10 Ways to Use and Apply in Maths

I’ve never wrote a ‘Maths’ blog before so this is my first attempt. I’ve spent much of my career in Y6 and one aspect I’ve worked particularly hard at is developing ‘Using and Applying’ (U&A) in maths. There are lots of definitions as to what U&A actually is however; I’m not going to get bogged down in this debate. In my opinion it’s less to do with word problems and more to do with reversing the transactional norm of a maths question. To clarify what I mean here is an ‘shape’ example:

Shape:

The staple diet of this area of maths is to label a shape with its properties. Nothing wrong with this except it can be a bit ‘dry’ and for the most confident learners presents little challenge. To reverse the process try this; give pupils a list of properties, ask them to choose 5, then to draw a shape to meet the criteria they have set. Immediately pupils have to be creative, they have to USE their knowledge and because the teacher has not given a specific shape, learners have a lot of choice.

10 ways to Use and Apply across the maths spectrum:

  1. Area and Perimeter: Give pupils the answer first and then ask them to draw the shape. For example, draw an ‘L’ shape with a perimeter of 50cm. The same approach can be used for area; draw an ‘L’ shape with an area of 25cm². To extend this further create statements to investigate; for example, Rectangles with a perimeter of 20cm always have the same area.
  1. Measures: Reading scales can be notoriously laborious and often too easy for the best mathematicians. Try this though. Give the pupils a ‘menu;’ create a table with three columns, the first column is the ‘start number,’ the second is the ‘end number’ and the third column is the ‘number of intervals.’ In each column place 5-10 numbers. The pupils now have a menu to create their own scale.
  1. Shape: When the class are learning about different types of shapes or categorising triangles or quadrilaterals the concept is often picked up rapidly. To move the learning on create simple statements for the pupils; the pupils then investigate whether they are true or false (or sometimes a bit of both!) and provide evidence to support their view. For example:
  • An isosceles triangle could have a right angle.
  • A square can only be split in half along a line of symmetry.
  • Two rectangles can never make a square.
  • Two squares always make a rectangle.
  • A rhombus is half of a parallelogram.
  1. Line graphs. This is a simple one to set up; discuss with the pupils how line graphs often tell a story. Give the pupils a range of ‘blank’ line graphs; only draw the X and Y axes and the line. Do not label anything or put values on the axes. Pupils can either tell the story or create a title. This is a great activity done collaboratively. Over years I’ve heard some amazing stories!

  1. Rounding numbers; in my experience this is the archetypal ‘they’ve either got-it or they haven’t’ type lesson and when they’ve ‘got-it’ it doesn’t matter how many decimals places your throw at them it doesn’t get their brains thinking. Instead give the answer and pupils predict what the question could have been; for example. 6.7 has been rounded to the nearest tenth, what could the original number have been?

  1. Multiplication. If pupils learn the ‘grid’ method in your school, you’ll know that some get through the calculations as quite-a-pace. By giving the answer first the thinking begins. For example, A TU x TU calculation gives an answer of 475. What could the numbers have been and what would the completed ‘grid’ look like?
  1. Co-ordinates. This is an effective plenary idea if the pupils have been learning to plot co-ordinates in all four quadrants. Imagine the classroom is a grid and label each corner/area with the numbers 1-4. Give the class a co-ordinate and the pupils move to which quadrant they think the co-ordinate lives!
  1. Time: Calculating differences in time can be quite tricky for most. However, for some pupils it comes quite easily. Instead of asking pupils to find the difference between the start and finish times, give the pupils the answer and either the start or the finish time. For example, the time difference is 3hrs 56mins, the finish time is 06:34 – what is the start time?
  1. Odd one out: This can be used across maths. For this example I’ll use fractions. Write 5 fractions on the board; assign a fraction to each table/group in the class. The challenge of the table is to prove why their fraction is the odd one out. Always ask for evidence to support their argument.
  1. Plan the plenary. Again this can be used for any type or maths. This is a great idea to challenge those pupils who finish in double quick time. Their challenge is to plan a simple game/activity to finish the lesson that MUST help everyone reinforce their learning. The pupils must lead the game/activity. This idea takes some time to embed, but once it does the results are incredible.

If you have any other ideas, let us know – or even better, write them in the comments box below so they can be shared!

The Thought Weavers.

Advertisements

Effective Feedback – PAIR marking

Effective written feedback – PAIR marking

 

I don’t remember much of the marking from my school days; but one ‘grade’ does stick in my head – I once got a D+ for a piece of work in geography. I was gutted, I worked hard in geography and Mr Machin, my teacher, seemed pretty decent or “sound” as I might have said then.

So why does this piece of marking stick so vividly in my head? Well, for one reason it damaged my fragile teenage ego (But really that’s just tough!) but the other reason is simple; there was no explanation for it – I didn’t know why the grade was so low and I didn’t know how to improve it. It was poor marking!

 

I’ve read a few blogs about marking and the first point I note is that marking really should be called feedback. The purpose of marking is to give feedback to learners to help them assess their progress and make improvements.

 Prof. John Hattie highlights the importance of feedback in his book ‘Visible Learning’ and the Sutton Trust ‘Teacher Toolkit’ corroborates this evidence. The key to feedback though is to get it right. Poor feedback doesn’t help learners and wastes the time of the teacher who writes it.

 

So what does ‘effective’ feedback (in the guise of marking) look like?

I’ve introduce PAIR marking at my school. PAIR is an acronym, not to be put into books, but as a guide to structure effective feedback.

 

The P stands for:

PRAISE – this is the most ineffective aspect of marking I see. ‘Good work,’ Well done,’ and ‘Brilliant’ are vague terms that offer no useful feedback to learners. There are some who argue that effective feedback has no room for praise, and to a point, I’m sympathetic to that view. However, praise can be highly effective when it acknowledges personal attributes. To justify this I would point to the work of Carol Dweck who explains that praising for effort and tenacity develops a growth mindset; a belief that you can get ‘brighter.’ Praising the thinking behind the learning can also acknowledge the mental effort afforded to the task.

 

The A stands for:

ASSESS assessment of the learning (not the task) is critical if the learner is to use the marking to gauge their progress. It is essential that the feedback is accurate and explains reasons behind it; for example – This is effective writing BECAUSE… is better than scribbling  ‘Great writing.’

 

The I stands for:

IMPROVE – This aspect of PAIR marking presents the student with an opportunity to improve their learning. The teacher offers guidance about improvement so that the student can reach the next step. Phrases such as ‘your next step is,’ and ‘to improve…,’ provide useful starters. I often pose questions to pupils, encouraging them to think about their learning and how they might improve it. Questions are particularly powerful for learners who find it difficult to reflect on their learning by themselves. Short ‘improvement’ tasks to address weaknesses/misconceptions can also be set to be completed at the start of the next lesson. Improvement can be explicit (e.g. ‘to improve…’) or implicit, where a question is posed to promote further thought.

 

The R stands for:

RESPOND – This is a great strategy to make feedback ‘Stick!’ The chance for the pupils to have their say! Pupils can respond in a number of ways; a signature to acknowledge they’ve read feedback; answer a question posed by the teacher; complete the short ‘improvement’ task; agree or disagree or maybe just a personal response. When pupils respond to marking this creates a learning ‘dialogue’ between the teacher and the learner; highly effective AfL!

 

What does pair marking look like?

Here is an excellent example of PAIR marking I saw in an English book the other day:

 

         Great resilience today. As a reader I was ‘hooked in’ because you varied the sentence starters. To improve vary the length of sentences.

‘How can I ‘PAIR’ mark every piece of work?’ 

A very sensible question and that’s never the expectation. I would recommend that 1/3 pieces of work should have every aspect of PAIR marking and for the others pieces use ‘PAR.’

My final piece of advice about marking is to keep it short, precise and meaningful as in the example above.

 

The Thought Weavers

 

The Mini-Plenary – Friend or Foe?

It wasn’t until a couple of years into my teaching career that I’d heard of a ‘mini-plenary.’ According to the local authority my lessons should have one. When I asked what that might ‘look like’ in the classroom I was given a garbled response about checking progress half way through the lesson.

“But what if I know that the children are doing just fine – why would I want to stop them?” I asked. The reply was short and sweet and straight to the point; “Because Ofsted want them!”

The ‘mini-plenary’ is very en-vogue at the moment, it’s a bit of an educational buzz-word (phrase) and I can’t remember the last time I made a lesson observation and didn’t see one (Or at least an attempt at one)

The problem with ‘Buzz-words’ in education is that they become so familiar to practitioners that they lose their meaning. They become the Boweneque “super, smashing, great,” feature of the educational world; said so many times the meaning is lost.

Getting back to ‘Mini-Plenaries’ then; they can be very useful. It is however, important to remember the purpose of a ‘Mini-Plenary’ is to:

 

  1.   Enhance the assessment of the teacher; ensuring the learning is meeting the needs of the learners
  2. Give the learners the opportunity to ask “How am I getting on?”
  3. Challenge the thinking of the learners.
  4.  Assist learners in target setting.
  5. Address whole class patterns of misunderstanding 

 

Too often Mini-Plenaries are for show; little thought is given to their timings, they become a show and tell session with little evaluative significance and are not intellectually demanding. Even worse, they become a trick to ‘show progress’ to an inspector every ten minutes; if we believe that pupils make progress this often and at this rate then we’re either exceptionally gifted educators or deluded.

Assessment for learning during the lesson should be ongoing; it doesn’t necessarily need a whole ‘slot’ with a ‘wizzy’ name to be useful. Assessment takes place at every stage in the lesson, whether it is with one pupil, a group or the whole class.

 

Effective Mini-Plenaries

The best Mini-Plenaries (for want of a better phrase) are intellectually demanding;  ask challenging questions of the pupils and ensure that when the learners get back to their task, they apply their new skills and understanding with greater authority and confidence.

 

 Ideas for the classroom:

  1. ‘Plenary’ questions display – great prompts for the teacher. The students will know they will be expected to respond to them as some point in the lesson – raising expectations.
  2.  Pupil led Mini-plenary – put the ‘Plenary’ questions on to key rings/cards with a ‘group’ leader who will then guide the discussion on each table.
  3. Review the success criteria – Are the prompts effective? How could we make them better?
  4. Peer assessment – students to pick one aspect of the success criteria for their partners/peers to work on.
  5. True or false statements related to the learning. Ask the pupils to move to a specified area of the classroom based on their response. Demand reasoning here!!

Mini-Plenaries are not a foe; the phrase is just over used (We suspect due to Ofsted ‘game’ playing) All of the above ideas should be part of learners’ experience in class, they don’t need a label; reflection is part of the learning process. Ultimately ‘Mini-Plenaries’ are for the benefit of the pupils, not just another box to tick on an observation form.

 

The Thought-Weavers

Preparing for Ofsted 2013

Last year I gave a presentation at the education show entitled ‘Preparing for Ofsted.’ I sifted through lots of Ofsted reports, founds patterns of ‘behaviours’ and looked for things inspectors seemed to be consistently asking for. I then created a slide show based on my findings.

In February 2013, Ofsted visited my school. As a result I’ve recently updated the slide show and below is the new updated version. I hope it will help you when your visit is due.

<div style=”margin-bottom:5px”> <strong> <a href=”http://www.slideshare.net/paceanderson/preparing-for-ofsted-2013-v2&#8243; title=”Preparing for ofsted! 2013 v2″ target=”_blank”>Preparing for ofsted! 2013 v2</a> </strong> from <strong><a href=”http://www.slideshare.net/paceanderson&#8221; target=”_blank”>paceanderson</a></strong> </div>

The Though_Weavers

Preparing for Ofsted!

Last year I gave a presentation at the education show entitled ‘Preparing for Ofsted.’ I sifted through lots of Ofsted reports, founds patterns of ‘behaviours’ and looked for things inspectors seemed to be consistently asking for and produced a slide show based on my findings.

In February 2013, Ofsted paid my school a visit. As a result I’ve recently updated the slide show and below is the new updated version. I hope it will help you when your visit is due!

Preparing for Ofsted! 2013

<div style=”width:425px” id=”__ss_12069324″> <strong style=”display:block;margin:12px 0 4px”><a href=”http://www.slideshare.net/paceanderson/preparing-for-ofsted-nec-2012&#8243; title=”Preparing for ofsted! nec 2012″ target=”_blank”>Preparing for ofsted! nec 2012</a></strong>

<div style=”padding:5px 0 12px”> View more <a href=”http://www.slideshare.net/thecroaker/death-by-powerpoint&#8221; target=”_blank”>PowerPoint</a> from <a href=”http://www.slideshare.net/paceanderson&#8221; target=”_blank”>paceanderson</a> </div> </div>

Lee of the ‘Thought Weavers.’

What Kind Of Restaurant Is Your Classroom?

Myself and David (AKA the Thought Weavers) love to play around with analogies, sometimes they help us get a point across and at other times people look back at us with glazed eyes. However, we really feel this one works and will hopefully help you think about your practice.

So here goes.

We think classrooms are like (or perhaps even should be like) a good restaurant. However, this is not always the case, sometimes they are more ‘fast food’ than ‘gourmet’

Let me explain some of the classic features of a ‘fast-food’ model of the classroom:

  • Pupils walk in with no-one to greet them
  • Adults talk really quickly; they’re impatient and want answers quickly.
  • The menu is always the same.
  • A diet of uninspiring food learning is supplied daily. (it does however hit all of the APP outcomes)
  • Pupils will never remember their favourite or lesson when they’re older
  • Standards are high because the criteria for judging them is so narrow. The ‘fast-food’ restaurant makes and healthy profit and the classroom produces high ‘standards’
  • The tables and chairs never move.
  • All posters and displays are professionally made by adults.
  • Differentiation is made by the words ‘small,’ ‘regular’ or ‘large,’ or in classroom speak; ‘poor,’ ‘average’ or ‘bright.’ (Although occasionally ‘G&T is on the menu)
  • Sometimes special menus/promotions are created, in schools these are known as ‘theme days,’ this is the only time when the menu is slightly more interesting.
  • Feedback is standardised and irrelevant. In the classroom this might be ‘Good Work’ or ‘Well Done’
  • No tips are given; the children will never go the extra mile.
  • Customers can never change the menu and ask for something a little different; in the classroom children get what they’re given.
  • There is no overt way of expressing pleasure or disappointment at the service provided.

On the other hand, a gourmet restaurant (or perhaps country pub!) model for the classroom might read as follows:

  • A friendly smile when you walk in.
  • Small talk at the table with staff.
  • The menu changes regularly and there are lots of daily specials
  • The meals (learning) are well deigned by experts who truly know what they are doing.
  • Great memories are created by the quality of service and friendly atmosphere.
  • Relationships with all adults and children are positive.
  • ‘Difficult’ customers are treated with dignity and respect
  • Standards are exceptionally high, because of the attention to detail at every step of the process.
  • If something special is required or someone wants to deviate from the menu it is celebrated and explored
  • Differentiation is the choice of the customer/pupils; there is a wide variety of activities/meals set out in a variety of ways.
  • Feedback is personalised and unscripted, it feels natural but authoritative.
  • Plenty of tips! Children bring in masses of things from home because they’ve been inspired in school.
  • Pupils can personalise the menus, giving feedback to the lead adult about their performance.
  • Pupils are encouraged to think about their decisions; they have time to evaluate the menu before making a decision

And so on…

Let’s make it clear. Classrooms are not restaurants and certainly shouldn’t be run as a business; pupils are not our customers, they are learners and we should be proud to facilitate their progress.

But, we feel the comparisons can be made. We believe that too often, the standards agenda pushes schools into a ‘fast-food’ model of education. Children deserve better! Whilst a ‘Gourmet’ classroom means hard work, it does mean that the children are the most important people and they will remember their experiences.

So how do you make your classroom ‘Gourmet?’

The Thought Weavers

Curriculum change!

The Thought Weavers at the BETT show.

Curriculum change is a hot topic in education at the moment and we had the privilege of taking part in a panel discussion at the ‘Educational Leaders’ conference as part of the BETT show. The topic for discussion was curriculum change. Prior to the discussion we were also lucky enough to hear the views of Tim Oates, the chair of the expert panel on curriculum review. This post represents our reflection on the curriculum review based on our prior understanding and our thoughts following the BETT show.

Before we offer our thoughts we have tried to make the following assumptions in an attempt to make our views as sensible and ‘objective’ as possible.

  • The review panel have the best interests of children when considering the new curriculum.
  • The new curriculum will be an attempt to give more freedom to schools (This is stated in the DfE website and in the interim report)

Prior to the show we both read the expert panel review report. We were heartened that it does mention extra freedom, learning to learn approaches and having a ‘school curriculum’ that is not prescribed by the new curriculum.

However, when we got into the ‘nitty gritty’ of the report, such as curriculum design, subjects and the organisation of key stages it soon became clear that this curriculum would have much more prescription than the current document. The irony of a 70 page report to inform us that we will have extra freedom was also not lost on us.

When we heard Tim Oates speak, this reaffirmed our worries. He quite openly told us the new curriculum will be thicker with more detailed learning outcomes. He also reaffirmed that assessment would be tightly linked to the curriculum to assessment, whilst this seems to make common sense, we think it reinforces the ‘teaching to the test approache’. He also mentioned that pupils should not be able to move on until one ‘block of content’ was secure; does this mean children will be held back as in the USA?

From the report and hearing Tim Oates speak we came to the following conclusions:

  • There is an assumption that pupils learn in a linear way, with one block of content being learned so that they can move onto the next block of content. Just how does that really work? For some pupils fractions are much easier than timetables, for other it’s the opposite, for some children using commas is much more developed than using full stops. How will they decide the order for these ‘blocks of content?’ Wouldn’t it be wonderful if children learned in systematic way? – But they don’t!
  • Another assumption is that other countries systems of curriculum design are better than ours. To begin with this assumption is based on narrow tests (e.g PISA) to evaluate maths, literacy and science; so where the does the ‘broad and balanced’ argument fit in? We feel they are just ‘cherry picking’ parts of other countries curriculum to support their own arguments. Tim Oates also stated that whilst we should look at other countries curriculum design we should not try to copy them. This is confusing.
  • Our other concern is the manner in which Tim Oates delivered his speech. In education, when children have one chance, passion is vital. We didn’t get a sense of passion from him, most questions were answered using reference to academic research. We have the feeling that the expert review panel are themselves frustrated under the intense pressure from government to produce a curriculum based on the ideals of Michael Gove.

When we took to the stage to sit with our panel, Tim Oates took his place in the audience. We discussed curriculum change and took questions from the floor. With regret Tim Oates was not able to stay for the whole panel discussion.

The key points raised by ourselves and the panel were:

  • With a narrow assessment system, no matter how schools are encouraged to have more freedom over the curriculum, children’s learning will always be channelled to towards getting the grades.
  • Ofsted’s remit is too wide. They seem to have the power to do what they like. Most of the panel agreed that it is Ofsted that set school policy, not the government.
  • Children’s learning should not be standardised
  • The curriculum review seems to have little direction.
  • The new curriculum will be more prescriptive than the current one.
  • A perhaps cynical point of view was that the curriculum review was an attempt to push schools into academy status.

The expert panel into curriculum change have been given a very difficult job. There remit is to design a core and foundation curriculum that will suit every student in England. The very idea of this, in our view is impossible.

Final thoughts…

With around 20,000 schools in England and many wonderful, creative and focussed professions, the following questions popped into our heads…

Why do we need a curriculum written for us?

Can’t we be tasked with creating our own curriculum, our own success criteria, our own pedagogical approach based on the needs of children we know very well within a community of which we are part?

Does the head of science need to be told what essential knowledge should be taught?

Would a new curriculum create a whole new wave of commercial products to support it?

Who really are the experts in education?

Can we really have personalised learning with a standardised curriculum?

To finish on a positive – no matter what the outcome of the curriculum review, nothing is more powerful that teachers doing what they do best; helping children to learn. The online collaboration through twitter and facebook etc will always be a more powerful force than any formal written document. When teachers collaborate and debate, children will always benefit.

Lee and David.