Showing posts with label strategies. Show all posts
Showing posts with label strategies. Show all posts

Friday, 2 February 2018

General Principles Of Challenge For Higher Prior Attaining Pupils

General Principles Of Challenge For Higher Prior Attaining Pupils

The National Curriculum states that 'teachers should set high expectations for every pupil. They should plan stretching work for pupils whose attainment is significantly above the expected standard.' My question is: are there general principles that underpin the setting of stretching work?

In this blog post I propose 6 general principles (there may well be more) to consider when thinking about how to challenge higher prior attaining pupils:
  1. More (and More Complex) Knowledge
  2. Provide Opportunities For Children To Demonstrate And Do Something With Their Knowledge
  3. Teach Masterclasses
  4. Remove Scaffolds and Support To Encourage Independence
  5. Communicate High Expectations
  6. Personalise The Challenge
Teachers can often identify the kinds of activity that they provide for pupils who are achieving highly, but it's more difficult to put a finger on identifying the general principles which might be applied when trying to challenge children. It's not too hard to call to mind a particular pupil and then recall the ways in which they've been provided for: writing an alternate viewpoint, encouraging debate in response to texts they've read or solving complex open-ended problems covering a range of maths domains, for example. But are there similarities between the subject-specific challenge activities that children are given? And is it actually all about activity, or something more?

Image taken from ronbassett.com
Bloom's Taxonomy and Knowledge

When teachers' thoughts turn to the general principles that might apply to challenging higher prior attainers (I'm avoiding the other 'a' word), they might often think of Bloom's Taxonomy and the so-called Higher Order Thinking Skills. And it's not a bad starting point; the taxonomy certainly has some implications here. David Didau and Doug Lemov have both written interesting articles about the issues with the taxonomy, particularly in its pyramid form. They both point out that without knowledge at the bottom none of the other skills can be exercised. The pyramid might suggest that reaching the top is the goal but at the same time the fact that the foot of the pyramid (knowledge) is the largest section, the foundation on which the rest is built, points towards the fact that a secure knowledge base is crucial. This in turn points us towards what might be the most important way to challenge higher prior attainers (HPA).

General Principle 1: More (and More Complex) Knowledge

Someone (maybe just a person on the internet) said "The more you know, the more you know you don't know." For those with a thirst for knowledge, this realisation that there is more to know spurs them on to learn more. If you have an HPA who has lapped up all the facts and information you've taught them so far, then surely a simple way to challenge them is to provide them with more information on the subject, or linked to the subject. It might be that this information is harder to understand, or relies on a good understanding of previous information (it will), but that's where the challenge lies for the child. I also think that the second category in the taxonomy should never be separated from the first: knowledge and comprehension should always be hand in hand - what good are facts, information and knowledge if not comprehended?

Contrary to popular belief the National Curriculum does support this principle. For example, in the maths curriculum it says this: 'The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage.' Although the focus is on NOT teaching more, it does acknowledge that for some children, this is a legitimate way forward. This then becomes an issue of pace - sometimes children will need to accelerate past something they are already capable of doing, other times they will need to work at something more slowly in order to ensure it really is excellent.

Bloom's Taxonomy and 'Higher Order Thinking Skills'

Where knowledge is definitely the keystone of any model relating to different thinking categories, I think it is probably arguable that the other categories don't need to be set out so hierarchically, or at least that children don't need to work through them in a linear fashion in every context. What I wouldn't argue with is that it is a good idea to develop thinking and learning in the other categories; I just don't think they need to be thought of as higher order skills. However, what might make someone a higher order thinker is the ability to demonstrate their knowledge securely across the range of categories in the taxonomy:


Image taken from getsmarter.com
General Principle 2: Provide Opportunities For Children To Demonstrate And Do Something With Their Knowledge

In that heading I mean to sum up the other categories of Bloom's original taxonomy: application, analysis, synthesis, evaluation. If knowledge (and comprehension of that knowledge) is what the other categories are built on, then the other categories are all ways of showing that the knowledge is understood. Having said this, when the skills outlined by the rest of the model are exercised there will be additional outcomes - they all provide opportunities for knowing to inform actions.

When it comes to providing opportunities for children to exercise a range of skills in these categories the verb-based revised taxonomy can be quite inspiring when it comes to designing challenging work. Taking just one verb, such as 'dramatise', can spark inspiration in the mind of the teacher who is planning work for HPAs. Every time a child is asked to do something with their knowledge in a different way there is the opportunity to take them out of the comfort zone and into the learning zone (or the optimal performance zone).

In addition to teaching new and more complex knowledge the National Curriculum suggests, in the maths aims section, that 'pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content'. This is an example of this second general principle.

General Principle 3: Teach Masterclasses

Whilst another principle of challenging HPAs might be encouraging greater levels of independence (more about this next), it is very difficult for us to become independent when doing new things. If we are going to provide children with new and more complex knowledge, and if we are going to expect them to do new and varied things with this knowledge, then we will need to teach them more. It might be that we teach either know-what (knowledge) or know-how (knowledge of how to do something, which leads to children learning a new skill) in these masterclasses.

Image taken from What Does This Look Like
In The Classroom? by Robin Macpherson
and Carl Hendrick
In their book Robin Macpherson and Carl Hendrick summarise that 'independence does not seem to be the best way to become independent' and that 'independent learning looks different at different stages, and develops as a continuum rather than having the nature of a spectrum'. They go onto point out that 'independence is something that is achieved and exercised by experts, and our students will have a long way to go to reach this level of ability. What we do as teachers along the way is vital, and requires a lot of scaffolding'. Our HPAs may have attained a certain level of independence (i.e. they may be able to easily do the work that the rest of the class are doing) but will need to be taught the things they need to know in order to become independent at the next level. Becoming independent in one thing does not automatically mean a child will be able to work independently at something more difficult.

General Principle 4: Remove Scaffolds and Support To Encourage Independence

The assessment frameworks for Year 2 and Year 6 use an interesting phrase with regard to our higher prior attaining pupils - they refer to 'working at greater depth within the expected standard'. Where children are still working within the expected standard independence is a good goal for them. They know what they need to know (know-what and know-how) and before being exposed to new material, or even material with some depth, they should be able to work without the aid of adults, scaffolded worksheets and so on. As discussed above, as soon as new knowledge is introduced, they will need scaffolding and support before they reach independence with the new knowledge and skills that they have learned. An analogy: the independent mastery of the making of a boiled egg doesn't mean that the preparation of a carbonara can be achieved independently without some form of instruction. This general principle definitely comes with a health warning: don't throw your HPAs in at the deep end just because they've demonstrated they can take a bath safely.

General Principle 5: Communicate High Expectations

Differentiation by outcome: my old favourite. But can we expect children to produce work of high quality if they don't know what it looks like to produce something that distinguishes it from work produced based on general expectations? No. Even if a child produces an exceptional piece of writing it is probably because they have set high expectations for themselves, expectations which have been defined by high quality literature that they have read themselves. In this example we see that the child has seen an example of how good something might be and have drawn up a set of criteria, albeit subconsciously, that they want to adhere to.

Most of us have to be intentional about producing something that is excellent - children will benefit from having high expectations clearly communicated to them so that they have a standard to work towards. Even if the idea is for them to produce something independently, perhaps especially in this case, it is necessary for them to know what the hallmarks of excellence might be in that piece of work. A model (it should be this good) or a list of criteria (it should contain or demonstrate these things) will probably suffice.

When it comes to high expectations, not only should they be communicated but children should be held accountable to them. Analysis of their own work (e.g. editing and revising) should lead to further improvements - they should not expect to produce excellence in a first draft. Indeed, this process of improving might be one criterion that is communicated to and required of HPAs.

General Principle 6: Personalise The Challenge

We often think of personalisation for lower prior attaining children. The curriculum even prioritises them saying that 'teachers have an even greater obligation to plan lessons for pupils who have low levels of prior attainment'. But we often forget that personalisation, tailoring if you like, might be a great principle for challenging HPAs.

Personalisation can come as a result of assessment - we find out that they know something or can do something already, and adjust their future learning accordingly. But personalisation could be more than this. We could take into account their interests, strengths and weaknesses, personality traits and so on. In order to engage them and encourage them to produce something excellent we might tap into their hobbies and interests. Conversely, in order to challenge them and to encourage them out of their comfort zone, we might not allow children, for example, to write yet another story if they are already demonstrating excellence in this area. In this case the child might be challenged to produce a piece of written work within another genre that they are less comfortable with.

Often, children who are working at greater depth will know what they find easy (and often what they find boring as a result) so it may be worth consulting the child about this in order to determine ways of working that might challenge the child. Sometimes a child might have ideas about how they want to challenge themselves which could be tapped into in classroom work.

Challenge for all

In reading this you may have been struck by the same thought as I had whilst writing it: shouldn't we think about these principles for all pupils? I think the answer is yes - we should seek to challenge all pupils, regardless of levels of prior attainment. With this in mind principle 6 becomes very important: the better we know the children, the better we can challenge them. Robert Bjork refers to desirable difficulty which is what we might think more simply of as pitching work correctly: the correct pitch will mean that work won't be too easy or too hard for the pupil who is attempting it. When work is set at this optimal point children will experience the correct amount of struggle which in turn leads to better retention and higher future performance.

If all we ever do is teach only HPAs new and more complex knowledge or ask them to do a wide variety of tasks when other children are doing similar tasks over and over, there will always be a set number of higher prior attaining pupils (most likely the ones who entered school already at an advantage due to other factors). If we want all pupils to have the chance to attain highly then we should ensure appropriate challenge for all, meaning that all the above principles apply to every child so long as principle 6 is taken into consideration first.

The challenge then for teachers is of course how they do this for each of the 30-or-so pupils in their class without falling into the old trap of three-way differentiation, attempting to provide 30 different activities or just giving up and asking all the children to do the same thing with no thought given to tailoring at all. Ongoing assessment and dynamic grouping is probably the simplest answer here, although within those dynamic (ever-changing) groups it is important to acknowledge that there are differences in need which might be better addressed by differing levels of adult support. This is still a real challenge, one which has workload implications, but taking on this challenge, most of us would agree, is absolutely central to our job as teachers.

Providing challenge for HPAs, and challenge for all children, is the greatest challenge teachers face.

Monday, 15 February 2016

>10%? (PPA Time)


A popular call as a solution for teachers' workload is for teachers to be given extra time at school within working hours to get more of the 'admin' done (throughout this post I will refer to planning, preparation, assessment, moderation and the like as admin). And it's not a bad idea. In fact it's something we do.

Guidelines suggest that a minimum of 10% of teaching time is given to teachers as PPA (planning, preparation and assessment), and it is a statutory right (more info here: http://www.tesfaq.co.uk/ppa#TOC-How-much-PPA-time-should-I-be-getting-). So, let's take a rough estimate of teaching time to be 25 hours meaning 2.5 hours of PPA time should be provided. Our children have 27 hours 5 mins of teaching time so our PPA time should roughly be 2 hours 45 minutes.

The first question to ask is, are you getting what you are entitled to? If not it is worth querying it with your leaders. Many teachers won't even stop to work out how much time they are owed.

The second point to consider is, is even 10% enough and what would happen if you were given more time? 

Our PPA time should be 2 hours 45 minutes, in actuality we get 3 hours 30 minutes. 45 minutes more than 10% of timetabled minimum allowance. As per guidelines this extra time is best referred to as non-contact time - it isn't protected in the same way as PPA time and as a result is designated for other meetings such as Pupil Progress Meetings and Appraisals. However such meetings occur only once or twice per term, leaving each teacher, most weeks, with the extra time to use for their own benefit. Phase Meetings take place during this time also but since all teachers in the phase plan together in one appointed room I find that the meetings become part-and-parcel of the PPA session, therefore taking up little extra time. Our PPA sessions are covered by a combination of senior leaders and HLTAs who teach PE, PSHCE and French lessons.

It's anecdotal but many of my colleagues have mentioned that they prefer to work in the mornings; it's when they feel most productive. Our long PPA sessions can only take place in the mornings. I use the hour before it starts and some of lunchtime to make the session even longer and I complete a great deal of work.

Our extra non-contact time is a gesture which is indicative of our leadership team's commitment to reducing workload. Obviously it still isn't enough time to get EVERYTHING done, but it's a helpful kickstart. The structure of our PPA time encourages collaborative working and the sessions are attended by senior leaders - our staff are vocal about how supported they feel by this set up. If you are a senior leader in a primary school I'd urge you to consider a similar scheme.

Oh, and don't forget the cake.

Photo Credit: mobilyazilar via Compfight cc

Monday, 4 January 2016

Times Tables: What is Knowing?

@tombennett71: There should be nothing controversial about a mainstream expectation for children to know times tables and we'll look daft if we dispute it.

And I agree. Apart, perhaps, from the part about 'know'. What does 'know' mean? Merriam-Webster defines 'know' thus:

  • to have (information of some kind) in your mind
  • to understand (something) 
  • to have a clear and complete idea of (something)
  • to have learned (something, as a skill or a language)
If a child, when they are tested on their tables in 2017, can choose their own version of 'know' then I definitely agree. When you've wiped away your tears of laughter after watching Nicky Morgan avoid answering 11x12, read what she said: "We are introducing a new check to ensure all pupils know their times tables by age 11." She says 'know'. The 'by heart', 'by rote', 'by memory' rhetoric has been added by the papers who gleefully reported the news, glad at the chance to stick another knife in the back of the profession. So, theoretically children don't have to know their tables by heart.

The reason why this issue resonates with me, and with many others, is that as a child, despite my dad's best efforts, I found it impossible to learn my tables by heart. And I still don't know them all today. What I can do is work out multiplication problems very speedily using Merriam-Webster's second, third and fourth definitions. I understand what happens when you multiply one number by another so I can solve a problem. I have a clear and complete idea of how timetables link to other areas of maths. And I have learned lots of methods (you might say skills) to help me to work times tables questions out before anyone realises I haven't memorised them.

The beginning of my journey out of times-tables-embarrassment-land was when I realised that my dad, at random moments during the day, in an attempt to keep the practice up, would only ever ask me what 6x6 was. So I learnt 6x6 (it's 36 - see, told you I'd learnt it). I soon realised that if I knew that then I could work out 6x7 really quickly.

The next step of my journey was my realisation, in secondary school, that if a teacher tried to get me to learn a method without explaining how and why it was working, then I wouldn't be able to do it. I had to understand the mechanics of the mathematical process in order to be able to solve problems. As my teacher took the time to model processes in a way that I understood them, I began to improve in maths. I started to enjoy it too. In fact, I started to think mathematically, could problem solve, reason and I sure was getting fluent. Recognise those three terms? Yes, the aims of the National Curriculum. If I had only learnt by heart the formula for finding the area of a triangle without understanding why it worked then I'd have been far less fluent and would not have been able to problem solve or reason. So why are so many teachers hellbent on getting kids to memorise stuff like times tables?

OK, if a child can memorise them then great, but teachers beware, I truly believe there are kids out there in year 5 right now who will be better supported this year if you teach them some tricks and tips so that instead of rapid recall, they can do rapid work out of tables. Take it from someone who knows.

Here are a few tips and tricks for how you can help those children once you've identified who they are (probably by giving them one of the hundreds of times table check practise tests that will appear online by the time the month is through):
  • Find out which tables they have learnt by heart - the majority of children will definitely have 2s, 5s and 10s.
  • Assuming children know 1s, 2s, 5s and 10s they already have good reference points for other tables. 3s and 4s could be taught using manipulatives such as Numicon shapes or cubes (or you can get really creative - Ikea's dogs' bums coat hooks are fun for 3s) to reinforce what is happening when multiplying 3 and 4.
  • When learning 4s and 8s make links back to 2 times tables. Lots of simple investigation opportunities here too i.e. Which times tables does the number 16 appear in? If the kids can make these connections themselves they will be more likely to learn skills that they can apply in a test situation.
  • Similarly link 3s and 6s together. Later they can be linked to 9s and 12s.
  • Teach 9s using the finger trick. Make sure children have identified the pattern in the answers: the digits in the answers add to 9 - do investigation so that they find this out for themselves.
  • Teach 11s by looking at the pattern in the answers. 10x11, 11x11 and 12x11 might be a bit more difficult so these might need to be learnt by heart - reducing the number of answers that need to be learned by heart is still helpful.
  • This might sound totally ridiculous... OK, it absolutely will, but Weetabix taught me how to work out my 12 times tables quickly. I know the pack sizes.  Each tube inside a box contains 12 Weetabix. You can get boxes of 12, 24, 48, 72. Help the kids tap into outlandish methods like this - maths in real life will be a saviour to many. So many kids need to know why maths is important and relevant to them SO THAT they can begin to understand it.
  • Your children probably are capable of retaining a few facts. I could always remember 6x6 which inspired me to learn my square numbers. Mathematically square numbers are interesting and are more likely to stick in the head (nice links to actual squares in geometry too as a model). Once you've learned square numbers the world is your oyster, especially if you know the square of 6, 7, 8, 9, 11 and 12. You can use those as a reference point and quickly add or take from them.
  • Many children will be able to get a feel for which numbers sound like correct answers and which don't. Some work on what a prime number is might help - children will learn to avoid 17 as an answer in a tables test because it doesn't sound right. They will begin to know that 56 and 42 do appear somewhere - this gives them a reference point to check their answers by. 
  • I use the idea of The Hard Tables. This reduces the number of times tables that children have to really worry about in year 5 and 6. The Hard Tables (even the name shows a child who struggles to memorise them that you understand their plight) are basically any problem (beginning at 6x6) above the square roots of square numbers i.e. 6x6, 7x6, 8x6, 9x6 and 12x6 (most children will know 10x6 and 11x6)
  • Give the children tests where you model a thought process e.g. "The question is 8x7. So think of your square numbers: 7x7 is 49 so you need another lot of 7. 49 add 7 is... is your answer one of those numbers that we know is an answer in the times tables? Does it sound right?"
Put me in front of the nation and ask me a times table question and I'll answer it right away. Not because I know everything up to 12x12 by heart but because I will THINK MATHEMATICALLY about the answer. I will demonstrate fluency as I link areas of my mathematical understanding together. I will demonstrate, invisibly, my ability to problem solve and reason. I will demonstrate that I 'know' my times tables without actually ever having memorised them all. I will be using one or two of the above strategies to get to answer. It will take me a fraction of time longer than someone who has memorised the answer, but out of the two of us, I'll be the one demonstrating better mathematical thinking.

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