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variation theory

CPA: using Cuisenaire to support pupils to develop fractional understanding

Louisa Ingram is a primary mathematics adviser for HfL

Identifying Fractions

To begin with, pupils need to become familiar with assigning a value to a rod and finding the fractional value of the other rods. A good starting point is to find the value of the white rod as this then allows you to find the value of all other rods. When the brown rod equals 1; the white rod is one eighth. Compared to dark green, the white rod’s value is one sixth. Against blue, it is one ninth and against orange one tenths etc. You can then start to apply this such as assigning the brown rod a value of 2. Through this you can also draw attention to fractions such as which rod is one half, one quarter, one third the length of etc. Continue reading “CPA: using Cuisenaire to support pupils to develop fractional understanding”

Making Every Question Count

Charlie Harber is the Deputy Lead Adviser for the HfL Primary Mathematics Team.

Do pages and pages of repetitive questions deepen our children’s understanding?

Teaching to mastery requires a mind shift on many different levels and presents many challenges (differentiation, whole class teaching, culture and ethos to name but a few). It is underpinned by a range of theories… You can’t explore mastery for long without encountering ‘Variation’ theories. There are two distinct variation theories (conceptual and procedural) which develop symbiotically to grow deep conceptual understanding in learners. These theories are used widely in the high performing East and South East Asian countries. They are exploited skilfully by teachers to expose the underlying structures of mathematics and allow children to ‘self-discover’. Continue reading “Making Every Question Count”

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