2 Key issue 2: What should be assessed and how should it be assessed?

Good assessment is seen as both valid and rigorous. Testing for validity means asking whether grades generated by a testing system represent a student’s achievement in the whole of mathematics. Can a series of timed, written tests at the end of a key stage assess all those things we think are important for students to learn about in school mathematics? Teacher assessment is often seen as having a lower status than the results of tests, even though it is more likely to be valid in these terms.

An over-reliance on the results of tests may lead to making generalisations and judgements about a student’s capability in all aspects of mathematics, based on the formal testing of a subset of what they are likely to know. For example, a grade ascribed on a short answer test may say little about an aspect of the topic that was not on the test, and says nothing about a student’s problem solving or creative skills in mathematics, nor about their ability to work in groups or engage in extended tasks. Perhaps all that can be said is that tests tell us about the capabilities of students to answer questions at a particular time and of a particular type (and in the conditions and circumstances of the test): no more and no less.

Reliability questions whether a student’s performance on a given test changes (or not) depending on the particular questions that are set. Ideally, assessments should give every student optimal opportunity to demonstrate what they know. In practice, however, tests have been found to be biased against students from particular backgrounds, socio-economic classes, ethnic groups, or gender (Pullin, 1993). Equity issues are particularly important when assessment results are used to label students or deny them access to courses or careers in the future.

Cooper (1998) conducted research using the English National Curriculum KS3 test questions, which suggests some potential lack of fairness in testing regimes. It is likely that these issues raised by Cooper’s research relating to assessment apply to all testing regimes. Consider the implications from this (and other) research, which shows that poorer children:

• … go into lower sets …
• … so they are entered for lower tiers of examination papers …
• … and therefore they have to answer more ‘realistic’ test items …
• … so they achieve lower test results …
• … so they are confirmed as being appropriately placed in lower sets for mathematics …
• … so they may experience a less rich mathematics curriculum, and will learn less content …
• … which restricts their opportunities to get high grades in examinations at the end of their schooling …
• … which restricts their career opportunities …
• … which means they and their family may be locked into a cycle of underachievement.