Monthly Archives: June 2017

BTL Surpass for online assessment in Computer Science⤴

from @ Sharing and learning

Over the last couple of years I have been leading the introduction of BTL’s Surpass online assessment platform for  exams in Computer Science. I posted the requirements for an online exam system we agreed on a few months ago. I have now written up an evaluation case study: Use of BTL Surpass for online exams in Computer Science, an LTDI report (local copy). TL;DR: nothing is perfect, but Surpass did what we hoped, and it is planned to continue & expand its use.

My colleagues Hans-Wofgang has also presented on our experiences of “Enhancing the Learning Experience on Programming-focused Courses via Electronic Assessment Tools” at the Trends in Functional Programming in Education Conference, Canterbury, 19-21. This paper includes work by Sanusi Usman on using Surpass for formative assessment.

A question for online exams in computer science showing few lines of JAVA code with gaps for the student to complete.
A fill the blanks style question for online exams in computer coding. (Not from a real exam!)

The post BTL Surpass for online assessment in Computer Science appeared first on Sharing and learning.

Visiting as metaphor – developing a framework for reflective practice⤴

from @ Cat's eyes

Gillies, D., 2016. Visiting good company: Arendt and the development of the reflective practitioner. Journal of educational administration and history, 48(2), pp.148-159.

 

 

 

Hannah-Arendt by POLISEA – CC BY-NC-SA

This paper offers a critique of the notion of ‘reflective practice’ in the context of initial and early-stage teacher education. Reflective practice is a term which is frequently used throughout the career of a teacher; it is a practice which is encouraged in teacher education programmes on campus and in school experience. It is also a requirement of students and serving teachers if they are to meet the standards for registration, as stipulated by the General Teaching Council of Scotland (GTCS). They are exhorted to: ‘reflect and engage in self-evaluation using the relevant professional standard’ (GTCS 2012a), and for the standard of Career-Long Professional Learning, to ‘develop skills of rigorous and critical self-evaluation, reflection and enquiry’ (GTCS2012b). In spite of this central focus on reflection, aspects of teacher development and practice may leave some students and serving teachers feeling that there is insufficient discussion in their instructional and practical experience of what reflective practice is or how it might be achieved. Neither do systems and cultures best support reflection in context: the current emphasis on the evidence-based, best practice or ‘what works’ agenda supports the technical-rational–instrumentalist emphasis on craft, skills, and a cause and effect approach to practice, which leaves little room for consideration of wider aspects of pedagogical approaches.
Gillies (2016) draws on Arendt’s theory of enlarged thought –a theoretical concept with considerable philosophical pedigree, as it relays back to Kant and Aristole – to offer a conceptual framework which supports a progressive development of reflective practice, especially with regard to early-stage teachers and student teachers. This, to me, seems to be an extremely helpful mechanism in teaching and learning about the practice of reflection, developing experience in the consideration of alternative perspectives (‘visiting,’ loosely, in Arendt’s terms), and coming to judgement, as a key component of reflection, of the value and merits of the perspectives under consideration.
Engaging with these perspectives, in Gillies’ and Arendt’s terms, is the ‘company’ we keep; however, there are caveats. Keeping company of only known perspectives might limit our reflections and leave us in an echo-chamber, where our own biases and beliefs are confirmed and justified. That might be a comfortable environment for some, but for others this is an opportunity for challenging, professional conversations and debate; for contesting accepted beliefs and for ‘enlarging our thoughts,’ in  Arendt’s terms.
Here is Gilles’ framework for reflection, based on the ‘visiting’ metaphor, offered by Hannah Arendt (Gillies, 2016, p157).
gillies

I’d urge you to read the article if you have, like me, wrestled with the disconnect between expectations and support for the development of reflective practice in the early stages of learning about teaching.

P.S. Hannah Arendt was a political theorist known perhaps most widely for her analysis of the origins of totalitarianism. This Open Culture link provides useful insights to her thinking via an interview and further links.

References

GTCS. 2012a. Standards for Registration. Edinburgh: GTCS.

GTCS. 2012b. Standard for Career-Long Professional Learning. Edinburgh: GTCS.

Gillies, D., 2016. Visiting good company: Arendt and the development of the reflective practitioner. Journal of educational administration and history, 48(2), pp.148-159.

 


FUTURE AS5ET: Calling all S5 girls who know they can change the world, and just as importantly, those who don’t⤴

from @ Education Scotland's Learning Blog

FUTURE AS5ET – A one day free conference for S5 schoolgirls, open to all secondary schools in Scotland.

22 September 2017,  Edinburgh International Conference Centre

The organisers, financial education charity Didasko and various investment management firms coordinated by Stewart Investors, are especially keen to encourage attendance of schools from outside Edinburgh,.  They are offering generous financial contributions towards travel for schools based outside of Midlothian area, and accommodation for those located more than 100 miles away.

The conference programme offers a wide range of seminars and key note presentation from inspirational speakers all around career opportunities in the financial sector.

Access the  programme here.

For more information please contact:

Ania Lewandowska, Senior Associate, Charlotte Street Partners

www.charlottestpartners.co.uk   @cstreetpartners

0 787211 8175

 

School leadership: stop shooting ourselves in the foot!⤴

from @ School Leadership - A Scottish Perspective

Let me say at the start of this post that I was a school leader for over 18 years and I loved almost every minute of it. School leadership was challenging, intellectually, emotionally and physically at times, but that was always a part of the allure for me. I entered teaching wanting to make a difference. I became a school leader to be able to make more of a difference, for more learners and families. I am not alone in this view and I have met, and worked with, many colleagues who feel exactly the way I do, about their role, the challenges and the opportunities it presents.

Yet, we have a problem in Scotland, and elsewhere, in that we are struggling to get people to apply for school leadership positions, especially headteacher ones. Why? is a question many of us within the system, and our employers, have been asking for some time now. When school leadership roles become available, there is often a dearth of suitable applicants.The answers people have come up with point to the nature of some of the problems, for me.

In my last few years as a headteacher, I was constantly told and often read, that we school leaders were a big part of the problem. We didn't 'sell' the job well enough and we were always moaning about the difficulties of the job, especially when faced by so much change, austerity, cuts, accountability and so on. We were told in no uncertain terms we needed to talk the job up more, stop moaning and complaining, and instead demonstrate how great the job was, and how people with talent and aspirations should aim to follow in our footsteps and become the next generation of leaders. The trouble with messages like this, if you hear them often enough it becomes easy to believe them, and start to think you are part of the problem, rather than a source of the solution.

I would contend that it is important that we are open and honest with future leaders about both the opportunities and the challenges. If we are having to sugar-coat the role there is something wrong with the role, or the people aspiring to such roles. School leadership is awash with opportunities, as long as you are aware of, and are prepared to face, the challenges that come with the role. Dealing with the challenges means acknowledging them and finding strategies and solutions for those you can, that still enable you to remain true to your values and principles as a professional educator. It doesn't mean pretending they don't exist. When aspiring school leaders see current leaders dealing with all the issues and tensions that currently exist in the role, whilst remaining up-beat and positive about  their ability to make a difference, they provide those aspiring leaders of the future with a model of what can still be achieved. If they can retain their sense of humour and their humanity in the role, so much the better.

It is my view that many of those who have been telling us that we are a big part of the problem, fail to detect any irony between their own actions and what they have identified as our own failings. Take inspections for instance. School inspections happen in the Scottish system, and just about every other, with a few notable exceptions. Finland for instance, but what do they know? The Scottish system of inspection is not as draconian as that found in many others, and aims to be more supportive, based around a professional dialogue that supports a school on its particular development journey. This is fine in principle, if you are accepting of inspection as a necessary part of the accountability agenda. However, what inspection is described as and what they feel like, is all but destroyed by the imposition of 'gradings' at the end of the inspection process. Inspectors may have been in a school for a number of days talking to teachers, learners, parents, partners and school leaders, all as part of the dialogue around school development that aims to help and support that school. However, at the end of the process a letter is written to parents about the process and findings, and whether the inspectors are confident about the school's ability to keep moving forward, accompanied by the 'grades'.

The effect of the grades handed out have an impact on all staff in a school, but the greatest is on the school leader. No-one else is identified in any inspection findings, apart from the headteacher or principal. The fact that these will appear in local media, just adds to the impact. I was contacted by a colleague headteacher recently at 12.40am about a recent experience she has had. She has worked her socks off for over twelve months trying to drive forward a small rural school in a remote area, and she felt that she had been kicked in the teeth by the 'gradings' that were going to be attached to her letter of findings following an inspection. I have two questions about this. the first is, What useful purpose does the attachment of such gradings serve in this process? If it really is a professional engagement and dialogue, it should be exactly that, to help inform a headteacher, and local authority about where a school is, with suggestions for steps to develop. Hopefully, this will confirm the headteacher and local authority view of where that school is as well. If it doesn't, then that should promote more professional dialogue between all parties. My second question is, what impact do you think experiences like this might have on headteacher recruitment? I really don't think it will help the situation. However, if people could see this process as really supportive and part of an ongoing professional dialogue, their view might change. If inspectors then issued a letter to parents stating they had visited the school, engaged with everyone, including the local authority, and were confident the school understood where it was, and where it was heading, in its development, there should be no need to place any artificial 'grading' onto the process. The letter might suggest when the school might next be inspected, as part of this ongoing process of engagement.

How this process might change in the light of the latest structural review occurring in Scottish education remains to be seen.


Most researchers, writers and school leaders understand the impact of school leadership on any school, in any setting. In Scotland 'Teaching Scotland's Future' penned by Graham Donaldson in 2011 addressed the issue of teacher education and leadership preparation. One of the key aspects of this was his consideration of the development of leadership at all levels within the system, and out of which emerged the formation of SCEL. The Scottish College for Educational Leadership. In its early days, as it found its footing, SCEL focused on senior school leaders, but quickly realised and recognised its responsibility for considering leadership at all levels in the system. Over the last few years SCEL has led the development of Frameworks and qualifications for school leaders and those aspiring to future leadership roles. In a short period it has grown, under the leadership of CEO Gillian Hamilton, and developed links with universities here in Scotland, as well as with academics and researchers around the world. Alma Harris spoke at the recent SCEL and GTCS awards ceremony in Edinburgh of how SCEL had improved Scoltand's standing and reputation around the world and how we should be proud of the work undertaken by Gillian and her team. SCEL has been considered one of the successes of Scottish education over recent years, and gave myself and others, great hope that we were developing an organisation that was going to grow future leaders, as well as help current ones develop further. I, of course, have to declare an interest, as SCEL helped my develop as a senior leader from 2012 onwards. I have seen, and experienced, the difference it has made and the impact it has had, so have many others. So it was with some dismay that we heard that SCEL was to be swallowed up by Education Scotland as part of John Swinney's Governance Review. What happens next we await to see, but many are concerned on the impact this change will have on SCEL, its work, and the attractiveness of leadership in Scotland.

If we are serious about addressing the issues around headteacher recruitment we have to stop shooting ourselves in the foot. We need systems and structures which support teachers and leaders, and which are seen to do so. What we need to get away from are cultures and systems that make it harder for school leaders to do what can be a difficult job, which constantly change so that politicians can show they 'are taking charge' and that 'the status quo is not an option' and which are low on trust and respect for the role.


School leaders are the best models for future leaders. We need to consider how we support them to be the best they can be, so they can help grown the next school leaders. Putting barriers in the way, and making the job ever more onerous and difficult helps no-one, and may be putting off more from stepping up.

School leadership: stop shooting ourselves in the foot!⤴

from @ School Leadership - A Scottish Perspective

Let me say at the start of this post that I was a school leader for over 18 years and I loved almost every minute of it. School leadership was challenging, intellectually, emotionally and physically at times, but that was always a part of the allure for me. I entered teaching wanting to make a difference. I became a school leader to be able to make more of a difference, for more learners and families. I am not alone in this view and I have met, and worked with, many colleagues who feel exactly the way I do, about their role, the challenges and the opportunities it presents.

Yet, we have a problem in Scotland, and elsewhere, in that we are struggling to get people to apply for school leadership positions, especially headteacher ones. Why? is a question many of us within the system, and our employers, have been asking for some time now. When school leadership roles become available, there is often a dearth of suitable applicants.The answers people have come up with point to the nature of some of the problems, for me.

In my last few years as a headteacher, I was constantly told and often read, that we school leaders were a big part of the problem. We didn't 'sell' the job well enough and we were always moaning about the difficulties of the job, especially when faced by so much change, austerity, cuts, accountability and so on. We were told in no uncertain terms we needed to talk the job up more, stop moaning and complaining, and instead demonstrate how great the job was, and how people with talent and aspirations should aim to follow in our footsteps and become the next generation of leaders. The trouble with messages like this, if you hear them often enough it becomes easy to believe them, and start to think you are part of the problem, rather than a source of the solution.

I would contend that it is important that we are open and honest with future leaders about both the opportunities and the challenges. If we are having to sugar-coat the role there is something wrong with the role, or the people aspiring to such roles. School leadership is awash with opportunities, as long as you are aware of, and are prepared to face, the challenges that come with the role. Dealing with the challenges means acknowledging them and finding strategies and solutions for those you can, that still enable you to remain true to your values and principles as a professional educator. It doesn't mean pretending they don't exist. When aspiring school leaders see current leaders dealing with all the issues and tensions that currently exist in the role, whilst remaining up-beat and positive about  their ability to make a difference, they provide those aspiring leaders of the future with a model of what can still be achieved. If they can retain their sense of humour and their humanity in the role, so much the better.

It is my view that many of those who have been telling us that we are a big part of the problem, fail to detect any irony between their own actions and what they have identified as our own failings. Take inspections for instance. School inspections happen in the Scottish system, and just about every other, with a few notable exceptions. Finland for instance, but what do they know? The Scottish system of inspection is not as draconian as that found in many others, and aims to be more supportive, based around a professional dialogue that supports a school on its particular development journey. This is fine in principle, if you are accepting of inspection as a necessary part of the accountability agenda. However, what inspection is described as and what they feel like, is all but destroyed by the imposition of 'gradings' at the end of the inspection process. Inspectors may have been in a school for a number of days talking to teachers, learners, parents, partners and school leaders, all as part of the dialogue around school development that aims to help and support that school. However, at the end of the process a letter is written to parents about the process and findings, and whether the inspectors are confident about the school's ability to keep moving forward, accompanied by the 'grades'.

The effect of the grades handed out have an impact on all staff in a school, but the greatest is on the school leader. No-one else is identified in any inspection findings, apart from the headteacher or principal. The fact that these will appear in local media, just adds to the impact. I was contacted by a colleague headteacher recently at 12.40am about a recent experience she has had. She has worked her socks off for over twelve months trying to drive forward a small rural school in a remote area, and she felt that she had been kicked in the teeth by the 'gradings' that were going to be attached to her letter of findings following an inspection. I have two questions about this. the first is, What useful purpose does the attachment of such gradings serve in this process? If it really is a professional engagement and dialogue, it should be exactly that, to help inform a headteacher, and local authority about where a school is, with suggestions for steps to develop. Hopefully, this will confirm the headteacher and local authority view of where that school is as well. If it doesn't, then that should promote more professional dialogue between all parties. My second question is, what impact do you think experiences like this might have on headteacher recruitment? I really don't think it will help the situation. However, if people could see this process as really supportive and part of an ongoing professional dialogue, their view might change. If inspectors then issued a letter to parents stating they had visited the school, engaged with everyone, including the local authority, and were confident the school understood where it was, and where it was heading, in its development, there should be no need to place any artificial 'grading' onto the process. The letter might suggest when the school might next be inspected, as part of this ongoing process of engagement.

How this process might change in the light of the latest structural review occurring in Scottish education remains to be seen.


Most researchers, writers and school leaders understand the impact of school leadership on any school, in any setting. In Scotland 'Teaching Scotland's Future' penned by Graham Donaldson in 2011 addressed the issue of teacher education and leadership preparation. One of the key aspects of this was his consideration of the development of leadership at all levels within the system, and out of which emerged the formation of SCEL. The Scottish College for Educational Leadership. In its early days, as it found its footing, SCEL focused on senior school leaders, but quickly realised and recognised its responsibility for considering leadership at all levels in the system. Over the last few years SCEL has led the development of Frameworks and qualifications for school leaders and those aspiring to future leadership roles. In a short period it has grown, under the leadership of CEO Gillian Hamilton, and developed links with universities here in Scotland, as well as with academics and researchers around the world. Alma Harris spoke at the recent SCEL and GTCS awards ceremony in Edinburgh of how SCEL had improved Scoltand's standing and reputation around the world and how we should be proud of the work undertaken by Gillian and her team. SCEL has been considered one of the successes of Scottish education over recent years, and gave myself and others, great hope that we were developing an organisation that was going to grow future leaders, as well as help current ones develop further. I, of course, have to declare an interest, as SCEL helped my develop as a senior leader from 2012 onwards. I have seen, and experienced, the difference it has made and the impact it has had, so have many others. So it was with some dismay that we heard that SCEL was to be swallowed up by Education Scotland as part of John Swinney's Governance Review. What happens next we await to see, but many are concerned on the impact this change will have on SCEL, its work, and the attractiveness of leadership in Scotland.

If we are serious about addressing the issues around headteacher recruitment we have to stop shooting ourselves in the foot. We need systems and structures which support teachers and leaders, and which are seen to do so. What we need to get away from are cultures and systems that make it harder for school leaders to do what can be a difficult job, which constantly change so that politicians can show they 'are taking charge' and that 'the status quo is not an option' and which are low on trust and respect for the role.


School leaders are the best models for future leaders. We need to consider how we support them to be the best they can be, so they can help grown the next school leaders. Putting barriers in the way, and making the job ever more onerous and difficult helps no-one, and may be putting off more from stepping up.

‘You and Me, all we want to be is lazy’⤴

from @ Just Trying to be Better Than Yesterday

Of all the things that have begun to happen to me as I get older, increasing claustrophobia is my most concerning. Whenever I’m in a position where I can’t see a way out – whether an exit or an excuse – I start to get anxious and feel my heart rate increasing. More and more , I avoid social occasions, certainly if there is likely to be a large crowd: more recently I’ve begun to dread larger CPD events, especially ones where the ‘presenter’ asks the ‘audience’ to do some work.  I feel the same way when Bruce Springsteen turns his microphone to the audience: ‘No, Springsteen. YOU sing!’

That feeling is probably the reason why online learning appeals to me. I can read things when and where I want: there is no one with flipchart paper or a microphone to put me on the spot. And, to cap it all off, I don’t have to tell anyone who I am or where I’m from or what I hope to get from the day. Seriously? If you’re running a CPD day and have to ask that then there’s a problem. Indeed, if you’re an educational ‘consultant’ and need that reassurance then you really need to up your game. If you’re selling your product you should be clear what it is from the start.

But online learning is much more appealing to me. Sometimes. The comforting delight in knowing that you can give up at any time means that, for the most part, I give up at any time. Never finish things, I dip in to blogs and research papers and find books, and get about half way through them and give in, learning lots of little things along the way. And, knowing I don’t have to ‘feedback during plenary’, it is massively satisfying. But it’s different when you’re an adult. I’m not sure how I would have got on if I had something like ‘Flipped Learning’ when I was at school.

That tendency to give up is probably why these things won’t work for everyone in schools. It is in our nature to be lazy. As Daniel Willingham says in ‘Why Don’t Students Like School?’, ‘Humans don’t think very often because our brains are designed not for thought but for the avoidance of thought.’ Some of my students may love online learning; some may hate it; most, I think, would love the idea but never find the motivation to do it on their own. Flipped learning makes a lot of in correct assumptions about the willingness of children to work in their own time.

So, while crammed classrooms are probably claustrophobic for some kids, it really is the best way for us to teach a class of thirty. It’s not perfect by any means but I’m yet to be convinced that more ‘open’ approaches to learning can work for every child. We have a responsibility to those kids who needs us most, those disadvantaged by background, and new, untested strategies are often vanity projects. Teaching them well, in the best possible way, is our duty. Let’s not take risks with that.


What do we mean by leadership?⤴

from @ Fearghal Kelly

In a recent post, I shared my realisation that many of us in education have been using the words ‘leadership’ and ‘promotion’ interchangeably. Since then, I’ve had many more conversations with many more folk about what we actually mean by ‘leadership’. What’s fascinating is that when talking to teachers, and others involved directly in education in Scotland, the vast majority agree with me that it’s often used to mean ‘promotion’ or ‘management’, and that it’s not necessarily something classroom teachers see as relevant to them – unless of course they’re going for that first PT post…

Even some of the language around education in Scotland still reinforces this concept of what is meant, for example ‘senior leadership’, ‘early leadership’, ‘first leadership position’. What’s even more fascinating is the few conversations I’ve had on this topic with people from outwith education. They’ve often commented that of course leadership is a component of all roles, no matter where they are in the hierarchy and they’ve shown genuine surprise when I’ve outlined how the word is often used in education.

So what do we mean by leadership? This is a question which I’m spending much of my time exploring and discussing. I posed this as the title of my presentation at the recent InnovateEducation event and I’m asking the question again this evening at Edinburgh, Midlothian and East Lothian’s Creative Learning Network’s series of Creative Conversations. That presentation uses a range of resources to explore the question (including quotations, images of kayaking, resources from my teaching, some of my work at SCEL, and a song about stew), but I also find the following quotation from a recent book chapter by Christine Forde and Beth Dickson of use:

leadership is a “lay everyday knowledge term not a scientific construct” (Forde & Dickson, 2017)

I personally sometimes wonder if we have over complicated the term ‘leadership’ to the extent that not only is it the preserve of those in promoted posts, it’s also quite a complex thing which can be off-putting to busy teachers. I know that when I was in the classroom, I was aware of leadership ‘theories’ and ‘styles’ etc. and even if I felt that these were of relevance to me (which I didn’t) I was, frankly, put off by what sounded like a lot of work to get to grips with them when I was busy with getting better at the job at hand. It’s for this reason that I like this quote as I’m drawn to the idea that leadership is a lay term. It is not the preserve of those of who have read and studied the term in depth, it is a term which is available to us all to use in our work and lives.

So, if we choose to use it, what might it mean? Again from Christine Forde and Beth Dickson:

Leadership is an interactional process where influence and power are exercised in different ways, in different locations by different people across an organisation. (Forde & Dickson, 2017)

I like this as it again captures the universal nature of leadership, whilst also highlighting the importance of relationships, influence, power and the variability of each. There are an increasing number of helpful sources such as this to reference in this regard, but this doesn’t always mean that this can easily be translated into the practice of those in education. So, how then can those of us who think that it’s important to encourage teachers to think of themselves as leaders, and crucially, convince middle, school and system leaders to support and encourage leadership go about achieving this?

I’ve been quite struck by the simple power of talking about all of this in the context of practice. I was asked to give a short presentation on teacher leadership at St. Andrew’s & St. Brides’s High School in East Kilbride earlier this month. It was kindly open to staff from across the area and it primarily consisted of me talking for about 45 minutes on my thoughts on all of this with a couple of examples from my own practice as a teacher and as an enquiring practitioner. As ever with a one-off short presentation, my fear was that this would have little or no impact on those who attended the session. In fact, I find that my imposter syndrome goes into overdrive upon completion of these sessions and I drive away convinced that everyone will have no doubt regretted having wasted their time turning up for that. I was pleasantly surprised therefore when I received some feedback from the session last week which included an almost universally positive response. I really appreciate the time taken by all those who shared their feedback and for the school for sending it through, but one comment in particular leapt out at me in the context of what I’ve been exploring in this post:

The presentation encouraged me to reflect and develop my own leadership skills, an area I had never really considered applicable as an unpromoted member of staff. After this presentation it was clear that effective classroom leadership can have a fundamental and lasting impact on our learners and this is something that I believe all teachers strive for.

Two things strike me about this comment. Firstly, that developing leadership skills had never been considered applicable to their role as a teacher (something I can empathise with) and secondly, a 45 minute presentation which primarily consisted of my current thoughts and past examples might have changed their mind on this a little and they are now able to summarise the point of all of this a lot quicker than I ever manage!

Perhaps therefore if we can all take a little time to share what leadership means to us and what it looks and feels like in our practice we can collectively redefine what we mean by leadership in education. I therefore will now go and give my presentation in Edinburgh and try my best to keep my imposter syndrome at bay.

Thank you again to the staff who sent me their feedback from the session at St. Andrew’s & St. Brides’s High School. I’m glad it was of use. 

Knowing and Understanding in Mathematics⤴

from @ Learning Stuff About Stuff

In order to investigate the current debate about knowing and understanding sparked by David Didau's post, I want to examine one small part of mathematics, which I happen to be teaching to a Higher maths class at the moment: finding the point which divides a line segment in a given ratio.

One way to approach this is to teach a formula:

The position vector of P, where P divides AB in the ratio m:n, is given by p=(na+mb)/(m+n)

If you know
  • how to convert a position vector to a coordinate
  • the convention that capital letters represents points and bold lower case letters represent corresponding position vectors
  • how to multiply or divide a vector by a scalar
  • how to add vectors together
then can probably now solve a problem such as:

Given that the point P divides S(3,4,-1) and T(5,8,11) in the ratio 3:1, find P.

At this point, a student knows how to find a point which divides a line segment in a given ratio. They may have no idea why this rule works. They may have no idea what a position vector is. They may have no idea what a ratio is. They may have no idea about the 3D coordinate system. Do they understand the rule?

In maths, it seems to me, knowing means being able to recall a particular mathematical result, such as the formula given above. Understanding means grasping to some extent the chain of previously established facts and causal links which lead to the given mathematical result being true. In this sense, knowing and understanding are different in maths.

You might say the "understanding" I describe is just more knowing. I disagree, because there is a categorical difference between knowing a particular fact, or set of facts, and understanding why that fact is true. The litmus test, for me, is that anyone could remember the formula given above. Most people could be trained to apply the rule to solve problems using the formula, provided the problems were stated in a fairly standard way. Only those who have already mastered a sufficient body of knowledge and understanding in maths would be capable of understanding what the formula is actually about, and why it works.

I suppose I am saying that understanding is about the connectedness of one's knowing. Maths is a domain in which this distinction is particularly evident, because it is relatively easy to learn a fact which has no connection to anything else you know. For example:
A Hermitian manifold is a complex manifold with a smoothly varying Hermitian inner product on each (holomorphic) tangent space.
I could memorise that, and regurgitate it. I have no idea what any of the mathematical words in the definition mean, apart from "complex" and a very vague recognition of "manifold". I don't understand this definition because it does not connect to anything else I already know (and understand through connections to other knowledge) in maths.

Knowing and Understanding in Mathematics⤴

from @ Learning Stuff About Stuff

In order to investigate the current debate about knowing and understanding sparked by David Didau's post, I want to examine one small part of mathematics, which I happen to be teaching to a Higher maths class at the moment: finding the point which divides a line segment in a given ratio.

One way to approach this is to teach a formula:

The position vector of P, where P divides AB in the ratio m:n, is given by p=(na+mb)/(m+n)

If you know
  • how to convert a position vector to a coordinate
  • the convention that capital letters represents points and bold lower case letters represent corresponding position vectors
  • how to multiply or divide a vector by a scalar
  • how to add vectors together
then can probably now solve a problem such as:

Given that the point P divides S(3,4,-1) and T(5,8,11) in the ratio 3:1, find P.

At this point, a student knows how to find a point which divides a line segment in a given ratio. They may have no idea why this rule works. They may have no idea what a position vector is. They may have no idea what a ratio is. They may have no idea about the 3D coordinate system. Do they understand the rule?

In maths, it seems to me, knowing means being able to recall a particular mathematical result, such as the formula given above. Understanding means grasping to some extent the chain of previously established facts and causal links which lead to the given mathematical result being true. In this sense, knowing and understanding are different in maths.

You might say the "understanding" I describe is just more knowing. I disagree, because there is a categorical difference between knowing a particular fact, or set of facts, and understanding why that fact is true. The litmus test, for me, is that anyone could remember the formula given above. Most people could be trained to apply the rule to solve problems using the formula, provided the problems were stated in a fairly standard way. Only those who have already mastered a sufficient body of knowledge and understanding in maths would be capable of understanding what the formula is actually about, and why it works.

I suppose I am saying that understanding is about the connectedness of one's knowing. Maths is a domain in which this distinction is particularly evident, because it is relatively easy to learn a fact which has no connection to anything else you know. For example:
A Hermitian manifold is a complex manifold with a smoothly varying Hermitian inner product on each (holomorphic) tangent space.
I could memorise that, and regurgitate it. I have no idea what any of the mathematical words in the definition mean, apart from "complex" and a very vague recognition of "manifold". I don't understand this definition because it does not connect to anything else I already know (and understand through connections to other knowledge) in maths.

mi:Space: Inspirational Learning Spaces⤴

from @ Education Scotland's Learning Blog

Last September schools in Midlothian undertook an innovative and exciting new project which would allow them to transform the way that they learnt in their classrooms. Through consultations with local architects, extensive research and planning in their classrooms the schools created their own inspirational learning spaces!

Throught the year the classes had the opportunity to undertake various projects which would help develop and enhance by their new learning spaces. The first project was a STEM eco-classroom project. This is a project created by the Engineering Development Trust to help the pupils to develop their science, technology, engineering and maths skills. During this project, the pupils were challenged to build an eco-friendly classroom. They needed to research eco-friendly classrooms that have already been designed in schools and then use this research to create their classroom in a way that helps the environment.

In an exciting opportunity for the schools, teachers were invited to a training session with VEX Robotics. During the session the teachers got to use programmeable robots, making them move, make sounds and flash their lights! This wasn’t just for the teachers as they went back to school and used the robots with the pupils who could programme them straight from their iPads. In March pupils from two Midlothian primary schools – Loanhead and St David’s – travelled to the National Exhibition Centre in Birmingham to take part in the VEX Robotics UK Challenge. The VEX Challenge requires teams to program robots to carry out a series of complex tasks while competing against 40 other teams from all over the UK. Both schools won awards for high level of competancy in programming their robots!

The final project that the schools undertook was a CSI inspired activity where the pupils had to solve the Mayberry Mystery Crime. They visited the Mining Museum in Newtongrange which was the scene of a terrible crime and using their skills they had to solve the mystery and name the culprit. To help keep the pupils working together they used a Yammer group to keep their investiagtions up to date!

Throughout the year lots of exciting work went on in the newly designed classrooms and you can find out more on the mi:Space Blog – https://blogs.glowscotland.org.uk/mc/mispace/