Models & Didactics on the Complete Mathematics Platform
Written by Mark McCourt Friday, 29 May 2020
Pupils make sense of new mathematical ideas from a range of models, metaphors, examples and instruction. This means teachers need to be equipped with a set of approaches that they can call upon in the classroom.
Well established models, tried and tested over many years, such as the use of Cuisenaire rods, double number lines, algebra tiles, Dienes blocks, geoboards and many more are central to the subject specific pedagogical knowledge for everyone teaching mathematics.
We are adding these models to Complete Mathematics, tagged against the appropriate mathematical ideas so that teachers have immediate reminders of powerful pedagogies for the lessons they are planning.
The specific technical details behind a mathematical idea – the building blocks of the idea itself – are critically important to understand and communicate precisely if pupils are able to make connections across the universe of mathematics as they grow and learn more. These technical details are known as the didactics of the mathematics.
Didactics act as a bridge between the teaching process and the learning process. An understanding of didactics enables teachers to translate the mathematical competencies they themselves have – the mathematics the teacher understands and can work with easily and without having to think – in to a communicated form of the mathematics such that pupils who have never before encountered it can make meaning and grip the idea at hand.
As Jim Fey writes in the seminal book ‘Didactics of Mathematics as a Scientific Discipline’ (1994) preparing mathematics for teaching can be conceived of as elementarization, that is, “the translation of mathematical concepts, principles, techniques, and reasoning methods from the forms in which they are discovered and then verified by formal reasoning to forms that can be learned readily by a broad audience of students.”
We are adding the didactics of mathematics to Complete Mathematics so that all teachers can readily access the technical detail of the ideas they are communicating and see how these mature over time.
These and further updates to the curriculum will be live on the Complete Maths platform in the next few weeks. Stayed tuned for further investigations into this release soon.
About the Author
Mark is the UK's leading authority on teaching for mastery. He has trained over 2000 schools in mastery models for schooling in the UK and overseas.
A leading figure in mathematics education, Mark has led many large-scale government education initiatives, both in the UK and overseas. Mark was a Director at the National Centre for Excellence in the Teaching of Mathematics (NCETM) and has also been a school leader, an Advanced Skills Teacher, a school inspector and a teacher trainer. He founded and was Chairman of the Teacher Development Trust.
Mark has extensive experience of mathematics teaching and learning across all age and ability groups, having taught students from age 3 to PhD!