What I see all the time…
Students work on a problem, the teacher goes through the answer on the board, students are told to make corrections in green pen if they made a mistake, and then we move on.
Everyone is happy with this arrangement. The students are happy because copying a correction in green pen requires no thinking. Teachers are happy because a sea of students silently correcting work can be construed as an indication that their explanation has made sense. And, of course, senior leaders are happy because these lovely green pen corrections are “evidence” of learning in books.
This seems sensible enough. But are green pen corrections effective in terms of the impact they have on student understanding?
The experiment
Fortunately, several schools I visited recently provided the ideal opportunity to assess the effectiveness of green pen corrections. These schools each do a retrieval Do Now at the start of their lessons, where the same topics repeat over the course of the week. So, if Question 1 on Monday’s Do Now is on the percentage of an amount, then Question 1 on Tuesday’s Do Now will also be on the percentage of an amount, but with the numbers changed.
The rationale is that students have an opportunity to think hard about a given topic over the course of the week, and as such, they should see progress in their understanding.
I’ll be honest, I am not sold on this approach. I would rather see students retrieve a wider variety of concepts in any given week, and the retrieval schedule for any single idea spaced out over a longer time period.
But, my objections aside, here we have a good way of testing the effectiveness of green pen corrections. Because, if a student struggles with a particular topic on Monday, but then does their green pen correction, then they should be able to get the question on that topic correct when it comes up again later that week.
Let’s see if that is the case by looking at this type of Do Now in operation in five different schools…
Example 1: Simplifying fractions
Here is a Year 7s attempt at Question 4 on simplifying fractions on Monday:
They got it wrong. But this is not a problem, because they did what they were told and made the correction in red pen (although, strangely, they have not simplified the fraction fully). Let’s see what happens on Tuesday:
Hmmm, they still can’t do it. But maybe on Wednesday the power of the red pen will kick in…
Nope. Last chance, let’s see Friday’s effort…
Unfortunately not.
Example 2: Rounding to significant figures
Maybe that was a one-off. So, let’s visit another school. This time we have a Year 8 student who is grappling with rounding to significant figures. On Monday, they struggle with that question and leave it out:
But the green pen comes to the rescue. Let’s see what happens on Tuesday:
They have still left that question out. Maybe on Wednesday they will nail it?…
Well, at least they have had a go this time. Let’s see what happens on Thursday…
Some progress!
Example 3: Simplifying algebraic expressions
Another school, another student, and another Do Now. This time keep your eye on the question about simplifying algebraic expressions by addition and substraction. They struggle on the first Do Now:
And then on the second:
And on the third:
And on the fourth:
Example 4: Place value
Ready for another one? Okay, here is a Do Now from a different school. Look at the first question which involved multiplying by powers of 10:
Four days later the student still cannot do it:
And neither can they three days after that:
Example 5: The equation of a straight-line graph
Keen for one more? This time let’s look at the book of a Year 11 student. Focus your attention on Question 6, where the student has to rearrange the equation of a straight line to work out its gradient.
The student has struggled, but has made the green pen correction. Will that correction help when they next take on a similar question?…
Not really.
Why correcting in green pen does not work… and what we can do instead
In each of these examples, the students have done exactly what they have been told to do: make corrections in green pen. But in each instance, that correction has not led to any improvement in learning.
I alluded to the reason at the top of the post: green pen corrections are easy. Correcting is a passive activity. Correcting is something you can do without thinking. Crucially, correcting also masks this lack of thinking because it gives the appearance that thinking and learning have occurred.
So, what is the solution?
First, we need to ensure we have a more accurate sense of who can and can’t answer the question correctly than asking for a volunteer or Cold Call gives us. In both of these scenarios, we hear from just one student, so we have no idea about the understanding of the rest of the class. In maths, a mini-whiteboard is a Godsend. Students can still answer the questions on a sheet or in their books, but when it is time to go through the answers, they copy their final answer to any given question nice and big on their board and hold it up for the teacher to see when instructed. This is a technique I call Book-to-Board. Now we can see the responses of all our students.
Let’s assume that understanding in the class is mixed, as it was in each of the examples above. Because the whiteboards have made the teacher aware of that, they can respond accordingly. I think a sensible approach is:
- Model
- Check for listening
- Recheck for understanding
Let’s look at each of those steps.
- Model
If there is confusion in the class, we need to offer our support. This support could come after canvassing some explanations from students, or after instigating a Turn and Talk, but it needs to come. And when it does, students need to have empty hands, eyes on the board, and our explanation needs to be clear and concise.
- Check for listening
Next, we need to check for listening. Students may be silent and looking at us – maybe even nodding – but are they really listening? If they are not listening, then they have no hope of understanding. There are a few ways to check. We could Cold Call a student and ask them to repeat the last part of our explanation. Or we could instigate a Call and Respond, repeating the first half of a sentence from our explanation and asking everyone to repeat the second half all at once.
These checks for listening are crucial to give us data that students are listening during our explanation. These checks for listening also – because they know they are coming – give our students an incentive to sustain their attention throughout our explanation. For more on checks for listening, check out my podcast with Pritesh Raichura.
- Recheck for understanding
This is the most important part. The only way we have any evidence that our explanation has been successful is to recheck our students’ understanding. “Does that make sense?”, or “Does anybody have any questions?” does not cut it. In maths, this check for understanding is often as easy as changing the numbers in a question, although I would always recommend planning this follow-up question in advance as it is one less thing to think about in the heat of a lesson.
We ask this follow-up question, and get mass participation (again, the mini-whiteboard is my go-to). This will give us evidence as to where understanding currently is. If students are still confused, we have a decision to make. Do we spend lesson time addressing the issue, or do we move on? If we move on, there is little point in including the question on tomorrow’s Do Now. Instead, we need to free up lesson time in the future to address the concept properly. If students nail the follow-up question, then it is still useful to include a similar question in a subsequent Do Now to ensure we separate performance in the moment from longer-term learning.
If the absence of evidence in books is a no-deal for you, your students, or your leadership teams then, by all means, crack out the green pen at any stage. Maybe after you have modelled the first question, or maybe to copy the follow-up question into books. But I stand firm in my belief that this is the least impactful part of the process of addressing a problem, and yet it is often where the correction process begins and ends.
