Strictly on the record;Mathematics

Jon Swain

Measurement of pupils' progress is vital. Jon Swain offers some pointers to perfect primary assessment

Some teachers get agitated when they hear the word assessment. But we have all been assessing children for as long as we have been teaching.

Assessment can take many forms and serve a variety of purposes. But it is a way of gathering reliable and systematic information about children's progress. It can be formative, which informs us about what the children are able to do, or summative, a summary of achievement. Whatever system is used, it should be:

* fit for the purpose - decide why you are assessing and who for

* reliable - capable of telling you what you want to know

* comparable - make fair comparative assessments

* developmental - tell you what the child needs to learn

* positive - tell you what the child can do

* integral - to the planning, teaching and learning processes.

The final point is particularly apposite. Recorded information about a child becomes valuable only when it improves the quality of the work. Thus assessment and planning are inextricably linked.

But to assess children's learning, the teacher must be aware of the learning potential and expected outcomes for planned activities.

The main areas are who, what, how, when and where to assess.


At various times you will want to, and need to, assess the whole class, a group, or an individual.


It depends on who you are assessing for. Assessment has most value for personal use, rather than where it is used in its summative form, as part of recorded information to be passed on to other colleagues.

Don't try to assess everything. Have a limited focus, use it to inform planning, and remember you have access only to part of what a child knows and can do. Attainment target 1 (AT1) will often be more difficult and more time-consuming than the other content areas, as much will depend on discussion and the child's ability to explain hisher thinking.

But although facts and skills may be easier to assess, a more complete and accurate picture of a child's mathematical ability will be formed by assessment of the conceptual structures and general strategies. Teachers need to know not only what the pupils find difficult, but why. Otherwise any action will probably be ineffective.

When it comes to assessment for general use, a fundamental problem has to be reconciled. Although summative assessments, linked to the level descriptions, are necessary, and an important complement to Government standardised tests (SATs) the greater the amount of meaningful, quality information passed on, the less likelihood it will be read, digested, and acted upon.

Millions of hours have gone into producing comprehensive assessment packages that have eventually been abandoned as unrealistic, impracticable and unworkable. We should be less specific and trust teachers to use their judgment.

We must also be aware of the limitations of summative assessment. It provides only a snapshot of what a child knows at a particular time - it doesn't mean he or she will still know it the next week, nor that the child can transfer the knowledge and skills. And nor does it show depth of understanding.

Some teachers have tried to record whether a child has covered the work, rather than understood the concepts, but this is of little help. This is a particular difficulty when we come to assess issues such as understanding of place value, where conceptual understanding is going to be irregular and slow.

Perhaps all that is really needed is a record such as the one shown below, using a score of 1-5 with 1 = excellent to 5 = very poor. The date must always be included.

When it comes to assessment for personal information, the recording may need to show more detail, such as a written comment, to inform the planning for the next stage.

Other areas to consider are on-going assessment of a pupil's personal qualities and attitudes towards mathematics. It is also necessary for the school, and for teachers, to assess the teaching methods and the materials they use.


One of the simplest, and most effective, ways of finding out what a child knows is to ask: "How do you do this?" Observation of attitudes to learning is particularly useful for AT1. Are the children co-operative and enthusiastic, and do they work effectively in a group, ask questions and so on?

Although many observations are going on continuously, they will sometimes need to be made on a more systematic basis, and with a limited focus. One way is to use the system of "pupil tracking", when you might observe two to four pupils for a week, recording what they are learning. For mathematics this may be broken down into smaller areas, perhaps of content or attitudes.

Another way is using pupils' self-assessments (which can also be linked to records of achievement), but probably the most frequently used method is the diagnostic written assessment.

Teachers use this method because, as with SATs, they are simple to set and, usually, simple to mark. They are also less open to interpretation, so more objective. But they give a limited amount of information. For example, just because a child can answer that 24+57 = 81, doesn't tell us whether he or she knows that, say, the 5, means 5 lots of 10 and not 5 units. Only when the child is questioned, will the qualitative information be communicated and made known.

Moreover, there may be further problems with written assessments which affect their validity and reliability. Are pupils always to be provided with an example? How will reading difficulties be addressed? Will consideration be given to the fact that some pupils may get bored and distracted, or may rush because they want to get out for playtime?


Much assessment will be continuous and ongoing. That does not mean continuous assessment is continuous testing - it is frequent, systematic observation and recording of progress, often with simple jottings in a daily record book. Again, it will often inform the next stage of planning.

So for personal use, the answer to "when" is "whenever the need arises", although be careful that you are not assessing so much that it is interfering with your teaching.

Colleagues should acknowledge the limitations of written assessments. It is far better to pass on information that is easy to understand, meaningful, manageable, and of genuine use. Most teachers wish to make their own diagnostic assessments, rather than rely on the judgments of others - indeed it is essential that they do so. But it will be of considerable use to hand over the following, which will constitute a record of evidence of assessment:

* a list of the areas of mathematics you have covered, linked to a rolling programme of work

* a list of your latest mathematical groupings

* a sample of work for each child showing the level of presentation

* the results of place-value assessments

* the results for SATs (where appropriate).

The place-value assessments at the school where I have been working are standardised written tests given to each year group twice a year, in October and April. It is intended that they will be used on a more personal basis, to see how effectively the children are learning, and the teacher teaching. It is important to build in a reviewing system of evaluation before introducing something else.


Much of the assessment will be classroom-based, alongside the children. But there may be times when you need to gain access to more qualitative, in-depth information, and this may require a one to one session.

Jon Swain was a deputy head of a junior school in Essex until Easter this year

* Assessment is an integral part of the teaching process.

* Effective assessments, have a planned, clear, and limited focus.

* Children's understanding is developing all the time, and any measure you use is only a snapshot.

* AT1 is more difficult to assess than ATs 2, 3 and 4. It is open to more interpretation, and is difficult to assess using pencil and paper methods.

* AT1 often tells you more than the other attainment targets as it's about children's thinking.

* The main, and best, use of assessment is personal, to inform planning for the next stage of learning, when it is formative, rather than summative.

* Summative assess-ments to be shared with other colleagues should be brief and easy to understand, or they will not be used.

* The limitations of written assessments should be acknowledged.

* Most of the time, assessment will take place through the observation and questioning. This tells more than marks on paper.

Register to continue reading for free

It only takes a moment and you'll get access to more news, plus courses, jobs and teaching resources tailored to you

Jon Swain

Latest stories