What colleague hasn't experienced that interminable moment in class, when the minutes spent correcting exercises tick by, putting off until tomorrow the objective of the day's session? And that's not all: students who are sure they've passed their homework talk about the chips in the canteen, next to those who, having done it more or less, don't understand the correction. In short, the learning-by-doing ratio is very low!
Capturing the attention of the students during this phase of the session is therefore a challenge. If the pupils are to be able to follow and understand the corrections, this phase cannot be the heart of the session and must be quick.
‘OK, but how much time do you need to correct the exercises?
From experience, I'd say that 25 minutes is already too much. It's easy to feel students' attention waning as the correction phase lengthens, whether or not they need it to make progress. In short, it's a tricky time for teachers, especially at the start of their career.
‘So you might as well not correct them in class, just give them the answer key...’.
Understanding an answer key is not that simple. The aim of an exercise correction phase is for the students to present their answers, discuss them and clarify any misunderstandings. So I think it's important to correct everything you give students to do in class, even when you're pressed for time. What's more, it's an effort that the students have made, and feedback on their work is of interest to them.
I propose that we discuss 2 points:
1. How can we avoid getting bogged down in the exercise correction phase?
2. How can we differentiate our expectations during the exercise correction phase?
1. How can we avoid getting bogged down in the exercise correction phase?
Limit the amount of homework per day, but give it very regularly
In a forthcoming post, I'll be giving my opinion on what homework should be. So we won't go into it here.
It's essential to anticipate the correction phase before giving pupils exercises to do outside the classroom. It should not be too time-consuming. Limiting the amount of time spent on correction means that few exercises are given, even though I think it's essential to give them frequently: after every session or so. Furthermore, the level of difficulty of these exercises should remain reasonable. Challenging some students who don't have maths help at home will discourage them.
‘Gosh, I'd have liked to give the students some challenging problems, which aren't just practice exercises’.
Of course, there's nothing wrong with that. However, if you want almost the whole class to benefit, you need to set up a special system. Here are two ideas:
Start solving the problem during a class session, with the whole class, and make it clear to the pupils that they may not manage to solve it despite their best efforts, but that it's OK as long as they've thought about it and kept a record of their research in their notebook.
If you want to give a really tough maths problem, you can give the class several weeks to solve it. And once or twice, organise an interim assessment of their research in class. It's not easy to organise, and it will be difficult to know who, among the students, has played the game or not. But for those who have, you'll have put them in a mathematical research situation, and that's what we're aiming for!
‘Why not, but what about the bulk of the exercises to be done at home?
The exercises to be done from one day to the next will be exercises to apply part of the lesson written in class. And we don't give too many, so that we don't spend the whole hour correcting them.
‘So how do you organise the correction phase?
Here are a few tips that have been tried and tested by many colleagues to speed up the correction of exercises.
The first tip is well known to experienced teachers: if an exercise involves repeating a technique, send several students to the board at the same time. If you want to take the time to explain, take the time to add fractions on the board while explaining, and send several pupils to the board for the following ones. This means that you need to plan the organisation of the board, the number of markers, etc. But I know that's not easy. But I know that comes naturally to you ;)
‘But how do I know if the exercise has been very successful or not? And who do I send to the blackboard?
Go round the rows, it's necessary to check the homework (see another blog post: How do you make sure that homework is done properly?), and what's more, you'll be able to estimate the level of success of the class on this exercise. You'll then be able to decide how much time you're going to allocate to marking, and which students you want to send to the blackboard. If an exercise has been passed by all or most of the class - dream on - you don't even need to correct it, you can congratulate the class and move on to the next one. For the two who didn't manage it, you can correct it next to them when a pupil comes to the blackboard or during tutorial time. And if you find that half the class has made the same type of mistake, send a pupil who has made the mistake to the blackboard, and take the time to discuss it, even if it means giving another example after the correction.
‘Sir, I found 24 and Maïa put 27 on the board’, said Joshua, “That's because it seems to me that 3 times 9 equals 27 and not 24 Joshua”, I replied.
You want to avoid this kind of dialogue. Especially as it's not just one pupil who will want to share his silly arithmetic error with the class. Here's a little idea for filtering out superficial questions. From experience, I've found that it works quite well, so I'll share: ask the students to correct each other in pairs, and discuss their disagreements calmly. Don't exceed one minute of intensive debate, no more is needed. They can correct each other's arithmetical errors and other blunders, and you can focus the correction on the deeper errors that you want to discuss with them.
‘What you're saying is for technical calculation tasks, but for exercises involving more writing, a geometry demonstration for example, it takes an inordinate amount of time to get a pupil to write his answer on the board.
Not wrong, but there are tricks. The least convincing one: if you feel that the pupil is going to take a long time copying down his notebook on the board, copy down his answer for him. They're certainly not the fastest at the blackboard! Next, I'd like to introduce you to a very practical tool: the visualiser. At the moment, visualisers are springing up like hotcakes in secondary schools, and with good reason. It's a camera on a stand that sits on a table. Connected to the computer in the room, it films and takes photos. The films and photos can be projected to the class in real time. For example, to avoid the time it takes to copy the answer on the board, you can place the exercise book under the viewer's camera and project. This allows you to comment on and correct the student's answer live, on the board or directly in the student's notebook. As well as being popular with the pupils - if you call your visualiser Véro, it's a guaranteed success from Year 6 to Terminale - it saves a lot of time: no more time-consuming copying of a notebook by a pupil on the blackboard while the class waits. Correction can begin immediately. Incidentally, the visualiser is not an expensive tool compared with the maths budget of schools.
In the same spirit, some colleagues take a photo of a pupil's notebook and project it. It's obviously more difficult to do this in class; while we're dealing with the technology, we're not running the session!
‘All right, but that doesn't stop students who have done their exercises without difficulty from getting bored during the correction and starting to do something else.
It's not an easy problem to manage. We're often on the edge during these corrections, and even if we get silence, many students have nothing to gain from the correction. In what follows, I'll show you how to solve this problem, even if it leads to others, but you're used to that ;)
2. How can we differentiate our expectations when correcting exercises?
Students who systematically succeed in the exercises we give them are generally the most independent and, statistically, they concentrate on maths problems independently for longer than students who have difficulty with maths. We might as well make the most of it! When correcting exercises, unless you want to rush it, it's not really appropriate for the students with the strongest maths skills to be systematically questioned. Firstly, the ‘right answer’ won't necessarily help the others to understand, and secondly, asking them systematically will set the session off at a very fast pace, and part of the class will watch the train go by... The students who are strong in maths might as well keep themselves busy.
Here's the proposal:
Stipulate to the class that those who have passed the exercises and are confident can do new ones. Gloups, ah yes it's true, you must have anticipated these new exercises, sorry... Tell them to check with one eye that they've done the exercises at home. And, of course, don't let them talk, as the teacher and other students will be working together on the exercises to be corrected while they work on the new statements.
‘But you're raving. A lot of them are going to go on to the next exercise without paying any attention to the correction, even though they didn't get it right. It's going to be a bloodbath!
I'd advise you to experiment. That was also my fear when I first tried this method. In fact, it works quite well. I think we underestimate students' ability to assess their own needs. In my experience, I'd say that some students move on to the next stage because they're too sure of themselves and they're convinced they've succeeded when they haven't. In the end, it's been the same for every student. In the end, each time it's been an opportunity to discuss with him his desire to rush and the fact that I won't think any less of him if he actively follows the correction of the exercises - incidentally, in my classes, it's always been boys, strange isn't it? On the other hand, what is less anecdotal is the opposite phenomenon, i.e. students who follow the correction because they lack confidence in their homework. You then have to convince them to trust themselves and move on. And strangely enough, up until now in my classes, the vast majority of these students have been girls. It's an opportunity for them to self-assess their work, so you might as well take advantage of it. What's more, by doing this, you show them that you trust them. Obviously, as usual, the circulation in the rows is essential to regulate this differentiated operation of the exercise correction phase.
‘But if they don't succeed in the exercises, that should generate questions, while we're doing something else with the rest of the class.
That's true, it's tricky, we're at least at level 2 of behaviour management in the classroom. No matter how much we explain to them that they shouldn't ask questions of the teacher or their classmates, they tend to do it anyway. Understandably, it's frustrating to get stuck, when the answer is probably on a nearby table or in the teacher's head. In short, it will take them some time to adopt the behaviour you expect for this phase of the lesson. You'll need to explain to them the reason for this behaviour: to allow students who haven't succeeded in their exercises to benefit from calm and the best conditions for understanding. And, if necessary, enforce these behavioural expectations through corrective action.
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