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CPA

RUCSAC pack your bags, let’s hit the bar instead

Charlie Harber is the Deputy Lead Adviser for Primary Mathematics at Herts for Learning.  She has  researched the positive impact bar modelling has on pupils’ access to worded problems.

Recent analysis in many schools and discussion with subject leaders confirmed what many teachers have long suspected, that many children have the procedural skills but they  seemed to abandon all reasoning  when they need to apply them once they are embedded in a word/story problem. Many schools in the UK use RUCSAC to help the children, but have you considered why that doesn’t work? Is there a better way, one which just doesn’t prepare them to answer questions in tests, but also deepens operational understanding, exposes misunderstandings and develops reasoning – empowering the children to discuss the mathematics?

Simply put, yes I think there is a better way – bar modelling. Continue reading “RUCSAC pack your bags, let’s hit the bar instead”

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.”

Take One Resource: The Counting Stick

Deborah Mulroney is a Primary Mathematics Adviser for Herts for Learning

In this blog the resource that we are focusing on is the counting stick. It usually has ten intervals but the type with four faces and divided in several ways are most useful. The main use is that it can be thought of as representing a three-dimensional empty number line.

Numberline 1

Continue reading “Take One Resource: The Counting Stick”

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”

Take one resource: the humble tens frame

Louise Racher is a primary mathematics adviser for HfL

The humble tens frame paired with double sided counters. Cheap, effective and perhaps a resource underused by schools in the UK. However, once you start using it you will soon realise the multitude of opportunities there are. The ten squares support pupils’ ability to benchmark from 5 and 10 and is a highly effective route to developing the idea of ‘ten-ness’ and the pattern of numbers leading to effective calculation and number sense. High performing jurisdictions such as Singapore use this model with pupils from a very early age; it is hugely popular in Singapore, America and now increasingly in Hertfordshire.

10s 1

Continue reading “Take one resource: the humble tens frame”

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”

Mathematical Voices

Rachel Rayner is a primary mathematics adviser for Herts for Learning.

How many times have you heard the following?

‘I only really understood maths once I started teaching it.’

We all recognise the importance of subject knowledge in teaching any subject. Many of our schools in Hertfordshire have been engaging with our advisory team to discover what that really means for mathematics. Together, we have wrestled with the fact that the subject knowledge we were taught ourselves may not have translated into the deep conceptual knowledge and understanding we are committed to exploring alongside our charges. That leaves us with personal knowledge gaps that we need to fill. Continue reading “Mathematical Voices”

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