The teacher projects a series of questions on the board; the questions all have the form of those previously discussed, except for the last one which is ‘4% of 30?’. An instruction is given that students should copy the date and title down and then work through the questions in order, once again showing ‘full working out’, and it is repeated that this work should be done individually and in silence. A student is picked to repeat the instructions back and then the class is told how long they have for the task, and they state that this is a maximum amount of time.
What may the teacher’s previous assessment have provided to inform them of the suitability of the class working through a series of questions in this manner? Is it appropriate for every student to begin in the same place, to complete every question? Is there sufficient challenge for students here? Is there sufficient development of mathematical thinking for students here?
Is there any scope for the teacher to makie changes from their plan based on what they have observed and assessed, or do they stay with their plan regardless?
What is gained and what is lost by not allowing any discussion?
What is the desired outcome when a task is presented with the structure of questions described here? How many questions of a similar type are enough to present to students? How many is too much?
The teacher praises every student for starting the task and they then circulate among the students. The students they initially select for one-to-one attention are the three who displayed the equivalent of ‘I don’t know’ during the preceding work on whiteboards. After a brief amount of time spent with each, those students then appear to answer some of the questions independently.
Is this the best method to offer support to students in this situation? What other approaches could be utilised?
How likely is it that these students are often if not always the first or among the first to receive individual support? If that is the case, what may cause this to happen?
As the students complete the work, the teacher then circulates amongst them, looks over their shoulders at what they have and are writing down and stops to offer both support and ask questions of a few.
What may inform the teacher’s decision about how to move around the room and in which order they visit students? What decisions may influence which students they select to spend longer with - has this been determined before the lesson or by information gained during it? How much variety from lesson-to-lesson is there in which students are selected for individual attention?
As the teacher is talking with one student, conversations between students start in two different places in the classroom. One conversation is about the mathematics being undertaken, one appears to be about a football match. The teacher stops their own conversation, praises the majority of the class for working well and following instructions, and says they now expect this to be true of all of the class. The conversations quickly stop.
In a situation such as this, what may be the cause of conversations both “on” and “off” task, despite the teacher’s instructions?
A very short time later, whilst the teacher is still with the same student and well before the stated time for the task has elapsed, a student puts their hand up and then tells the teacher they have finished; a few other students also have put their pens down and are nodding. The teacher briefly says something to the student they are with and then tells the class to finish the question they are on whilst they go to the front and get the answers ready to project. A short time later, the answers are projected and the students are told to mark their own work. They are told that if they got any wrong answers, they should copy down the correct answer and try and work out where they made their mistake.
Based upon this description, to which students has the time given for this task been based upon? Does the teacher know that sufficient time has been provided for all? What message may this be sending to the class about how their lessons work and who they are for?
In this lesson, if students do not understand the work, where does responsibility lie? What strategies have been developed for this situation, and what may be witnessed or evident to make this clear?
How likely is it that students ask for help if they are stuck in a lesson such as this? What classroom culture facilitates this, and what signals are there that such a culture does or does not exist?
What has been done here to help build students’ confidence in themselves as mathematicians?
Next: lesson ending and final reflection
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