Mary Myatt writes about a joke concerning two men in a bar. One says: “I’ve taught my dog to speak French.” “Really?” says his friend, “let’s hear him then.”
“I said I taught him – I didn’t say he’d learnt it,” comes the response.
Herein lies a profound pedagogical truth: despite our enormous efforts, learning does not naturally follow teaching.
As teachers, we cannot define our success merely by the clarity of our instruction or exposition of a concept or process; we also cannot jump straight from instruction to students independently applying their knowledge to a task that will consolidate their learning. This very often fails. Therefore, we need to structure practice in a way that enables them to succeed.
Cognitive Load Theory (CLT) provides ample insights into how we can do this well (Sweller et al, 2011). One key approach, CLT suggests, is through worked examples.
In the first of two articles, I explicitly focus on worked examples that include “backward fading”, considering its application in both English and maths. I will then outline a general pedagogical framework to support leaders of teaching to equip their colleagues to use this in practice.
How should we use worked examples?
Seen as the most important of the CLT effects, Sweller and his colleagues see worked examples as an effective way to applying their findings in the classroom and structuring elements of lesson design.
The general premise of worked examples is that instead of giving students a set of problems or a complex task to do straight after initial instruction, it is important to provide multiple examples of completed tasks, alongside instruction, that are similar or the same as the ones they will do independently.
This is an important clarification of the strategy, as some have seen worked examples as an alternative to providing instruction. For example, instead of explaining new knowledge out of the context of problems or a complex task, teachers have interpreted worked examples as the way to teach new knowledge. This is an error.
As Ollie Lovell (2020) writes: “Worked examples refer to the guided practice that students do following a teacher’s initial exposition.” Over time, elements of the completed problem can be removed to increase independence, but this is only after initial instruction, not in place of it.
In short, worked examples, after teacher instruction, provide a way for students to see how new learning is applied to complex problems and tasks. Worked examples do not replace clear explanations of key concepts and new knowledge.
When teachers provide several examples that slowly remove elements over time, following simple step-by-step explanations, students can see at each stage how they can apply what they have learned in context.
Adapting work from Lovell (2020), here are the key steps of this idea of backward fading which is proposed by CLT and the work of Sweller.
- Teacher provides instructions of new idea or concept
- Teacher models worked example
- Students practise worked example (slowly fading key elements out)
- Students practise similar problems
Worked examples and backward fading in context
Before I offer two examples of what this looks like in practice (in maths and English), there are two important points. Worked examples and backward fading should always be used to combine new knowledge that is learned, implied by the learning objective, with the later independent work that students will be doing.
For example, when students are learning how to apply column methods using addition and subtraction to worded problems, it is worthwhile making sure that this is done in small steps. If worked examples are only one-step problems (involving one calculation), independent practice also ought to involve one-step problems as opposed to a variety of different types of problems.
It might be that two-step problems are introduced later but this needs to be supplemented with teaching, worked examples, and backward fading that includes these steps.
Next, it is important that students are provided with clear steps to success that can be replicated when they are solving problems for themselves. When a worked example is provided and an explanation is coupled with this, the instruction ought to follow steps that are repeated for each example and then used in independent practice. This ensures that students can consider carefully each step they take, and if they get stuck they have an easy reference to keep coming back to.
Maths
Let’s take long division as an example to explain how worked examples and backward fading can be used. The first step begins with the teacher clearly explaining what long division is, why it is important, and then, crucially, explaining a worked example, step-by-step, like the one below.
It might be that the teacher shows several examples. Then they can show a few examples with certain steps removed, talking out loud about how they will be completing each step.
Then a question can be displayed and the teacher can complete the whole thing. It is important that the steps that have been followed first time round are constantly referred to throughout this explanation by using worked examples and backward fading.
Once this is done, teachers can provide students with partly completed examples for them to do independently, structuring practice in a way that means students complete slightly easier problems than the final one the teacher modelled or begin problems that have no scaffolding at all.
What about those who are not ready to work independently?
At this point, many teachers will think of those who, after all of this instruction, still don’t understand what to do. The trick here is to reach a point where almost all students are able to do it by themselves. If you are left with two, three or four students who are still struggling you can release the rest of the class for independent learning while you do further work with this small group.
In my experience, sometimes students who lack confidence need one or maybe two more questions and then need to have a try themselves. Often, when they have a go they find they are able to do it.
If students are still struggling, give them a prerequisite task (in this case, short division). If they can master this, move them on slowly to long division by beginning with calculations that use simpler times tables.
Worked examples and backward fading could be used in this context by the teacher explaining the process of long division alongside a worked example, then doing another calculation that is part-completed and then doing one with no example at all, describing step-by-step how it has been completed each time.
Once there are clear steps in place and these have been explained to students, elements of a completed example could be removed. A simple questioning round can be included which will serve as a formative assessment tool to identify any misconceptions or problems:
- What’s missing?
- What would go here?
- What should I do next?
English
Likewise, in English, completed worked examples and backwards fading sits neatly within the highly recommended LEAD approach to teaching grammar:
- Link... to current content
- Example... teach through examples and non-examples
- Apply... to current writing
- Develop... deepen current understanding to a range of contexts
The “E” stands for “examples” and this framework suggests that long-winded explanations of key grammatical terms is a waste of time. Instead, students need to see the word class, examples of it, and develop their use of it in context.
Equally, non-examples can be helpful to expose students to the boundaries of the new knowledge and explicitly teach misconceptions. After showing multiple examples, teachers can fade-out key elements and do a similar questioning round to that detailed above in our maths case study.
Short formative assessment tasks can then be used to check student understanding and adapt instruction accordingly. Let’s look at an example of this.
Embedded in a unit of writing on developing discussion texts, students need to learn how to use conjunctions and adverbials to combine two opposing points of view.
To do this, it is important to reteach conjunctions and adverbials to activate prior learning. Then, teachers show an example of how a conjunction could be used to combine two opposing views and also an adverbial.
This should be done several times, following steps that are repeated. As mentioned, it is worth making sure that students see where certain conjunctions and adverbials don’t work and why this is the case, ensuring that explicit misconceptions are taught at this point.
Then students can co-construct sentences using conjunctions and adverbials with their teacher and their peers. This provides an opportunity for teachers to check understanding and students to practise their ideas.
Then students can be released to create their own. Importantly, the practice at this point ought to be isolated – students should not be writing whole paragraphs and instead should be practising this skill in isolation from a wider extended piece of writing. This ensures that students become fluent in using these conjunctions and adverbials in such a way that when they are writing independently they can do so without extraneous cognitive load.
‘I do, we do, you do’
This is the language we use as a school when we plan for worked examples with backward fading. The reason for this is twofold.
First, it provides teachers with a clear way to structure worked examples in lesson time. In turn, this also means that students are able to develop an understanding of how the teacher will explain how something is done, building metacognitive language to describe the learning process.
Here is a simple table, mapping out how “I do, we do, you do” works in general terms for maths and English.
|
| CLT and Worked Examples | Maths | English |
| I do | Teacher completes problem or shows how new knowledge is applied in context. Often one example is not enough and multiple examples should be provided, following simple steps which students can follow | Teacher completes a one-step addition or subtraction worded problem following clear steps for students to follow They then complete another problem to draw out any nuance in the problems that the students will encounter later on | Teacher completes sentences that use subordinating conjunctions – because, before, after – thinking out loud as they do this |
| We do | Teacher does a few more problems with students using cold-calling and probing questions to check understanding while also engaging students in the process of completing problems with the steps in mind | Teacher, with the help of students, will complete two to three more problems It might be they make intentional mistakes to draw out misconceptions so that these can be explicitly addressed Teacher can also check for understanding at this point from select students who exemplify key pupil groups | Teacher does a few more examples with students, making intentional mistakes throughout and checking the understanding students have at this point |
| You do | Students are given the opportunity to try out a few problems with lots of feedback from the teacher. This often involves a few problems before the teacher draws students back together ahead of releasing them to do independent work | Teacher provides three or four one-step addition or subtraction problems for students to solve before drawing them back together ahead of their independent practice Teacher circulates throughout to check for understanding | Teacher provides two to three more simple sentences and then enables students to complete them using a conjunction and subordinate clause Teacher circulates throughout to check for understanding |
Conclusion
To move our teaching to learning, worked examples and the language of “I do, we do, you do” can provide a helpful way for both teachers and students to apply new learning to the context of complex tasks.
In the second of these two articles (which you can find here), I want to look at the weaknesses of this approach and suggest an additional way to use worked examples.
- Robbie Burns is a teacher and assistant vice-principal for teaching and learning at Bede Academy in Northumberland. He has written for a range of publications on primary education and curriculum. Read his blog via www.howthenshouldweteach.wordpress.com and follow him on Twitter @MrRRBurns. Read his previous articles for Headteacher Update via https://bit.ly/htu-burns
Further information & resources
- Atkinson et al: Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, (70,2), 2000.
- Lovell: Sweller’s Cognitive Load Theory in Action, John Catt Educational, 2020.
- Sweller, Ayres & Klayuga: Cognitive Load Theory (vol 1), Springer, 2011.