Two big ideas (but six concepts)

Equations- Formulae – Identities

Sequences- Functions – Graphs

• An equation is : : A connection indicating equality between 2 expressions

x - 4 = 9 (with a limited or finite number of solutions)

• A formula is: A formal rule expressing a result Area = Length * Width

• An Identity is: An equation that is true for all values of the variables.

x² – y² ≡ (x – y) (x + y)

• A sequence is: an ordered list of numbers (called "terms"), such as 2,4,6 … which often leads to a generalisation expressed algebraically

• A function is: a rule that gives value for a variable (called the dependent variable) that corresponds to specified values of one or more independent variables. What is confusing is that we use an equation to state the relation between two variables, so, the equation y = x² is actually a function

• A graph is: a pictorial image of the connection between two or more variables.

A review of the key algebraic teaching ideas suggested that three ideas were:

1) relating reverse operations to equation solving;

2) pictorial equation solving;

and 3) using both arithmetic and algebraic approaches to solve problems.

The process of simplifying expressions, the understanding of equality and the use of word problems to given context and reality is all important when beginning the algebraic learning journey.

From the above it is evident that the educator needs to pay particular attention to the specific challenges in certain topics of algebra learning. The challenges are a direct result of the structural nature of algebra, cognitive gap, and to some extent the absence of teaching approaches.