I change my methodology based on the pupils sat in front of me but the elements that make it up remain the same. I like to incorporate fun and laughter and a sense of competition with oneself in order to improve. I like to start with some settling questions a pupil can answer and then some questions about the lesson of that day to see what the pupils starting knowledge is. I might then model the skill the pupil needs to progress and we can work through some questions together. At the end of the lesson I would use some form of assessment to find out what the pupil knows now.
I have been teaching in an inner city school in cardiff for the last 10 years. Before that i did a year of supply teaching and tutoring. The pupils I taught at that time were aiming for a grade C. All of them got either the C or improved it to a B. Since then I have worked with age groups from 12 to 18, from the bottom set to the top and produced a range of resources designed to help pupils who are struggling in a traditional maths setting.
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