Response to the proposed materials for secondary maths HODs
(from the Consultation Community)
13th Sept
I gather some substantial re-working has been going on and that re-drafts will be posted in due course.It is very sad I haven’t been able to talk to anyone during this process – but we are where we are and I am now worried that you will end up posting something which I will have to further criticise and I don’t want to be in that position.
So it seems only fair to you that I try and express some of my understanding of this subject, which I what I will do, in real time in the odd moments when I am able to do so over the next couple of weeks.
Tonight’s post is by way of pre-amble, so you can contextualise the experiences I bring and therefore be able to better judge its relevance to others and your project.In essence I feel that my experience complements what I have seen from the team, and it is a shame we cannot work together to understand the dynamics between our experiences.Instead it seems best in the circumstances that I speak as a lone voice. This has obvious disadvantages – the written word is a very limited medium in many ways and it leaves me vulnerable and exposed.There is a duty of care for the team in that you have a responsibility either to take on board what I say or to justify why you do not need to.The advantages are that anyone can read these thoughts (and some may even be interested enough to do so) and that if I am not clear or need to think more carefully anyone can point that out and I will respond.In theory there should be an advantage that I can construct my thoughts carefully and only publish after careful consideration but anyone who knows me understands that my world does not allow me the time to do that, so I must write in real time.
So what is the experience I bring?
Firstly, I am a strong academic of the management of mathematics education (given that this discipline does not really exist).My credentials for this are that I grew up in a home where my father set up one of the first degree courses in management.We reflected together heavily on the ethics and efficacy of what he was doing over the years.Thus when I finalised in management at Cambridge and studied Management and Leadership of Education during my MEd, I did so as a critical analyst rather than as an ordinary participant.And of course in the latter case I was also working in mathematics education and so that was my frame of reference and interpretation.My husband has an MBA and I use his reference material, as well as keeping up with the latest techniques through MindTools.
Secondly, I have experience in mathematics teaching and leadership which contrasts and challenges the mould which seemed to emerge from your first draft.The descriptions you wrote were appropriate for well managed large secondary schools with streamed sets and a large team of mathematics teachers, delivering strong results according to the old program of study and assessment criteria.I’ve never worked in a school like that – instead I’ve worked in schools in transition, schools with staff shortages and serious resource problems and schools with exceptionally challenging cohorts.I felt alienated by the picture of excellence in maths leadership generated by your work and I know at the discussion day others felt similarly excluded.
I think it is possible to create a vision of excellence in the management and leadership of mathematics education and supporting materials which transcend these barriers.In this thread I’m going to try and explain how I believe this is possible.But I needed to start with a post which gives you the context for those which will follow.
14th September
Tonight I have one clear point to make, which runs through all my thinking and analysis of management and leadership in maths education, so in true lecturing style, I will tell you it, I will explain it and contextualise it and than I will tell you it again.
Say it:
In planning mathematics education it is extremely useful to make a deliberate and determined split between two forms of mathematics education.The first form is the teaching of key mathematics vocabulary to aid the communication of ideas and of core techniques for the purpose of fluency.The second form is the nurturing and development of students as mathematical thinkers and of their connected mathematical understanding.If you analyse the new programs of study, it could be said that section 3 lies within the first form of mathematics education while sections 1, 2 and 4 lie within the second form.
Explain it: part 1 of 3 – the background to the technique of splitting concepts
It is essential in the definition of concepts that we challenge the vocabulary we are using.When we use words are we clear what we mean?Do we all mean the same thing when we use the same term?These processes of discipline in using languageare sensible and obvious.What is less obvious is that sometimes we use one word thinking it refers to one concept when in fact it refers to more than one concept.By splitting our concept and our vocabulary we gain much greater insight into our subject and make greater progress with it.And so it is with maths education.But before I go further into this I want to explore a different part of management theory where this has been done with great effect.
Explain it: part 2 of 3 – a rich and powerful example of the technique of splitting concepts.
One of the key components of management studies is the study of motivating employees.Now this theory made little holistic progress until Herzberg pointed out that we have a natural human propensity to see motivation and de-motivation as being equal and opposites within the same concepts.So if someone is de-motivated, giving them a good incentive will somehow more than balance that out and they will end up being motivated.What Herzberg did in a disciplined way was to separate motivation and de-motivation as concepts.So the opposite of being motivated is not being motivated.The opposite of being de-motivated is not being de-motivated.This led to much more powerful insights into how to deal with de-motivation and how to increase motivation than had previously existed (obviously you can find more on the internet about Herzberg should you wish to do so).For me this is a lovely example of concept splitting because I have often found maths teaching to be both incredibly motivating and de-motivating at the same time.And while motiviation and de-motivation are clearly linked, the segregation of concepts is valid because these things do not just balance each other out to leave me ‘neither motivated nor demotivated’.
Explain it: part 3 of 3 – the validity of this split
Now I leave motivation and de-motivation aside and return to maths education.The split I propose is one which I have used in many forms and contexts over the years both in practice and in academic articles and in the form I now present it in and I have found it to be robust.Much of my work has been about the synthesis of the two forms of maths education and I have found that in order to exploit the benefits of their synthesis it has always been wise first to consider them to be separate entities.
Conculsion: Say it again and name it:
The purpose of this post is to clearly define and explain a split which I make in my definition of maths education.To understand what I say about excellence in the leadership and management of maths education you have to understand this split because I will often refer to it.So once again the split is:The first form of mathematics education is the teaching of key mathematics vocabulary to aid communication of ideas and of core techniques for the purpose of fluency.The second form of mathematics education is the nurturing and development of students as mathematical thinkers and of their connected mathematical understanding.I’m going to call this split ‘The Hanson Split’ in order to keep this definition tight and to prevent it being used fluidly.
15th September
Hmmm, dunno why that last paragraph swapped into caps - that's not what I intended. Anyway. Now I've given a context and defined a concept I intend to use, I'll get going.
Part 1: A head of mathematic needs to ‘understand the journey’ of their department.
‘Understanding the journey’ and ‘Having a strong narrative’ are phrases which came to me from my mentor Geoff Faux, who has advised and mentored a wide variety of departments over the decades. This is different from having a mission statement.
Firstly, understanding our journey demands that we focus on where we have been, both that we may cherish and recognise strengths which may otherwise be lost and that we may avoid repeating our mistakes.
Secondly, I picture the journey as being a walk through the mountains.Sometimes we buckle down, we know what we have to do, we sweat, it hurts and we get on with it.And when we pause we take in the view, both for the enjoyment of the variety of the scenery and to help us get our bearings.When we reach summits we pause to absorb the sunshine, rest properly and to take time plot and understand the next part of our journey.Sometimes it rains and the weather is unkind and over time I have learned tobe at ease withthe wind and the rain too.I find this metaphor offers me comfort and helps me contextualise and be at ease with my experiences, which is why I offer it to others.I understand that it will not be relevant to everyone.
Thirdly, the narrative of our journey as a mathematics department gives us a meaningful shape to our future.We define things to strive for which are worthwhile to us and we always have the sense that when we achieve them we will enjoy their fruits and then plot another meaningful course.
Before going on to explore how we each learn about our journey I must pause to reassure you that I am not blind to the obvious problems heads of departments in plotting a meaningful course.I will address those soon.
So how do we go about learning to ‘understand our journey’.At PGCE level students are often given the opportunity to reflect on and contextualise their own mathematics education.My OU masters degree demanded that I did this more rigorously and through my observations of and conversations with other teachers I began to have a picture not only of my own history but of our shared history.I understood that much of my colourful variety of experience in my own history was generated by the focus on the second form of mathematics education which dominated developments in the 1970s and 1980s.I saw how the Woodhead view of education, OFSTED and the national curriculum had, in many regions such as my own, swept all this away as we moved to a narrower focus on the first form of mathematics education – or in many cases – teaching to the exam.I understood the consequences of and reasons for this shift through the experiences of those involved.
We had two competing philosophies, each competing for the same time, resource and commitment of staff.Each philosophy had its merits, its intrinsic logic and its problems.But the two philosophies were extremely hard to reconcile and easily made enemies of each other.In understanding this I saw the essence of the key struggles of the second half of the 20th century – the conflict between a socialist state, where the freedoms of the individual are curtailed for the greater good of the needy and the liberal philosophy of individual freedom.And in seeing this parallel I found my own clear way forward with this struggle.Because technology and, more importantly, communication technology, has bought us in the 21st century a reconciliation between these philosophies.As technology has taken the strain of ever more complex methods of the organisation of society, it has become possible to create systems which provide support and structure for the needy while allowing great freedom for most.
And so, as a head of department I resolved to use technology to allow students to take responsibility for the first form of mathematics education, shifting my role to being more supportive (with encouragement and consolidation in class) although of course initially I had to chase the lazy.This shift created time and energy to explore many aspects of the second form of mathematics education, within which I found previously unimagined benefits for my students.
I take the time to describe this because I think this part of my journey may now be relevant to many HODs who are trying to understand the present and next stages of their own journeys.I don’t go into details because the details will be different for everyone.But within these details there will be communalities which we can enjoy exploring together through our shared literature and the discussion forums.
Having a clear sense of your own journey is essential in the processes of interacting positively with external forces which try to mould you.
16th September
Part 2: On assessing quality (the journey from unsatisfactory to outstanding?)
These resources have the stated purpose of supporting the journey towards excellence in the leadership and management of mathematics departments.Therefore it is important that we analyse and understand our assumptions about this progression.
Much of the language and thoughts of teachers today have been moulded be the OFSTED assessment criteria against which we are all judged, so we must first reflect on the validity of these criteria.When OFSTED was first conceived it was decided that it was necessary that it had written criteria against which all teaching should be assessed.Both this idea and the specific criteria which were generated were highly controversial.Then, as now many schools chose instead to use systems of disciplined noticing and communication to support their lesson observations.Specific gradings were only considered necessary for teachers who were required to improve or leave the profession, such as trainee teachers and those about whom there were serious concerns.None-the-less, OFSTED decided it was appropriate to grade all teachers.