CMTP: Changes in Mathematics Teaching Project

Home / Department organisation / Purposes and effects of assessment details

Purposes and effects of assessment in year 7 and 8: details

FH used adapted versions after a major (but polite) row about whether they should test what had been taught that year to see if students had understood, or whether they should use tests which provided an NC level for each individual. They did the latter because the majority of teachers wanted to have a sense of students' NC levels.

During the project, the use of self-assessment and peer-assessment became commonplace at LS and SP. We know from observations that these forms of assessment were included in many lessons in FH but we never heard it being discussed.

SP refused to test until forced to do so when their SMT interpreted 'assessment for learning' to mean 'testing every half term'. SP's response was to develop extended 'milestone tasks' which were investigative in nature and needed the use of core curriculum knowledge. They then used a standard test at the end of Year 8 but without any special preparation - much as a snapshot which they understood to be the original purpose of SATs tests.

LS used commercially-produced tests which covered the same material as the standard tests, yet each question challenged conceptual understanding rather than procedural application. There was a high-quality discussion about what made a test useful for students and teachers:

• the questions reminded everyone that they needed to focus on both knowledge and interpretation
• some students could do tests better if the print was a good font and size and the paper is buff-coloured.
• students need tests that let them show ALL they can do, not just answer some given questions
• good questions 'catch' a wide range of understanding
• some students have high CATs scores, but do not know much, so they need questions which challenge their thinking
• tasks must allow students to demonstrate and use their resilience
• teachers wanted to assess thinking, reasoning, resilience, resourcefulness etc. and hence had to be precise about what these mean in a test context.

On several occasions teachers remarked on the ways in which their students tackled test questions. There were three main themes:

• Many students devised their own methods for multi-stage standard test questions, especially those for which they had not been taught the subject matter⁵. Students could use creatively what they had learnt in primary school. Answers were often well-reasoned, even when lacking knowledge, and they showed resilience in trying various approaches.
• Questions that looked as if all you had to do was apply a method were well-answered where it was obvious what to do, but not in situations in which you had to decide what to do. Teachers agreed that they did not often introduce questions which forced students to decide what to apply, and how to do this. They discussed how to help students include application of knowledge in their usual teaching approach (see point 1).
• Sometimes students knew more in one aspect of mathematics than was asked for on the test. This could lead to results that did not show the full extent of their knowledge.

When discussing students who applied some procedures in the wrong order, teachers suggested that they had tried to learn a procedure without awareness of what each step achieves, or that they are trying to behave as if they were fluent before really being fluent. Students might think "in tests I am supposed to just 'do' things, so I shall just 'do' them". The implication for teaching is to give more explicit help about how to prepare and what to do in tests, rather than reteaching procedures.

Teachers expected students to use particular techniques when they may not have had much experience of having to decide what to use, and when, and how to use them. They asked 'how often do we give a mixed bag of non-standard questions so that they have to make these decisions?' In some questions there was progression between question parts, and students did not spot this or use it: 'how often do we offer a progression of questions in class?'

The test questions used in LS all involved multi-stage reasoning and non-standard applications. These require the initial analysis of the question and discussion about how to approach it; some teachers do this with all problems presented in class, but perhaps had not been explicit about 'this is the kind of thing you need to do on your own when faced with a test question'.

A special kind of application was identified in geometry questions, where students knew the relevant facts, and had some geometrical reasoning experience, but had not realised that they had to decide for themselves how to apply them in test questions.