### What is an integer?

Here are some ideas pupils need to learn about integers: •A number represents a quantity. An integer is a type of number. An integer represents a quantity. •Integers are useful in representing quantities and includes opposite sense. For example, going up 5 floors and going down 5 floors can be represented by +5 and -5…

### What is algebraic thinking?

In my post Arithmetic and Algebra, I wrote that it’s how you solve a problem that tells whether you are doing algebra or arithmetic, not the problem itself. Here’s a description of algebraic thinking that I think teachers in elementary school mathematics might find useful especially when they are teaching about numbers and number operations:…

### Levels of understanding of function in equation form

There are at least three representational systems used to study function: graphs, tables and equations. But unlike graphs and tables that are used to visually show the relationships between two varying quantities, students first experience with equation is not as a representation of function but a statement which state the condition on a single unknown quantity.  Also,…