Dear Elizabeth Truss- why conceptual understanding of calculation matters.

Today, I had the horror of reading the speech made by Elizabeth Truss to the North England Education Conference on Thursday.  This speech advocates, amongst other things, the almost forced return to the teaching of algorithm calculation methods.

I initially felt very worried after reading this, and this afternoon decided to pen some form of response to Elizabeth Truss, which you can find below I’ve decided to blog this, an ‘open letter’ if you like,  as I would be very interested in what you think :)

A bit of background here-  my Mathematics Specialist Teacher second year project is on developing a conceptual understanding of calculations with a focus on division, and I have been meaning to (and still will) blog more about this.   I also feel I need to put a reminder that these views are my own and not necessarily those of my employer etc etc…

Anyway, my thoughts are below…

Dear Elizabeth,

I read with quite considerable alarm the speech you made to the North England Education Conference on the 17th January 2013.   As a committed teacher, who wants their children to not just learn facts but develop understanding, this speech made me feel very un-easy.

In your speech you state that children must learn to speak the ‘language of maths’- something which I fully agree with- we need to develop a conceptual understanding of maths within our children, so that they are able to effectively use and apply their mathematics skills, and are able to problem solve beyond the dreaded and much over taught  ‘word problems’.   I would like to address just some of these issues from your speech.

Let’s first tackle your accretion that those ‘new’ methods which are based on conceptual understanding do not allow for progression- are you able to provide evidence of this?   By their very nature the methods taught in many schools now are rooted in the structure of our number system- and therefore can easily be extended to any number.   Children frequently do this themselves-  for example, when taught how to subtract by finding the difference on the number line for  2 digit positive numbers, they are easily able to extend this, often independently,  to subtracting larger numbers, decimal numbers, negative numbers and indeed time intervals.  The same applies for division by grouping/chunking,  and multiplication using the grid method (which, in reality  takes multiplication back to what it is- an array)

The ‘algorithm’ methods bode  little resemblance to what is actually happening with the numbers.   Can you explain why long division works?   There is no logic to these methods- they work by simply following n a set of instructions, which, to many children at least, ‘magically’ end up with the correct answer-  and I believe this means children will struggle to extend these methods.  After all, maths is not ‘magic’.

You correctly state that no-one can predict when a child will experience the ‘light bulb’ moment- but by removing the conceptual understanding behind calculation, you will be virtually eliminating the chance of this happening- as a child will not truly be able to say ‘ahh…I understand’- all they will be able to say  is ‘I can follow the method…’

There is a considerable bank of research evidence showing that the ‘new’ methods which foster a conceptual and relational understanding of number and calculations lead to far greater accuracy and confidence than the ‘traditional’ algorithm based methods.

In fact, you don’t have to go far to find evidence of this- for 3 pieces of leading research in your very own county of Norfolk[i] have consistently shown that methods which foster conceptual understanding ‘win’ when it comes to children being able to calculate accurately.  Surely it is  by using methods based on a conceptual understanding that children are more likely to spot their errors- for they actually ‘see’ what they are doing to a number, rather than just robotically following a set of instructions ‘just because it works’.   And further research clearly states the importance of developing conceptual understanding.[ii]   Can you provide research to prove that these methods lead to greater errors as implied in your speech?

Of course, this is not the first time you have heard this.  Many groups and organisations have tried to explain this before, and many of us responded in a similar vein to the (absolutely appalling in parts) draft curriculum published in March 2012.  Indeed, the joint response[iii] to the proposed curriculum by the Association of Teachers of Mathematics (ATM) and the Mathematical Association (MA), which together represent some of the leading thinkers when it comes to mathematics education, clearly states and provides evidence for the need to develop a conceptual understanding and not rush to formal algorithms too quickly.   Could I suggest that you re-read this response and ask if the new version of your curriculum addresses the many issues raised within it before it is released in a few weeks time?

The government has spent money on, and now continues to support the Mathematics Specialist Teacher Program, of which I am now in the second year, and this very program, designed to ensure that each primary school has a mathematics specialist and therefore raise the standard of mathematics teaching, advocates conceptual and relational understanding and the calculation methods which are based on these.

Indeed, these ‘new’ methods are, in fact, nothing ‘new’- leading academics, backed up by research, have consistently proven the case for relational understanding (Skemp, 1976[iv]).     Without methods based on this understanding you constantly find in classrooms that children who struggle with maths find the algorithm methods incredibly confusing and are unable to use them.

I also take great issue with your statement that these methods are not efficient.   These methods may not be efficient for you- I’m guessing because you are not comfortable with the method, nor do you probably have the conceptual understanding of number which underpins these methods- this is demonstrated by your rather lax explanation of these methods in your speech. This is of course, not surprising  as they are different to the way you were taught.

But for the children who are taught these methods they are efficient.  They, used alongside robust teaching of mental strategies, which themselves are rooted in a conceptual understanding of our number system allow for efficient and accurate calculations in all four operations (yes, whilst they would work for any calculation, even the most simplest, it’s never been advocated to conceptual based written methods ‘blindly’ used for any calculation), .   Surely a method is only efficient if it means the child is actually able to get the correct answer?  

East Asia, and specifically Singapore,  is, yet again, used as an example by you as a country where things are done ‘right’.  So are you proposing we import all of this teaching, if so, let’s first look at  Singapore’s mathematics teaching,  which includes a very refreshing approach to the purpose of mathematics teaching (for the solving of problems) , which encourages mathematical thinking and includes the Singapore  bar methods for calculation and solving problems-  based on a conceptual understanding of number and can be which can be seen to be similar in its thinking to the conceptual methods taught by teachers in the UK.

You state that parents are not able to understand these methods.  Yes- these methods are different to the way in which most parents were taught themselves at school, and it is the job of the school to ensure that parents are aware of the different methods taught in school- something that many schools do through successful calculation events, in which many parents realise for the first time themselves what division, subtraction, multiplication or addition actually means.   Once aware of the new methods and the reason behind them, parents are normally, in my experience anyway, very supportive.    But despite this, are you therefore creating a maths curriculum for parents?   I would assume that a curriculum is meant to be written for the benefit of the pupils not their parents?     Children understand and are able to easily explain the conceptual methods they are taught, they are accurate when using them and can use them ‘quickly’-  this is what matters to me as a teacher.    (It is also worthwhile pointing out that in only a few years time our new parents will, themselves, have been taught the conceptual based methods- so we could end up with the same problem in reverse!)

I am also not advocating the complete abolishment of the use of algorithm methods, however ideal that would be, as I appreciate this would never happen- but do believe it is about using the right methods, backed by conceptual understanding, at the right stage for the child.   For many children, the forced  introduction of algorithm based methods in primary school when they do not have this conceptual understanding is too early, and will ruin their chances of actually understanding maths and increase their chances of  becoming one more of adults who say ‘I can’t do maths’  (when they are normally really saying ‘I don’t get maths’)  that you refer to in your speech (I agree by the way, that is an awful attitude to have!). [Of course, the converse is true, for a few children, they will be 'ready' and be able to extend their conceptual understanding for the traditional algorithms by the time they leave primary school- surely we should be reactive to the child?]

There is one glimmer of hope in your speech- that the new curriculum will state that children must be taught efficient methods- and I could argue that by teaching the methods based on conceptual understanding, that these methods are the most efficient for the children I teach.

But, then you state that, from 2016 children will achieve a ‘method’ mark only if they have used the ‘prescribed’ algorithm methods.   [By the way, what will this mark be awarded for?  as by the very nature of algorithm methods there is little margin of error.]

This means you are effectively forcing schools to take a calculated ‘gamble’- do they solely teach the algorithm methods, which they know (as backed up by research as stated earlier) will lead to a far greater error rate  but which will pick up a ‘method’ mark,   or do they stick to the research proven methods, which they know children will generally stand a higher chance of getting the correct answer, and therefore two marks, but with the risk that if they do not arrive at the correct answer they will be penalised for using a method which they do not understand?

All this strikes me as change for changes sake- a dangerous change which  stands a good chance of reducing our children’s ability to calculate and solve problems, but which will please many traditional conservatives and elements of the press who do not understand the real issues in mathematics education, and a change which, yet again, erodes the professional judgement and expertise of teachers.    Please do not think, as I am sure someone will be quick to suggest, that teachers are simply resisting change.   I am not  teacher who resists change and am more than happy for change, and embrace it, after all teaching has to be a profession where we are constantly moving forward.  But change has to be positive change that will have a positive impact on the education and lives of the children which I teach- and I, as many teachers do,  believe this change certainly will not.

Of course, there are many more things in your speech which were incredibly worrying, but I do not have the time to get started on, for example, why rote learning times tables up to 12 times is unnecessary (the structure of our number system means that tables up to 9x would be sufficient) or why children’s ability to think mathematically can be increased by calculator use (but not by dependence on calculators .   What your speech simply proves, is yet again, this government is not listening to what teachers and leading academics are saying- but why am I surprised?

TH


[i] Borthwick, A. and Harcourt-Heath,M (2007) Calculation strategies used by year 5 children. Proceedings of the British Society for Research into Learning Mathematics’  27 (1)  pp. 12-17 (available online here)
Borthwick, A, Harcour-Heath,M (2008)  Are we nearly there yet? Accessed online http://cattell.bltnorthants.net/files/2011/06/Y5_article_2008-911.dochttp://cattell.bltnorthants.net/files/2011/06/Y5_article_2008-911.doc   19.01.12
Borthwick, A. and Harcourt-Heath,M (2010) Calculating:  what can year 5 children do?  Proceedings of the British Society for Research into Learning Mathematics’  30 (3)  pp. 12-18  (available online here)
[ii] Nunes, T. Bryant, P., Hurry, J. and Pretzlik, U. (2006) Fractions: Difficult but Crucial in  Mathematics Learning http://www.tlrp.org/pub/documents/no13_nunes.pdf
Nunes, T., Bryant, P. et al (2009) Development of Maths Capabilities and Confidence in Primary  School https://www.education.gov.uk/publications/eOrderingDownload/DCSF-RR118.pd
fNunes, T. Bryant, P., Watson, A. (2010) Key Understandings in Mathematics Learninghttp://www.nuffieldfoundation.org/key-understandings-mathematics-learning

[iv] R Skemp: ‘Relational understanding and instrumental understanding’, Mathematics Teaching, 81.

Let’s get ‘appy- why teachers should take note of apps.

On Wednesday 30th January, I’ll be at BETT with 6 of  my digital leaders, where we’ll be having fun exploring the exhibition as well as leading a series of  ‘themed’ presentations, seminars and takeovers.   Our theme this year, which was chosen by the children before I submitted our LearnLIVE proposal, is around the use of ‘apps’ (of all kinds!) in education. 

We’ll be leading a LearnLIVE session, ‘Let’s Get ‘Appy- how the app generation can use apps to enhance, extend and motivate learning.   at 12:15 in Gallery Room 7, as well as different things on the show floor, full details of what we’ll be up to can be found on the children’s own BETT Blog.   Of course, if you are around at BETT on the Wednesday we’d love to see you- so do come and say hi!

A couple of weeks ago, I was asked to write an article for ICT for Education  around the theme of our seminar session, which I wrote alongside the children who are presenting at BETT.  This is due to be included in the next issue of their magazine, and, after a few who had read the article felt it should also be blogged,  I have permission to post a version of  the article on this blog.    I have to say, I don’t profess that any of this is groundbreaking , especially for many of the readers of this blog, but hopefully it is a useful read none the less.

So here it is- I’d be really interested in your views, and hearing how you use apps in your classroom :)

Let’s get ‘appy-  why teachers should take note of apps.

 App (noun)- a self-contained program or piece of software designed to fulfil a particular purpose; an application (Oxford English Dictionary)

It’s been nearly impossible to miss the surge of ‘apps’ both on devices and web based over the past couple of years.  Many of us have a smartphone and/or tablet, and these devices are becoming increasingly common in schools.   There are also a large number of ‘web apps’ which can be accessed on practically any web-enabled device, including desktops and laptops, and therefore it is no surprise that an increasing number of teachers are starting to exploit the power of apps.

The App Generation

The children we teach are ‘natives’ to this technology, I like to think of them as the ‘app generation’- apps are nothing new to them, and they are growing up in a world which many predict will be increasingly powered by apps.  The vast majority of the children we teach will own an app based mobile device [an additional note- on the return to school, I discovered that half my class received some form of tablet for Christmas!].     Bayleigh, 10, adds “We use apps all the time on our iPod touches and phones at home, so it makes sense for teachers to use them to help us learn”.

Apps are often very simple to use, but despite this are often extremely powerful tools.  Adam, 8, explains “It is dead easy to do things on apps, like put together a movie, or create a digital poster that would take me ages to do on proper computer programs”.    Give a child a new app and they will soon become experts on the app- often within minutes.

Children also enjoy using apps in school, and they can be a very powerful tool to engage children in their learning.  Isobel, 11, comments “Children love using apps in school, especially on mobile devices.  They make learning so much more fun and allow us to do things that wouldn’t have even been possible before”.

It’s free!

Apps are, for the most part, either free, or at worst, very cheap, especially when compared to their desktop counterparts. On top of this, nearly all apps offer free updates, enabling you to always have the latest version of the application.  Pretty much most functions performed on a computer can be accomplished through a device and/or web based app, meaning in an increasing number of schools you will find no ‘traditional’ software beyond the operating system is installed on their computers.

The possibilities are endless.

The possibilities of what can be achieved in schools through the use of apps are practically endless, and the children have shared their top 10 apps with you at the end of this article.

During our LearnLIVE session the children will share how apps can be used to develop specific skills, how they can be used to enable them to present their work in creative ways, how apps can be a powerful tool in them recording their learning and how they can be used to allow greater learner interaction and for children to ‘replay’ key teaching moments.

When combining the use of different apps together, their power only increases.  For example, last term, we ran a fully functioning ‘news room’ in Year 5, using only apps on our tablets, which allowed us to create a constantly updating news website  (http://bit.ly/woodlandsnews), and we will explore some more ways in which apps can be used together during our session at BETT.

Homely Apps!

However, I think ‘apps’ really come into their own when you exploit their potential to build home-school links and enable more meaningful work to be completed at home.

Most blogging platforms have apps for mobile devices, which make blogging about work completed in school even easier and accessible to children than before.  Photographs of that super piece of writing/maths/other piece of work can be uploaded,   and using apps such as Vimeo, Audiboo and Soundcloud, sound and video files can be easily captured, making sharing learning in school with the wider world, quite literally, child’s play.

Many head teachers are starting to exploit this ease of use by creating ‘well done’ blogs, showcasing to the world work that has been sent to them for a head teacher award.  [http://bit.ly/appypraise1- Gaywood Community Primary School and http://bit.ly/appraise2- Heathfield CPS for examples].

Paul Shanks, head teacher of Gaywood Community Primary school shares that  “Using apps such as WordPress, Vimeo and Audioboo means that we can share children’s work more readily with parents/carers.  The Praise and class blogs can be updated immediately, with parents often aware of children’s achievement before the end of the school day.  Twitter and Facebook integration enhance this further as we then have direct contact to majority of parent/carers and can supply direct links to the blogs. The impact on learning has been significant as children are keen to be on the Praise blog”

Great possibilities also exist if teachers begin to ‘accept’ learning completed on apps, whether they be web based or device specific, for learning completed at home.

Bayleigh adds “Apps are just another way for us to show our work” and apps should therefore be seen by teachers as another, valuable way for children to share their learning with their teachers.  For example, a simple request to do some research about our forthcoming space topic can turn into information videos , or learning from a school trip can turn into a cartoon - all by the power of simple to use apps.

Children as App creators.

Finally, it is now even possible for children (and indeed teachers!) to easily create their own apps.  There are an increasing number of services out there which allow you to create apps, which can be accessed as web apps on any mobile device, or (often for a fee) even published as ‘real’ apps to the different app stores.

The children’s favourite tool for allowing them to create their own apps is AppShed .  Adam explains “It’s quite easy to create your own app on AppShed, you do need to think carefully about how you want your app to work and what needs to go where, but when you’ve done that creating the app is easy.”    Apps have been created by children from Year 3 upwards, and the pleasure of seeing their own creation being available as a web app on anyone’s mobile device is great to see!

Apps are on the rise, and the potential they have to transform learning cannot be ignored, the only question left is how will you use apps in your school?

See you at BETT!

I’d be really interested to hear your views, and how you use apps in your classroom :)

 

==

The children’s top 10 apps can be found below…

Read more…

Should we be ‘exemplifying’ ICT?

Yesterday I shared my draft ICT ‘curriculum‘ (which perhaps on reflection isn’t quite a curriculum, more a framework, or scheme of work…)  and have had some fantastic discussions with various people about it (thankyou!).

One key question that kept popping up when I was working on the documents, and has formed the basis for some interesting discussions over the past 24 hours, is

Should (primary) ICT coordinators exemplify, or plan, their curriculum/scheme of work?

I thought I would share my thinking on this, and  I’d be very intrigued to hear what you think!

In the documents I shared yesterday, there is, purposefully, no ‘lesson by lesson’ break down of the how the objectives and key skills should be covered- at one point when I began to put the documents together there very nearly was this level of detail, but then I moved away from this thought.

I intended the documents to set out the skills and experiences that the children in our school should gain as they move through the school.   I really believe that these must be delivered in a meaningful context, preferably linked into other curriculum areas and our cross curricular themes, and this, for me, was the final convincing factor in not exemplifying the objectives and key skills.   What I would hate is for staff not to make the most relevant and applicable use of technology just because it didn’t fit within the more detailed scheme of work which I had laid down- just like sometimes tended to be the case with the QCA schemes.  I may not select the best tie-in with themes and other work

I also thought that I wouldn’t expect someone to plan my English, Maths or any other lesson for me, or indeed set these out on a lesson-by lesson basis.    I really feel that  without staff themselves incorporating ICT into their planning, we are never going to reach the ultimate goal of what Naace are describing as ‘3rd Millennium Learning’- where ICT is a seamless, valued and effective part of teaching and learning in our school (well that’s my own interpretation of 3rd Millennium learning anyway!).

There was also an interesting discussion along these lines in one session at the  Naace Hot House about the lack of exemplification in the Naace framework, where it was felt that exemplification would have limited the impact and ultimate goals of the framework.

The vast majority of the objectives and key skills in the documents I have put together will have to be delivered not through the ‘ICT Lesson’ but through day-day teaching- and the ultimate aim is that discrete ‘ICT Lessons’ are a thing of the past within the next few years.  In KS2 we are having an ICT lesson (well a timetabled session in the computer suite) for this year at least- but hopefully in the future this can be dispensed with, whilst ensuring the ICT curriculum is still covered fully.     This is also why I decided that I wouldn’t suggest we buy into an ICT scheme (despite them being some very good ones like Switched on ICT around), as the units in any of these schemes didn’t match up with any of the cross curricular work going on in school.

However, I am very mindful that, in my school context,  this will need support to enable it’s implementation. The KS2 yearly overviews I think help slightly with this, which for next year suggest which skills may be best delivered in the ‘contextual skills based ICT lesson’- but I am expecting that these documents will be ammended by the year group teachers and evovle ove rth eyear.  I am going to part exemplify the first block of ICT planning for each year group, so that we can hit the ground running,  and offer support to all the staff in planning the remainder of the years ICT.  My digital leaders will also hopefully help with some of the more skills based support for staff too.

But, of course, I’m not saying that ICT should never be exemplified, and I may well be proved very wrong over the next year.   I know for many schools this is a way that works very well, and that ICT is still embedded across the school-for example @xanov/’DigitalTeacher’ blogged about his approach back in February,  it is all, of course, down to school context.

So what do you think?  Should we exemplify ICT?  I’d be really interested to hear what you think!

 

A New ICT Curriculum- First Draft

Over the past few weeks, I have been working on creating a new ICT Curriculum for my school.   It’s been a long process,  but I”m pleased to say the first draft is finally completed and I wanted to share this with you- to see what people think, to help it improve, and also for others to use if it is indeed useful :)

I’ve uploaded all the documents that comprise our new curriculum onto google drive, and you can access it here .

The main document is called ‘ICT Curriculum- Main Document’- which (helpfully!) is second in the list on Google Drive!

Before I go any further I definitely need to acknowledge a few people/documents!   When creating the curriculum I found the Noroflk ICT Curriculum created by Jill Duman (Norfolk ICT Advisor, tweets as @NorfolkTeachers) invaluable, and parts of the curriculum are copied from this document (but often with some amendments to fit our school circumstances).   I have also gained lots of inspiration from lots of people on-line, including @ianaddision (and his super new book and ICT planning website) and @simonhaughton.   As well as all these people,  the Naace Third Millennium Hot House event I was lucky enough to attend last week really helped with the creation of the curriculum and lots of the ideas shared at the event have been Incorporated into the curriculum (more about that below)

So a bit more about this document…

My School context – obviously has a lot to do with the curriculum- ICT in school needs development to ensure it is emebded throughout the school and day-day teaching, and this curriculum is intended to be a stepping stone towards this aim.  Some parts of the curriculum are down to be covered in specific year groups in 2012-13 only or from 2013-14 onward- this reflects the current skill set of the children in our school and what we need to develop.

As the foundation- I took the new Naace ICT Framework - after exploring the framework at the 3rd Millennium Hot House event, I really believe it is a great document and a good foundation for any ICT curriculum.

However, I felt the 5 areas of the framework themselves were not enough to provide the necessary guidance for staff and to ensure that children receive a broad and balanced ICT curriculum- I see it more as a (very valuable!) ‘philosophy’ for ICT.    I therefore decided to split the actual curriculum into 8 key skills-  Using a Computer, Using the internet , Communicating and Collaborating, Creating and Publishing, Digital Media, Programming and Control, Modelling and Simulations and Using Data.    I have to admit I agonized a lot over what these key skills should be and what the objectives and key skills should be, but hope I have managed to strike a good balance.

Each element of the Naace ICT Framework will permeate through each of these areas, and it may be that teachers will be asked to identify the different elements of the Naace ICT framework in their planning.

I decided to set out the Key Skills and Objectives for each of these areas per year group, which hopefully shows a good progression as we move through the school.   The idea is that the vast majority of these objectives will be met through work and projects in other subjects.

However, as a school we have taken the decision to timetable each KS2 class with an hour in the ICT suite- this serves many purposes- resource management (especially until we get our refresh) as well as guaranteeing that each child will experience one hour of ICT each week.  This will be delivered as contextual skills based lessons with the real focus on developing a specific skill, and these skills will then be applied across the curriculum.    I have therefore decided to, for this year at least, produce a ‘guide’ for each year group of which objectives may be best delivered as part of this ICT ‘skill’ time, and a rough number of hours for each skill-  this can be found in the ‘Curriculum Overview- year by year’ document.

Given this approach, a lot of the skills are taught and then expected to be used throughout the school- for example website creation is only taught as part of the ‘skill sessions’  in year 4, but applied and developed in Year 5 and 6.

The curriculum takes a ‘bend’ towards what would traditionally be thought as as ‘computing’ in Year 5+ 6, and lots of ideas from the Third Millenium Hot House, including the super RoboMind ideas shared by Nick Jackson are incorpoated here,  I have also incorporated what for many people was the biggest ‘take away’ from the event, application creation using the amazing Appshed.

[E-Safety is, of course key, and is subject to our separate E-Saftey policy and schemes of work]

So, I’d be really interested to hear what you think- is there anything missing? Am I barking up the completely wrong tree?  You can access the documents here  and of course, I’d be happy to share editable versions of the documents if they would help anyone!

TH

PS- The Naace 3rd Millennium Hot House event was fantastic- lots of others have blogged in detail about it, and you can find their super posts by following the links below:-

 

 

 

The concept of ‘exchange’

As you may know, I am currently nearing the end of Year 1 of Cohort 3 of the MaST (Mathematical Specialist Teacher) programme.

This has been a really interesting ‘course’ so far- with lots to think about and it has already had a big impact on the way I approach my maths teaching.

We met tonight for our last ‘Local Meeting’ of this academic year, and along with a review of the year, we discussed the concept of ‘exchange’ in mathematics.   This has really made me ‘think’ and I wanted to share some of these thoughts below- partly as a way of organising them, but also as I’m interested, of course, in what other people think/make of them.

This has come from discussions which various people have had with John Mason, a leading academic (whose writings on learner mathematical powers forms a substantial basis for much of the MaST programme) and I’m hoping that he will be publishing a paper about this concept soon!

So here goes- hopefully some of this will make some sense!

First, to try to explain what I think ‘exchange’  means in this context-  the act of changing something into something else at a ‘set rate’- for example the act of changing 5 1p coins into a 5 p coin, 4 5p coins into a 20p coin,  10 units into a ‘ten’   etc

I guess the overiding question I am left with is do we really ever teach the concept of exchange?   and if not, I guess, does it really matter? 

A few examples were shared with us to try and explore the concept, so I thought I would share these below…

For each of these examples, we were basically told to imagine the counters operated in Base 5- I think this helps break any ‘reliance’ on what we, as adults, already know and understand.

First, imagine you had 8 blue counters, and you could exchange each blue counter for 3 red ones.

This could be represented in the way shown below:-

Does this representation make sense to you?  Would you have represented the exchange in any other way?  What would a child, say in EYFS for KS1 do?   Does it matter what way you organise and represent this exchange?

Now imagine you have a different situation- you have 23 green counters, and you can exchange each 5 green counters for 2 orange ones.

Now how many orange counters can you ‘have’?

My, along with many other people tonight, initial answer  was 9.   But we were later convincedthat the ‘answer’ is most probably 8 (taken, at least, on the most simple level)

However I found 8 to be a clearer answer when represented like this- this again leads me to question if how we represent ‘exchanges’ effects our understanding of them…

Do you think a child would have answered that question as 8 or 9?   I’m going to try it out, along with some other exchange based activities before the end of term to see what my Year 4’s think.

Of course, the argument goes that you can’t ‘split’ the 2 counters- it’s an exchange ‘rate’ of 5 for  2 after all.  But this caused quite a bit of cognitive conflict tonight- and left us wondering if the exchanges (our base 10 system, money etc) which the maths we teach relies upon can be the root of some children’s difficulties in understanding number.

So back to my initial question- do we teach the concept of ‘exchange’ and does this matter?

In short, I think my answers are- no, the concept of exchange probably isn’t taught as much as it maybe should be in schools- we tend to assume that children are naturally ‘secure’ in making exchanges- however can we really assume this when our number system relies on this concept of exchanges?

And as for does this matter-  I think it just might… but am not sure what or indeed how, we should go about addressing this- hopefully this is something that John Mason will share when/if  he writes about this in depth…

So- that’s what’s got me thinking tonight-  I’d be really interested in your views on this!  (if, by any miracle it made any sense ;) )

TH

ICT Curriculum Themes…

I’ve just ‘officially’ taken over ICT leadership at school- which has suddenly given me lots of things to think about and sort out!

One of them is mapping our existing ICT coverage (which I suspect will be very patchy) and then looking at how we move forward next year.

This has got me thinking about how our curriculum should be structured- it needs to fit fully into our cross curricular teaching- with ideally no, or very little, ‘discrete’ ICT lessons.

I’ve began to develop some key ‘themes’ which will need to be covered throughout the school-  I’ve taken my ideas from a range of sources- commercial schemes, the current national curriculum and things I remember seeing/reading over the past few months and my initial thoughts are below, together with my initial very rough brief explanation for staff…

Using the internet and e-mail-   Researching, finding information etc…   Sending and receiving e-mails.


Creating and Publishing:
- Anything that involves presenting information in some way using ICT-  word processing, presentations, blogging, websites etc…  

Digital Media-  Photo editing and image manipulation, video and video editing, animation (with an appreciation that some animation is also programming)

Programming- making something ‘happen’ using a computer.

Using Data-  Spreadsheets (including using formulas), Databases and any other work which involves either sorting, presenting or manipulating data of some sort.

E-safety- Keeping safe when using computers and the internet.

I would be very interested to here what you think- have I missed anything out (especially EYFS/KS1)?  Are the themes to broad or could they be reduced further?

My next (much bigger!) steps are to take these themes and begin to map the progression year on year, to provide an accessible framework for teachers to incorporate into their teaching.

TH

I’m back blogging!

I’m back…

Yes, I know I never said I was going anywhere….but as some of you may have noticed, my blog has been neglected since January.

This has been for a range of reasons, but primarily due to the school where I work being placed into Special Measures, and the whole host of  ‘things’, extra pressure/stress/work  etc that this brings with it.   Partly due to our ‘category’ I have also felt the need to be even more careful about what I share about ‘general’ school things.

But now two things have changed which means I feel I have more I can blog about, and more importantly more that may be interesting to read ;)

  • I’m now ‘officially’ ICT coordinator- this brings a whole host of challenges, given the current ‘state’ of ICT in our school.  Lots of exciting things are already happening including the trial of eye-pads and the recruitment of digital leaders.  I am also starting the process of reviewing and re-writing our ICT curriculum and mapping the coverage from reception-Y6.
  • I’m about to start my whole school project for the MaST (Mathematics Specialist Teacher) program.   I have a focus on calculation  methods and representations  (well the official working title is Developing conceptual understanding of number through representations- with a focus on written calculation methods.) 
So hopefully I’ll have lots more to blog about- with a focus on ICT and maths of course :)
Tim
PS- Whilst this blog has been a bit neglected, my class website/blog certainly hasn’t ;)
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