Educational Designer

The argument that students need experience of unstructured, open-ended tasks - with authentic problem-solving elements in which the correct ‘tools’ to use are not immediately obvious – has been made elsewhere. One challenge is that such tasks tend to have a range of solutions of equal validity but different levels of sophistication. In mathematics, for example, a problem may be soluble by a simple ‘guess and check’ approach at the expense of more ‘elegant’ and generalizable algebraic or graphical approaches. Although the learning aims of the lesson probably included the more advanced solutions, the ‘easy’ solution can’t be rejected and students may have difficulty in seeing the ‘payoff’ from a ‘harder’ solution. Specifically telling students to, say, “Solve it using linear equations” destroys the problem-solving elements of the task.

While the students are fictitious and the work has sometimes been created by the design team, it is inspired by actual student responses observed during trials and uses extracts copied from real work where possible. It reflects common mistakes and misunderstandings observed in real students as well as rarely seen, but desirable, sophisticated techniques.

Students could also compare and critique each other’s work, and this is also a feature of the MAP lessons. However, using ‘designed’ sample work ensures that students see the more sophisticated solutions and learn to recognize common mistakes. Also, having fictitious students to criticize can help avoid social tensions intruding on the learning. Some of the implications of these resources for teacher behavior are discussed in Evans & Ayalon (2016).