Tuesday, July 28, 2015

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). 

Sunday, July 12, 2015

Getting my maths on



I was very lucky to attend the NZAMT conference on a scholarship from NZAMT. In other words, I had a fantastic opportunity to spend four days at a maths teacher conference, learning amongst some pretty serious mathematicians. As with most conferences however, things can be a tad overwhelming as we try to make sense and learn from each session, trying not to forget the new ideas they shake loose. I take notes at every conference I go to however, often these notes go to waste as life gets busy. As a result, I decided that with this conference, as well as the notes I usually take, I would summarise each session with a single question to help jog my memory around the ideas or goals each session gave me. You will notice that these are all phrased as 'How might we ... ?' questions. How might we is a great tool I picked up from the design thinkers and books such as A More Beautiful Question. How might we suggests possibility and action.

So here are my questions:

  1. How might I develop my knowledge of advanced mathematics?
  2. How might I improve the quality and quantity of feedback students receive in my modules?
  3. How might I enable more evaluation of methods for more discerning problem solvers?
  4. How might I reach backwards, aka, make sure students get to the exciting contextual maths at the beginning rather than a goal to work towards at the end?
  5. How might I help students to develop better representations of mathematical ideas?
  6. How might I challenge my students to find mathematical patterns in more everyday situations?
  7. How might I use PPDAC to support development of mathematical art work in my upcoming cross curricular module with art?
  8. How might I use testing data to be a mores responsive, adaptive teacher?
  9. How might I expose my students to data science earlier?
  10. How might I encourage and enable more students to 'play' with data?
  11. How might I empower my students to be more independent learners through the use of video?
  12. How might I extend the concepts that I am teaching to bring more mathematical awareness?
  13. How might I create innovate and engaging electronic internal assessment tasks for my NCEA students?
It seems that his was a far more powerful way to summarise my notes as looking over these questions I feel ready to prioritise my next steps and tie them to my professional goals for the year.