is a multiple choice response system with the benefit that it only requires a single device with the Plickers App and a set of response cards of the students. Each response card has a printed QR code and its alignment allows for four possible responses. The card is rotated such that the desired multiple choice letter or number is placed at the bottom. The App uses the devices camera to read the code and record the individual responses. As each QR code is unique individual responses are recorded and graph is produced showing how many responses resulted for each option. Plickers provides a cheap alternative to costly electronic ‘Clickers’ and its novelty factor and ease of use enhances engagement. As with any multiple choice style solution the quality of the questions or prompts will determine the quality of learning which results. Creative use and avoidance of entirely closed questions/responses will produce better results.

By Nigel Coutts
 

Collaborative Learning with Google Docs

Something is missing from my classroom lately and I am quite happy to have seen it disappear. It is the traditional line at the teacher’s desk formed by students awaiting feedback on a recently completed piece of writing. What has replaced this is our use of Google Docs and Slides as a tool for the collaborative development of ideas from initial thinking and strategising through to final editing and refinement. It has introduced a new workflow to the class that both streamlines the process of providing feedback, allows for greater detail and transforms the process into one that is richly collaborative.

Students selected images that represent places described in a novel we are reading, Google Slides allows this to be shared and collaboratively analysed. 

Students selected images that represent places described in a novel we are reading, Google Slides allows this to be shared and collaboratively analysed. 

A typical writing task will begin with a prompt. This is designed to have the students thinking and identifying possibilities. Sometimes it is a provocative statement other times it is a series of sample pieces designed to act as models for the writing that will come. In the past week students read a set of poems about heroic freedom fighters. Each poem was placed into a Google Doc and the students were asked to read all three independently and then select the one which they felt was most compelling. They used the commenting feature in Google Docs to reflect on the poems and identify devices used by the poets to engage their audience and construct meaning. Having looked at the pieces of the poems they then selected a thinking routine from the website www.rediquest.com. They used this thinking routine to analyse the poem as a whole and to reflect on its effectiveness.

The next step introduces two layers of collaboration. Firstly, they share their document with a number of classmates who now use comments to reflect on their peer’s analysis of the poem. They ask questions that probe for closer analysis and greater detail such as “What makes you say that?” and add ideas that might have been missed. through  this process the students share insights and gain a deeper understanding of how the poet has communicated their ideas and emotions with an audience. After some refinement and editing of the analysis this document is shared with me and I add my comments to the mix. Each student now has a collaboratively produced analysis of the poem they chose, one that they own and have played a part in developing at each step but one that is more detailed and of greater utility to them than the original produced independently.

The next step is to write a poem of their own using the poems they have read and the analysis they produced as a guide. Once again Google Docs is used and students begin drafting their poems in ways that make sense to them. Some choose to begin with lists of words, others start straight into drafting possible lines to later be assembled into stanzas. Once they have a draft they are reasonably happy with, they share that with me. I encourage them to share early in the process so that I may offer feedback before they are heavily committed to an idea and unwilling to make changes. I am able to add comments and make suggestions, they see these and adjust their writing or in some cases decide to stick with their idea. Comments appear alongside the document linked to a piece of text and can be more detailed than what may be scrawled in the margin of a student's  book. It is important that this is true collaboration and that they understand I am just adding my ideas. I would never want a student to think that their ideas are of less value than mine. As they continue to write they can choose to resolve the comments I have added or to reply where they feel some clarification is required. It becomes a very efficient conversation and they are able to deal with each piece of feedback in their time and without having to join a cue and wait for me.

One of the key advantages is that I see the process of writing. I can see which lines they are editing, the changes they make, the ideas they try and then abandon. The students benefit from my feedback but do not have a document covered in red ink. The final document is very much theirs. By the time they have finished and resolved each of the comments and suggestions they have a clean document ready to publish. At this point or often earlier in the process they can share their document with their peers and I can invite other teachers to read the piece as it evolves. My students are able to benefit from feedback from multiple sources and my colleagues are able to see how ideas have evolved within lessons that they will teach. Templates developed for a lesson can be quickly shared between classes and we can now see how students have made use of these templates and scaffolds as we share completed and partly completed samples.

Google Slides is becoming the go to platform for collaborations between groups of students. We are using this platform more for drafting ideas that incorporate text and images rather than as a tool for producing slideshows; a digital scrapbook. In many cases a rough outline is provided or alternatively a set of prompts may be offered. One recent lesson involved students identifying Mathematical concepts within a set of images. Each image was placed on a slide and groups of students were assigned to each image. Their task was to identify the mathematics present and add information to the slides that would make this visible. The conclusion of the lesson was to share what had been found back to the class. Another set of lessons asked students to locate images which they felt reflected places within a novel we have been reading. (See image at top of page) Each student produced a slide show of images and added their responses to the thinking routine “I see, I think, I wonder”. Once complete they shared their slideshow with a classmate who used comments to ask questions, offer feedback and add their voice to the analysis. In each instance the collaborative experience produced a richer learning experience.

The ultimate version of this style of collaboration are the “Coding Journals” the students are producing as they learn to programme robots to deepen and demonstrate their understanding of geometry. Each student is producing their “Coding Journal” using a Google Slides document as an initial template. Various slides have been created by their teachers to frame their initial thinking and provide some structure. Students add to this and make adjustments to suit their needs. Importantly each journal is shared with the teachers and with a set of peers who can all add feedback and also benefit from the shared learning. The “Coding Journals” are both evidence of learning and scaffold for future learning, a truly collaborative effort and the sort of tool that would be of benefit in real world settings beyond school.

All this online collaboration could be imagined as cold and impersonal compared to face to face discussions. The reality is that the conversations we do have are now much more focused and meaningful. I am more aware of what the students are up to, I can view their learning readily in advance of a conversation with no need for them to stop while I read their work. When they do stop to share work with a peer it has already been shared and read and they have had time to consider the feedback they will provide. The resulting conversations between students are focused and to the point.

The final piece of this collaborative effort is that as a group of teachers we have started using Google Docs for our programming and our annotations. We each use a single Google Document for this process and after each lesson add our reflections and observations. As we all have access to this constantly evolving document we can easily see how a lesson worked for a colleague. This information can then guide our delivery of lessons we are yet to teach, suggest new or additional resources and it provides opportunities to quickly and easily make adjustments to what will be our programmes for next year. The process is proving to be much more useful than the previous practice of annotating a printed programme and we are finding that the social nature of reflecting on our teaching to be most rewarding and even enjoyable.

As always I thank the team of teachers that I work and learn with. The ideas shared here are very much a product of our collaboration and I am continuously in awe of my colleagues capacity to deliver quality learning experiences.

By Nigel Coutts

The poem below was produced by a Year Six student using the collaborative process described here.

The Right to Fight
Malala Yousafzai


Basic rights
A definite no more
Fight for them
Fight for us

The day was new
When she spoke up
She fought for them
She fought for us

Inspired the world
A voice so small
She fought for them
She fought for us

Until that day
She could have died
We fought for her
She fought for us

The shot fired
The blood shed
She fought for them
She fought for us

Silence unknown
The world alive
We fought for her
She fought for us

Home she came
Glory bound
She fought again
She fought for us

We fight for her
She fights for us
We fight for them
She fights with us


By Sophie of 6C

Why banning technology is not the answer

There is something about human nature that draws us towards dichotomous patterns of thought; an all or nothing, us or them style of thinking in which an option is either good or it is bad. In such a model complexity and subtle nuance with multiple possible outcomes and routes towards a goal are ignored. The field of educational technology is one where such a pattern is evident and recent ban on technology by a Sydney school shows how this style of analysis can have a significant impact on student learning.

A ban on technology is an approach that is guaranteed to draw a response. Fortunately, perhaps most have quickly derided this move labelling the decision antiquated and out of touch with reality. Sugata Mitra tweeted ‘Here is how to get things completely wrong.’ and Julie Lindsay’s response is well worth reading.  Others have agreed with the decision and pointed towards student distractibility, online bullying and results on standardised assessment tests as indicators that such a ban is warranted. Beyond the hype of a ban on technology such a decision reveals a disappointing approach to education and learning that goes beyond the use of technology, a belief that learning is something that is intolerant of distraction.

Within the debate there are aspects of Dr Valance’s argument that have merit even if his response is misguided. Education is a social activity, driven by conversation and communication. Discussion, debate, argument, questioning and provocation are powerful elements of learning and an important part of what contributes to a dynamic and engaging learning environment. Where the argument falls down is when it is associated with a belief that the inclusion of technology in this mix will be to the detriment of a positive learning environment. The assumption is that access to ‘devices’ will be such a distraction that real learning will not occur.

To make this assertion a number of premises must be agreed to. Firstly, the face to face component must be seen as of lesser worth and be less engaging to the individuals than is the content delivered by their devices. It must also be accepted that it is not possible for content delivered by the device to be integrated with the face to face component and that it is not possible for this integration to add value. It must be accepted that other distractions such as a notepad, book or events taking place outside a window are significantly less than that presented by a device and that while we have developed strategies to manage other competing distractions we are incapable of managing distractions from devices.

Each of the premises upon which Dr Valance’s ban is predicated seem rather flawed. Surely high calibre teachers are capable of engaging students in discussion of topics so compelling that distractions of any nature are ignored. Our aim should be to build learning environments which are highly engaging, relevant and valued by all involved, if the learning is only relevant to the teacher then perhaps it should be changed or its significance to the students made clear. Understanding how our connected devices bring new opportunities to make connections beyond the four walls of our classrooms is an essential understanding to be developed. Effective teachers will show their students the power that such connections offer and encourage students to make full use of all of the tools at their disposal. As David Perkins of Harvard argues in ‘Future Wise’ digital tools should be included among the tools we use for learning. Connected devices should inject new opportunities, knowledge, data, influencers and thinking into our debates and add value not distraction.

The question of student distractibility is worth further exploration. The reality is that students have always found ways of distracting their attention from learning experiences that they have not valued. Passing notes, gazing out the window, doodling in the margins, reading a novel secreted under a desk, allowing the imagination to wander are past times every student has engaged in. Should we ban notepads in case students use the paper to pass notes? Do we ensure desks are clear of books which may cause distractions, walls clear of displays, windows covered by blinds all so that the students have no choice but to focus on us and to ensure that our lessons have nothing to compete with?

Much of this debate is centred around what has emerged as traditional uses of computers. This model sees our devices as replacements for existing modes of communication and as tools for accessing information. Texting, messaging, internet access and social chat are the limits of such a model. All of this has value and brings new opportunities for connectedness and collaboration on a global scale. But this model is limiting and limited in its understanding. Tracing back to Seymour Papert’s vision for computers within learning we see new opportunities for us to think about how we learn, how we think and how we construct knowledge. With the rise of algorithmic thinking, machine learning, artificial intelligence and an increasing need to understand how computers and networked data influences our decision making students need to move beyond using computers for content consumption or even creation and shift towards understanding how they function. As Papert asserts in Mindstorms ‘learning to communicate with a computer may change the way other learning takes place.’ (read more about ‘Computational Thinking')

Technology does not need to be a part of every aspect of our lives. We need to learn when it is the best tool, when it plays a part on the sidelines and when it is best left out of the equation. We need to see it as the tool that it is and understand how we may best use it to extend our capabilities. As teachers we need to reveal to our students how technology can assist their learning, how it can empower them and how it can if used inappropriately hinder. We need to understand the affordances of technology and utilise this knowledge to our student’s advantage allowing them to extend their learning beyond the classroom as they become connected learners. In doing these things we maximise student learning and ensure our students are prepared for the world beyond school. Blanket bans and oversimplifications of the debate around technology’s place serve no one except those fearful of a world where they as the teacher are no longer the centre of attention.

By Nigel Coutts

The Power of Teams

Sometimes it is worth stating the obvious, giving time and thought to what we easily take for granted. In doing so we name the things we value most and give them the value they deserve. The value of teams is one such ideal, we know that teams have value, we probably even know what it feels like to be a part of a great team but too often we take this feeling as understood and don’t stop to consider what makes it worth chasing.

Presently I have the pleasure of working with a great team of teachers within a strong Junior School. A team of teachers who inspires and challenges each other towards success and growth. We are a core group of five teachers with strong connections to a team of amazing specialists who work together to prepare our Year Six students for the challenges of Senior School while ensuring the students' experience of their final year in the junior School is memorable. We are a diverse set of individuals with varied backgrounds, strengths, interests and personalities. As a team we are able to act as a cohesive unit with a shared understanding that allows us to take differing patch to the same destination.

Collectively we are united in a love of learning. We each enjoy the opportunities that new situations bring to us and we know that we have much to learn. We also understand that we each have things that we can teach each other and this ensures a mutual respect that is genuine. This love of learning and valuing of our collective wisdom is evident in our approach to problem solving and planning. No one person has the answer, no one voice need dominate, the best answer is the one that emerges in response to the problem. Daniel Wilson, of Harvard describes this as ‘Emergent Leadership’ where the wisdom of the group is the key to solving complex problems. This property of an effective team is perhaps the one most frequently missing and one that is most required if education is to transform itself to meet the challenges of a post-industrial revolution era.

As a team we also understand that there is a job to be done and that it can be no single person’s responsibility to do it. A week at camp showed how this value within a team can triumph even when things don’t quite follow the game plan. Working within a team where everyone is accountable and everyone understands the importance of their actions allows for distributed leadership to take hold. Tasks no longer need be assigned because the team will identify the needs and take the appropriate actions. For this to happen every member of the team needs to have agency to take action and not feel they need to play a game of 'guess what the boss wants’. Agency within teams is critical for their success.

The culture of a great team is infectious and will be naturally inclusive of new members. For our camp the team grew from five to over twenty and yet the culture of the core team remained and spread. Our enthusiasm caught on and the team was able to incorporate new members without effort because we all knew where we were going and how we would get there. Culture triumphs policy and a strong team culture based on trust and respect is supreme.

When working in a great team, leadership can almost disappear. Observe a group of people working together and if it is clear who is in charge you are most likely watching a manager at work. In great teams where the value of every member is equally respected the leadership is distributed, the team is able to function towards its goal with little direction and the results are phenomenal. With a great team the productivity will far exceed what a well managed team can ever hope to produce as every individual contributes their very best and no one is waiting for the next set of instructions.

Great teams value each others success and share responsibility for mistakes. Effective teams understand that mistakes happen as a part of the learning process and the only way to avoid them is to never try anything new; clearly not a viable option. Great teams also acknowledge the success of individuals and understand that when a team member achieves success it reflects well on the whole team. If your team members are doing well it is a sure sign of a healthy team, celebrate the success.

Effective teams understand that team members have lives beyond the team. Empathy and understanding are the cornerstones of great teams and supporting each other with the challenges that life throws your way is essential. Every team member will have differing needs and understanding that and respecting the complexity of our modern lives allows teams to be supportive of each other beyond the confines of the workplace. It is not always about the job, sometimes a team needs time to stop and talk about life, the conflicts the craziness and the things that make us human.

Lastly and perhaps most difficult, teams build the capacity of their members and that means sometimes creating the conditions that allow team members to move on to new and bigger challenges. Learning and personal growth is important and part of the process that all tams go through and the eventual result is that team membership will change as members seek new experiences and challenges beyond the team or their present situation. In a great team the need for a change of scenery is lessened by the opportunities inherent to the teams functioning but building the capacity of individuals members and the collective capacity of the team are essential elements.

If you are part of a great team cherish it and take the time to name and value what makes it great. Amazing teams do not happen by accident and maintaining their spirit is the responsibility of every member.

 

By Nigel Coutts

Beyond consumer based ICT

There is a change taking place in how schools approach ICT, one that has been coming for some time but is at the point of moving into the mainstream. A subtle but powerful shift that sees ICT build connections with the Maker Movement as a tool for solving what Bronwyn Moreton speaking at the ICT Educators of NSW conference describes as the ‘I wish it would . . .’ moment where a learner discovers that their technology doesn’t do everything they wished it would.

For a long time, ICT in the classroom was a mix of internet based information tools, some desktop publishing and for the adventuresome multimedia design, video and photo editing. This placed the user for the most part as a consumer of content or a user of software packages and more recently Apps. The skills required of these users would be found in user manuals and tutorials and revolved around learning the particular idiosyncrasies of various pieces of software. Skill with Microsoft Office, internet browser and Apples iLife suite of tools for video and photo management would suffice for the majority of users. With the rise of tablet computers such as iPad, Android tablet and Microsoft Surface the App economy has driven the required skill set down further as ICT moves firmly into the consumer device market.

This was not always the case. In computing’s early days when Steve Wozniak was a member of the ‘Homebrew’ computing club it was about problem solving to get the hardware and software to do what you wanted it to. Computer Geeks blended the skills of electrical engineers with software developers to get the early machines to power on. Computing at this time involved manipulating the core components of breadboards, processors, inputs and outputs all of which is well hidden from view in modern machines which are tightly focused on a pleasing 'out of box' experience. But as attendees at the ICTE NSW conference saw repeatedly a change is coming, we are moving back to tinkering with the hardware. Coding and electrical engineering are opening new opportunities.

Recognising the need for young people to understand computer coding and seeing a gap in the available software MIT (Massachusetts Institute of Technology) developed Scratch. The aim is to provide a simple coding environment that allows students to literally assemble blocks of code in a digital environment in much the same way that they would assemble wooden blocks in the physical world. The drag and drop nature and friendly block design makes coding readily accessible and the user gets immediate feedback on their designs. Many students have been introduced to coding thanks to Scratch and others have followed a similar path with tools becoming available for all major platforms. The trouble with Scratch is that at some point learners will need something more and traditional response is to move on to more involved coding solutions such as Python.

There is an alternative route however. Move the students on from Scratch to using it to programme physical devices that they create using Arduino. The beauty of Arduino is that it allows low cost access to hardware that encourages user developed code. Arduino boards are a system on a chip meaning that the whole computer is on one board and to this you can connect other components such as lights, sensors, motors and speakers to give the system additional functionality. With Arduino the students are not just using a computer they are making and programming it. Arduino is just one of the ways that physical computing is making a come back. Other players include Raspberry Pi which was one of the first system on a chip type computers to grab the attention of the mainstream thanks to its low price point and functionality that matches many computers from as little as five years ago. Raspberry Pi gives its users access to fully functioning operating systems from the Linux environment and the latest versions will run Windows 10. The low cost and bare bones nature of the Raspberry Pi encourages tinkering in ways that laptops and desktops don’t.

Another way into this world of physical computing is through robotics. This is an area where the benefits are coming from increased consumerisation of robots and the availability of ready to go robots. This removes barriers to entry and allows younger users to experience what is possible with a programmable robot. Children in Prep Schools can use Apps like Scratch and Blockly to programme a robot and see immediately the effects that their code has on the robot’s movement. At more advanced levels students are able to design complex code that integrates feedback from the robot’s sensors with logical operators. As student expertise moves beyond the capabilities of consumer robots there is cope for them to use combinations of Arduino and Raspberry Pi type computers with sensors and motors to create bespoke robots of their own design.

As is the case with the whole Maker Movement the spirit of sharing and collaboration ensure that a rich support network has evolved. For those with a passion for tinkering with computers this support network is bound to answer your questions. Having spent a Sunday learning with some of the ICT educators of NSW this willingness to share expertise and learn collaboratively was most evident in everyone I spoke with. For teacher and learners beginning their journey into physical computing and coding there is no need to be alone.

 

By Nigel Coutts

Hold your ideas lightly

The history of teaching is littered with ideas that have come and gone. In their day each was the new bright hope, set to transform what we do as teachers and how our students learn. Each new idea had its supporters and detractors and each in turn was replaced by an alternative or simply disappeared from view. Those who have experienced this ebb and flow of ideas have learned to approach the shiny and the new with caution and yet we have all encountered ideas that are so compelling it is difficult to ignore. How might we approach new ideas and innovative practices in ways that ensure our students benefit?

Effective schools and teachers engage in a process of action research even if it is not thusly named. It is a process that can be as simple as identifying a need, imagining or identifying a solution, putting it into action and observing the results. Applied as a methodology for improving practice through cycles of research, implementation, evaluation and reflection it can provide valid research data. A key benefit of action research is that it is closely linked to practice and involves practitioners as researchers ensuring a close connection between the research and its implementation. In action research it is very likely that those implementing the new strategy will have a solid understanding of its research basis, the problem it aims to address and the result it should achieve.

Action research fits nicely into a design thinking approach. There is much in common between the two methods and one could see design thinking as a structure for action research. At the core of both approaches is the identification of a problem the development of a planned response, the implementation of the plan and deliberate reflection. Both should include opportunities to adjust the plan at various points and when looked at as a cycle it should be clear that the process need not be linear or have a set end point. Fluid movement between action, evaluation, planning and questioning phases allows both action research and design thinking to respond to discoveries mid cycle and for adjustments to be made.

For the evaluation of new ideas both models hold real advantages. Thinking outside the box is all very well but thinking is best when it has a degree of structure and some level of organisation and it is this that action research and design thinking provide. For collaborative efforts the structure provided and the labels attached to various phases of the process can help team members identify where they are in their endeavour and where they are headed next. A key ingredient is that in these models the process is highly iterative in nature and the ideal solution or even the clear articulation of the problem is not likely to occur with the first cycle. Understanding the iterative nature of action research or design thinking is critical for success and a contributing factor for long term group cohesion.

The sharing of ideas with colleagues is for many a process not undertaken lightly. The more of our individuality, passion and effort that is invested in the idea the harder this process of sharing can be. We want our ideas to be understood, appreciated and accepted. When we contribute ideas to an action research process it is natural to hope that they will be included in the groups planning. Feelings of disappointment when they are not are natural but this is not a productive response within an iterative process. We need to hold our ideas lightly.

Those of us empowered by a growth mindset are perhaps more open to sharing our ideas. If our idea is not what the group is looking for we are able to move quickly on to the next idea without a negative reaction. Our ability to let go of our ideas decreases as our commitment to them increases and this commitment is directly related to the time, effort and emotion we have invested. To this end Ewan Macintosh urges us to share our ideas early, before we are too committed to them to listen to constructive feedback. If we share early, at a point where the idea is developed sufficiently to be understood by others who can provide us with feedback we may be more open to incorporating these new perspectives into our thinking.

Sharing early requires more than individuals who are open to the idea, it must be backed by a culture that accepts ideas should be shared before they are fully baked. Such a culture accepts that ideas might have rough edges, missing details, errors and imperfections. Such a culture is a natural fit with action research as it is one that encourages ideas to be tested and worked on without fear of failure. If the culture of a place is not accepting of failure in its action research efforts, it is not possible to try truly innovative ideas and efforts at safe innovation are unlikely to produce significant changes worthy of the effort. Fear of failure amongst individuals on action research will produce other negative consequences such as group think where divergent ideas are kept private and staff fall into patterns of trying to guess what their supervisor wants them to contribute.

One effective strategy for action research within larger organisations can be to trial multiple competing solutions at once with teams testing different approaches to a common problem. This connects nicely to an iterative process and can accelerate the research process as multiple options are tested and understood in parallel. It can also unlock our competitive natures when the ideas are compared and evaluated. A clear understanding, that it is the idea being assessed and not the individuals who researched its application, is essential. In cases such as this teams must hold their ideas lightly and accept that ultimately not all ideas will transfer into policy or future practice.

A willingness to hold our ideas lightly may also help avoid the scenario where the ultimate solution is a hybrid of multiple ideas formed not for its best fit to the problem but as a compromise between divergent groups. A willingness to let go of parts or all of our idea and accept that it may not offer the best solution is not easy but a necessary step towards maximising the benefits of action research. Perhaps hardest of all is letting go of our ideas when we are the ones who must make the decision. For leaders this is part of the job; a willingness to accept ideas from all channels will allow us to respond in the best possible way and to select the right path even when it is not the path we had envisioned. The capacity of an organisation’s leadership to share ideas early, listen to feedback and respond accordingly will have a powerful effect on the organisation’s culture and ability to innovate.

In the spirit of holding my ideas lightly I invite comments or feedback on how this article may be improved or why it should be deleted. I look forward to the discussion.

By Nigel Coutts

 

The new concrete materials for mathematics

Since the time of Cuisenaire rods or before that counters and buttons students have benefitted from the use of concrete materials in their mathematical learning. The combination of strong visuals and the ability to physically manipulate groups of objects has allowed students to move from purely physical representations of number concepts to increasingly abstract representations. This pattern of first experiencing a concept in the physical world before shifting towards symbolic representations has allowed countless students to grasp the fundamentals of mathematics. Effective teachers have always been able to maximise the benefits of this pattern ensuring that their students can not only produce the right answer but have a solid understanding of the mathematics behind it. 

In the age of computers and now tablets there have been many efforts to transfer this effective learning pattern into the digital world. Skeuomorphic representations that take digital renderings of real world objects and place them onto screens for manipulation through the computer interface have had some success in this area but an additional layer of abstraction is added that purely physical manipulations lack. Shifting the physical objects into the digital world may bring new affordances to the devices used but fail to transform the learning that was already possible with concrete materials. What was needed was a relationship between the digital and the physical that would enhance the quality of learning possible. With new tools such as easily coded robots, augmented reality and 3D printing this is a possibility that is beginning to emerge. 

One interesting option is the iPad system and related Apps made available by ‘Osmo’. In this the camera on the iPad is reconfigured to capture images from the area immediately in front of the device as it sits in a stand. The software allows for virtual objects on the iPad screen to appear to interact with objects placed or drawn in front of it. One of the Apps available presents the challenge of manipulating the trajectory of a virtual ball using objects placed or drawn in the real world space in front of the device. Students learn through an iterative process of altering angles of incidence and by adding or removing objects how the trajectory of an object can be altered. The software allows for complex interactions to be simulated and tested with immediate feedback provided on the screen. Other Apps allow students to manipulate Tangrams with added benefits occurring as a result of the augmented reality. Another App bridges the gap between the physical and the abstract by allowing students to manipulate real objects while the device reveals the associated abstract representations. Osmo brings an added dimension compared to purely digital Apps that attempt to do the same thing as its physical dimension invites collaboration. Students will want to sit and play with the physical objects and though the manipulations of these experience gradually increasing levels of engagement with symbolic representations.  

Learn more about Osmo

Sphero is another interesting way to take mathematics out of the digital world and allow it to blend with the physical. Sphero is a small spherical robot that can be controlled directly using a phone or tablet, can be programmed or can be used as a controller or interactive object with augmented reality games. Beyond the fun that comes from using Sphero like a remote controlled toy is the potential to use it to explore concepts within mathematics. This process is likely to begin with lessons that require students to programme their Sphero to complete a maze. Constructed on the floor with tape, cardboard or with a mixture of made and found obstacles mazes allow students to explore aspects of measurement of length, area, angles, time and speed. Unlike purely digital solutions that target these concepts Sphero brings a real connection between the code and the movement of the robot. Students engaging with Sphero will take measurements in the real world with traditional tools such as metre rules and protractors (preferably oversized ones), use that information in the digital code environment and then make adjustments based on the path taken by the robot. Again success is supported through an iterative approach with immediate and natural feedback. These feedback loops where the students are quickly shown what works and what does not are judgment free and ensure continued engagement with the problem and with each failed attempt revealing something new about the task while allowing the students to laugh at their robots misadventures. That students are learning to code while they are developing their understanding of mathematical concepts is further bonus. Beyond the maze activities are options for an exploration of how the robot may be programmed to complete artistic pieces that combine its movement and ability to change colours into robotic ballets that could include collaborations with other robots.  

Learn more about SPHERO

You can’t mention links between digital worlds and physical reality without mentioning 3D printing. For explorations in STEAM the increasingly affordable 3D printer brings the opportunity to design objects in a physical world and then print a real model that the students can hold. So many mathematical concepts from mass, volume, capacity, scale, ratio, and 3D shape can be explored in this way and links across key learning areas can be readily explored. For design thinking tasks the potential to have a physical prototype of an idea brings a tangible dimension that reveals ideas in new ways showing how imaginings in the virtual world translate into the real world. Increased accuracy of 3D printers is allowing for objects with great precision which means it is possible to print parts of machines with moving and interlocking cogs. Software is available now that will show how these moving parts will interact in a virtual world thus enabling testing of designs in this space prior to printing.  

In each case here there is a linking of learning in a digital space with the manipulation of creation of real world objects. instead of moving further away from the use of concrete objects blended environments suggest that mathematics teaching may be most successful when a mix of digital and physical is enabled. It may not be time to throw away those Cuisenaire rods and oversized set squares just yet, they may have a new part to play in the emerging terrain of mathematical learning.  

 

By Nigel Coutts