Research-based guidance and classroom activities for teachers of mathematics

Algebra arrows (function machines)

This Java Applet on the Freudenthal Institute for Science and Mathematics Education (FIsme) website allows learners to set up their own arrow diagrams to construct functions and inverse functions.

The boxes need to be dragged onto the screen and linked by clicking and dragging the arrow heads to join the boxes. Input can be numbers or letters, and output can be given as values or as expressions involving numbers or letters as input. All the operations are unary (this means they act in one variable only) so can be turned around to solve linear equations.

The Applet also offers squares and square roots. Some critics have said that the function machine/arrow diagram approach can embed a ‘left-to-right’ misconception of reading algebraic expressions. However, because this Applet can be set to give the correct conventional expression for the selected sequence of operations it can be used to contradict a ‘left-to-right’ tendency rather than embed it.

Go to the Algebra arrows Applet on the FIsme website >>