# Populating the Framework

- Cambridge Mathematics
- Consultation
- 4 - Populating

### QUESTION 4: populating the framework

The two dimensions of the framework that have already been defined through this consultation are the domains in maths, as discussed in Question 1 (how to cut the maths) and the progression in learning, largely age related but not necessarily so. This time I'm thinking about what to actually put in the body of the framework. I worked with Mike Askew on various different models and one we were taken with was that espoused by Kilpatrick et al 'Adding it up: helping children learn mathematics' who set out five strands:

(1) Conceptual understanding refers to the “integrated and functional grasp of mathematical ideas”, which “enables them [students] to learn new ideas by connecting those ideas to what they already know.” A few of the benefits of building conceptual understanding are that it supports retention, and prevents common error

(2) Procedural fluency is defined as the skill in carrying out procedures flexibly, accurately, efficiently, and appropriately

(3) Strategic competence is the ability to formulate, represent, and solve mathematical problems

(4) Adaptive reasoning is the capacity for logical thought, reflection, explanation, and justification

(5) Productive disposition is the inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

Of the five strands we thought strands 1, 2 and 4 could be particularly useful descriptions to map a landscape of maths (whilst strands 3 and 5 we would reserve for another dimension). For example, on the journey to multiplicative relationships with whole numbers, we might put 'factorising' as an example of strand 2 whilst 'generalising from patterns of factors and multiples' could be strand 1 and 'using the associative and distributive laws to simplify calculations' might be strand 4.

I'd welcome your thoughts on whether these are appropriate aspects on which to focus.

(NRC, 2001, p. 116) National Research Council. (2001). *Adding it up: Helping children learn mathematics*. J Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press

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