Tag Archives: education

Stop Teaching Calculus!

 

Recently I was privileged to be part of a discussion between two of my trainees on the Distance learning PGCE. This course, apart from being transformative for many of us (students and teachers), is also based upon the premise of ‘The Community is the Curriculum’. I purloined this phrase from Dave Cormier, and have been heavily influenced by his #Rhizo MOOCs over the years.  Emma and Stephanie (yes, these are their real names) are happy for me to re-post the discussion here. Our G+ Community is a closed group – perhaps it shouldn’t be but there we are -so I am unable to provide a link. Do continue the discussion using the comments below.
This was Emma’s first post:
For anyone else looking at maths, I stumbled upon this guy really like his ideas. He challenges the purpose of maths. Thought it would be a good link to mastery and problem solving.
Stephanie replied – and this is what piqued my interest and curiosity to watch the video. Before this I may not have entered the discussion and would probably have just left them to it. I thought that I didn’t have anything productive to contribute as mathematics teaching is not my specialism.
Thanks for posting this Emma.  Have sat through the whole thing and I have to say that I disagree with some of his opinions.  He says that computers are the only way forward in mathematics but agreed ‘times tables are somewhat useful.’  He would have been brought up learning his times tables over and over again due to his generation – something which maths in primary education is returning back to.  Therefore, do you not need to have the basic maths embedded, to be able to move forward and progress to doing mathematics on a computer?  Maybe technology is the way forward, but as demonstrated with his phone – it is not ready for us yet.
As soon as I watched the video and thought about Stephanie’s response I realised that the debate resonated so well with my reading and research during my PhD. Why do I seem to find John Dewey at every turn?
Here is my contribution.

Thanks Emma for posting and Steph for your challenging critique. Why is there a chasm (according to Wolfram) between mathematics in education and maths in the world? Does the answer lie in the separation between the abstract and the concrete (the knowing and the doing). A reading of Dewey can help here, as he recognised the problem of education and schooling.

“On the other hand, if an experience arouses curiosity, strengthens initiative, and sets up desires and purposes that are sufficiently intense to carry a person over dead places in the future, continuity works in a very different way. Every experience is a moving force. Its value can be judged only on the ground of what it moves toward and into”. (Dewey, 1938, p. 37-38) – Experience and Education.

Wolfram demonstrated the fallibility of computers during his demonstration, and he failed, in my view to reposnd well to Jon Snow’s question on this. He is also , again in my view, looking down the wrong end of the telescope. From his perspective he already has his ‘facts’ learned probably by rote and continued practice at school, yet he rejects the premise that they should be taught in schools. is that a risk worth taking? Perhaps we need to hear from a mathematician who was taught entirely by experiential learning (Montessori etc).

Experiential Learning theory implies the continuous interaction between the person and the context with reflexivity at the heart of learning from experience. However, there is a significant difference between the ideal and the reality. Stott (1995), commenting on Dewey’s influence on educational practices in North America puts it thus:

“Dewey’s educational experiment-revolution designed to bring democracy to North America has not been successful: its humanistic promises lie unfulfilled, and classroom group activities can be even more oppressive and less growthful than superior class instruction. Education is at the crossroads”. (1995: 32)

I find his conclusion troubling when listening to the recent ideological debates around Traditional v Progressive education (see here:http://www.independent.co.uk/news/education/education-news/nick-gibb-teach-children-important-facts-not-joyless-processes-minister-urges-a6859401.html ).

…but for me Dewey’s pragmatism, and Wofram’s endorsement  entail an enlightened profession that connects the knowing and the doing. Are we there yet?

Dewey, J. (1963) Experience and Education. New York: Collier Books.
Stott, L.(1995) ‘Dewey a Disaster?’. International Journal of Research and Method in Education. 18 (1), pp.27-33.

Those of you familiar with the networked power arising from twitter spats around progressive v traditionalist teaching may, like me, become more optimistic about the next generation of teachers – as I am when working with Emma and Stephanie.

A summer reading (and viewing) list for aspiring teachers.

Summer reading

The Architecture of Inclusive Assessment: Power, Risk and Participation

Ann Winter (find her blog here) and I recently presented our ongoing research at a conference hosted by the Pedagogic Research Institute and Observatory at the University of Plymouth (PEDRIO).

The following post represents the conversation that Ann and I held during our presentation. The resulting short paper is published here.

We thought we would reproduce it in our blogs, to give it a wider ‘airing’. We would be grateful for any comments and further discussions.

The post is represented as a conversation about the development of our ideas for the theme ‘Inclusive Assessment’. Most of our conversation was conducted online using @padlet and face to face during visits to Oldham Library, The Hepworth Wakefield, and Shibden Park .  We were experimenting with the notion of dialogue as assessment (perhaps not when we started, but certainly as we went along). Ann’s voice and mine are therefore separated as subheadings.


The Status Quo

ANN

Thinking back to when we started preparing our abstract Alison, we held our discussions and exchange online through Padlet, which now gives us a chronology of our thinking and ideas. Following my initial reading I think I coined the phrase ‘Initial Assessment (IA) has landedjanus lightly’ and it did with me as it was intuitively appealing, especially coming on the back of my involvement with the BA(Hons) Health and Community Studies (HACS) students during the 2013/14 academic year.

Couple the diverse range of assessments (mind maps, reports, e-portfolios, individual and group presentations, essays and group workshops and portfolios) with the use of dialogic and written feedback it felt as though the diversity and differences in and between the students had been acknowledged in the assessment planning.  A further opportunity to invite third year students into the traditionally closed academic space of assessment design reflected engagement with students in a new dialogue and perhaps went a little way in developing shared meanings and understandings.

I’d accepted IA as a ‘good thing,’ and saw the anticipatory assessment variation and flexibility along with the engagement with students as a marker for IA whereas you were bringing in talk of risk, confidence, knowingness and policy architectures.

I recall Alison that we found ourselves agreeing with Waterfield and West (2010) that the meaning of IA has been taken for granted and having a status as an idealised target.

ALISON

Our initial conversations about the innovative, diverse assessment practices on the HACS course, and the impetus that the abstract call gave us to think more about assessment design, brought my PhD thesis into a fresh domain. I had been concerned about the ‘taken for granted’ assumptions about what is considered to be good pedagogic practice for some time. I recall being keen to challenge you Ann to look behind the design into the power relations surrounding participation and engagement in assessment. These were difficult conversations as it felt a little iconoclastic to suggest that the materiality of ‘inclusive assessment’ may fail to benefit the students that it is designed to serve.

Do you agree Ann that once we read Waterfield and West we found an anchor for our thinking – particularly the proposition that ‘inclusivity’ was an appropriate term and words such as elasticity, slippery, double meaning (Waterfield and West, 2010). Ann, can you take us through the contribution of Graham and Slee?

ANN

Graham and Slee (2013) challenge the reader to recognise an ‘invisible centre’ which entails constructions, otherness and marginal positions from which exclusions arrive and how reform agendas tinker at the edges to produce the appearance of inclusivity. A really pertinent question raised is whether we focus on how we move forward with inclusion or whether we make the invisible visible through deconstruction and disruption.

As such, Derrida’s statement that, ‘language bears within itself the necessity of its own critique’ (Derrida, 1967: 358) is particularly pertinent to inclusive education, for the movement is troubled by the multiplicity of meanings that lurk within the discourses that surround and carry it.


The Trigger

parkhill

ANN

Multiple triggers prompted a deeper probing into the use of the word inclusive and IA. I found myself immersed in an ‘alphabet soup’ of Universal Design, UDI, UD, and UDL and began to feel uncomfortable with some of the IA discourse. Terms such as ’ bringing in’, ‘marginalised’ and ‘core’ appeared to simplify a complex social construct of difference, disability  and diversity and the deep structural, architectural mechanisms within teaching, learning and educational organisations.

Robert Mace, the  architect acknowledged as the founder of universal architectural design, felt that ‘the term universal is unfortunate… as nothing can be truly universal; there will always be people who cannot use an item no matter how thoughtfully it is designed.’ (Mace 1985: 4)

I was reminded of Graham and Slee’s (2013: 289) observations that talk of including can only be made by those occupying a position of privilege, and, that talk seldom revolves around recognising and dismantling that vantage and the relations of power and domination sustaining it.

Mace appeared to be calling for more than strategic rhetoric and a ‘technical fix,’ when he  called for architects to review everything, recognise features that could be barriers and design all products to be usable to the greatest extent possible by everyone.

ALISON

This was another turning point for me as I began to link architecture, design, and power. The history of the Park Hill estate in Sheffield provides an analogy for this, where the architects felt a great sense of democratic idealism during the design of Park Hill. However it was only in the act of ‘living in’ these structures that the social and emotional costs became clear.

As teachers designing inclusive assessment, promoting engagement in inclusive assessment practices, and fostering participation, I wanted to caution about the reassurance of ‘knowingness’ (Smith 2006: 23). I thought about my research into confidence and risk for trainee teachers, and felt that there were parallels conceptually for this theme. Ann, I know that we spent a long time trying to find a conceptual framework for our paper. Then I suggested the power cube.


The Quest

ANN

don qixoteI vividly recall you bringing the Power cube to our discussions Alison, and about that time I was questioning the use of the word inclusive, preferring universal. I saw many similarities in the histories of UD and IA, and found the new Design for All European architecture philosophy of full integration and nothing less, refreshing and perhaps signposting us towards a design for all pedagogy.

Perhaps this relates to confidence and risk Alison, where we can either ‘pursue inclusivity through assessment practice…’ (Waterfield and West 2010) or ‘review everything and pay attention to all aspects’ (Mace, 1998).  I was anxious that having experienced assessment variability and flexibility in the first year of the course, we were placing the students in a liminal space – a space of transition betwixt and between traditional written forms of assessment and the experience of diverse assessment practice.

I likened the phenomenon to Deleuze and Guattari’s urban nomads (1988: 482), we were student and academic nomads in a shared space where we were looking to translate the complex language and social practices.

However, I was also reminded of Hargreaves’ (2003) description of teaching practices as deeply embedded scripts reflecting life experiences and taken-for-granted assumptions, and saw the power cube as a way into having conversations, disturbing academic and learner scripts and creating further shared space opportunities.

Alison, is this where you see a potential for the power cube analysis bringing about real change?


The Surprise

ALISON

Yes Ann, in as much as it provides a tool for thinking that avoids the 2D of cause and effect. “If we do this” than inclusiveness will be the result. I was pleased to be able to bring the power cube into our discussion, as it allowed us to view assessment design from a range of perspectives, all of which create real dilemmas for teachers. Revealing the forms, levels and spaces of power sheds new light on the development of trust, confidence and risk-taking for students, particularly if we accept the premise that assessment has become a function of an HE that increasingly serves a market economy. I think we decided then to focus on the impact on the student of institutional change (flexibility in assessment mode), uncertainty (choice of assessment mode) and risk in the decision-making behind assessment choice.

Forms of power

Here I focus on visible forms of power. These can be visible such as the way that assessment is codified in programme and module specifications. They are visible because they become the way that we recognise the field of action in relation to assessment. They are both necessary to and a function of the curriculum. Before we begin to design inclusive assessment we need to acknowledge that students do not have easy access to these visible forms of power.

Participation and decision-making is not accessible by all, so the resultant products and processes are restricted to those with access. The success of specific change to products and processes is a result of prevailing interests of those who have access and can participate, not those who can’t (i.e. students and sometimes teachers).

To be able to challenge the prevailing discourses behind IA design and practice students and teachers need to use their voices in a mobilising action through visible channels. However one dialectical dilemma here is that students are diverse, and representation channels are often complex and take time.

Are our students able to articulate their issues, and do they have the resources, organization and agency to make their voice heard? If others speak for them, they may, themselves be caught up in the visible forms of power.

Ann, in your work with the students how did your decision to use mind mapping impact on the students

ANN

The surprise for me was that the students didn’t appear to want a different form of assessment. They’d anticipated written assignments and this was a nuisance an added risk in a high stake context. The regular essay format was their overwhelmingly preferred default assessment mode and they were perplexed, anxious about the very different choices involved in making a mindmap. A very small number of them didn’t want to learn something that they hadn’t expected and didn’t know was going to happen. It was risky, somepowercubething new and challenging.

The anticipated freedom and openness of creating a mindmap was tempered by the student’s requests for guidance in how to make their branch, label, content, colour and design choices. These choices were not easy for them as they were unfamiliar ones. Paradoxically, the freedom originally envisaged became more disciplined and bounded as they strived for familiarity simplicity and structure in support of their choices. I liken my role to that of a choice architect (Thaler and Sunstein, 2009) providing a structure and feedback in order to simplify their choices and collaborating with them in making difficult choices easier.

Eagleton’s (2008) research includes MRI scans which show how the affective network (limbic system) lights up when a student is engaged and motivated, challenged, excited and interested. These areas light up when there is a novel learning task demonstrating a high level of cognitive activity; conversely, when a learning task is practised and familiar, the brain shows much less activity in these areas, because it has developed routines to reduce cognitive load.

This was also the time Alison when we spoke about graduateness, employability, learning outcomes and quality as well as students taking the ‘path of least resistance’ in assessment choice. You introduced me to the concept of ‘knowingness’ and Smith’s identified features as over-confidence and premature urge to completion and closure.


The Critical Choice

ALISON

When we design inclusive assessment we are embarking on a quest for ‘knowingness’, where the student is able to meet the learning outcomes that have been set for them without knowing them as individuals. In the search for evidence of what is known about a topic. This lack of what Smith calls ‘contingency and finitude’ may actually work against inclusivity, rather than be a support to it, especially when we seek to inculcate confidence through assessment design. It is worth noting that for educational institutions, confidence is also relative to the culture and dominant discourses of a changing world. Wain (2006:37) suggests that institutions, fearinguncertainty and risk, are far from confident in what Smith (2006:23) called their ‘knowingness’. They are constantly seeking reassurance through ‘the language of skills and competencies, of measurable outcomes and transparent transactions in their decisions’ (Wain 2006:39).pooh bear

There could be a paradox here I suppose, in that in developing confidence a certain degree of openness and risk is required whereas the institutions may be risk averse and therefore favour a very bounded (competence based) approach.

“In short, the modernist – some would say Enlightenment – quest for equity and efficiency drives contingency from the university. Along with contingency much else disappears: principally the possibility of a relationship between a particular teacher and a particular pupil of the kind that Plato presents so carefully and movingly in the early dialogues. Such a relationship is, as Rorty writes, a matter of ‘‘the sparks that leap back and forth between teacher and student’’ (1999, p. 126).10 Such sparks are the source of the realization of forms of human freedom that otherwise cannot be imagined” (Smith 2006:30).

So tell me Ann, what choices did you make, and how did those choices enfold contingency for the students? Can you talk me through the experience with the BSc students?

ANN

The quest to improve things for all students and as W&W identified, the ‘taken-for-granted’ definition of IA has created a ‘Just Do It’ organisational approach. Particularly  as it resonates with current agendas around widening participation, DDA, equality and the QAA Codes of Practice.  However, when introducing the concept of knowingness Alison, you challenge some/many of the unspoken assumptions around IA, thus reflecting the ‘causal elasticity’ and ambiguity identified by Waterfield and West in the SPACE project. The danger is that as Graham and Slee (2013) identify we can tinker at the edges producing an appearance of inclusivity whilst the centre from which exclusions arrive remains invisible. Hence the relevance of a power analysis in identifying and exploring multiple power dimensions that affect IA, ie the ‘invisible constructions’ (Graham and Slee, 2013).

Co-constructing assessment criteria with BSc (Hons) 3rd year students was also an exciting opportunity to share and have a dialogue about academic language and expectations alongside students own ideas of what they wanted to achieve through a specified form of assessment. Both limitations and opportunities often unknown to students were opened up to debate and academic words deciphered, resulting in student led assessment guidelines and form to a pre-specified assessment form ie report. A shift from margins of assessment forms to a more central role for students, a space for traditionally marginalised voices, acknowledgement of the different identities of students and their difference.

Does this bring us to the point of where we are now and what’s next Alison?


The Resolution

ANN

I’ve changed. Initially I took IA at face value, a good idea, no, a great idea, I was asking why we hadn’t taken action like this before now. I do however; still have concerns about associated meanings with the word ‘inclusive,’ and its overriding use in considering choice and flexibility in the forms of assessment. However, it is more than this; it’s about power, privilege and difference (Guo and Jamai, 2014).

IA permeates my practice with students and the opportunities to have dialogues with students around assessment practice and form illuminates how IA creates an opportunity not just to give students choice but to involve them in co-creation of meaningful, assessment forms.

Selected references

Deleuze, G. and Guattari, F. (1988). A Thousand Plateaus: Capitalism and schizophrenia. London: Continuum.

Eagleton, M. (2008). Universal design for learning. www.ebscohost.com/uploads/imported/thisTopic-dbTopic-1073.pdf

Eraut, M. (2000). Non-formal learning and tacit knowledge in professional work. British Journal of Educational Psychology 70: 113-136.

Graham, L. and Slee, R. (2013). An illusory interiority: Interrogating the discourse(s) of inclusion. Educational Philosophy and Theory 40(2): 277-293.

Hargreaves, D. H. (2003). Education Epidemic: transforming secondary schools through innovation networks. London: Demos. http://www.demos.co.uk/

Mace, R., L., Universal Design, in Designers West. 1985. p. 4.

Smith, R. (2006). Abstraction and finitude: education, chance and democracy. Studies in Philosophy and Education 25(1): 19-35.

Thaler, R. and Sunstein, C. (2009). Nudge: improving decisions about health, wealth and happiness. London: Penguin.

Wain, K. (2006). Contingency, education, and the need for reassurance. Studies in Philosophy and Education 25 (1): 37-45.

Waterfield, J. and West, B. (2010). Inclusive Assessment: Diversity and inclusion – the assessment challenge. Plymouth University.

Powercube site: http://www.powercube.net/

HD Trailer « Schooling the World

Check out this website I found at schoolingtheworld.org

Recent Changes in Intergenerational Mobility in Britain – Sutton Trust

1 December 2007

Research Report – 190kb PDF

The vast majority of England’s most socially selective state secondary schools are non-grammar schools, a major review carried out for the Sutton Trust reveals today. However, England’s remaining grammar schools are currently enrolling half as many academically able children from disadvantaged backgrounds as they could do.

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Education Mobility in England – The link between the education levels of parents and the educational outcomes of teenagers – Sutton Trust

1 April 2010

Research Report – 840kb PDF

A report and discussion based on research by John Ermisch and Emilia Del Bono from the Institute for Social and Economic Research at Essex University

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Critical thinking In the classroom


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21st Century Teaching and Learning: 10 Uses of Wordle for Learning

http://mpbreflections.blogspot.com/2010/09/10-uses-of-wordle-for-learning.html 

 

Have a go with Wordle, its so cute.

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