Abstract
The professional development of mathematics teachers needs to support teachers in orchestrating the mathematics classroom in ways that enable them to respond flexibly and productively to the unexpected. When a situation arises in the classroom which is not connected in an obvious way to the mathematical learning intentions of the lesson, it can be challenging for the teacher to improvise so as to craft this situation into an opportunity for doing and learning mathematics. In this study, as teacher-researcher I maintained a record of unexpected situations as they arose in my own secondary mathematics classroom. Details are given of four unexpected situations which I found ways to exploit mathematically, and these are analysed to highlight factors which may enhance a mathematics teacher’s preparedness for dealing with the unexpected. The results of this study indicate that deviating from the intended lesson to exploit an unexpected situation in which students have shown some interest can lead them into enjoyable and worthwhile mathematical engagement.
Highlights
The mathematics classroom can be a complex and dynamic place in which unexpected situations may take even an experienced teacher by surprise
I reassured the class that I was joking and as the class seemed still engaged by this exchange, I asked: “Hey, do you think there could be two people in the room with exactly the same number of hairs on their heads?” Some immediately called out “No way!” and I suggested that they discuss this question in pairs. It was at this moment that I recalled noticing that an “unexpected situation” had arisen, as this study was not in my mind at the start of the lesson
Exhorting teachers to be flexible and responsive to contingent classroom situations goes against the grain of much current teacher education and professional development (Foster, 2013b)
Summary
The mathematics classroom can be a complex and dynamic place in which unexpected situations may take even an experienced teacher by surprise. Xi–xii), teaching is “full of unexpected events, un-looked-for surprises, and unanticipated twists and turns”. He insists that “the one thing teachers can expect with total confidence is uncertainty” While this never-a-dull-moment aspect of teaching might at times be stimulating, it can present the teacher with major challenges. An increasing body of research, over the last 10 years, has addressed mathematics teachers’ contingent behaviour in the classroom
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