Assessing Mastery at KS3
The NCETM has recently produced a set of Key Stage 3 Mastery Assessment Materials to complement those available for primary teachers. In this article we look a little at the rationale behind the materials and share some experience of teachers who have used them.
Have you read the recent EEF guidance report, Improving Mathematics in Key Stages Two and Three? It offers eight key recommendations with a focus on ‘improving the quality of teaching.’
The first of these recommendations is to
- use assessment to build on pupils’ existing knowledge and understanding
and the eighth recommendation is to
- support pupils to make a successful transition between primary and secondary school.
How do we, as secondary teachers, support pupils as they move from KS2 to KS3? How do we find out what they know and build on it? Are we aware of the high expectations of the new primary curriculum? You may have already noticed the impact that the increased focus on fluency in primary school has had on your current Year 7s.
As well as building fluency in calculation, primary pupils are expected to reason mathematically.
Have a go at this question from this summer’s KS2 SATs:
Did you calculate the volume of the cube, or did you use reasoning to simplify the calculation? What do you think your Year 7 students did when faced with this question last summer?
The EEF guidance report mentions that
‘one large national study of primary attainment in England found that, at the end of Year 7 - a full year after the transition to secondary school - pupils’ performance on a test of primary numeracy was below their performance at the end of Year 6’
and poses the question:
‘Are primary and secondary schools developing a shared understanding of curriculum, teaching, and learning?’
In order to help develop a shared understanding, and to support teachers of KS3 to smoothly continue the journey started at primary school, the KS3 Assessment Materials have been explicitly designed to follow on from the NCETM’s Primary Assessment Materials that have proved immensely popular with teachers, now downloaded over 1.3 million times. The questions allow teachers to find out what children in their class already know and so build on this in their lessons. Questions that offer pupils a chance to reason mathematically, and to expose what they know so that the teacher can build on it, are time consuming to create so the Assessment Materials are designed to assist teachers in this.
The KS3 Mastery Assessment Materials document (published as a PDF for easy printing) is divided into sections that address many of the content statements in the KS3 Programme of Study. It is designed to be used in different ways, each giving students an opportunity to show what they know or have learned.
Used as pre-assessment to find out what pupils know already, you might predict what errors you think the pupils will make, then use the questions to find out if they do. Focus on listening to what they’re saying rather than correcting mistakes for a while, then use this to inform the focus of the content, and the starting point, when you come to teach it. It’s worth noting that this not only shows what pupils can’t do, but also gives an opportunity to find out what they can do.
An example of using the questions in this way comes from one teacher who was preparing to teach her class a unit on angles in polygons and who used this question from the Geometry and Measures section:
During the discussion that followed, she unexpectedly found that a number of students in the class shared the unusual misconception that a regular polygon with ten sides should have angles of 10°. She was able to tailor the next lesson to explicitly explore and address this misconception with the class.
She plans to return to the same question midway through the unit, or towards the end of the unit and ask the students to correct or improve their work, or talk about how they’ve changed their mind.
While this misconception was not one that the teacher had come across before, some misconceptions are common and can be predicted and explored using questions like those in the booklet. An interesting task at a department meeting might be to choose one or two questions, such as those below, and discuss the misconceptions that might be exposed when they are given to a class:
You might choose to use some of the questions in the booklet as an assessment task at the end of a section – maybe through homework questions for pupils to give a written explanation of their methods, or to stimulate a discussion between pupils to challenge their understanding. One teacher who used this question:
as a consolidation task at the end of a lesson on finding percentages of amounts found this comment in one of the pupils’ books at the end of the lesson:
The document is intended to provide a source of questions that expose misconceptions and show pupils’ understanding. A good starting point might be to show one of these questions on the board in the last five minutes or so of a lesson, sit on your hands and listen to what your class think. In listening carefully to their responses, you may find that you’re better equipped to start the next lesson, building from what they already know.