Mathematical reasoning consists of five parts;
arithmetic, algebraic, proportional, geometric and trigonometric, and statistical and probabilistic reasoning,
and all of these involve verbal reasoning.
Compare the five parts of mathematical reasoning with the five subject content areas of GCSE Mathematics;
Number (arithmetic is from the Greek word for number – arithmos), Algebra, Ratio, Proportion and Rates of Change, Geometry and Measure, and Statistics and Probability.
It is easy to see then, that learning GCSE Mathematics is all about learning to reason mathematically.