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Is mastery just a passing fad?

 

Nicola Randall, Mathematics Teaching and Learning Adviser at Herts for Learning

Before I even start to tackle this question, I think it is helpful to clarify what we mean by ‘fad’ and the best way I could think of doing this was to consider some examples.

  • Leg warmers worn anywhere other than inside a dance studio: fad
  • No make-up selfies: fad
  • Replacing actual laughing with the word “LOL”: fad
  • Dressing as clowns and scaring people: fad

Continue reading “Is mastery just a passing fad?”

Why dodecahedrons hate CPA.

Rachel Rayner is a Primary Mathematics Adviser for Herts for Learning

For a blog about the CPA approach click here.

Yes, teachers do label their fixed ability groups by shapes…still. Yes, pupils do end up in the circles group from the age of five and in some cases in the teacher’s head, younger.  And yes, it damages.  We are all by now familiar with the work of Carol Dweck and the idea of fixed and growth mindsets.  But in maths at least this fixed ability grouping or setting persists in Primary, despite the evidence that it can be detrimental to those pupils designated ‘circles’ or ‘triangles’.   Continue reading “Why dodecahedrons hate CPA.”

Reflections on Introducing Middle School to the Concrete Pictorial Abstract Pathway

Louise Racher is a Primary Mathematics Adviser for Herts for Learning.

I am pretty lucky. I get to “do” maths all day every day.  Gone are the days when I used to teach PE, history, geography, English … and so on, as well as dealing with hormonal Year 6 children … to have the permission to think about one thing only, mathematics, is an indulgence.

I am still learning, and changing my opinion about which approaches will make the biggest difference, that will continue to change I am sure. What I do know is that the experiences I had in school were not good enough.  Rote learning, procedures with no reason, struggling to keep up, sometimes copying my neighbour to get me through the lesson, because maybe I will be OK on my own tomorrow.  I am passionate about the use of manipulatives across the Primary phase, and into the secondary phase.  So, to have the opportunity to talk to teachers in a middle school and really sell my passion was a great opportunity.  Continue reading “Reflections on Introducing Middle School to the Concrete Pictorial Abstract Pathway”

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”

The ‘CPA’ Approach

Rachel Rayner is a primary mathematics adviser for HfL

One of the most fundamental learning theories to be implemented within any mastery classroom is the ‘CPA’ (Concrete, Pictorial, and Abstract) approach. It was first proposed by Jerome Bruner in 1966 as a means of scaffolding learning. The psychologist believes that the abstract nature of learning (and this is especially true in mathematics) is a “mystery” to many children. It, therefore, needs to be scaffolded by the use of effective representations. He saw that, when pupils used the CPA approach, they were able to build on each stage towards a fuller understanding of the concepts being learnt and, as such, the information and knowledge were internalised to a greater degree. This allowed the teacher to build upon this secure learning. Bruner, and others, demonstrated that each stage of the approach acts as a scaffold for subsequent and connected learning. Continue reading “The ‘CPA’ Approach”

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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