In some selective school and scholarship tests they may test mathematics and then also mathematical reasoning.
In general, and from experience with these tests, mathematics is just the knowledge of formulas and whether you are up to date in the knowledge of mathematics that the curriculum for your child’s year level prescribes. For example, if you’re in Year 9, you’re supposed to know fractions and maybe some linear equations. They’re mathematical concepts.
However maths thinking or mathematical reasoning is a slightly different thing. It’s using mathematics to reason through a problem and find a solution. That means, you won’t get something like this:
2 x 5 + 10 / 2 = ?
This is too direct and pretty much tests your ability to calculate.
Instead, with mathematical reasoning questions, you might get a question like this:
Kris rides on a jeep at a steady rate to the market and walks to home at a different steady rate. Her total travel time was 28 minutes. If she rides on a jeep both ways, her total travel time would be 14 minutes.
If she walks both ways, her total travel time would be?
(Question sourced from www.examsuccess.com.au online mathematics course for selective and scholarship exam preparation).
So the main difference is that mathematical reasoning asks you to find out which operators to use and how to solve that problem USING maths, however, usually mathematics is usually the knowledge of mathematical concepts.
So, which one does the ACER test? It depends on the test involved. Looking through publicly available ACER tests, it seems that they really test mathematical reasoning (as it’s harder) but they call it just mathematics.
Tip for your exam: Know your maths for your curriculum level and above, but also think about how you can APPLY the maths you have learnt to different scenarios.