After this second example is completed, another question is written on the board: 60% of 40? The teacher tells the class that they wish everyone, without exception, to answer the question on whiteboards and reveal in the usual way after a countdown. They tell them that everyone, without exception, must attempt this, and that all students must show working out exactly as written on the board. The teacher asks if anyone has any questions before they begin; two students put their hands up. The first student picked shares that they already know the answer, can’t they just write the answer down? The teacher shares that there are many reasons why we show our working out, including that it is important for examinations, that it will help them with harder questions, and that it will also make it easier for the teacher to help if needed.
Given that this is neither an examination nor - apparently - “a harder question”, are these valid reasons to present here? If the primary motivation for this working out is that the teacher can observe that students are apparently following and applying the method they have introduced, would this solely not be enough of a reason to present to students?
When do and when do you not show your methods when answering questions in mathematics? What is your motivation for doing so, or not doing so? What dictates the level of detail included?
The second student states that they ‘don’t get it’; the teacher responds that they should try their best and that they will help them soon.
What strategies can students be encouraged to implement when they do not ‘get’ something? When is it appropriate to vocalise these, and when is it not? How could a mathematics classroom operate so this becomes second nature to the point the statement is less likely to be made?
The teacher then instructs the class to answer the question in silence, and tells them they have twenty seconds. When the time elapses, the teacher asks everyone to reveal their answers. The teacher’s head movements indicate that they are scanning the whiteboards, where it is evident to the observer that most students have reproduced similar working out to the teacher and obtained an answer. Three students have written the equivalent of “I don’t get it” or incomplete methods. The teacher thanks the students and tells them to put their whiteboards down, before sharing that the correct answer was 24 and that as they were happy with what they saw, the class is going to proceed to practice questions to be completed, in silence and individually, in exercise books.
After stressing the importance of working out, if the teacher then only emphasises attention on the 'correct answer' what are they implictily telling the class?
Is individual work moved to at this point because the teacher has assessed that “the class” is in a position to do so, or because the plan - whatever its source, as previously questioned - dictates this is the point to do so?
If this move is a result of the teacher’s assessment, what number (or proportion) of the students not displaying what they wanted is considered acceptable in order for this to still happen?
As will be described, the teacher goes to the three students to offer individual support at the outset of the next section. What other strategies could have instead been potentially implemented to support these students?
Next: individual work
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