How mathematical ideas develop in children

First steps in learning a mathematical concept

Learning occurs by linking and connecting a new idea to something that is already known.  New vocabulary is mostly learned in context with words or actions already known to the student.  In math, students need to be able to physically see and manipulate the task in order to learn it.  Being able to visualize the task and remembering it is building conceptual knowledge.  That is why ladders, number lines, and fingers are popular teaching tools in counting–students need to be able to see something to count.

In other words, teachers should first represent the new task with physical objects, drawings or other visual representations.  Then the teaching is in linking the objects to the problem, as in, showing the students how the math problem relates to what they see in front of them.  Then, once students can understand the problem and can explain it, students should then ‘act’ on it, and solve the problem.

Teach students how to act on math problems, not how to answer them

What is particularly unique in math is how concepts are related to each other (addition is related to multiplication, subtraction is the inverse of addition, etc).  It is important that students understand these relationships before they are taught how to find the answer.

In short, teachers should first teach in quantities (physical objects), then teach the symbols and language, and then teach the link/connection between them.  Students should then be able to visualise the task (problem) and explain it in their own words.  Finally, students should practice over and over to automatise the procedure.  However, a student may have a learning difficulty in any or all of these areas, which needs to be catered for.

Growth Points for Four Domains of Number

Growth Points for Four Domains of Number

DEECD Maths Developmental Continuum


Below is a link for comparing the VELS curriculum to the new Australian curriculum in mathematics. has developed comprehensive curriculum guides for AUSVELS. They offer a free preview, but to get unlimited access you or your school will need to purchase a license.


Copyright Dr. John Munro 2013