Research-based guidance and classroom activities for teachers of mathematics

Notations and conventions

Notations and conventions is a theme within quantities and algebraic expressions. Links to relevant activities and resources are on the right hand side of this page. 

Letters can stand for labels (e.g. ABC as the vertices of a triangle), givens (e.g. a, b and c as lengths of sides of a triangle), unknowns (e.g. x in 3x+5 = 20), variables (e.g. x and y in y=mx+c), parameters (e.g. m and c in y=mx+c) and constants (e.g. c in y=mx+c), and some letters (e.g. e, g, π) have specific constant meanings.

  • Students construct their own meanings such as:
  • letters are shorthand for objects, e.g. a = apple
  • letters have fixed meanings, e.g. area = l x w (so l=length and w=width)
  • letters can be seen as alphabetic codes, e.g. a=1, b=2 and therefore p < q etc.
  • all expressions have to be conjoined, so 3a + 5b = 8ab
  • 3m could mean 3 x m, but 32 does not mean 3 x 2, and 3m might also mean ‘3 metres’

To understand the need for rules of notation:compare the different answers obtained by different interpretations to see why rules are necessary.

To understand conventions: explore how different expressions work using computer algebra.

Research shows that holistic ways of relating algebra to situations are successful in helping students to learn the procedures, meanings and uses of algebra. Holistic teaching combinesarithmetic, algebra, data, graphs and functions side by side.