Inquiry learning - 3 reasons why

A few months ago, a rather juicy discussion erupted on a Facebook teacher group I belong to based on the graph above. One of the comments that really stood out for me was from another educator who said:

"It's evidence like this that makes me worried about the 'new' style 'open learning environments' that seem to be the vogue for schools being built at the moment. Is the 'student led, open inquiry' style of teaching going to erode progress that has been made?"

It seems that inquiry learning is often at the pointy end of the debate when discussions of academic achievement are had. Direct teacher instruction still seems to work best. The thing that many people forget however is that this works best for some things, certainly not for everything. Hattie's work in Visible Learning (as far as I understand it) looks particularly at achievement data. As does most other research because achievement is easy to measure. The thing with this research, is that it does not look at all the other measures of success, like how happy a student is, their sense of autonomy over their learning, how successful the student is beyond a school context, and most importantly, how passionate the student remains about learning. Although academic achievement may contribute to these things, it is important that we see its limitations, particularly when we start passing judgements on different and new styles of learning.

One of those new styles of learning that is frequently under fire is inquiry learning. Personally, I am a big advocate for inquiry learning because as I see it, there are a number of reasons why inquiry learning is appropriate for this day and age:

Inquiry develops student ability to understand the ‘culture of inquiry’ within a discipline or paradigm and use it to problem solve:Inter-disciplinary learning might be trendy right now, but it is important not to forget the many good things that each learning area does offer. Science has a particular way of asking questions, a particular way of seeing the world. It is precisely because of this 'culture of inquiry' in science, that we have been able to make all the stellar advances in medicine, space travel, technology etc. The same can be said for the 'culture of inquiry' within other disciplines too. Hence, inquiry learning allows students not just to learn about the knowledge that science, history, etc. has gained through its particular cultures of inquiry, but it allows them to learn to use this to seek answers and solve problems for themselves, by drawing on each discipline's culture of inquiry. Hence, they learn how knowledge is constructed in that discipline. 

A simpler way to think about this is that each discipline offers a range of toolboxes with which to solve problems. We should not just be teaching the students what each toolbox has built already, but rather, how they can use the toolbox to build and repair things for themselves. Additionally, because inter-disciplinary studies have become increasingly important, (eg. climate change, nanotechnology, etc.) we should also be developing students' abilities to mix tools across toolboxes, but do so deliberately knowing full well the power and limitations of each tool.

Develops student ability to critique their research decisions:In the post-truth age of fake news and social media, the age old philosophical question of 'how do you know?' becomes infinitely more relevant and critical for the everyday person. And so, the methods by which we find truth and knowledge becomes critical. If students have spent their entire lives consuming content that is provided by schools, they will be inculcated to consume without question elsewhere too. In order to understand the difference between opinion, perspective, information, fact and fiction, we must understand what actually counts as knowledge, the context in which we can rely on this knowledge, and the limitations of knowledge. And learning about this is not the same as developing the capacity to do this, the former just provides more content to consume. Hence, inquiry learning if done well, develops student capacity for critical thinking about far more than a content or concept focussed question easily examined in an exam. 

To get back to the toolbox metaphor, students need to learn to use each of the tools in their toolbox for the right reason, knowing that a hammer and a mallet although similar in appearance, are not the same.

Develops student ability to critique the validity of ideas, models, representations and sources:
So your students are able to navigate to a trusty source of knowledge on the internet, or can spot a biased article. You didn't really think that was enough did you? There is not a discipline under the sun that claims that its knowledge is absolute or complete. Hence, we should be developing students' ability not to think in absolutes or in final answers, but rather, to think critically in understanding the strengths and limitations of all ideas, models, representations, perspectives, opinions and knowledge.
This not only contributes to students' understanding of disciplinary concepts, but it might also contribute in helping them become better democratic citizens. After all, in the world's current political climate, I think it is safe to say that we need more people who can critically evaluate ideas, take on multiple perspectives, and recognise limitations of ideas (just think Trump's border wall!). The ability to recognise the limitations of knowledge, also enables students to see where they might contribute in the world beyond social media and click-bait garbage. If we want students to see and live beyond the instant and momentary famous of Instagram and Snapchat, then surely we must show them other ways they can contribute and leave their mark in the world? 

To use our toolbox metaphor again... Not every space that we construct with our tools is of equal quality, and even the best quality can never be perfect. There is always room for improvement. Being able to see the strengths and weaknesses in the spaces that we have constructed allows us to make better judgements about what to use a space for, how to use it and even, when not to use it.

In reference then to the fellow teacher who asked the question at the start of this post; 'Is the 'student led, open inquiry' style of teaching going to erode progress that has been made?' I have to ask, what might content driven, direct teacher instruction be eroding?

"...the only definite outcome is uncertainty"

The only thing we do know about the future is that is is uncertain. It surprises us. In our own lives and society, we know that unexpected challenges, problems and opportunities arrive. People and society is faced with everything from poverty and abuse to ISIS, climate change and natural disasters such as earthquakes and tornados. This doesn't even begin to talk about the uncertainty that we have about where technology will take us next. If for just one day, you were not allowed to use any technology that was invented in the last 15 years, what would your day look like? There would be no Facebook, no iPhone, so I would actually have to take a GPS with me. There would be no Netflix. Wait, there would be no YouTube. There would be no Wikipedia. Things are getting serious now. I would probably have to listen to a CD - oh the limitations to my playlist size! Scrutinise any part of your day, and you will notice the enormous influence that technology has had on our lives. Would we have been able to predict twenty years ago just how great the role of technology in our lives would be? You could try and argue with me, but if you just think about how many power outlet points there are in any given room in a house built this year compared to a house built twenty years ago...

"When contradictions, complexity and chaos
 combine with accelerating change the only
definite outcome is uncertainty"

Ziauddin Sardar sums up the ideas of uncertainty and complexity in today's day and age beautifully in his must read article, Welcome to the postnormal times; "When contradictions, complexity and chaos combine with accelerating change the only definite outcome is uncertainty"

It seems strange that the only thing we really do know about the future, is that it is riddled with uncertainty. Yet, in schools we seem to do little about preparing students for uncertainty. Instead, we give students timetables to tell them where to be every minute of their day. We tell them the learning objective at the start of the lesson so that they know what to expect and what to learn. We teach to a test or assessments, and we get upset if the questions surprise us. As teachers, we prepare our lessons, plan them out. In fact, how many schools and departments have the planning for the whole year ahead laid out, bit by bit? We are available to help students out when they get stuck. We tell student which strategies to use, what books to read and what thoughts to think. Before students learn to think about uncertain student finances, babies and children, political instability, we ask them what they want to be when they grow up. Then we ask them to make enormous investments in degrees that may or may not be useful as the market is too uncertain to know what will actually be useful. We help students believe that they just need to stick to the plan, and the all will be OK. There is no shortage of articles and research available about the disjoints between education and the workforce, both at a school and higher education level. Is it just me, or are the things that we teach, the ways we teach, actually doing the complete opposite of preparing students for coping with the unexpected and uncertain? And that's without getting me started on the helicopter parents!

I often hear teachers and parents talk about preparing students for the future. However I wonder if we have really thought about what this means. Does it mean teaching and learning of Shakespeare and Pythagoras as we have always done? But much like the economic ideas of continuous growth, that we perhaps try to do it better? Does it mean that we teach students coding and robotics? Perhaps it means that our schools should teach with devices, type those essays on Google Docs? Perhaps even collaborating on a Google Doc? Does it mean that we focus on things such as collaboration, problem solving, creativity, innovation?

So what then does teaching for and with uncertainty look like? It seems fitting that I am uncertain! However, my current approach to uncertainty involves rapid iteration and deep reflection. Hence, here are some of the things that I have tested and tried with various levels of success over the past year:

• Design Thinking, the Scientific Method and PPDAC: You might wonder what these two have in common... As I see it, Design Thinking, the Scientific Method and PPDAC are problem solving approaches. Where Design Thinking uses empathy to solve problems, science and maths uses objectivity to solve problems. By teaching using these (and other) approaches side by side, I hope that my students begin to understand processes of problem solving, rather than simply looking for an answer. I hope that they learn to distinguish between the pros and cons of problem solving approaches, and learn to apply each approach accordingly. Or perhaps even to mix approaches when the moment is right.  In class, we explicitly discuss problems together and talk about what the best problem solving approach might be. 
• When teaching maths in particular, sometimes I give impossible problems. Problems that can not be solved because I did not give enough information. Or sometimes I give problems with too much information. Sometimes I give problems that I have not yet taught the skills for. These problems are usually followed by reflections where we discuss our responses to uncertainty. Some of us get defensive, some of us act like we know when in fact we don't (and then sound very ignorant!), some of us simply give up, get distracted or even get angry. We talk about what might have been a better approach. We talk about what we could have done, alternative approaches. 
• For some time now, I have also been an a fan of programmes such as Art Costa's Habits of Mind. This approach gives students strategies for 'knowing what to do when you don't know what to do'. It enables students to coach themselves through challenges by having strategies to draw on when they don't know what to do. 
• Simulations: This year I was fortunate enough to co-teach with Steve Mouldey. Together, we ran an alien planet invasion simulation in class where students had to make decisions for themselves in a highly complex environment. This meant that students had to deal with real uncertainty and complexity on the fly. Without a doubt, this was some of the most powerful learning I have ever seen for a group of students. You can read more about this simulation here. 

Of course, as most of my experiments in the classroom goes, they only raise more questions...

• If schools valued the ability to cope and thrive in uncertainty, would they want to measure it? How would it be measured?
• What other approaches could I try to help my students cope and thrive in uncertainty? What does best practice for teaching and learning with uncertainty look like? Can there even be best practice for uncertainty?
• How do my students feel about uncertainty? Do they feel as uncomfortable 'not knowing' as the adults?
• Are teachers able and willing to work in a space where they don't 'know', a space where they too are uncertain? Are teachers able to challenge and redefine their identity as the one who 'knows' the answer? 
• Why is uncertainty so uncomfortable? Why is uncertainty often associated with the negative rather than the positive? 
• Is it foolish to be/act certain about the future?

With so many more questions, it would appear the the only thing I am certain about is that uncertainty is a key to thinking about Education Futures. Perhaps you are more certain than I? How do you think we might prepare students for a society fundamentally different than ours, so different that we can not know what to prepare them for? How do you think we might prepare students for uncertainty? Or perhaps, you think we shouldn't? 

Buzzwords are not enough

Visitors to Hobsonville Point Secondary School's beautiful, new modern learning environment are often distracted by the broad open spaces, the bright furniture. However, visiting the school with students in action leaves one with a completely different experience of a modern learning environment. Here are just two examples from my teaching for term three that illustrates this point.

What's a Squircle?

This module combined visual arts and mathematics. Students were exploring geometric properties of shapes, and using these to create screen prints. Using translation, rotation, reflection and in some cases, enlargement, students have created their own tessellations. Students then took a step further and completed a detailed write up, explaining the mathematical principals behind their work of art. 

Student work from 'What's a Squircle?'

 Age of Ultron

This module combined social sciences and science. Together, we have been looking at some of the ideas that sit behind artificial intelligence. In science, we unpacked some of the ideas around circuits including components of circuits, insulators, conductors, types of circuits etc. In other words, the very basic physical aspects of how machines, including smart machines are constructed. Steve Mouldey, my social science co-teacher for this module looked at the sustainability aspects of the rise of the machine, including automation and smart machines. He touched on ideas around economic, social and environmental sustainability. Student learning experiences in this module included modelling of Moore's law and the related chess board problem (see video and images below). We had the team from Thought-Wired in to talk to our students about machine learning. as well as playing with some breadboards, Arduino and also making some wobblebots (checkout the Mindkits website for gear). We deconstructed old computers and servers. Students have even had a go at constructing various parts of a policy statement for New Zealand regarding Artificial Intelligence. 

Student work from 'Age of Ultron'

So what?

I know that the students in 'Age of Ultron' were not just engaged in deep thinking about current, topical ideas, they were engaging with evolving ideas (we have a timeline constructed in class where we track artificial intelligence news as it is released throughout this module). The students were constructing ideas and questions together in spaces and ways where there is no textbook telling them about a single answer, or how to think. These students were dealing with the true complexity of the real world, not some contrived, oversimplified, fake version, and this includes everything from policy statements, killer robots, and even the ethical and social implications of sex robots. In contrast, the students in 'What's a Squircle?' were using existing knowledge of geometry, translation, rotation, properties of shapes etc. to create new meaning, new ideas, new interpretations. Students were not just replicating a method, they explored a method and applied it to create something completely new. Throughout the process, students were able to experience the real problems that occur when physically applying rational mathematical concepts. Students could recognise how two disciplines could find a way to work together.

Intended as a brief snap shot of my practice from last term, I realise that I could easily have turned this post into a buzzword bingo experience. Maker Ed? Check! Authentic and relevant context? Check! Learning from experts (other than teachers)? Check! Project based learning? Check! Elements of design thinking? Check! Blended learning? Check! Robotics and coding? Check! Assessment for learning? Check. Again, much like only looking at the beautiful modern learning environment spaces of schools like Stonefields, Hobsonville Point or Albany Senior, none of these genuinely capture the true complexity of what is going on. Too often in education, we grab the buzzword by the handle, and we leave the very important thinking, the bulk of the suitcase behind (thanks to Creativity Inc. for this metaphor). We look for answers, for recipes, for programmes, rather than actually engaging with the deeper thinking about what is going on, for our students, in the world, in the future. What would our practice look like if rather than talking trends, rolling out literacy programmes and preparing students for the working world (one that is changing so rapidly that this almost seems meaningless)?

The two modules above certainly tick many of the boxes around modern learning practice. I also know that the students were for the most part, highly engaged, they were learning and enjoying it. But is this enough? I hope that the learning experiences that I design changes the way the students think. I hope that the learning experiences I design enables students to collaborate, not just cooperate. I hope that students can recognise diversity (in people, in information, in knowledge, disciplines, experiences, etc.), learn from, and draw on the strengths and weaknesses. I hope to help students discover their passions, so that they may turn them into purpose. I hope to help students tackle challenges, to create brighter futures for themselves, for each other, and the world. I hope that I awake intellectual curiosity and determination. 

Given these hopes, there is no literacy programme roll out that will cover it, and no buzzword without the bulk of its meaning and context that will allow me success. There is no recipe that will allow me to meet these goals. There is however Dr Seuss; "Think left and think right and think low and think high. Oh, the thinks you can think up if only you try!". Here's to term four being about taking the thinking about my practice to a whole new level. Join me?

Subject teacher identity crisis

I was super excited when just before the holidays, this topic won the poll for #edchatNZ night:

What's the point of subjects in an age of wicked problems where collaboration rather than isolation will help us solve them? 

The archive for the chat is here and the 10 minute debrief podcast will be here in a few weeks with our other podcasts.

So what is the point of subjects? Or learning areas? Except for at university, it's not like we ever experience situations that require our subject knowledge in isolation. And anyways, what percentage of the students that we teach in this way become academics? And on top of that, so much of what students have to learn at school is completely google-able. So what exactly is the point of memorising something that you will just google later anyway to check that you have remembered it correctly? And who decides what students need to learn anyways? There are entire fields of knowledge that are completely excluded from the school curriculum, despite their enormous relevance and importance. And then, most students still learn subjects in isolation, despite the academic world currently contending with the fact that the traditional disciplines are not sufficient for our current world. Things like climate change, sport psychology, biomedical engineering and more span many disciplines and can not be viewed under the umbrella of a single academic discipline. And on top of all of that, the sheer volume of human knowledge is expanding at an enormous rate, one that means we add more an more into textbooks but understand less and less in great depth. (For an extended argument of how knowledge has changed, with references, see the summary of my reading below).

The question then becomes, what exactly should we be teaching? And for me, in a school with more flexibility that anywhere else in the country, what should I be endeavouring to teach? How should I teach it given the shifts in knowledge and academics? What is best for my students? Will they be disadvantaged if I do not teach them to value knowledge and the disciplines in the way that society has thus far? Or, will they be disadvantaged if I do teach them in this way? What should be prioritised?

All of this is enough to give a subject teacher an identity crisis. And it appears that to some extent I am having one. For some time now, I have felt uncomfortable with calling myself just a maths or science teacher. I feel that what I do and what I teach, is so much broader that the narrow image that people often apply outside of education. At Hobsonville Point I have worked alongside social science teachers, physical education and health teachers, visual arts teachers, dance teachers and more. As a result, I often end up teaching about these things too, combing my subject knowledge in ways that give problems more meaning. More often than not though, I have no idea about many of the things that our students have questions about, even in my subject areas. Considering that our students have asked questions that stumped climatologists, have been the kind of questions you could do a doctorate about, it's hardly surprising that I often can not answer them. What I can do though, and I like to think I do this well, is teach them how to find out. Now lots of teachers teach research. But I would like to push things a little further...

I am increasingly coming to the conclusion that having done science is pretty useless on its own. So is having done maths or social science. A bold statement I know, but let me explain. You are presented with a problem. It might be a small problem, it might be a large problem, it might even be a wicked problem. I can then draw on 'the way we think or act in science' to help me solve the problem. For example, I might make a hypothesis, collect data, analyse the data and then draw a conclusion. This allows me to determine whether my hypothesis is true or false. However, we all know full well know that in an organisation, country or community where we have to make decisions on behalf of others, that an understanding of different perspectives becomes useful. Hence, I might draw on the way that social scientists use knowledge to add a different lens to my data that I collected. I might view the data from different perspectives. Either way, the problem did not require me to remember some facts, but rather, it required me to draw on different ways of thinking. In this way, the old subject hierarchy disappears too, because rather than thinking that English or Science is more important than Performing Arts, in this way, we recognise that each has a particular way of thinking that can be employed as needed.

To get back to the idea of 'helping students to find out'... More and more I have been thinking about how I might get my students to do something more meaningful that simply consume the knowledge of others. To move beyond shallow research projects. What would it look like if my students were producing knowledge, if what they were finding out was not google-able because that knowledge simply didn't yet exist? What if my students were able to draw on the different ways of thinking from the diverse disciplines to combine them in unique and novel ways, to generate new ways of knowing, new things to know, to solve complex problems, to answer beautiful questions, or one day, maybe solve a wicked problem?

Blue hexagons are science ideas whilst social science hexagons are ideas from social sciences. The yellow post it notes explain the links between the ideas on hexagons.

Summary of notes about the nature of knowledge:

Networked knowledge

One of the contributing factors to the need for a systemic change in our education system is the change that knowledge has undergone since the establishment of our education system. For much of the history of formal education, reproduction of existing knowledge has been one of its core goals (Bolstad et al., 2012). This is evident in the approach that schools and teachers brought to the implementation of the current New Zealand Curriculum.  The release of the current New Zealand Curriculum document saw the introduction of the ‘front end’, a range of future focussed outcomes. However, it was found that teachers were more likely to engage with the ‘back end’, the achievement objectives relating to content, rather than the future focused outcomes (Hipkins, 2009).   As mentioned previously, the educational ideas from Plato’s Republic underpin much of our education system today, and as such; Plato’s ideas of knowledge to some extent underpin our education systems. This is evident in the presence of the academic curriculum, which is often creditedto Plato, a curriculum based on the best of human knowledge (Gilbert, 2005). However, the arrival of the Knowledge Age has meant that the nature of knowledge has fundamentally changed (Gilbert, 2005; Weinberger, 2011) need more sources, hence, suggesting a need for a change in our approach to knowledge in schools. As Weinberger (2011) puts forward; “Our most important institutions are being shaken by questions about knowledge that we thought were as firmly settled as those institutions’ marble and concrete foundations” (Weinberger, 2011)

The Changing Nature of Knowledge 

Where knowledge has previously been described as limited, true, actionable, the new nature of knowledge can be considered to be networked, dynamic, exponential and diverse (Bolstad et al., 2012; Gilbert, 2007; Weinberger, 2011).

Networked 

The new nature of knowledge is that it has become increasingly networked, or as Gilbert and Bolstad (2008) puts it, knowledge is “a product of networks”. Consequently, as Weinberger (2011) argues, the non linear nature of knowledge means that it has become “too big to know”.  Layered on top of the network is what Weinberger (2011) calls filtering forward rather than out. He illustrates this with the following example; in the past, knowledge was carefully edited for publishing in a journal or a book. Hence the publishing industry acted to a large extent as a filter, filtering much out. Bookstores and libraries then also applied a further filter. We were limited by what ‘fit’. This is further evidence with findings from the Andres, Zenter, and Zenter (2014) from the World Bank who found that internet growth in a country led to reduced consumption of paper used for newspapers and printing. In contrast to the confinement of knowledge to printed mediums, Weinberger (2011) explains that today we are more likely to filter forward than out, what doesn’t make it through the filter is often just a few clicks away in the background. In other words, at no point is knowledge filtered out, but rather filters share a node in the network, each node still connected to the easily accessible vast network of knowledge. Add to this, that our knowledge is no longer limited to the final refined, edited, reworked professionally published versions (Weinberger, 2011), but that we share ideas in their infancy, we share drafts, alpha and beta versions. In fact, some go as far as advocating for sharing the draft versions, the process of their work (Kleon, 2014) whilst others suggest that the networked medium means that we can share explanations of knowledge, making it more accessible intellectually (Barker, 2000). Thus, the network allows us gain more complete knowledge, however, at all time confronting us with the idiom of pulling on a loose that results in more and more unravelling.

Dynamic and Exponential 

Of course, if we are no longer publishing only the final versions, and we are no longer limited to publishing through traditional publishers, the rate at which knowledge grows is bound to escalate. The Library of Alexandria in the 3rd century BC was believed to house the sum of human knowledge  (Cukier & Mayer-Schoenberger, 2013).  By comparison, YouTube suggest that 300 hours of video is upload to their site every minute (YouTube, 2015).  In schools, we can see this trend occur too. In 2012 there were only two schools with a creative commons policy, whilst in 2015 the number was nearing one hundred (McGregor, 2015). Even the volume of scholarly journals have seen an increase, the average length of articles increasing by 80% from 1975 to 2007 (Cope & Phillips, 2009). Of course the nature of how scholarly articles are being distributed and published is also changing. As Cope andPhillips (2009) indicate, and as is echoed by Weinberger (2011), reports, conference proceedings, drafts published to personal websites and blogs are becoming increasingly popular over journal articles due to their immediacy and more often than not, open access. Adding to the growth of scholarly knowledge, is the increasing contributions from corporations (Cope & Phillips, 2009). This is bound to increase again with the rise of big data, as corporations seek to make sense of the increasing amount of data they have collected. As Cukier and Mayer-Schoenberger (2013) points out, big data allows us to “experiment faster and explore more leads.” Hence, the pace at which the sum of human knowledge is growing by leaps and bounds (Sardar, 2010a), but also the immediacy with which it is needed and used bears further clues to the changing nature of knowledge.

Diverse 

A further quality of knowledge is that it has become increasingly diverse. More diverse groups are generating knowledge and more diverse knowledge is produced. As pointed out above, knowledge is no longer produced largely by universities and research institutes. Instead, as well as schools, hospitals, corporations and government, social networks are now commonly being utilised for knowledge creation, as it facilitates collaboration between scholars and amateurs (Biesta, 2007; Cope & Phillips, 2009). As a result, the diversity of those creating knowledge has shifted. Cope and Phillips (2009) call this a democratisation of knowledge.  Of course, there is a second level of diversity that comes into play here, that of knowledge itself becoming increasingly diverse. Some argue that knowledge produced from universities still holds the epistemological monopoly (Biesta, 2007), additionally, academic journals are characterised by their discipline or sub-discipline (Cope & Phillips, 2009). However, despite these more formal knowledge institutions, Cope and Phillips (2009) draws our attention to the fact that rise of interdisciplinary fields and problems such as climate change has led to the breakdown of these epistemological and disciplinary barriers. Thus, not only have the types of knowledge increased in diversity, but also the cross over between disciplines. Outside of academia, there is also enormous diversity in knowledge, as Weinberger (2011) puts it, “we can see – or at least are led to suspect – that every idea is contradicted somewhere on the web”. Even in statistics, big data shows us those data points that sit outside what we think we know, as a result adopting correlation rather than cause (Cukier & Mayer-Schoenberger, 2013).  It is these ideas about the diversity of knowledge that might lead to experts such as Bolstad et al. (2012) to argue that “21st century citizens need to be educated for diversity – in both the people sense and the knowledge/idea sense.” Both the nature of knowledge and those participating in its creation is diversifying.

Refereces

• Andres, L., Zenter, A., & Zenter, J. (2014). Measuring the Effect of Internet Adoption on Paper Consumption World Bank Policy Research  
• Barker, S. (2000). The End of Argument: Knowledge and the Internet. Philosophy and Rhetoric, 33(2), 154-181.  
• Biesta, G. (2007). Towards the knowledge democracy? Knowledge production and the civic role of the university. Studies in Philosophy and Education, 26(5), 467-479. doi: 10.1007/s11217-007-9056-0 
• Bolstad, R., Gilbert, J., McDowall, S., Bull, A., Boyd, S., & Hipkins, R. (2012). Supporting future-oriented learning and teaching - a New Zealand Perspective: New Zealand Council for Educational Research. 
• Cope, B., & Phillips, A. (2009). Signs of epistemic disruption: transfomrations in the knowledge system of the academic journal The Future of the Academic Journal: Elsevier Science. 
• Cukier, K., & Mayer-Schoenberger, V. (2013). The Rise of Big Data: How it's Changing the Way We Think about the World. In M. Pitici (Ed.), The Best Writing on Mathematics 2014 (Vol. 92, pp. 28): Princeton University Press. 
• Gilbert, J. (2005). Catching the Knowledge Wave? The Knowledge Soceity and the future of education.Wellington: New Zealand Council for Educational Research. Gilbert, J. (2007). Knowledge, the disciplines, and learning in the Digital Age. Educational Research for Policy and Practice, 6(2), 115-122. doi: 10.1007/s10671-007-9022-1 
• Gilbert, J., & Bolstad, R. (2008). Disciplining and Drafting, or 21st Century Learning? Rethinking the New Zealand Senior Secondary Curriculum for the Future. Wellington: NZCER Press. 
• Gilbert, J., Bull, A., Stevens, L., & Giroux, M. (2015). On the Edge: Shifting Teachers' Paradigms for the Future. In TLRI (Ed.), (pp. 18): TLRI. Hine, D. (2014, 6 March). 
• What good is information?aeon.  Retrieved 15 July, 2015, from http://aeon.co/magazine/technology/the-problem-with-too-much-information/
• Hipkins, R. (2009). Reshaping the secondary school curriculum: Building the plane while flying it? National Survey of Secondary Schools 2009. Wellington. 
• Kleon, A. (2014). Show Your Work!: 10 Ways to Share Your Creativity and Get Discovered: Workman Publishing Company. 
• McGregor, M. (2015, 14 July). [Creative Commons Data]. 
• Sardar, Z. (2010a). Welcome to postnormal times. Futures, 42(5), 435-444. doi: http://dx.doi.org/10.1016/j.futures.2009.11.028
• Sardar, Z. (2010b). Welcome to the postnormal times. Futures, 42, 435-444. doi: 10.1016/j.futures.2009.11.028 
• Weinberger, D. (2011). Too big to know. New York: Basic Books. YouTube. (2015). Statistics.   Retrieved 15 July, 2015, from https://http://www.youtube.com/yt/press/statistics.html
• Zucker, J. (2014). World Views: Creating Significance of Learning in the Classroom. The Councilor: A Journal of the Social Studies, 71(1). 

Yoga and maths. One and the same?

Image Source

I had a rather unusual maths lesson today. Keeping in mind that I have been focussing on well being for my students and I in various capacities, I thought working in some yoga in a maths lesson seemed like a really good idea. Also, working in a cross curricular team with the Health and Physical Education department, it seemed like a unique opportunity for students to physically experience concepts, rather than just talk about them, or worse, just be told about them.

1. Bryce my co-teacher in this module started with a theory introduction about yoga. Building on the ideas of aggression versus competition from the previous week, he explained how western culture has influenced yoga particularly in respect to competition. We also talked briefly about how yoga had been sexualised. With the Health and Physical Education focus on social and cultural factors, there was lots to talk about. West vs. East type stuff!
2. We then went on to about half an hour of yoga. Really basic stuff but finishing off with five minutes of careful breathing exercises. At the beginning, students were told that the idea was to focus on yourself, not on anything or anyone else. The goal was to clear your mind completely, or if you struggled with this, to only focus on your breathing. 
3. Students answered some reflection questions about doing yoga. For example, what does yoga look like, feel like, sound like? Which Hobsonville habits are in use when doing yoga? Purposeful fit really well here because of the importance of focussing your thoughts, breathing and movement. 
4. We returned to class where I read students an extract from Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers.
   "Shunya means zero in our language. But it also relates to the Buddhist philosophical concept of the void, which is called Shunyata. You see, zero, the number, and the Buddhist emptiness - the goal of mediation and an ideal striven for on the road to Nirvana, or enlightenment - are one and the same. Emptiness is a deep philosophical concept, and from it we get zero." As part of exploring the idea of numbers representing things, we also took a moment to discuss the question, "Are numbers real?". This was fascinating and lead to a remarkably heated debate. 
5. From this, we then explored the idea of zero and it's importance in more depth. Students could choose one of two questions to work on. The second is a problem from NRICH maths.  Through this, students were able to begin making sense of place value. They also developed a really clear understanding of the idea that our numbers are only a symbol, and these symbols are representations. Zero is representation of nothing, or the clear mind we were all attempting to have earlier in the lesson. At the same time, five could be represented in a number of ways. I feel like this was great preparation for the algebra concepts later this term as in the past, I have often seen students struggle to wrap their heads around why we introduce letters. I hope that seeing beyond the symbol might be useful.
6. Finally we finished the lesson Steve Mouldey style, with a "what if" question. What if zero was never invented? Although some students could still only grasp at some basic ideas, it was really exciting to have a student ask whether we would have negative numbers without zero. 

Choice of questions students had to work on. 

It's peculiar to think that maths has been influenced so heavily be eastern religion, philosophy and religion, yet more often than not, we have separated the emotional, people aspects from maths entirely. Instead, it is often presented in a rather sterile way. The ideas that we encounter on a daily basis as far more connected than we realise at first glance. It really made me wonder, how much of the 'content' that is so valued in schools, has actually lost all its romance because we have stripped it from its context?

Preview

Turns out planning a conference keeps one a bit too busy to blog regularly. However, I thought I would just share a quick preview of what I am teaching this term.

There is no I in team

Bryce's team work game in action
We are looking forward to having students analyse their behaviour!

On Wednesdays this term I will be teaching with Bryce. Bryce will be doing PE and Health while I will be doing statistics. We started the module with some team building games. Students were then able to reflect on the experience using a google form. The same google form was also then used as a means to establish prior knowledge about statistics. Students then worked in groups to have a go at analysing the results from the google form.

Population Explosion Project

Thursday afternoon is my SPIN (special interest module), that I offer by myself. This spin is a maths module, however mixed up with one of my personal interests - anthropology. We started the session by watching the first few minutes of a video from the fantastic and entertaining statistician Hans Rosling. Students were then asked to generate questions from what they had just watched using a question grid and dice. We will be using their questions throughout the term to inform our statistical inquiry and hopefully draw some conclusions. 

Shout out to Cindy for this fabulous resource

Student selections of their most complex and most interesting questions

Apocalypse now

Apocalypse now on Friday is a module that I will be teaching with Steve Mouldey. In this module, students will be examining socio-scientific issues, however particularly looking at 'wicked problems' specifically outlined in Steve's current read - NZCER's Key Competencies for the Future. Students started the lesson simply by brainstorming in groups everything that is wrong with the world. They were then asked to sort these into groups with descriptive titles and then asked to provide a description of each category. Students were  then given time to explore the resources (videos, articles etc.) that Steve and I curated. Even on day one, we already had some interesting discussions about different perspectives when gay marriage came up as a topic. Steve couldn't join us, however but we made sure to keep him in the loop using our module hashtag on Twitter #apoclyps. Our visitor in class, the lovely Alyx also made sure to share the events. 

Volanoes

V is for volcanoes in the A to Z challenge...

Welcome to Auckland, New Zealand, a city built on a dormant volcanic field. As a result, we have 53 volcanoes in Auckland. There is also Rotorua, one of my favourite New Zealand cities where you can visit geothermal tourist attractions, or just watch the steam rise and the mud bubble in a local public park. This is of course a wonder land for a girl who used to collect rocks. My mum tells me that we used to have arguments when she unpacked my far too heavy school bags because I wouldn't let her throw my rock collections out. Apparently I insisted that each one had a special colour, a special shape or something else special.

Public park, Rotorua New Zealand

This term, I will be working with Sally and Pete on a module called The MASTER behind the chef. We will be exploring our geological past, present and future through food and maths. Since every year, I identify my insufficient knowledge of Māori language and culture as a professional development need, I am really looking forward to working with two educators who are role models in this field.

Even more so, I am excited to explore the great impact that these beautiful but vicious features of our landscape have had on New Zealanders. As a tourist in New Zealand, you can have corn cooked in a geothermal pit as Māori did in their past. A friend of mine has a tiny garden at the foot of Mount Albert, another Auckland volcano. She rarely buys vegetables because her soil is so fertile due to the volcano on her doorstep. Just as Māori found value in the geology of the landscape, so too can we find value in it now. There are parts of our knowledge about volcanoes that have evolved, but there are also parts that stayed the same. The New Zealand Curriculum requires that all students should learn about how scientific knowledge changes over time, and so, I am looking forward to a great term exploring the ties with which geology connects New Zealand past, present and future.

Rotorua, New Zealand

Rangitoto Island, Auckland, New Zealand

Learning 2.0

L is for Learning 2.0 in the A to Z challenge:

At Hobsonville Point Secondary School, we want to personalise learning. We want our kids to love learning. And we want the learning for both academic and personal dispositions to be rigorous. You might be curious about how a public secondary school is trying to achieve this. So here is the cheat sheet...

Start with Claire's blog post that describes the different structures of our school. Then read Megan's blog post that describes the anatomy of our learning hubs. And then, read through the modules we are offering for term two. In short though, modules cover the curriculum whilst learning hubs is where we develop the whole learner and where we make and develop our connections with families.

We still teach maths, english, science and so forth. But we do things a little differently. For example, you can choose how you do your maths and science in term two... So everyone is learning about maths and science, but you can choose to do it it in a visual arts context, a food and culture context or a social science context.

You might wonder what this looks like in practice...Below is a comparison between one of the modules I taught this term with Ros MacEachern called Larger than Life. You can see that I still taught statistics, however I just wrapped it in a context. And this clever wrapping allow us to personalise whilst providing rigour and curriculum coverage.

What we do: Maths at HPSS	New Zealand Curriculum
Modules take the place of subjects at HPSS. A module combines two or three subject areas. Students who have additional interests in maths will be able to gain extra coverage in  SPINS (special interest modules) which focus on extended coverage of learning areas	The New Zealand curriculum dictates what all students across the country should be learning at school From the New Zealand Curriculum: In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations.
Larger Than Life: (combining English and Maths) Under the English component of this module, students produced their own blog or vlog. Students in this module: Analysed graphs based on the content of their blogs/vlogs. E.g. Students who were blogging about gaming looked at graphs of console prices over time. Entered the amount of ‘hits’ from each of theirs sites in a spread sheet Posed questions about the amount of ‘hits’ that we were getting as a class. E.g. Did YouTube channels or blogs of the students in our class have the most hits? Did the boys or girls in our class get more hits? Calculated the averages to determine the answers for the questions above Begin to manipulate a spread sheet to input formulae and produce graphs	In statistics students will: Interpret statistical displays Use a calculator to determine averages Undertake a statistical investigation Flow chart from NZ Maths http://www.nzmaths.co.nz/elaborations-level-five-statistics

Of course, because the learning for every student looks different, we need to make sure there is consistency across the modules. This is gained from the learning design model which was constructed by pulling the New Zealand curriculum to pieces and the putting it back together again. Just one term in and most of the students are able to verbalise the main parts of the model and understand its process on driving learning.