Getting right answers is important. If your bank made mistakes on your bank statement you would rightly be angry. You don’t want air traffic control making mistakes about the flight you’re on.
But equally sometimes mathematics is about getting answers that are close enough. Measurement is based on approximation. If I say I am 1.63 metres tall what I’m really saying is that I’m 1.63 metres to the nearest centimetre. If a recipe asks for 250ml of milk, then in reality I can only measure out approximately 250 ml of milk. Do your learners understand this? Should they?
If learners think that maths is about getting right answers they are likely to find it harder to accept uncertainty, to seek out alternatives, to engage in more open investigation. Analysis of real data often involves levels of uncertainty, for example when looking at correlation, or trying to establish causal relationships. There is a great deal of mathematics underlying research into climate change, but a great deal of uncertainty about precisely what conclusions to draw from this. Do we help our learners understand this?
The Primary Framework’s discussion paper ‘Mathematics and the Primary Curriculum’ concludes with the following suggestions for what mathematics teaching should offer:
• provide children with a balance of exploration, acquisition, consolidation and application
• ensure that children experience the excitement of learning mathematics
• direct and steer children to explore, identify and use rules, patterns and properties and model this process
• build in frequent short and sharp periods of practice and consolidation
• engage with children’s thinking, giving sufficient time for dialogue and discussion and space to think
• demonstrate the correct use of mathematical vocabulary, language and symbols, images, diagrams and models as tools to support and extend thinking
• give well-directed opportunities for children to use and apply their learning
• teach children how to evaluate solutions and analyse methods and understand why some methods are more efficient than others
• pause and take stock to review children’s learning with them
• model with children how they identify their learning skills, and manage and review their own learning.
‘Getting right answers’ is embedded in the list, but there is much else besides. What opportunities do learners have to develop understanding of this wider picture in your classroom?