# 4 Mathematical Reasoning and concept strands

**Reasoning progression in mathematics learning.
**

For educational success at key stage 4 and beyond pupils need to develop the formal operational thinking defined by Piaget (see page 6). In order to see how this could be facilitated the level of thinking demanded for each achievement in secondary school mathematics was assessed.

**Concept strands**

The Thinking Maths lessons cover the 6 key concept strands in the KS3 National Curriculum:

**Number, Algebra, Ratio, proportion and rates of change, Geometry and measures, Probability and Statistics**

Each activity is designed to give the opportunity for formal operational thinking within an identifiable concept strand, while also linking to other strands. The contexts have been chosen to allow two or three different levels of achievement, depending on pupils’ current level of development, rather than having just one ‘objective’. For example, although only a few lessons focus on ‘proportion’ (within the multiplicative relations strand) as the main aim, it is addressed as a subsidiary aim in many others.