Session

3. Using worked and partially completed examples

This session will take approximately 45 minutes to complete.

Session overview

In the previous session we looked at effective strategies to introduce new knowledge to pupils. The aim of these strategies is to avoid overloading their working memory, therefore giving pupils a better chance of learning and remembering the information. This session will explore a further method to achieve the same goal:

  • Using worked and partially completed examples

Using worked and partially completed examples

A worked example is a problem that has already been solved for the pupil, with every step fully explained and clearly shown. The beauty of a worked example is that they make visible an expert’s problem-solving solution, and then this is shared with the novice pupil as an example to learn from.

They also free up the pupil’s working memory by shifting the focus from finding the correct answer to understanding and learning the steps in the example. This means that they are more likely to recall how to solve this type of problem when they are faced with it in the future (CESE, 2018).

When you are creating a worked example, you are not aiming to reduce the complexity of the knowledge being learnt and remove any of the academic rigour around it. The knowledge will remain complex and pupils will need to partake in effortful thinking in order to understand it. But worked examples are effective at removing any extraneous information and distractions that would stop pupils being able to think deeply about each step of the process. With the support of the example they can focus instead on the content and exactly how an expert would solve it.

Effective worked examples often share the following features:

  • They offer a clear structure and reasoning behind the steps shown
  • They take pupils through the problem to its logical conclusion without any step being left to interpretation
  • The teacher talks through their reasoning, sharing their expert thinking and understanding
  • After studying a worked example, learners require practise on their own to provide them with feedback on whether they have learned it or not

Partially completed examples are worked examples that have had some steps left blank for pupils to complete. They allow the teacher to direct the pupil to where the practise needs to take place. The idea behind a partially completed example is that you are directing pupils to where you want them to focus their thinking.

Listen to Ben Riley from Deans for Impact talk about why worked examples can be so effective in reducing the risk of overloading the working memory. He also talks through a worked example of how to solve a crossword puzzle, modelling how he would share his thought process aloud as he would do with his pupils.

Worked examples – Benjamin Riley

Video transcript

In this module, I’m going to talk with you about a particularly useful insight from cognitive science around creating something called a ‘worked example’ and why it can be so useful to you as a teacher.

So let me start first with a very simple definition of what a worked example is. A worked example is simply a step by step explanation of how to solve a problem. That may seem obvious and sound like easy to do but it’s actually quite interesting to explore how to do it effectively as a teacher. And rather than talk about that in the abstract I thought I’d take a bit of a chance here and actually try to create a worked example here in this video with you around solving crossword puzzles. Now I know immediately some of you just groaned and have, what, nothing to do with this and a few of you might also already love doing puzzles and this might seem a bit redundant so I apologize to both of you but trust me I think if we explore this together you’ll find it interesting and think about how it can apply to situations, anything you might want to teach. But I actually think crossword puzzles contain an awful lot within them that help explain our cognitive architecture and I’ll explain that as we go along.

Ok so let me start by saying if I wanted to teach you how to solve a crossword puzzle what would I not do, what would be a bad example? Well, one thing that I certainly wouldn’t do is give you a bunch of crossword puzzles with the clues already filled in and say study these. That, I think, would probably not improve your performance in solving crossword puzzles at all and the reason for that is you’re not actually going to be learning a strategy for how to solve the problem. You’re going to be learning at best what some of the answers to some clues are but unless the puzzle contains that same clue again it’s really not going to be very helpful. So worked examples are not just about giving students the answer, it’s really about figuring out a process and making it very explicit what that process is so that students can use that to sort of alleviate their cognitive burden when they’re solving a problem that may appear new and novel to them.

So let’s dive in, let’s say for now that I’m going to try to teach you, give you, a worked example for solving a crossword. So here’s the first thing that I’d start with: I’d look for all the clues that are what I call ‘fill in the blank’. Here’s an example: let’s say in the crossword we’re doing three across is PRIME blank now my guess is many of you immediately started thinking of what could follow this PRIME. I suspect many of you immediately thought ‘Minister’ a few of you who are hungry may think ‘rib’ and perhaps a few Star Trek aficionados thought ‘directive’, but my guess is for those of you are in the UK, Minister is the first thing that came to mind so let’s just take a look here. We’ve got a box with I believe eight letters I’m just gonna see if that fits. Good idea to usually do this in pencil but lo and behold: Boom! Minister. Great, so that would be step one and it’s worth thinking about just for a second why would we want to start with blanks like that and the answer is, my opinion, the creator of the puzzle has actually made your cognitive load a little bit easier by giving you half the information you need already. For whatever reason, those sort of clues are usually the ones that people immediately go to because again it doesn’t tax as much of our memory and our consciousness as some of the other clues will, which we’ll come to in a second. So, we might go through the puzzle, see all of the fill in the blanks, see how many of those we can solve but what will we do next? Well, we might then turn to attacking the three-letter clues. So, let’s for example look at one that I’ve created for this puzzle. 17 down has ‘TV in the UK’. Think about that for a second. Right, you’ve got it right I’m sure many of you immediately thought BBC. Now why would we start with attacking the three-letter clues? Well, it’s because there’s only three letters. And so again we’re looking for ways to make puzzles easier for us to think through rather than more challenging. So, starting with the three-letter clues after the fill in the blank should help us fill in the puzzle in ways that will make it a little bit less taxing on the cognitive process that we’re doing. Now again we are doing effortful thinking, that’s good, and we’re pulling things from our memory into our working memory in order to solve these clues.

One thing I will just note for crossword puzzles too is if there’s little things you might learn or put into your worked example like clues that have acronyms in them typically have acronyms as their solutions. It’s things like that when you’re starting to teach somebody something that you want to make that very explicit. You can allow them to discover it on their own by doing this over and over again but why not make it easier up front? In time they will learn it and then it will become sort of their background knowledge but it’s really important with a worked example or frankly when teaching anything to try to be as explicit as you can when first introducing a concept to a pupil.

So now we’ve populated our puzzle with a few solutions we can look at it and see where do we have what I call ‘first letters’ and that is what I mean where some of the letters that we’ve filled in give us the first letter for one of the other clues. So let’s just imagine for a second that there’s this clue, five down, and it says ‘luxurious autos’. Now if you’re like me you might immediately think, ok, Mercedes Benz, you drop down and it’s like ooh that’s promising that looks like a lot of letters. Looks like about eleven here but you try to type Mercedes or write Mercedes and that doesn’t fit and or say Mercedes Benz is too long. Hmm! Have a look – it’s tough right? Now, what if I told you that our Prime Minister solution crossed with this and so that we actually know the first letter in this. The first letter is ‘R’. Gotta think for a second. My guess is that a lot of you just thought of the answer to this. The answer is Rolls Royces. How elegant is that? Of course, they break down a lot but this is not to disparage British engineering. So, this is a worked example that I’ve rapidly created here of how I might teach people to solve crossword puzzles. Look for fill in the blanks, attack the three-letter and then find first letters. Now here’s the thing about teaching – there’s a lot of different ways in which I could have created a worked example for crossword puzzles. There’s no one way to do it. The key is to think about why it’s important to step through all the processes for your students and to understand that for them encountering new things like this are gonna be things they might naturally resist and that we’re actually trying to alleviate as much as we can in the early stage of something, the cognitive effort that it takes and that’s the joy of teaching is that there is no one way of doing that and for basically everything that you might teach you’re gonna be responsible for figuring out and imagining how to create a worked example like this to help your students.

Worked and partially completed examples in action

In this section you will hear from teachers explaining why they have found worked and partially complete examples useful for focusing pupil thinking and sharing their expert knowledge. You can also see examples of teachers using worked examples in action in their classroom. Select videos to view that are most appropriate to your phase.

Hear from English Teacher Joseph Craven as he talks through how he incorporated a worked example into an end of unit lesson to support pupils to effectively answer an exam question.

Worked examples – Joseph Craven at Northern Education Trust

Video transcript

Worked examples are a hugely important part of the learning process. They offer a model of expert thinking and processing and they demonstrate how an expert would apply their knowledge when working to answer a question.

They are also beneficial as they give the teacher an insight into their pupils’ perspective when faced with solving a new problem. It can be difficult to know how to answer a question or how to effectively break down a task if it isn’t something you’ve worked through and completed yourself. As a teacher you should be considering your pupils’ prior knowledge and then tailor the worked example to be built on this and accessible to them. There’s also the old danger of providing worked examples that aren’t replicable. There’s no end of teachers who have spent an hour writing a worked example to a question that a pupil has 20 minutes to answer, meaning that the quantity and quality of the response isn’t actually a replicable model. You will course naturally take a little longer to create the example to ensure it includes everything you want to demonstrate and to ensure it is designed in a way that will alleviate some of the load placed on the working memory. However, as the expert, it shouldn’t take you much longer to create than it would take your pupils to answer.

Worked examples can be introduced at almost any point as a learning tool, but I typically use them in English once the class are secure in all the foundational concepts and then I used the worked example as a way of demonstrating how to pull all that learning together. I like to think about them almost as an apprenticeship model:

  • Here’s a beautiful example
  • Here’s a master craftsman crafting a beautiful example
  • Let’s work through the process of crafting a beautiful example together
  • Now you create a beautiful example and I’m here to help if needed
  • Now you create a beautiful example independently

In the example shared below, it is important to know the class were already familiar with the topic. We’d been working on the opening of ‘An Inspector Calls’ for a few weeks, and they knew the characters, the opening of the narrative and so on. With this in mind, and a secure foundation of knowledge on which to build, I felt a worked example would help me demonstrate how they could pull all this learning together when answering an exam question.

The worked example was actually written by a very able pupil from the previous year, and expertly demonstrated the learning points I needed the class to pick up. The dissection shown underneath the example shares the focus and rationale for each step of the process. It’s structured as an effective paragraph (a clear point, valid evidence that’s embedded, explanation and analysis with a zoom in on a specific word, some technical terminology, and a link to the whole text). I talked through this with the class, sharing my thoughts on why this is such an excellent example at each stage. Following on from this, we would create a further example together, then the pupils would attempt an example independently. At this point I can see what steps in the process individuals have remembered. At other times, I’d produce the initial model myself, but I’d very much want to ensure that it’s of a practicable, replicable quality and length.

Worked example

At the beginning of the play, Priestley presents the inspector as an enigmatic, almost wilfully nondescript figure. After all, the description of him wearing a ‘plain darkish suit’ contrasts sharply with the ‘tails and white ties’ worn by the Birling men, just as the inspector’s habit of speaking ‘carefully, weightily’ contrasts with Birling’s speech-making, despite his claim that he doesn’t ‘often make speeches at you’. Priestley clearly intends the inspector to be juxtaposed with Birling. The two are both male and of an age, but their behaviour is as significantly different as their appearance – Birling is ‘heavy-looking, but it is the inspector’s ideas and language that allow him to speak ‘weightily’. There is, in addition, nothing specific about the inspector’s clothing or appearance, just as there is very little sense of personality or clarity in terms of his symbolic function at the beginning of the play, and the inspector’s speech seems direct and purposeful, unlike Birling’s long-winded and opinionated rant. Perhaps Priestley intends for the inspector to be defined through his function rather than his ego, something of which Birling seems incapable.

Exam or teacher model-response dissected

Point:

At the beginning of the play, Priestley presents the inspector as an enigmatic, almost wilfully nondescript figure.

Evidence:

After all, the description of him wearing a ‘plain darkish suit’ contrasts sharply with the ‘tails and white ties’ worn by the Birling men, just as the inspector’s habit of speaking ‘carefully, weightily’ contrasts with Birling’s speech-making, despite his claim that he doesn’t ‘often make speeches at you’.

Explanation/analysis:

Priestley clearly intends the inspector to be juxtaposed with Birling. The two are both male and of an age, but their behaviour is as significantly different as their appearance – Birling is ‘heavy-looking, but it is the inspector’s ideas and language that allow him to speak ‘weightily’. There is, in addition, nothing specific about the inspector’s clothing or appearance, just as there is very little sense of personality or clarity in terms of his symbolic function at the beginning of the play, and the inspector’s speech seems direct and purposeful, unlike Birling’s long-winded and opinionated rant.

Link/development:

Perhaps Priestley intends for the inspector to be defined through his function rather than his ego, something of which Birling seems incapable.

Hear from Secondary Geography teacher Ashley Philipson as she explains how she used a partially completed example to support her pupils to explain the formation of coastal erosion.

Video script – Ashley Philipson talking about partially completed examples

The final version of this video will be available from spring 2021, as the publication of this programme was fast-tracked in response to disruptions to this year’s initial teacher training.

A partially completed example is similar to a worked example, but with some information missing. It is used to help reduce cognitive load when pupils are learning new content or a new skill. It is a form of scaffolding to develop expertise as it allows the pupils to add to the answer themselves, developing the explanation of a key concept. I would use this strategy at a point in pupils’ learning where they had previously seen a fully worked example, or as a scaffold for a task.

I recently used it to support pupils in a task where the outcome was to explain the formation of erosional coastal features. At the beginning of the lesson, I verbally explained the formation of a wave cut platform and supported my explanation with photographs and relevant diagrams. I used the acronym SPED, which stands for Sequence, Process, Explanation and Description, as this helps to break the answer down into smaller components. Throughout the explanation, I checked for pupil understanding through questioning. Once I was satisfied that pupils were ready to begin, I explained the task to them.

They were given a partially completed explanation of the formation of erosional coastal features and were asked to complete it. This involved developing some points further and including additional detail that was missing. The level of detail missing varied for different pupils according to their current understanding on the topic. This ensured that pupils were able to focus their learning on key points without experiencing working memory overload. It developed pupils’ understanding as they were required to identify what was missing from the partially completed example and therefore understand what is needed to give a full geographical answer.

When planning this activity, I began by creating a good explanation that followed the structure of SPED and contained fully developed points. I then removed the information that I wanted the pupils to practise recalling. This ensured their recall focused on key learning points and skills that we had been working to develop.

To see worked and partially completed examples in action in the classroom, click on the relevant link below. When watching, consider the following questions:

  • What did the teacher want the pupils to learn?
  • How did the worked or partially complete example support this?

Early Years example:

In this Reception lesson, the teacher utilises the support of his TA to work through how to complete and solve a doubling task.

Worked and partially completed examples – Early Years

Primary example:

In this KS2 lesson, the teacher builds on the pupils’ prior knowledge of decimals. In writing the sentence for the pupils, the teacher partially completes the example, directing pupil thinking towards the missing numbers and the relationship between them.

Worked and partially completed examples – Primary
If you require an audio description over the video, please watch this version: Worked and partially completed examples – Primary [AD]

In this written exemplification, a KS2 Maths lesson incorporates a partially completed example. The teacher directs pupil thinking and addresses a common misconception.

A worked example used in year four maths

Using worked examples.

Year 4 place value lesson to include decimals (tenths). During independent work children were given the task below. The first example is completed for them. There is also another question completed further down to address possible misconceptions around asking for a value of a 0. Children could then explain that this was a place holder.

Worked examples:

Year 4 place value lesson introducing tenths. Children often enjoy looking for your mistakes and are keen to put them right. Explaining what is wrong allows them to develop skills of self-explanation which is shown to deepen understanding.

Secondary example:

In this KS4 lesson, the teacher uses a worked example to demonstrate how to fully answer an exam question. He has created the answer himself and is now talking his pupils through it and sharing his expert reasoning.

Worked and partially completed examples – Secondary
If you require an audio description over the video, please watch this version: Worked and partially completed examples – Secondary [AD]

During your next training session, you will work with a partner to create and review a worked example for an upcoming lesson.

Activity

You are now going to create a worked example of your own, outlining how you would solve the math problem below.

As you do this, remember your learning from previous sessions and incorporate the following into your example:

  1. Break complex material into smaller steps.
  2. Ensure that each step removes any extraneous information and offers a clear structure and reasoning.
  3. Think aloud your expert reasoning in order to share this with the pupil.

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Once you have completed your worked example, click here to view a version of a worked solution to this problem.

Reflect on an upcoming lesson that would benefit from a worked example. Prepare to discuss this lesson at your upcoming training session.

Related ECF strands

How pupils learn

2.9 Worked examples that take pupils through each step of a new process are also likely to support pupils to learn.