Exploring mathematical representation
This is something I feel passionately about... It is the relationship between graphs and functions/equations/expressions. Students sometimes like the algebra but make no connection with the graph and I think teachers can accentuate this problem by seeing an obvious connection. I let my top set year 11 explore the relationship between a quadratic function and it's graph. They used completing the square, the quadratic formula and factorising into double brackets to explain how the graph was behaving in relation to the function. They could then move onto making predictions of a graph just by looking at the function. For kids in KS3 this should be done with straight line graphs, dedicating a few lessons to the discovery of gradient and y-intercept. Give students a sheet with a few guided questions and bring the discussion together later. A great way to do this is to have groups of four and then get two of each group to be nomads so at ten minute intervals they move to other groups so they can spread their views while also listening to others'. Also packages such as geogebra will help students to explore and explain. To just go through a step by step process of drawing a table then entering x-values and finding y-values then finding coordinates and blah blah blah helps no one and doesn't forge any connections. There is so much to do on this topic and expand into! Please let me know if you have any good ideas to do this! mrmathlete