Mathematics is conceptually based... not skill based. Understanding of one concept is needed to understand another concept, and another concept, and another concept…. 

Existing Professional Learning covers:

     * Problem Solving
     * Algebraic, Additive and Multiplicative Thinking
     * Instrumental vs Relational Thinking

Many children (and indeed adults) have gaps in this relational understanding of mathematical concepts and so their learning plateaus.
Children in the first three years of school think additively - this means thinking in terms of Addition and Subtraction.
Following these years, children begin to think multiplicatively about Place Value, Multiplication and Division and Fractions - this means thinking in terms of Multiplication and Division.
As Jacob and Willis, pointed out at the MERGA Conference 2001 'Unless teachers consciously help children develop multiplicative thinking, which goes well beyond repeated addition, it may not happen for many children.'

To teach for deep understanding requires the teacher to have deep understanding. This is particularly true when teaching mathematics.

The Mathematics professional learning resources, and the Teaching resources at A Learning Place A Teaching Place, will deepen teacher understanding as the teacher is developing their students’ understanding.

Mathematics involves much more than computation and calculation. Mathematics involves explicitly and intentionally thinking algebraically, additively and multiplicatively in appropriate situations. We think algebraically as we look for patterns in relationships in our world. Additive thinking involves thinking in terms of addition. Multiplicative thinking involves thinking in terms of multiplication - in orders of magnitude.

Mathematics may be taught and learned instrumentally or relationally. Instrumental learning involves possession of a rule and the ability to use it. Relational learning involves knowing both what to do and why.  

The Teaching and Professional Learning resources here at A Learning Place A Teaching Place, provide Scope and Sequences and Concept Sequences, allowing teachers to teach children to think mathematically, and to learn maths relationally. The resources will not only enhance your students’ mathematical thinking and understanding, but yours too! Browse now!