Maths Related Miscellany

Maths teaching has been my primary focus throughout my career. I have been blessed with opportunities to teach in some great schools, learn from and work with talented and expert maths teachers in a variety of contexts.

As a perennial tinkerer and someone who is often better at generating ideas than following them through, there are various maths related projects I have worked on, some of which have made it to a usable form. The online maths tools and sites that are available are detailed in the projects section, where I also write short posts explaining each tool and the purpose behind it.

Here are other things that I have worked on, often for the dual purposes of supporting other maths teachers and clarifying my thinking.

Number to Algebra Concept Pathway

An attempt to clarify and connect concepts of number together and to their generalisation in algebra, through four chains:

  • The arithmetic-to-algebra spine: Place Value → Laws of Arithmetic → Area Model → Division → Fractions → Factors and Primes. **
  • The equality-to-algebra spine: Equality and Equivalence → Variable as a Concept → Expressions, Equations, and Identities.**
  • The proportional reasoning pathway: Multiplicative Reasoning → Division → Fractions → and onward into ratio, proportion, linear graphs, and trigonometry.
  • The generalisation pathway: Laws of Arithmetic → Scaled Tables → Generalising from Patterns → Variable → Expressions, Equations, and Identities.

The framework rests on six unifying principles:

  1. Number is structured
  2. Operations have meaning
  3. The laws of arithmetic are the grammar of the framework
  4. Algebra grows out of arithmetic
  5. Fluency comes from understanding as well as practice
  6. Representations reveal structure, and pupils should move fluently between them

None of this is new. I am drawing on well established mathematics and widely respected pedagogy. Many teachers will recognise much of what is here as consistent with what they already do. My hope is that this is helpful with developing the precision and accuracy in teaching, that scaffolds as many pupils as possible to successfully understand these crucial concepts.

Explore the Number to Algebra Concept Framework