Reflecting on my pedagogical development

I finished my undergraduate teacher training in 2006 and I was taught many traditional pedagogical strategies, however, I was also taught the NSW Quality Teaching Model (QTM) and it was perhaps my first step towards realising the importance of reflection in my teaching practice.  I was constantly reflecting on the lessons I taught and how they were engaging students in aspects of the QTM.  As technology became a bigger part of my teaching practice, it became evident that the pedagogical strategies I implemented and utilised might have to change more as well.  

For a few years now I have been researching and reading up on heutagogy and andragogy.  I am always keen to investigate new ways to teach content and skills to my students.  Technology has been a huge catalyst in me doing this.  I realised early on in my career that technology was entering education institutes at a rapid pace and that there was going to be a need for teachers to develop further skills in ICT integration and that how we taught would also change.  

It was when I did the Intel Teach Essentials Master Trainer course that I realised just what kinds of pedagogical strategies would be required to harness the potential of technology and teach students who were engaging with technology more and more every day.  This PD course looked at problem- and project-based learning and how to integrate technology within it.  This was the first time I had learned about PBL and I quickly saw it as a valuable pedagogical strategy for the 21st century.

What is the significant position and place of pedagogy in education?  What is it in reality?  What should it be?  These questions came to mind as I was reading Lingard et al. (2003),  Zammit et al. (2007) and DET (2003).  Where is pedagogy placed within our current education system?  Is it placed in high enough a position?  I don’t think it is in reality.  When I look at the Australian school system as a whole, the focus is always on content… cover this, cover that and culminate in a test at the end.  Do educators today think of pedagogy as simply the foundation strategies they learned about when they were studying to be a teacher initially, but something that they don’t need to consider as much with experience?  Perhaps they do.

The QLD education department seems to have it going in the right direction when in their ‘Pedagogical Framework – FAQs’ they emphasise that: 

The State Schools Pedagogical framework policy requires every Queensland state school to develop a school pedagogical framework. It needs to be informed by research, yet respond to the local context.  From 2013, each school is required to enact a pedagogical framework that is collaboratively developed with the school community and aligned to state and regional requirements. This requirement is listed in the P–12 curriculum, assessment and reporting framework.” (p. 1).  

However, when I went to the NSW Syllabus website for the new NSW national curriculum syllabus documents, I did not see the word ‘pedagogy’ anywhere.  Where is the value placed on pedagogy in the new Australian curriculum? 

I believe that school plans should be made with pedagogy in the forefront of leaders’ minds.  Pedagogy is not just classroom teaching and learning strategies, it is the ‘art and science’ of teaching.  It is the facilitation of students and teachers alike, expressing and reproducing their learning with creativity and individuality.  It is the psychology, philosophy and specifics of how to teach and learn, how we process information and what we do with that information.  That is more important than the content we teach, because it carries into life beyond the classroom.

REFERENCES

DET, N. (2003). Quality teaching in NSW public schools. Sydney: Professional Support and Curriculum Directorate.

Lingard, B., Hayes, D., & Mills, M. (2003). Teachers and Productive Pedagogies: Contextualising, conceptualising, utilising.Pedagogy, Culture & Society.  11,3, 399- 424.

QLD Department of Education, Training and Employment, (n.d.). Pedagogical framework — Frequently asked questions. [online] Available at:     http://education.qld.gov.au/curriculum/pdfs/pedagogical-framework-faqs.pdf [Accessed 2 Sep. 2014].

Zammit, K., Sinclair, C., Cole, B. Singh, M., Costley, D., Brown a Court, L., Rushton,K. (2007). Teaching and leading for quality Australian schools: a review and synthesis of research-based knowledge.  Acton, A.C.T.: Teaching Australia, Australian Institute for Teaching and School Leadership. LB1727.A8.T45

Features and qualities important to pedagogical models

I have long had an interest in pedagogical and instructional design models and the elements of them I have looked for, as evidence of their quality, has been guided by these questions:

  • Does the model provide adequate scaffolding for a learning experience?
  • What is considered most important, content or pedagogy?
  • Are students’ getting the opportunity to demonstrate higher-order thinking skills?
  • Is ICT considered as a supporting tool in the process and experience of teaching and learning?
  • Is there room for flexibility, adaptability and differentiation?
  • Is there room for student self-regulation to be facilitated and encouraged?
Photo by David Jones, from Flickr.com, Some rights reserved

Photo by David Jones, from Flickr.com, Some rights reserved

When I consider pedagogical models, I consider all of these and more, often thinking of the NSW Quality Teaching Model.  As a leader in technology integration in teaching and learning, I never consider pedagogical models without considering how it scaffolds ICT integration.  Technology is still such a gimmick and there is still somewhat of a novelty to its use within the classroom, however, it is not always integrated with solid instructional design as its foundation.  That is why my interest has been in models of pedagogical design and instruction that help provide that foundation that both encourages ICT integration and enables it in a smooth and undertaking way.  My most frequently referred to pedagogical models are: TPACK, ADDIE model, the NSW Quality Teaching model, Bloom’s taxonomy, inquiry-based learning model and problem- or project-based learning models.  I find each of these great foundational models for integrating ICT into pedagogy, for reasons outlined below.

TPACK – This model is comprehensive at outlining the connections between pedagogy and technology, between pedagogy and content, and between content and technology, as well as all three intertwined.  It places content as the most important element in this pedagogical model and seeks to establish solid foundation in content and activities before technology interferes.  Technology is seen as the supporting actor, the tool to enhance outcomes further.

Bloom’s Taxonomy – This model does not make suggestions as to how technology should be implemented in the model’s original format, however, the verbs offered in the model, suggest active ways that technology can be utilised.  Students can create, analyse, synthesise and discover new knowledge with technology.

Inquiry-based learning model – This model has stages for creation and for discovery or investigation as well.  Much can be discovered and investigated with resources available on the Internet.  Reflection and discussion are also important features of Inquiry-based learning and can be facilitated through the integration of technology as well.

Problem-based learning model – A model that allows students room to self-regulate their learning and to utilise a number of technologies to assist them in solving a problem or developing a product.  PBL connects students with real-world problems and audiences and leaves room for differentiation and flexibility as well. 

Photo by Alec Couros on Flickr.com Some rights reserved

Photo by Alec Couros on Flickr.com Some rights reserved

In the 21st century, students need to develop a certain set of skills: collaboration, communication, creativity, critical thinking, and information fluency (Dede, 2010).  We are said to be in the age of knowledge, the knowledge society, and this requires the development of “1. knowledge construction, 2. adaptability, 3. finding, organising and retrieving information, 4. information management, 5. critical thinking and 6. team work” (Anderson, 2008 in Voogt & Roblin, 2010, p. 1).  Pedagogical models of the 21st century need to include these skills and need to integrate the mode in which 21st century learners most frequently learn and engage with new knowledge and information, which is technology.  I think some pedagogical models cater well for that explicitly and some may only provide a shel from which to interpret the nature of ICT integration.

  

REFERENCES

Dede, C. (2010). Comparing frameworks for 21st century skills. 21st century skills: Rethinking how students learn, 51-76.

Voogt, J., Roblin, N. P. (2010). 21st century skills. Discussienota. Zoetermeer: The Netherlands: Kennisnet.

Important aspects for education and for a curriculum in the C21st

In one of my uni courses this week we were asked to reflect on the question: “What do you see as some of the important aspects for education and for a curriculum in the C21st?”.  It’s something I often think about but here are some of my thoughts at present.

71878108_709b04c40d_mIn July of this year, I attended the annual Ann D Clark lecture at Penrith’s Joan Sutherland theatre.  This year’s speaker was Presidential Chair and associate dean for Global and Online Education, Yong Zhao.  Yong was very thought-provoking and inspiring and spoke a lot about current aspects of education and curriculum and how they are not necessarily appropriate for the need to create entrepreneurial and creative students.  He raised some very valid points and in his book, World Class Learners: Educating Creative and Entrepreneurial Students, he dedicates an entire chapter to why a common curriculum and set of standards will not help our current and future generations of students.

The mission statement provided in the newly implemented Common Core State Standards (CCSS) of the US indicates that one purpose for its implementation is “to compete successfully in the global economy” (Zhao, 2012, p. 26).  Should the 21st century curriculum and other aspects of education be focused on the economy?  Well, I guess that it is the economy that keeps jobs alive and generally helps society to keep going as it has for so long.  Zhao also goes on to delve into the newly implemented Australian National Curriculum, and when he compares it to the US CCSS he finds that they have very similar rationales, being that they intend to create “equity, efficiency, and quality for all students to compete successfully in the global economy” (Zhao, 2012, p. 28-29).  The globalisation aspect for education and curriculum appears to be critical in the eyes of some.  Does the Australian National Curriculum foster and enable this?

3620335406_691b16543e_mWe are in the knowledge management age and that of globalisation as well so I believe personally that education, and certainly the National Curriculum, should provide opportunities for students to enter into this world with the knowledge and skills needed to be creative and entrepreneurial citizens.  Chinnammai (2005) says that students need to become global citizens, “intelligent people with a broad range of skills and knowledge to apply to a competitive, information based society” (p. 1).  Does the new national curriculum provide a broad enough scope of skills and knowledge applicable to an information-based society?  I don’t think so, I think it is far too content heavy and that students and teachers alike, get lost in the content and learning for the sake of exams, that they do not develop the necessary skills required by a global citizen.

Chinnannai (2005) also points out that “The introduction of technology into the classroom is changing the nature of delivering education to students is gradually giving way to a new form of electronic literacy , more programs and education materials are made available in electronic form, teachers are preparing materials in electronic form; and students are generating papers, assignments and projects in electronic form” (p. 2).  However, what guidelines are included in the national curriculum to guide the expectations of what students should be able to do with technology when they leave school, in order to be global citizens.  I believe that technology is a critical part of 21st century education and beyond.  Any national curriculum should include a continuum of skills that students develop as they progress throughout their schooling, that will guide their acquisition of technical skills required when they leave school.  It can’t be all content focused, we have to be realistic about what they crucially require when they enter the workforce and other study areas.  I therefore also believe that 21st century education systems, and certainly the national curriculum, needs to provide scope for differentiation and individualised pathways of learning and development to cater for all students’ needs, abilities and future endeavours, regardless of a special needs or giftedness.

References

Chinnammai, S. (2005, November). Effects of globalisation on education and culture. In ICDE International Conference.

Zhao, Y. (2012). World class learners. Educating creative and entrepreneurial students.

Education up in the clouds

Watching a TED talk this morning by Sugata Mitra, on a project I had heard about before, reaffirmed my own beliefs that our current school system is not set up to cater for the 21st century.  Sugata is a software engineer, innovator, pioneer and educator who resisted the pull of the schooling system that the British empire initiated and that has become the norm, and he tested the boundaries of expectations and discovered amazing possibilities if we just put aside the default settings of teaching and learning.  In his TED talk, ‘The Future of Learning’,  Mitra boldly proclaims that “school as we know them are obsolete” (Mitra, 2013, 2:55) and “the education system is wonderfully constructed but not needed anymore… it’s outdated” (Mitra, 2013, 2:56).  I believe he is right.

Mitra (2013) placed one computer in a hole in the wall of his office and let the local children engage with it in an unguided and free way.  What ended up happening was that students started to teach each other how to browse he internet.  He tried the experiment again and again, getting similarly surprising responses.  When he eventually decided to create a serious hypothesis and test it out the results were astounding.  He placed a computer, with lots of information downloaded onto it about DNA replication, in a remote Indian village and hypothesised that none of the Tamil-speaking children would be able to learning about DNA replication with materials only provided in English.  After several months, some periodic testing, and an older student providing prompts in the form of questions, the children were able to achieve 50% on their DNA replication test.  There was no teacher, the students taught themselves and taught each other and they broke down the barriers that we might think would prevent them from learning the material.

Do we have this same approach and mentality when we teach? No we don’t.  Do we provide a stimulus, and then let them go for it, digesting and discovering resources for themselves and making meaning from it? I really want to be the type of teacher who enlarges the territory of learning for all of my students, who knows no limits in terms of what students might achieve.  Who are we to say what they are capable of?  The ‘hole in the wall’ experiment Mitra conducted went against all expectations and educational norms but it produced astounding outcomes and results.  He goes onto say in the later half of his video that the notion of the Grandmother method and encouragement proved to be the key in the experience of he DNA replication project.  The Grandmother method, he explained, was the addition of a 20-year-old student who stood behind the children engaging with the resources on the computer screen who asked them questions as simple as, “what are you doing now?” and “how do you do that?” and encouraging them.

From that one experiment with the older student, Mitra decided to engage as many British grannies as he could for another project.  The Granny Cloud, as they have become known, are available via Skype whenever a child needs them and simply provides encouragement and questions to encourage in this ‘self-organised learning environment’, which Mitra (2013) says “are basically broadband, collaboration and encouragement put together” (16:56).  It is from this that Mitra (2013) has determined his vision for the future of schooling. “My wish is to help design a future of learning by supporting children all over the world to tap into their wonder and their ability to work together. Help me build this school. It will be called the School in the Cloud” (19:32).  It’s a fantastic idea and the ideal way to take hold of the potential we have to learn collaboratively in the cloud.


 

references

Mitra, S. (2013). Sugata Mitra: Build a School in the Cloud. [online] https://www.ted.com/talks. Available at: https://www.ted.com/talks/sugata_mitra_build_a_school_in_the_cloud#t-35640 [Accessed 15 Sep. 2014].

Philosophy for teens?

Another question I asked myself yesterday as I was reading was, ‘Should philosophy be taught in high schools?’.  I asked myself this question in response to a sentence I read in Kalantzis and Cope (2012) that said: “The logistics of their form [test] are such that they end to measure discrete knowledge items distilled to clear-cut and isolable facts and aphorisms drawn from theories and, specifically, items that can be adjudged right or wrong.  These may not be the best things to be measuring in an era when the questions are at times complex and ambiguous, facts contestable and theories open to interpretation.” (p. 86)  We are in an era where the prevalence of information, stimulus materials and theories are running rampant and in which teenagers are exposed to much more thought-provoking materials in the media than ever before.  I asked myself, whether it was an age in which it might be appropriate to equip students with some knowledge and skills in philosophy?

According to the Catholic Encyclopedia at www.newadvent.org, philosophy can be defined as: “the general science of things in the universe by their ultimate determinations and reasons; or again, the intimate knowledge of the causes and reasons of things, the profound knowledge of the universal order”.  We are living in the ‘knowledge society’, the ‘knowledge economy’ and the era of knowledge management so it seems appropriate that we address the need for our next generation to take hold of the knowledge of these things. Apparently, according to my research, there are many high schools in Europe teaching philosophy and one site, called PLATO, gives this reason for doing so: “Philosophy can and should be taught in high school because this is the ideal time for students to engage its questions, arguments, and methods of thinking.” (Plato-philosophy.org, 2014).

In some ways, we are already teaching students about philosophy and equipping them with philosophic knowledge and skills in the implementation of ethics classes, religious education, and in other pedagogical practices such as inquiry-based learning and problem-based learning.  However, how can we extend the philosophy skills students develop and be intentional in teaching it?  Well, in Victoria, The Victorian Association for Philosophy in Schools (VAPS) has a vision to see students learn to be philosophers, “stimulating open and inquiring communities of philosophical exploration, in which students develop the art of questioning and acquire conceptual and reasoning tools” (Gelonesi, 2011).  VAPS have been crusading as well for the inclusion of philosophy in the new Australian National Curriculum, with the justification that “if young Australians are to be successful learners who are able to think deeply and logically, then young Australians will need to acquire the basic skills of philosophical inquiry: logical thought is, after all, the special provenance of philosophy” (VAPS, 2013).

It’s such a big discussion, and I could go on and on exploring and writing about it, however, for now it has got me thinking and I definitely want to pursue more philosophy study and would support and advocate for it within schools.  Much of the general capabilities in the Australian curriculum have been founded on philosophical principles and are related to philosophic concepts, therefore, it would be highly possible to be more intentional in integrating such important skills into our students’ learning.  Would love to hear what others think about this topic?


REFERENCES

Gelonesi, J. (2011). High school philosophy. [online] Radio National. Available at: http://www.abc.net.au/radionational/programs/philosopherszone/high-school-philosophy/2918446 [Accessed 11 Sep. 2014].

Plato-philosophy.org, (2014). Teaching High School Philosophy : PLATO: Philosophy Learning and Teaching Organization. [online] Available at: http://plato-philosophy.org/getting-started/teaching-high-school-philosophy/ [Accessed 11 Sep. 2014].

Vaps.vic.edu.au, (2014). The National Curriculum: The Case for Inclusion of Philosophy in the National Curriculum. [online] Available at: http://www.vaps.vic.edu.au/curriculum/national-curriculum [Accessed 11 Sep. 2014].

A new 21st century pedagogical model

This is something I have pondered for years, a new model, a 21st century model, for understanding and implementing best practices into teaching.  We were asked to consider this in the course I’m doing called ‘Advanced Pedagogy’, and as an online learning designer, I have been very heavily into instructional design models and models for creating new learning experiences.  I’ve explored many of these, and other learning models, on my blog over the years but the few that have particularly stood out to me are:

  • The TEC-VARIETY Model
  • TPACK
  • Hybrid learning model

In the 2014 K-12 Edition of the Horizon report, hybrid learning was outlined as a mid-range trend, and this involves utilising a range of teaching and learning modes to facilitate experiences for students that produce quality learning outcomes.  A quote I found particularly valuable from the report said:

“Schools that are making use of hybrid learning models are finding that using both the physical and the virtual learning environments to their highest potentials allows teachers to further personalise the learning experience, engage students in a broader variety of ways, and even extend the learning day.  Hybrid models, when designed and implemented effectively, enable students to use the school day for group work and project-based activities, while using the network to access readings, videos, and other learning materials on their own time, leveraging the best of both environments.” (p. 12)

I think that any model we utilise pedagogically needs to be flexible, agile and adaptable to the needs of all learners.

Another point I think is important in any model is that it is progressive in nature or provides some sort of continuum on which to base the starting point of learning about something new and the mastery of something.  I think that students need to have something to aim for, so having a model that presents a continuum will provide teachers with guidelines on which to frame learning and progression of.  Like the progression through syllabus stages, e.g. stages 1-6, however, more micro progressive.

The TEC VARIETY model is one that was developed to address motivation and engagement in online learning, but which I feel is applicable to all teaching and learning if considered in the right light.  The model is an acronym for the following: tone/climate, encouragement, curiosity, variety, autonomy, relevance, interactive, engagement, tension and yields.  Each of these elements have been researched and proven to have significant effect on engagement and motivation.  More can be read at www.tecvariety.com

The TPACK model is also a favourite of mine and one that I feel is crucial in the 21st century.  It is a holistic model that comprehensively covers how to work seamlessly with content, pedagogy and technology in curriculum design and its about understanding how each combination of the three work together to create a model for 21st century learning.

Will work on visuals for my combined ideas and the most important ones but as I was reading another one of the course readings, it mentioned other elements that I thought might be relevant for a new pedagogical model.  Kalantzis and Cope (2012) conducted research that was published under the title of ‘New learning: a charter for change in education’ and in it they said: “The transformed economic system emerging from the current financial crisis will require human capacities that only education can nurture, based on deep knowledge, practical imagination, creative participation, intellectual inquisitiveness and collaborative commitment” (p. 83).  These words immediately stood out to me as essential elements in a new pedagogical model for the 21st century but what would they look like in the classroom?


 

REFERENCES

Johnson, L., Adams Becker, S., Estrada, V., and Freeman, A. (2014). NMC Horizon Report: 2014 K-12 Edition . Austin, Texas: The New Media Consortium

Kalantzis, M., & Cope, B. (2012). New learning: a charter for change in education. Critical Studies in Education, 53(1), 83-94.

The evolution of policies framing ICT integration

A reading I did this week was titled ‘Framing ICT, teachers and learners in Australian school education ICT policy’ (Jordan, 2011), and it serves as a study of the evolution of ICT policies in Australia since the ICT was first included in the vision for Australian education, over 20 years ago.  It was a very interesting read and I observed a few things as I read that were quite provocative.  Below is the timeline essentially, of the policies developed:

  1. In 1989, the National Goals for Schooling, developed by State, Territory and Commonwealth Ministers of Education in Hobart, followed by
  2. The Adelaide Declaration on National Goals for schooling in the 21st century came along in 1999, then
  3. In 2000, the Ministerial Council for Employment, Education, Training and Youth Affairs (MCEETYA) endorsed the Learning in an Online World: The School Education Action Plan for the Information Economy.
  4. In 2005, MCEETYA reinvented it as Contemporary Learning – Learning in an Online World, as well as,
  5. Pedagogy Strategy – Learning in an Online World (MCEETYA, 2005).
  6. A political campaign drove the implementation then of the A Digital Education Revolution in 2007, endorsed by Rudd et al.
  7. MCEETYA followed up the DER with The Melbourne Declaration on Educational Goals for young Australians in 2008.

Here is a little more detail on each:

  1. National Goals for Schooling (1989)
    1. “provision for students to develop ‘skills of information processing and computing’” (p. 417)
  2. The Adelaide Declaration on National Goals for schooling in the 21st century (1999)
    1. “Goal 1.6: that upon leaving school, students should ‘be confident, creative and productive users of new technologies, particularly information and communication technologies, and understand the impact of those technologies on society’” (p. 418)
  3. Learning in an Online World: The School Education Action Plan for the Information Economy (2000)
    1. Supported the above goal from 1999
    2. Aligns ICT directly to the idea of an ‘innovative society’
    3. “Harnessing these technologies for learning is vital. Australia’s future as an equitable, imaginative and economically strong knowledge society depends upon it.” (p. 420)
    4. Specialist skills are needed that are appropriate for the information economy
    5. Students will be engaged in ICT-rich programs and students gain employment-related skills for the information economy
    6. ICT integration needs to be purposeful and involve intentional and explicit teaching of skills
    7. Teachers need to commit to the vision of ICT implementation in education
    8. Teachers need professional development
  4. Contemporary Learning – Learning in an Online World (2005)
    1. Statements and strategies formed the ‘Learning Online Suite’, a part of a broader action plan
    2. Aligns ICT directly alongside the 21st century
    3. ICT creates new possibilities and opportunities that are both local and global
    4. Bullet points are used to show certainty
    5. Engaging with ICT is second-nature to young people and they need interactivity in learning
    6. “Learners are dependent on teachers having ICT skills” (p. 427)
  5. Pedagogy Strategy – Learning in an Online World (2005)
    1.  ICT integration is foundational to the economic and social prosperity of Australia and will transform education and training
    2. “A framework to assist teachers to plan and implement ICT into pedagogical practice” (p. 423)
    3. ICT drives change
    4. ICT is an outcome of change
    5. ICT is most applicable to the efficiency activities of teachers
    6. Teachers have to ‘catch up’ with students
    7. Teachers are the one who “will determine the extent to which the possibilities offered by technology are realised in educational settings” (p. 428)
    8. ICT transforms pedagogy
  6. A Digital Education Revolution (2007)
    1. “We need to ensure that Australian schools are able to provide students with the tools they will need to live and work in a world shaped by technological change” (p. 419)
    2. “Aligns ICT with notions of a ‘world class education’” (p. 420)
    3. Limits the transformational nature of ICT to the classroom education and learning
    4. “Constructs a utopian representation of a future education enabled by ICT” (p. 422)
    5. Uses both words that imply certainty and ‘possibility’
    6. Prepares young people for the ‘jobs of tomorrow’
  7. The Melbourne Declaration on Educational Goals for young Australians (2008)
    1. Claims ICT as a critical part of successful learning
    2. Aligns ICT directly alongside the 21st century
    3. “[...] learners are motivated to use ICT, suggests that teachers ‘should take advantage of this [students'] increased motivation [to use ICT] to achieve more equitable educational outcomes for all” (p. 427)
    4. ICT will enhance the outcomes of students

There are many commonalities throughout the policies, such as the emphasis on the notion that ICT will enhance learning and that there is a need for new skills to be developed.  The discussion in the article about the language used was interesting and how there was often the use of strong, certain language, juxtaposed with language that demonstrated some level of uncertainty, e.g. ‘possibilities’ and ‘potential’.  It seemed to progress from the earlier policies of considering the potential of ICT, to the DER, which claimed with an abundance of certainty that it’s policy would be revolutionary in preparing students for their entire future.  There was a varying level of focus placed on the future in each of these policies as well.

A lot of the policies seemed to take the position that students find the use of ICT second-nature and that there is no problem on their part, engaging with technology in their education.  However, much of the responsibility and need for change was placed on teachers and the education system as a whole in most of the policies.  Its not as clear cut as they would like to convey and it should be considered that if we assume students are tech-savvy, they could be left behind and be caught playing ‘catch up’ as much as they claim teachers to be doing.


 

REFERENCES

Jordan, K. (2011). Framing ICT, teachers and learners in Australian school education ICT policy. The Australian Educational Researcher, 38(4), 417-431.