**Training teachers through inquiry**

**Nichola Sowinska** devised the prompt above for a two-day course she was running at the London Metropolitan University (UK). The students were on the Subject Knowledge Enhancement programme prior to starting a teacher training course. The initial questions they posed about the prompt gave Nichola an insight into their levels of mathematical knowledge and creativity. Nichola reports that the students assumed the equation was quadratic before realising in discussion that the power of *x* did not have to be two. The inquiry developed, with the use of **@****Desmos**, into exploring quadratic equations fully and analysing the differences between graphs of equations with even and odd powers.

**Jamal King**, one of the students, thought the course was very well delivered: "The style of learning, being different to the traditional, really encouraged the class to engage in discussions to find solutions." Nichola adds that the success of the inquiry in the context of teacher training was twofold: "It opened the students' eyes to a different pedagogical approach. It also allowed them to put the formulas they remembered from school into a deeper context and understand links which they had not had the opportunity to make before." Reflecting on the times she has used inquiry, Nichola remarked: "Every time I teach in this way I am always surprised at what my students can do."

**Nichola Sowinska **is a maths teacher in Peterborough (UK). She is studying for a Masters degree at the Institute of Education, London. You can follow Nichola on twitter **@NixxSunshine**.