Developing a departmental approach to worked examples
An example from a school I was supporting
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Overview
This is the second in a series of posts that attempt to shine a light on some of the support work I am fortunate enough to do with the maths departments I visit. Posts will include:
Developing a departmental approach to… worked examples (this post)
For more information about my CPD, departmental support, and coaching, please visit here.
Developing a departmental approach to worked examples
What we sorted first
During my first few visits to the school, we worked on using mini-whiteboards to ensure mass participation and improve checks for understanding during the Do Now in much the same way as I described here. All members of the maths department subsequently nailed this. Do Nows were short, sharp and effective, with colleagues quickly moving on when they had evidence that understanding was secure, and intervening when the mini-whiteboards revealed students were struggling.
It was important to get the Do Now sorted before moving on to worked examples. The Do Now sets the tone for the rest of the lesson, and I would argue it also is easier to check for understanding and respond in this stage of the lesson than amidst the complexities of modelling.
What their worked examples looked like
Lesson drop-ins revealed an inconsistent approach to worked examples. Here are some things I saw:
Some teachers asked their students to copy down the steps of the first example (the I Do) as the teacher was modelling, some asked the students to wait until they have finished, while others didn’t make it clear either way and so some students copied during the model whilst others waited.
Some teachers were taking the lead during the I Do section and explaining to students what to do. The issue here is those teachers had no evidence that students were listening. Other teachers were regularly asking students to predict the next step during the modelling process. There were two issues here. First, only a few students were called upon to answer, so who knows what the other students understood. Second, because students were being asked questions about something new to them, many students got the questions wrong and the process took a long time.
Some teachers did the I Do on one slide, and then asked the students the We Do on another slide, other teachers split their board in two. Among that latter group, some had both the I Do and We Do questions visible from the start, whereas others revealed the We Do later.
When it came to the We Do section, some teachers asked students to complete it in their books, whereas others were using mini-whiteboards.
Such a variety of approaches is common within a department, but as I argued in this post, unless student outcomes are consistently high, I think a more prescripted approach is called for.
The four principles of worked examples
The Head of Department and I sat down and agreed upon four key principles that we wanted everyone’s worked examples to adhere to. The four principles were:
Empty hands, eyes on me when modelling
Check for listening when modelling
I Do on the left, We Do on the right, and only reveal the We Do after the I Do
Assess the first We Do on mini-whiteboards using Step-by-Step
How do these compare to your worked example principles?
Let’s look at each principle in turn.
Empty hands, eyes on me when modelling
I remain convinced that it is a bad idea to ask students to copy down the worked example as the teacher is modelling it. Students’ eyes are looking down at their books instead of toward the board, and their attention is always on the previous step they are copying instead of the current step the teacher is explaining. So., we decided that everyone would insist that students empty their hands and look at the board for the duration of the modelling (the I Do) phase of the worked example phase.
Check for listening when modelling
We decided to try a new way of doing the I Do. Teachers would take the lead during the initial model and not ask students to speculate on things they had not yet been taught. In other words, they would not check for understanding at this stage. But, in an effort to sustain student attention and also gather valuable feedback, they would check for listening throughout the modelling process.
The difference here is subtle, but important. Asking students what is a good first step to solve an equation is a check for understanding. Explaining to students that a good first step to solve an equation is to subtract 3x from both sides, and then asking a student what is a good first step to solve the equation is a check for listening. The latter is a prerequisite for understanding, and students need to be held to account if they are unable to answer correctly.
I Do on the left, We Do on the right, and only reveal the We Do after the I Do
Following the I Do, comes the We Do, which is students’ first opportunity to see what they have understood from the model. We agreed on a common split-board setup, with the I Do on the left and the We Do on the right so the teacher could draw students’ attention to the similarities and differences between the examples. Furthermore, we agreed that everyone would only reveal the We Do question after the I Do has finished to keep students’ attention focussed on one question at a time.
Assess the first We Do on mini-whiteboards using Step-by-Step
We agreed that it is important to get data from all students during the We Do. Asking for a volunteer or Cold Calling one student to see what answer they got means we run the risk of assuming their answer is representative of the rest of the class, and misunderstandings are likely to remain hidden. As is often the case, the mini-whiteboard is a maths teacher’s best friend here.
We agreed to use the mini-whiteboards in a specific way that I call Step-by-Step. Instead of giving students, say, an equation to solve for the We Do and asking them to do it from the start to the finish, we ask them to write only a very specific thing on their mini-whiteboards, such as the first operation they will do to both sides of the equation. Students hover their boards face-down when ready, and reveal their answer on 3, 2, 1…
The teacher then responds accordingly, either confirming the correct answer or remodelling and rechecking if students are confused. They then ask students to add the next step to their mini-whiteboard ready to be checked as they build the solution one step at a time.
Step-by-Step does three valuable things:
Step-by-Step reduces the amount of information a teacher needs to take in on any mini-whiteboard check. If 30 students have completed several steps on their mini-whiteboards, that is simply too much data to analyse in the few seconds boards are in the air, so things are likely to get missed.
Step-by-Step shows the teacher exactly where in the process students are struggling, allowing them to intervene and respond accordingly. If we try to assess several steps all at once, we end up having to play detective and working back from potentially lots of different final answers to see where the problem lies.
Students have more opportunities to feel successful. This should not be underestimated. If we only assess the final answer of a multi-step process, then that is just one chance for students to feel successful. If, however, we assess several steps, that is lots more opportunities for students to taste those all-important moments of success.
What do you think of this approach?
How does it compare to your worked examples?
The CPD session
I had the department together for 90 minutes that afternoon. I asked them first to reflect on their worked example process. The question I posed was this:
How easy would it be for a student to lack effort or understanding during your worked example and you not pick up on it?
I then presented each of the four principles, sharing the rationale behind each. Next, I modelled what this might look like for two upcoming topics, fraction operations and rounding, so colleagues had concrete examples for topics they would be teaching soon. The members of the department were my students, and it always amazes me how much people’s attention heightens when the checks for listening kick in:
Today we are going to learn how to multiply fractions… what are we learning today… Mrs Green?
I then addressed any concerns colleagues had. Time was the big one - would this take too long? - along with worries that the constant checks for listening and whiteboard checks would disrupt the flow of the lesson. But everyone was happy to give it a go with one class of their choosing for one week.
Colleagues spent the final 30 minutes planning exactly what this would look like in that class. They then had an opportunity to rehearse their checks for listening with their partner. Rehearsal, as ever, was key. Checks for listening were new, and it was important colleagues got a chance to practice this in front of one pair of friendly ears, rather than doing it for the first time in the lions’ den of a Year 9 class.
What happened next?
I was in school the very next day, so could see this new process in action. Every single member of the department gave it a go, which is not always the case.
One colleague introduced checks for listening by telling the class how many times Newcastle won the FA Cup in the 1960s and then asking a lad (a Sunderland fan) to repeat it back to him. Another colleague explained the rationale behind the Step-by-Step approach, and then demoed top-class technique by hovering the mini-whiteboard and holding it above her head.
There were, of course, teething problems. One colleague included checks for understanding alongside checks for listening, and when students struggled with these (as they had not yet been taught the concept), the pace and flow got derailed. Another colleague was horrified at how little her students were actually listening, which is of course the point of doing the checks. Students moaned about having the hold their mini-whiteboards in the air so much, but these were the very same students who loved passively copying down examples from the board.
All in all, it was a success. Colleagues will meet together in a week to reflect on what is working and what isn’t, and I look forward to visiting the school later in the year to see how this process has evolved.
How does this compare to your worked example process? What do you like, and what don’t you like?
How does this compare in terms of the level of direction in your department?
Let me know in the comments below!
🏃🏻♂️ Before you go, have you…🏃🏻♂️
… checked out our incredible, brand-new, free resources from Eedi?
… read my latest Tips for Teachers newsletter about checking for listening to see if your explanations are clear and concise?
… listened to my latest podcast with Ollie Lovell and Zach Groshell?
… considered booking some CPD, coaching, or maths departmental support?
… read my Tips for Teachers book?
Thanks so much for reading and have a great week!
Craig
You only have one area to process auditory information in your brain (Jared Cooney Horvath) and when you are reading/writing you are using that processing power for the talk in your head. No point asking students to copy down and listen to you at the same time.