Category Archives: Professional

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/

The Scottish Curriculum: A Beginner’s Guide⤴

from @ Learning Stuff About Stuff

There is no universally agreed meaning for the term "curriculum" as applied to the education of children and young people. In academic circles it is a highly contested concept, and covers everything experienced by children and young people, within or without formal education. To an average parent, I guess it means "the stuff schools are going to teach children and young people". From this perspective, Scotland has no national curriculum. Scotland has no national framework which spells out explicitly what knowledge schools should teach children and young people. We used to have one, called 5-14, but it was decided that this was too prescriptive.

Instead, the Scottish Curriculum for Excellence has a series of statements called the Experiences and Outcomes, which make vague, implicit references to the knowledge we expect young people to acquire, wrapped up in highly general statements about what we expect young people to be able to do, and what we expect them to experience. The general vibe in our curriculum is that specific facts are unimportant - temporary stepping-stones to be skipped over on the way to developing generic transferable skills such as "creativity" and "problem solving". The curriculum is blind to the widely recognised fact that such generic, transferable skills do not exist.

Here is an example, from the Social Studies E&Os:
I can explain why a group of people from beyond Scotland settled here in the past and discuss the impact they have had on the life and culture of Scotland. [SOC 3-03a]
When teachers across Scotland first saw these E&Os they were, of course, aghast, and began creating local "schemes of work" or "progression frameworks" which did actually spell out what they were going to teach. In some areas, this work - the work of actually creating a curriculum - was undertaken at a local authority level, whereas in others it was left to individual schools, departments and even teachers.

As far as I am aware, no work has ever been undertaken nationally to audit these local curricula. No one knows the extent to which pupils across Scotland are being taught the same or different things.

Thankfully, some sanity was restored when it came to the creation of the new qualifications (the Nationals and rewritten Highers) which pupils sit from the age of 16. These eventually spelled out content, albeit somewhat sparsely and grudgingly amongst the pages of talk about the development of higher-order thinking skills:

Teachers were then able to refine the curricula they had created for younger pupils, by working backwards from these somewhat-clarified endpoints. The sparse nature of the content documentation explains why it is considered so valuable for Scottish teachers to become exam markers - they are then privy to more detailed discussions about exactly what constitutes assessable knowledge, what constitutes a valid explanation etc. The rest of us have to reverse engineer this detailed information from the published marking schemes of past papers.

Latterly, John Swinney, the Education Minister, has attempted to streamline Scottish Curriculum documentation by the creation of "Benchmarks". These are supposed to be more explicit and useful than the E&Os. Judge for yourself - here are the relevant benchmarks relating to the Social Studies E&O above:
  • Provides at least two simple explanations as to why a group of people from beyond Scotland settled here 
  • Describes at least two impacts immigrants have had on life and culture of Scotland.
To describe this approach as problematic would be charitable. We are still left wondering which immigrants, which explanations and which impacts we should teach. Our "curriculum" is mute.

With the publication of the benchmarks, the politicians now seem to feel our curriculum is fixed, and we are moving on to a major reorganisation of governance structures for schools. We are fiddling while Rome burns.

What’s Up, Docs? Digital Technology in English.⤴

from @ Just Trying to be Better Than Yesterday

As  an English teacher I get no greater pleasure when I see a classroom full of children engrossed in a book. Whether that is a focused ten minutes on their own choices or hanging on every word of Macbeth, books are what got me here and books are what it should be about. So when it comes to tech, I’ve always approached with caution. With any new ‘innovation’, I always begin with two questions: will this help reduce my workload rather than increase it and will it genuinely be a better way to teach kids stuff? If the answer to either of those is ‘No’ then I’ll ignore it.

I have real concerns that some of the major international tech firms are looking on at Education in the UK and are rubbing their hands with glee. So much money; so much possibility. The blind swallowing of this thing called ‘21st Century skills’ often disguises the fact that good learning is good learning no matter the tools we have in front of us. But is it incumbent on us all to find out what might work for our classrooms and ourselves? Perhaps. Again, approaching with caution – and a firm eye on the price tag – is key.

Having said that, though, it is our professional responsibility to utilise the best strategies for our classrooms. Using effective tech is already part of what we do in Scotland. The Government issued document ‘Enhancing Learning and Teaching Through the Use of Digital Technology’   states that: Digital technology is already embedded within Scottish education. It has a place within Curriculum for Excellence, Initial Teacher Education and the Professional Standards set by the General Teaching Council for Scotland (GTCS).’ So, knowing that, I have always tried to use the best resources I could find for my classes. The danger comes, however, when we use tech just because it is there.

I have recently been dabbling with the  ‘Classroom’ suite of tools from a very big tech company. For writing in the senior school I have begun to see it as hugely impressive. Our students have to produce a Folio for Higher and National 5. Using Docs this term has allowed me to follow progress very closely, to mark and assess as they go along, and avoid the chasing up of late bits of paper. It both cuts down on my workload and helps the students to make progress. Sold. I would never use it with younger kids; they need to write accurately with pen or pencil before they should move on to more focused tools but for seniors it works really well.

As teachers we should be able to assess how tech works most effectively. Kids have loads of gadgets but are not as tech savvy as we may be lead to believe. In fact it is often  lazy assumption. They have tools with great power. Whether we can tap into that or not remains to be seen but we should find out of ourselves. Tech, if anything, should allow us to extend the classroom, providing genuine opportunities for learning. If it doesn’t do that the we should leave it alone. And get back to the books.


iPad in my classroom 2016 – 2017⤴

from @ wwwd – John's World Wide Wall Display

Although there is over a month left of my first year in the classroom for a while I though that I’d start writing this as if I leave it till the summer… 1

I am lucky enough to be teaching in a 1–2–1 classroom. 15 pupils spread across primaries five, six and seven.

I’ve probably not done as much with the iPads as I could have this session, stepping back into the classroom after a few years out has been ‘interesting’, teaching a multi-composite has had it challenges too.

The last time I was in school the classrooms had 2 desktop PCs, we shared a lab of desktops and a trolley of laptop. This was a great provision, but 1–2–1 is quite different.

The iPads are original Airs. They have individual ‘school’ iCloud accounts and the pupils use their glow accounts for emails, online storage (O365) etc.

Apps are distributed via a free meraki MDM account. The devices are not in DEP. I ask pupils to request app that they want. And not to install them themselves. Obviously they could if they wanted to. We have a few restrictions, movie age for example, set from meraki but the devices are pretty open.

App notes

Some brief notes on the main apps we have used this session.

  • Drawing, Brushes Redux & Tayasui Sketches
    • learning about layers, illustrating, art. Tracing images of all sorts is very popular with pupils in spare moments. 2
  • Whiteboard Some of the pupils prefer a real one though.
  • Camera
    • recording learning (photo & video)
    • illustrating work (poetry) 3
    • presenting work (markup)
    • photography, casual learning about craft
    • video, casual learning about craft
  • Notes
    • writing, as the year has gone on we have written more in notes and less in other apps.
    • drafting, especially useful for blogging as removes any distractions.
    • collaborative writing, it is easier to airdrop a few notes that setup online document.
  • Safari, having an always to hand reference book, media library etc. Brings a lovely set of problems with it, copyright, fact checking and distraction. Updating the school blog and e-portfolios should be easier when everyone has a browser to hand.
  • O365 through glow. I’d decided to use these office tools this session. At that point I could have used the Apple ones, but would, then, have had to pay for the apps. I could have used Google, but would have had to organise accounts.
    • Microsoft Word, used for writing, especially for presentation and if work needs printing. Now we often start in notes. Early on we tried a lot of handing in of work via sharing in O365. Had a lot of problems with work going missing, documents not fully syncing. Some of this might have been confusion round saving (locally, Onedrive,auto, manual) some due to poor bandwidth. Now I ask pupils to start in notes, moving to word for formatting and adding images.
    • Microsoft OneNote, after early problems with Onedrive & word I decided to use Onenote as a virtual, handout/worksheet/jotters solution. When it works it is great. Unfortunately, for us, it doesn’t work consistently. I have persisted, for months. One of the most frequently used apps, but am probably going to look at other solutions next session.
      • I’ve blogged about the problems and spent a fair amount of time trying out solutions suggested by other glow uses, twitter folk and the Microsoft team.
    • PowerPoint, we have used a little. Most often as a choice for personal projects. I think I’ll try Keynote next session as is now free.
    • Microsoft Sway, we have dipped into sway, I’ve not found the pupils as excited by the app as other glow users have reported. Might be the way I’ve explained it?
  • LEGO® Movie Maker, a nice free stop motion app. we used this for some maths shape work and a whole class Tam O’Shanter movie. 4 I think the app has been discontinued a great shame
  • iMovie, for editing videos, science reports, animations. Some of the pupils are very keen on trailers in any spare moments, golden time and personal projects. 5
  • 5SecondsApp – Animated GIF Create & Search – Animated GIF Create, occasional fun for the blog often in combination with MSQRD. 6
  • Padlet has great potential, but our bandwidth seems to be too poor for this.
  • MyScript Calculator – Handwriting calculator – Handwriting calculator, some of the class like this, others prefer the google one in the browser.

If I was limited to the number of apps I think we could have got by with stock software, Safari, Notes and Photos will get you a long way. I’d add iMovie next.

The app I’d like to find is the simplest audio recorder that would allow pupils to listen to, record and share audio. It is a pity that Apple voice memos is limited to the iPhone. We have used boss jock junior a bit this session, but I think I’ll try the free version of ferrite next, unless I find something simpler.

Workflows

Attempts to distribute, gather and organise.

Over the session I’ve used OneDrive, OneNote and latterly experimented with Apple Classroom. These all have their strengths and weaknesses.

Pupils creating documents in OneDrive and sharing with me was the way we started. The obvious problem is organisation. We tried both sharing documents through OneDrive and emailing back and forward. Emailing proved to be the most successful, we had a lot more failures with sharing, as noted above, it’s hard to tell if these are problems with the syncing, pilot error or due to lack of bandwidth. Emailing brings organisation problems.

The main app I’ve used this session for distributing and collecting information has been OneNote. Apart from a few dislikes of the way the software works, no grouping in particular, the concept of how OneNote should work is great. Unfortunately We’ve lost data, had slow syncing and a lot of errors thrown. Even when working with a small group of 10 pupils, getting work to review back from all of them in a timely fashion has been a struggle. We have quite often lost work completely.

The possibilities of the class notebook are wonderful. Pupils record and assess their own reading on the one page. I can use the classnote book tools to click through them all listing and adding my 2 pence worth easily. I can had out maths ‘worksheets’ with a video of myself working through the problem embedded. The pupils work can organised and accessed easily. Unfortunately it doesn’t always work for us.

Recently I took the iPads out of meraki management to allow us to test the Apple Classroom app. The best practise for doing this is to have the iPads in DEP, The Device Enrollment Program, and supervised in an MDM (e.g. meraki). Unfortunately our iPads are not in DEP and they would have to be wiped to do that. I am not doing that at this stage in the session.

Instead I got the pupils to remove the MDM management and join a manually created classroom. Compared to the onenote workflows described above the classroom is quite limited. There is no organisation of media, text etc. The killer feature, for me, is that sharing is done locally, via Airdrop, without needing to get data out to the internet. So far I’ve just used it to distribute and collect files, notes and media files of all sorts. This is lightning quick, and so far I’ve had no problems. Longer term I need to figure out how pupils work could be organised, both on their iPads and mine. Notes has a simple folder system, but it could get pretty messy over time. I wonder if iOS 11 out this autumn will help, either with improvements to the Notes app or the new Files app that integrates with OneDrive?

Next Session

There is a lot to think about. I avoided the Microsoft classroom this session, it felt a bit too complex for me and seemed to still be evolving. Quite glad as MS classroom is going to be replaced by Teams. I am wondering it if will be any more successful than OneNote in my situation.

Next session Glow will also give use access to the Google suite, I’ll be interested in seeing how that plays out. My personal use of google apps has lead me to feel that they are lighter weight and faster to sync than O365 but I’ve not used them in the classroom.

I am also, now they are all free, thinking that switching to the Apple ‘office’ apps would be a good idea. I certainly find pages and keynote easier to use on iOS than Word or PowerPoint. 7

I am tempted too by Apple classroom, the quick local transfer seems like a good idea.
From the distribution to pupils, just using the notes app with the classroom Airdrop, where you can send to the whole class or a group is a great improvement over OneNote. On iOS or mac the OneNote classroom lacks the ability to send to groups which Apple Classroom has. The success and speed of Airdrop beats O365 via the web hands down (not surprising). Tables I’ve missed a little and it would be nice to be able to record audio straight into notes. It is simple enough to record in another app and insert into notes.

Ideally I’d love the simplicity and speed of Notes and Airdrop to be extended to add some of the organisational features on OneNote classroom.

I am a bit disappointed that I’ll start next session still unsure about the best way forward. Google will not arrive in Glow until September. MS teams is not yet ready for use.

I am looking forward to trying all of this out, but mindful that swapping out workflows is not as easy for our digital natives 8 as it is for me.

  1. Yup, this post has taken at least 3 weeks to mature. It is a bit of a grab bag but has helped me think things through.
  2. Art Gallery – Banton Biggies a lot of this is made in Brushes.
  3. Kennings, we know about animals – Banton Biggies
  4. Scenes From Tam O’Shanter – Banton Biggies
  5. Video – Banton Biggies
  6. RedNoseDay Animated Gifs – Banton Biggies
  7. Personally I am not a frequent user of office apps. I would never open word, pages or google docs just to enter text. Drafts would be my iOS productivity tool of choice.
  8. I found the pupils are really quick in learning some digital things, but I don’t think that includes organisation.

Proud⤴

from

Last night I gave the following speech to introduce the review of the year at our Celebration of Achievement evening.

Back in December I was given the great privilege of becoming acting head of teaching and learning in the secondary school. Teaching and learning are at the heart of what we do in school. Our excellent team of staff works to ensure that all of our pupils develop skills for learning, skills for life and skills for work so that they grow into the best possible versions of themselves.

As a school we are judged partly through the assessments and exam results that we produce and there is no denying that these are important. Formal qualifications are the currency that allow our pupils to compete in a world where opportunities are sometimes hard to come by.

I recently spoke in an assembly about Richard Branson, the self-made multi-millionaire who left school with nothing and made it nevertheless.

Whilst in some ways he is an amazing role model, particularly for those with dyslexia, he is also in other ways unhelpful because he is one in a million. Qualifications on the whole do matter and it is for that reason that we want all of our pupils to leave school with the absolute best results that they can.

But being the absolute best is about more than just qualifications.
In our Learn to Learn and PSE classes and our assemblies, we focus a great deal on the idea of being reflective learners and of using all situations, both in and out of school, as learning opportunities. The successes and mistakes. The highs and the lows.
Our pupils know that being the best is also about being helpful, being loving, being understanding and being a good human being.

You are about to see a presentation that celebrates the highlights of the past school year and shows, alongside all the other huge achievements in the room tonight, why our school is amazing and why having my job is an absolute privilege.
There will be some things missing: please don’t be offended but just understand that in 15 minutes, we have just produced a snapshot.

This is the work of the students who are presenting it and a few others behind the scenes.

The quotes your will see are from our Learn to Learn sessions and assemblies and will give you a flavour of the ideas that we encourage our pupils to explore.
I will now leave you in the very safe hands of the students.

The presentation that the pupils presented was slick, professional, moving and entertaining and they did themselves and the school proud.

I am so very lucky to do the job I do.

 

 

 


Microcast 8: Thoughts On Sonant Thoughts Ep 29⤴

from @ wwwd – John's World Wide Wall Display

Audio comment on the Microcast Sonant Thoughts – Episode 29: Focused

This is a quick try of an iOS workflow. The idea is to quote and comment on a podcast. The content was a one take job. Steps:

  1. Listen to podcast
  2. Copy URL to audio file (I grabbed it from my RSS reader FeeddlerPro
  3. Open in safari
  4. Save to Dropbox
  5. Open in Ferrite
  6. Trim to quote
  7. Add audio comment
  8. Save to iCloud
  9. Back in Safari upload to blog, create post etc

Could probably speed things up using workflow to create post.

Id love to see an app to simplify this. I don’t think it is really a practical solution. Much quicker to move to desktop.

Benchmarks – the value of collaboration⤴

from @ Education Scotland's Learning Blog

A blog by Lorna Harvey, Acting Senior Education Officer
for Numeracy and Mathematics

Last year ( August 2016), we published draft Benchmarks for literacy and English and for numeracy and mathematics with the aim of providing clarity on the national standards expected at each level of the Broad General Education. We wanted to make clear what learners need to know and what they need to be able to do to progress through the levels, and to provide guidance that would support consistency in teachers’ and other practitioners’ professional judgements.

By publishing the Benchmarks in draft, we wanted to ensure we had time to consult with the very people who would be using the Benchmarks. We were committed to developing guidance that would hit the mark and achieve our aim of providing clarity.

From the outset we were keen to hear from as many practitioners as possible and we wanted to make sure anyone wishing to provide feedback felt confident that they could be as open and honest as they wished. To achieve that we set up an anonymous online consultation, but we also planned a number of face-to-face sessions allowing for more depth to our discussions and the opportunity for people to ask questions.

A number of National Network events provided opportunities for practitioners from across Scotland to contribute to this consultation process. This included the National Literacy Network, the National Numeracy Network and the Principal Teacher/Faculty Head Forum for Mathematics. Colleagues from SQA were involved in many of these discussions.

Some people decided to get together with colleagues and offer suggestions, while others wanted to provide their individual response. Whichever way people chose to provide feedback, it was extremely valuable. It was great to receive insight based on practitioners’ engagement with the Benchmarks in their education setting.

Together with my colleagues across Education Scotland , I worked on collating the results and analysing the feedback before making relevant changes to the Benchmarks. A number of stakeholders had offered to be involved in further consultation so we shared the updated Benchmarks and gathered more feedback as part of the process.

And then we had them. The final Benchmarks, shaped by practitioners and providing the clarity that we had been aiming for. A real collaborative effort.

We have now published the Benchmarks on our National Improvement Hub and would encourage practitioners to familiarise themselves with the documents before they begin using them in their setting. It’s also worth having a look at the ‘change’ documents we developed which clearly show where changes have been made from the drafts. There is also a frequently asked questions document.

We have uploaded a broadcast on the National Numeracy and Mathematics Hub which provides background information, advice and guidance on using the Benchmarks. The majority of this broadcast is relevant for all practitioners and there is a specific numeracy and mathematics input also. This broadcast could be used at an In-Service day in August to raise awareness of the Benchmarks and support professional discussion and planning.

We will be providing seminars at the Scottish Learning Festival in September as well as a Yamjam – where practitioners are invited to engage in an online discussion about the Benchmarks.

We would like to say  a huge thank you to all the practitioners who supported the consultation process, working with us and engaging with the drafts to provide valuable feedback to help shape the final documents

using Excel’s LINEST function⤴

from @ fizzics

The period (T) of a simple pendulum can be calculated using where l is the pendulum length and g is the gravitational field strength. Using a single value of length and period, we can determine the acceleration due to gravity.  However, it would be better experimental practise to vary the length of the pendulum and ... Read more

Edinburgh International Book Festival⤴

from @ Education Scotland's Learning Blog

Baillie Gifford Schools Programme – 21-29 August 2017

What’s the Big Idea?
The 2017 Edinburgh International Book Festival Baillie Gifford Schools Programme challenges young minds to question, imagine and wonder. The programme brings together well-established writers, illustrators and performers from every corner of the globe, along with some shining new talent.
The programme is full of activities that will entertain, educate, enthral and inspire everyone from P1 pupils to teens and teachers, including events with bestselling illustrator Kristina Stephenson, Olympic cyclist Chris Hoy, picture book events for the youngest primary school pupils, and a Relaxed Event for pupils with Additional Support Needs.
You can find more information, download the full programme and book tickets on the Book Festival’s new Learning Site: learning.edbookfest.co.uk