The end is nigh: notes on the History of Maths

For most teachers this date is the end of term but could it be the end of the world as well?

If you search this date on the internet you’ll get nearly 2 billion results. There is even a web-site specifically dedicated to this date and the doom laden prophecies associated with it.

The main source for all this is the ancient Mayan calendar. The Mayan civilisation was dominant in Central America from about 200 BC to 1540 AD. They used 3 different calendars. There was a religious one, the Tzolk’in, based on a year of 260 days (20 lots of 13 days) and a secular one, the Haad, based on 365 days. This was made of 18 months, called ‘uinals’, of 20 days. To this was added 5 days called ‘the period with no name’ symbolised by chaos. You were thought to be cursed for life if you were born during these 5 days. The religious and secular calendars synchronised once every 52 years, about the length of a lifetime. This is an interesting exercise in calculating the Lowest Common Multiple of 260 and 365 (=18980 days or 52 secular years).

Image copyright of Roy Niswanger

The Maya were phenomenal at astronomical calculations even without the means to measure parts of the day. Their solar year works out to be equivalent to 365.242 days compared to our current value of 365.242198. It is more accurate than the Gregorian calendar we use (365.245 days). The Gregorian calendar, introduced by Pope Gregory XIII in 1572, attempted to allow for the solar year being just under 365 ¼ days long (as used in the Julian calendar from 45BC which brought in the leap year). The Gregorian calendar leapt forward 10 days and said leap days would not happen every century, unless the year was divisible by 400 (so 2000 was a leap year but not 1900). It took a while for some to adopt the Gregorian calendar, especially non-Catholic countries. It didn’t happen in Britain until 1752 when there were riots as people demanded to have their stolen days back.

Mayan name	B’ak’tun	K’atun	Tun	Winal	K’in
Days	144,000	7,200	360	20	1
Approximate solar years	394	20	1
Note that the system isn’t uniformly base 20 with a tun being 18 x 20 not 202

The Maya had another calendar, used for long periods. It was based on a year of 360 days, a tun. A k’atun was 20 tun and a b’ak’tun was 20 k’atuns or about 394 years. On 21^st December, we will simply move onto the next b’ak’tun.

The date 21^st December 2012, in the Mayan long calendar, will be 13.0.0.0.0.  Suggestions that there will be a cataclysm are generally denied by modern scholars of Mayan history, so you’ll need to prepare the lessons for next term!

Don Hoyle

Animate your lessons!

Too often, the first unwelcome obstacle a teacher has to overcome when entering the classroom is the inertia of disaffected students, students who arrive expecting to be bored and, as is generally the case with self-fulfilling prophecies, who get exactly what they expect (and, some might say, deserve!).   This is not to say that your lesson is in any way uninteresting.  In all probability, you will have given it considerable thought, possibly having worried about it all weekend, but, let’s face it, if your students arrive with such a profoundly negative attitude, then you really are up against it!

So what can be done?

One solution is to open with an exciting starter activity which raises the emotional level of the class and thus, hopefully, ignites a spark of enthusiasm which will propel them through the rest of the period.

Animation is one way of creating that spark ... as, I hope, the accompanying four minute animated film, ‘Fire!’, will illustrate. The objective of this film is to introduce an intensive session about what students should look for when faced with the challenging task of responding to a GCSE English examination question which requires them to analyse a writer’s use of language in order to create effects.

Download class activity plan here

Download 'Fire' lyrics here

If you have a quick look at this animation, and then compare it against the high-tech, high budget productions of internationally renowned film companies, you will immediately realise that it is certainly not Pixar-perfect!  However, I have tried and tested it in class and, despite the fact that I have only been competing with Pixar, Disney and DreamWorks for the past eight months, never having made a film of any description prior to March 2012, it certainly grabs the attention of my students – not least because they are often excited (one might even say animated) by the fact that I made it.  And this leads to such questions as:  ‘How did you do it?’, ‘Did you write the song?’ and ‘Is that you singing?’  Well, it certainly isn’t me singing but, at this point in the proceedings, it doesn’t much matter because we are all sufficiently enthused to progress with the rest of the lesson.

So just in case you are interested in spending some of your spare time pushing the boundaries of both your teaching and your creativity, just how do you do it?

Well, your first task is to download a free trial version of a suitably powerful and affordable animation programme.  You could make a web search in order to see what is available.  The one I use is a 3D programme called iClone Pro 5 and the 30 day trial version is available from:

http://www.reallusion.com/iclone/iclone_trial.aspx

Once you open the programme, it will offer you the option of surfing through some of the online tutorials (on the Training Resource tab) which contain relatively simple projects designed to familiarise you with the iClone workspace.  This is well worth doing – otherwise, you will be faced with the daunting task of somehow bringing life out of a most visually unappealing putty-grey screen. Below is the link to the tutorials bank should you wish to peruse it:

 http://www.reallusion.com/reallusiontv/ic/tutorial.asp

Of course, if you are animating, you will also need to experiment with sound.  The soundtrack to ‘Fire’ was initially recorded on a Yamaha PSR 8000 synthesiser but the vocal was remixed on a totally free recording programme called Audacity:

http://audacity.sourceforge.net/

Audacity includes many first class editing tools and special effects and, most importantly, enables multi-track recording – so you don’t have to get your performance right in one take, which can be very frustrating when trying to record a five minute script which, through nerves, you keep botching in the final paragraph!  Once successfully recorded, there is the facility to export your masterpiece as an mp3 file which can then be imported into iClone.

Another very useful iClone product, again available on a trial basis, is 3D Exchange:

http://www.reallusion.com/iclone/3dx/3dx_trial.aspx

This programme allows you to make use of the thousands of free 3D models created and uploaded by animation enthusiasts.  These are available from the Google 3D warehouse:

http://sketchup.google.com/3dwarehouse

iClone 3D Exchange will enable you to select from this massive range of content and then convert your chosen 3D models into iClone files which can then be imported into your animations.  In my film, ‘Fire!’, the shimmering silver moon and the sleek and stylish Dodge Viper GTS are courtesy of the creative talents of such generous enthusiasts. The alternative, of course, is to make all your own models – but that could prove to be very time-consuming … and could we well be regarded as over-stretching the boundaries of dedication!

A further useful piece of software to consider is a text to speech (TTS) programme such as Natural Reader or Neo Speech.  If, like me, your voice is so uninspiring to listen to that you certainly wouldn’t want to subject your students to it more than once, this could be the perfect solution for you.  Such programmes allow you to convert text into one of a number of very convincing speaking voices with accents which can range from US to UK and German to Arabic.  So, for example, let’s say that you teach history and you want to bring Karl Marx to life.  iClone would enable you to create a Karl Marx look-alike avatar and your TTS software would allow you to paste in quotes from the great man himself which, for argument’s sake, you might have copied from the Internet.  Your TTS software could then articulate these in a genuine, if rather heavy, German accent – so subtitles might be advisable!  As with Audacity, your TTS software should then allow you to convert your sound file to mp3 which you can then import into iClone and thus allocate to your Karl Marx avatar:

‘History repeats itself, first as tragedy, second as farce’ … and thirdly, of course, as animation!

Natural Reader can be found at:

http://www.naturalreaders.com/index.htm

And Neo Speech can be found at:

https://ondemand.neospeech.com/

Again, as with iClone, you can try before you buy.

Finally, you will need a video editing programme such as Windows Live Movie Maker (but, if your computer is reasonably new, do have a quick check that it has not already been bundled in with your operating system – it was with mine):

http://windows.microsoft.com/is-IS/windows-live/movie-maker-get-started

You will have to save each change of camera or each change of scene in iClone as a separate file and then render (export) each file, preferably as an AVI file with MJPEG compression.  Windows Live Movie Maker will then enable you to stack each of these exported scenes in the order that you would like them to appear in the finished film.  It will also enable you to meld them together via such neat transitions as ‘Fade in’, ‘Cross fade’ and ‘Flip’.

If you feel daunted by the prospect of familiarising yourself with so many new programmes, then you might initially begin by experimenting with only one; just download the trial version of iClone Pro 5 for now and see how you get on.  However, if you’re really pressed for time and even this seems a step too far, then why not simply take advantage of the thousands of animations (and other short films) that the ever-growing army of enthusiastic amateur (and professional) film directors regularly upload to Youtube.  Type your chosen topic into the search box and you might well be very pleasantly surprised by what is out there.

But if you are really are up for the challenge, animation is fun … and seriously addictive.  Furthermore, you can upload and publish your own creative output - on Youtube, of course.  So, if you are looking for a wildly creative new hobby that could open up all sorts of doors – real as well as virtual - then this might be the perfect holiday project for you!

Peter Morrisson

Class activities for child nutrition

November 5^th to 9^th was National School Meals Week. This year, it coincided with the publication of a survey by the Local Authority Caterers Association, which examined parental views about nutritional standards in free schools and academies. The survey revealed that 57% of parents did not know if their child’s school was meeting the nutritional standards set by the government. The majority of parents also said they would welcome the introduction of an independent body to monitor schools to ensure that standards are being met.

Knowledge of nutrition is an extremely important aspect of working with young children and forms a significant part of both the Level 2 Certificate and Level 3 Diploma for the Children and Young People’s Workforce, particularly:

L2:       Unit MU 2.8 Contribute to the Support of the Positive Environments for Children and Young People

L3:       Unit EYMP 3 Promote Children’s Welfare and Wellbeing in the Early Years        

Food and Mealtimes in the Early Years also forms a whole unit (Unit 14) of the new Edexcel BTEC Level 3 National Diploma in Children’s Play, Learning and Development (supported by the forthcoming Collins student textbook). This unit also emphasises the importance of working with parents in helping children to develop healthy eating habits and attitudes towards food.

Many of your learners will have studied food and nutrition on a variety of other courses and may already be familiar with the main principles of a balanced diet, the nutritional content of different foods and the role of different nutrients in the body. It can therefore be challenging to keep the topic fresh as well as specifically relevant to the early years. The School Food Trust (http://www.schoolfoodtrust.org.uk) provides a wide variety of learning resources in addition to many of the current policies about food and nutrition in the early years, which I have found very useful.

The School Food Trust Guide “Eat Better, Start Better” (2012) provides a range of information about healthy eating for young children, including food choices and portion sizes. The Food Groups table (Download here) can provide a useful starting point for your learners to refresh their knowledge about the main food groups and nutrients. Working in pairs or small groups, learners could begin by completing the blanks in the table. This could be followed by the case study (Download here), where learners could analyse the food intake of a typical five year old and make suggestions for improvement. You could even ask your learners to keep a personal food diary and analyse their own food intake over a few days. I have often found this leads to a few surprises, with learners looking at ways to improve their own diet!

Another important focus for food and nutrition in the early years involves an awareness of individual dietary requirements, including cultural or religious restrictions and food allergies and intolerances, which are common in young children. The School Food Trust provides a comprehensive chart (Download here), which summarises some of the main religious dietary restrictions. Learners could use the chart as a reference tool to complete the associated task in planning meals and snacks for different children.

For more independent study, your learners could investigate different food allergies and intolerances at:

http://www.nhs.uk/conditions/food-allergy/Pages/Intro1.aspx

The same website also has a section on healthy eating recipes, which I have used with learners to research and create a fun recipe book for children.

http://www.nhs.uk/Livewell/5ADAY/Pages/Recipes.aspx

With increasing concerns about childhood obesity, it is perhaps more important than ever for learners to be fully aware of their responsibilities in helping children to develop healthy eating patterns in the early years.

Janet Stearns, Lecturer in Early Childhood Studies, former Lead Examiner for CACHE

Codes and Communications - Primary Maths

You’d normally associate English with communication but maths has an almost equally important role to play. This series of activities introduce children to codes and communication.

Activity One – Sequences and codes

LO:  To be able to recognise simple number patterns and sequences
        To be able to identify the next term in a sequence and state the progression

The simplest sequence is counting on in ones which we do from an early age but what is tricky in those tender years is to recognise the relevance of the name of the number to what it actually signifies. It’s learning a new language where a group of five objects is named by the word ‘five’. Sequences gradually get more difficult, from counting in 2s, 3s and so on to ones where it’s squares of numbers or cubes or where the next term is algebraically calculated.

The easiest way to identify the progression of a sequence is to calculate the difference between the terms.
Show the children this example:

0, 1, 3, 6, 10, 15 and ask them to tell you the progression

They should identify that it goes up by 1 then 2 then 3 etc.

This is a sequence of triangle numbers but they don’t need to know that to be able to work out that the next two terms will be 21 and 28.

Try these with them, asking them to identify the progression then the next two terms.
a) 1, 3 ,7, 13, 21, 31
b) 2, 4, 7, 9, 12, 14, 17, 19
c) 0,1, 1, 2, 3, 5, 8, 13, 21,  (a tricky one)

Codes are an interesting use of number, especially if you match the alphabet with the numbers 1 to 26. This is a simple code but allows the children to begin to understand the principle. Use it to get them to write their names in code and use the cipher to work out whose name is which.

Talking Point: The idea of a code is that it’s a secret between people who want to share messages without others knowing. The simple code we've just looked at makes it easy for others to intercept messages. How could we make it more difficult?

The children should suggest changing the numbers that go with the letters either randomly, in which case the recipient would need the cipher or progressively by making A be 4 and B be 5 for example.
Ask the children to change the original code progressively and see now if anyone can decode the names.

At Home:  Devise your own code and write a message using it for the teacher to decipher!


Activity Two – Base Numbers

LO: Understand that although our number system is effectively metric, you don’t have to count in hundreds, tens and units
      Understand how base 2 numbers (binary) can be used to express numbers

Base numbers dropped out of the primary curriculum a long time ago but may be making a comeback!

Whilst many are of little use except in codes, binary code; using 1 and 0 to represent numbers, is used in computing across the globe and is fun to work with.

Write these numbers on the board:
1 = 1
10 = 2
11 = 3
100 = 4
101 = 5
110 = 6
111= 7

Talking point: Ask the children if they can work out how the numbers match. If they struggle place the numbers in places with the place value headings as question marks. This will help them to consider what value each digit might be.

Once they have realised that the place value headings are 4s, 2s and 1s, ask them to rewrite a selection of base 10 numbers up to a hundred, predicting what the extending place value headings might be.

They should notice that whereas in base 10 the numbers in each place holder can only go up to 9 before beginning again and adding a digit to the next column, in binary (base 2) it can only go up to 1.

Extension or At Home: Numbers can operate from any base so ask them to write out the numbers 1 – 10 using base 3. You should get the response:
1, 2, 10, 11, 12, 20, 21, 22, 100, 101


Activity Three – Morse Code 

LO: Understand how binary numbers can be expressed by a series of on/off commands or short or long pulses
       Understand how Morse code uses a binary system to convey messages

Morse code was one of the best inventions in the field of communications – a quick and simple way to communicate using dots and dashes. You’ll notice that Morse code is almost a binary system with dots and dashes representing the 1s and 0s. A dot was a quick pulse on a transmitter whilst the dash was a longer one.

A great activity for the children to do which involves translating Morse code into binary and then base ten numbers giving an excellent code that they can use between themselves.
The Morse code alphabet is as follows:

Taking the letter A for example, if a dot is a 0 and a dash a 1 then A would be 1 in binary and base 10, B – dash, followed by three dots would become 1000 in base 2 and 8 in base ten. C would be 1010 in binary and so 10 in base 10, D would be 100 and so a 4, and so on.

The code for ‘dad’ would be 4, 1, 4 and for ‘cab’ would be 10, 1, 8

Ask the children to continue working out the letters of the alphabet. There are one or two which duplicate so can they suggest a way around it?

At Home: Ask the children to use their code to write a message to a friend.

Dave Lewis - Primary Teacher

Take a look at: Collins Big Cat: Code Making, Code Breaking

Secondary English - Escaping the Ego-sphere

It may sound like something out of Dr Who but, if anything, the Ego-sphere is the polar opposite of the Tardis.  It might look pretty big from the outside but it’s an extremely limited dimension when you are stuck inside it.  So what are we talking about here?  Well, it’s an alternative reality, a sort of hyper-space in which the only thing that shifts faster than the speed of light is the individual’s attention span.  

Unfortunately, it is inhabited by many (though certainly not all!) of our teenagers  and can result in them becoming so disengaged from reality that they often fail to make the grade, both educationally and socially.

Considering the cocoon of self- indulgence that a significant number of children are brought up in by our society – heavily protected rights, scarcely enforced responsibilities – this is hardly surprising.  Nor is it surprising that a European table of children’s well-being published in 2009 ranked the UK 24^th out of a total of 29 countries.

The factors highlighted as responsible for this lamentable situation were mainly socio-economic.  However, as any sane psychiatrist could tell you, extreme ego-centricity, especially when combined with a reluctance to engage in any productive activity, is a guaranteed recipe for personal unhappiness.  If you give no real meaning to your life, then it stands to reason that your life will have no real meaning.

So, can our children be rescued from the Ego-Sphere and helped to get safely back down to planet Earth?

Well, at one time, the solution to the twin evils of egotism and indolence was religion … which is perhaps why students from more traditionalist countries tend to be more educationally dynamic and socially productive than many of our own youth.  But in an increasingly materialistic society, in which the national concern is not spiritual advancement but the pursuit of so-called ‘material well-being’, the remedy may lie in how we approach the teaching of such humanities subjects as English.

Of course, this is not a new idea, but it is well-worth a revisit.  As Matthew Arnold declared well over a century ago:

“Good poetry does undoubtedly tend to form the soul and character; it tends to beget a love of beauty and truth in alliance together; it suggests, however indirectly, high and noble principles of action, and it inspires the emotion so helpful in making principles operative.”

So, next time we are studying a text prescribed by some examination board, and preparing for some lofty assessment task that requires a dry academic analysis via Point, Evidence and Explanation, let’s also try to remember that great literature affords a profound insight into human nature – both that of ourselves and of our fellow human beings.  It may sound dreadfully old-fashioned, but it teaches the difference between right and wrong by frequently portraying tragic life outcomes based on the poor decisions made by self and others, outcomes which we would often do well to consider on a deeply personal level.

Perhaps, in between the hustle and bustle of exam preparation, we could find some time to encourage our students to really think themselves into a character’s situation and consider:

• What is the nature of my dilemma?
• How did I get here?
• Is it my fault I got into this mess?
• Can I get out of it without causing indefensible injury to somebody else?
• What harms have I caused?
• What kindnesses have I done?
• What do people think of me?
• Are their views justified?
• And, most importantly, has my life been of value?

Basically, it’s called empathy – the practice of regularly trying to view the world from another person’s perspective. And some sage advice to all of those imprisoned in their own oppressively limiting, very personal little Ego-spheres – and not all of them, by any means, teenagers  …  I’m no saint myself!  – why not give it a try?

Peter Morrisson

Chocolate, school inspections and irreversible changes

To Manchester for a conference on “Can all schools be good?”  It’s an intriguing title for a conference as well as being a topical question.  Think about it: one of the outcomes for a school inspection is ‘good’.  This is an absolute term, supported by criteria.  Logically all schools could be good (or none of them).  However ‘outstanding’ is relative, though it is also supported by criteria.  Having all schools being outstanding doesn’t make sense (unless they were outstanding in different ways).

Chair of the conference was Professor Mick Waters, from Wolverhampton University.  Mick is one of the good guys in education, having a strong background in teaching, school leadership, local authority work and then at QCA.  He’s perceptive, rooted in rock solid principles about what constitutes effective learning and is very witty.  It’s a winning combination.

One of his suggestions was that the outcomes of inspections should simply be either ‘good’ or ‘not good.’  He’d recently put his car in for its MoT test and had been told that it had passed.  “What, no outstanding features?” he’d responded.  It’s a good point; if schools are letting kids down that’s not right.  However, a multiple category system implies a normal distribution curve of outcomes for various schools.  This limits outstanding outcomes for fear of debasing the term.  Inspection outcomes being good or not doesn’t stop schools seeking to excel but means they would do so in other ways.

One of his other concerns about inspections though is that it may distort what teachers seek to do with pupils and, more specifically, may lead them to focus upon ‘generating evidence’ rather than on genuine learning.  Mick told the story of observing a lesson in which pupils were looking at the idea of reversible and irreversible changes.  One of the examples they considered was that of melting chocolate.

He asked the pupils sat near him whether it was reversible or irreversible and they decided it was reversible.  Upon probing they suggested that this was so because if it got hot it melted and became a liquid but if it was cooled down it went back to being a solid.  But what would it taste like, he asked, the same?  Oh.  Don’t know.  Well, what about setting jelly? Irreversible.  Why? Because if you make jelly and it sets you can’t get back to the solid lumps in the packet.  Well – you put it in the fridge to help it set; what would happen if you heated it? Not sure.

At this stage the lesson could go either way.  One would hope that some practical work would follow with pupils exploring questions and finding out about the different ways that materials behave.  There’s a risk however that their earlier responses are simple captured as “evidence of making predictions” and that no such deep learning subsequently takes place.

Now, I’m not naïve about this.  Schools need good inspection outcomes and they need evidence to secure them.  However, inspections, like exams, can’t measure everything.  Sometimes in science authentic learning involves activities that are less neat and sometimes messy.  We have to be true to our principles about what we know to be good practice and go to that place.

Ed Walsh

Childcare - Activity plans for Health and Safety

The whole early years sector has recently been shaken by the tragic deaths of two young children.  A three year old died in September after becoming entangled in a rope on a slide at York College Nursery and a nine month old baby choked to death at a nursery in Greater Manchester on October 23^rd. Heartbreaking accidents like this serve as stark reminders about the importance of health and safety when working with young children and perhaps provide a good opportunity to review some of the key principles with your learners.

Teaching health and safety can often be challenging. Learners need to know about health and safety legislation and how it applies to the early years workplace, but it can be a very uninspiring topic to undertake in the classroom. It is vitally important to help learners make practical links with their different placement experiences and support them in the process of understanding their own responsibilities.

Health and safety forms a very important component of both the Level 2 Certificate and Level 3 Diploma for the Children and Young People’s Workforce, particularly:

L2:       Unit MU 2.4 Contribute to Children and Young People’s Health and Safety

Unit TDA 2.2 Safeguarding the Welfare of Children and Young People

Unit PEFAP 001 Paediatric Emergency First Aid

L3:       Unit CYP 3.4 Support Children and Young People’s Health and Safety

Unit SHC 34 Principles for Implementing Duty of Care in Health, Social Care or Children’s and Young People’s Settings

Unit CYP 3.3 Understand how to Safeguard the Wellbeing of Children and Young People

These units cover a wide range of topics around health and safety, including legislation, safe working practices and dealing with emergencies. The assessment tasks include both knowledge-based and competence-based evidence and this can be supported with class activities, which encourage learners to make relevant links with their placement experience.

For example, the activity “Assessing Hazards” (attached) will encourage learners to investigate the health and safety procedures in their placements and talk to early years staff about the practical implementation. Learners can then share the information with each other in class and discuss key aspects of best practice. This could be followed up by the activity “Design a Webpage” (attached) which the learners could undertake in groups, sharing their ideas and experiences.

The two case studies (attached) offer the opportunity for learners to apply their knowledge in different practical situations and to discuss and reflect on the implications of keeping children safe in early years settings.

The new BTEC National Qualification in Children’s Play, Learning and Development (supported by the forthcoming Collins student textbook) includes a unit on health and safety practice in early years settings, with an emphasis on policies, procedures and risk assessment. To achieve a Distinction grade in this qualification, learners must show that they can:

Assess the ways in which legislation and procedures in early years settings contribute to children's health and wellbeing.

Evaluate the extent to which risk assessment contributes to effective early years practice in a selected early years setting.

Evaluate the extent to which policies and procedures for response to emergencies in early years settings contribute to children’s health and safety.

In the aftermath of these recent tragic deaths, it seems timely to review how critically important it is for learners to fully understand the significance of these criteria.

Activity worksheet 1

Activity worksheet 2

Case study 1

Case study 2

Janet Stearns, Lecturer in Early Childhood Studies, former Lead Examiner for CACHE

Scattering the Plenary

One of the great aspects about the teaching profession is that no two days appear to be the same and that there are always opportunities to try things out even after many years and thousands of lessons.

There is much to celebrate in the success of the three part lesson which is now firmly established across the country.   Ideas for zappy starter activities can be found in a myriad of resources and the Collins Freedom to Teach resources are great for giving teachers lots of ideas to captivate the interest of students the moment they arrive in a classroom setting.  Having mini-whiteboards and post-it notes ready for solutions to be presented at the front of the class always seems to be a winning idea.  Asking students to subdivide the whiteboard into four sections with a whiteboard pen is great to ask four distinct questions before the work is wiped. For example, top left write down the cube root of 343, top right work out a third plus a quarter, bottom left what is 15 squared, bottom right calculate the square root of a million.  Now check with a student sitting next to see and where there is a different answer, convince your neighbour that you are correct.

I have recently looked more closely at the whole strategy of a lesson plenary in the context that even if a topic has been taught clearly there are sometimes issues with the big challenges of recognition and recall which are, in part, addressed by revisiting key topics in a well-defined scheme of learning.  Within the new OFSTED framework, a lesson moving towards ‘outstanding’ requires considerable pace, challenge and innovation among other aspects and a sequence of six or seven episodes that fit well together to enable considerable learning progress to be made.  There is an increasing awareness of the need for a sense of ‘Awe and Wonder’ of mathematics and the role it plays in the world around us;  therefore an additional  ingredient is a need to contextualise the mathematics and give it a sense of purpose and elegance.  Students are often intrigued for example when I mention that the Fibonacci Sequence can be found in the DNA of a spiders' web or the pattern of a nautilus shell.

Following the start of a new academic year and the arrival of a new Principal at Frome Community College, I decided to give a special focus to incorporating student-led mini-plenaries into a lesson to enhance what has been accomplished  so far in the lesson and give a sense of shared ownership of the education journey.  This has worked especially well when a no-hands up strategy has been deployed.  With the assistance of data-rich recording systems including FFTD and test scores, differentiation can be successfully achieved by targeting specific questions for named students.  A few times during the lessons, students have been asked to list two or three key points or ‘Key Learning Moments’ so far either to the person sitting next to them or to the overall class. During my lesson observation by OFSTED I asked year 9 students to have a brief learning conversation with the teaching assistant and let him know what has been learned – with the other students listening carefully.  I have sought to bring as much variety to the student led mini-plenaries as possible;  sometimes, a volunteer has come to the whiteboard to list a key point – sometimes I have asked students to have a ‘news update’ in pairs then requested one pair to talk to another two students.   Sometimes I have asked for one key point from the last ten minutes - or one point from the last ten minutes that might not be completely understood.

Having a focus on multi-plenaries this term has been especially illuminating;  something I thought was very clear has been not so clear – sometimes the interpretation of the past twelve to fifteen minutes has generated higher level questioning techniques or has moved the focus onto something unexpected.   One aspect of this past half-term has been striking;  student led mini-plenaries are an integral part of many successful lessons and highlight the fascinating aspect that they serve to address the challenges of recognition and recall that may exist even when a topic has been clearly taught.    Students taking ownership of the refocus on lesson objectives and the learning journey can help them look back and look forwards with increasing confidence and self-steem.

Christopher Curtis