„A nice example, taken from lower-secondary education, illustrating this point, is the pocket money problem:

An and Susan are saving money. An already has $ 50 and receives $ 2.50 each week, while Susan gets $ 4 each week and saved $ 26 up to this moment. After how many weeks will they have the same amount of money?

Mathematical professionals will immediately translate this little fairy tale into the ‚real‘ world of algebra: 2.5x + 50 = 4x + 26 with solution x = 16.

Students who are offered such problems before any theory about linear equations is presented, will choose other strategies.

Create two tables in which the amounts of money are compared week after week. Some will make shortcuts in this table, because regularities are recognized and used.

Or a dynamical setting in which students solve this problem just by reasoning: At this moment Susan is $ 24 behind An. Every week she gains back $ 1.50 So after 24 : 1.50 = 16 weeks they are equal.

Even after linear equations are instructed in a formal, algebraic way, many students will use the contextbound strategies to solve contextual problems. For most students the contexts are the real world and the formal system is a not-so-fairy-tale.“

van der Kooij, H. (1998). Useful mathematics for (technical) vocational education. In Proceedings of ALM-5. London: Goldsmiths College, University of London