Improving learning in mathematicsImproving learning in mathematics

PD6: Using formative assessment

Aims of the sessionThis session is intended to help us to consider: the reasons for assessment; the differences between formative and

summative assessment; some difficulties commonly experienced with

formative assessment; alternative methods for formative assessment; the type and quality of feedback given to

learners; the implications that assessment has for

teaching.

We assess learners to: diagnose difficulties and so inform teaching; celebrate achievement, rewarding effort and

success; motivate learners by showing them what we

value and what they still need to learn; select learners for groups, courses, careers; maintain records so that teachers or parents

can be informed of progress; assess teaching methods to see which work

more effectively.

Summative and formative assessment Summative – summarises and records

overall achievement at the end of a course, for promotion and certification.

Formative – recognises achievements and difficulties at the beginning or during a course, so that teachers and learners can plan appropriate action.

How do we assess formatively? Think of two learners, one who is finding

the topic straightforward and one who is finding it difficult.

Describe these learners’ strengths and difficulties to your partner in detail.

Explain how you know about these strengths and difficulties.

What evidence do you have?

Difficulties in formative assessment Teachers’ tests encourage rote and

superficial learning. Questions and methods are not shared or

critically reviewed. Quantity takes precedence over quality. Marks and the grades take precedence

over constructive advice. Learners are compared with one another;

personal improvement is devalued.

Feedback to learners serves social and managerial functions, often at the expense of learning.

Teachers tests imitate external tests, and enable predictions to be made rather than to identify learning needs.

Collecting marks to fill in records is given higher priority than the analysis of learners’ work to discern their learning needs.

Little attention is paid to the records of learners’ previous assessments.

Difficulties in formative assessment

Improving formative assessment Watch and listen before intervening. Assess groups as well as individual

learners. Use divergent assessment methods. Share objectives, encourage self- and

peer-assessment. Give useful and constructive feedback. Change teaching to take account of

assessment.

Divergent assessment strategies

Questioning with mini-whiteboards.

Learners producing posters.

Divergent assessment strategies

Learners assessing work. Produce work that contains common errors. Ask learners to imagine they are teachers. Ask them to mark the work. If they think that a mistake has been made:

underline the mistake; write the correct answer by the side; try to explain the thinking that led to the

mistake and write advice to the person who made it.

Divergent assessment strategies

Learners producing a mathematical dictionary for a topic. Give learners a list of words or phrases

relating to a particular topic. Ask learners to:

write down a full explanation of the meaning of each word or phrase;

create an example showing how the word or phrase should be used.

Divergent assessment strategies

Learners making up their own tests.

Towards the end of a topic, each group of learners: writes down the two most important ideas in the

topic; makes up a question that would test whether or

not someone understands each idea; produces a perfect answer and a mark scheme.

Assemble the questions into a test. Make sure learners know that the test is made up of their questions, and that they do the marking.

Divergent assessment strategies

This test was devised by learners.

Learners producing a short revision guide for a topic.

The revision guide should explain key terms and words; provide worked examples of problems and

questions for the reader to try; show examples of where the ideas are used in

everyday life; provide full answers at the back.

The guides can be exchanged and checked by other learners.

Divergent assessment strategies

Learners interviewing each other.

What do you think you were expected to learn in this activity?

What have you learnt? What are the most important ideas? Explain one of them. What did you feel you understood well? Give one

example. What did you find hard to understand? Is there still something you are confused by? What mistakes did you make? Why did you make them?

Divergent assessment strategies

Useful feedback: focuses on the task, not on marks or grades is detailed rather than general; explains why something is right or wrong; is related to objectives; makes clear what has been achieved and what

has not; suggests what the learner might do next; describes strategies for improvement.

Meeting the needs of all learners

‘When we try to meet the needs of learners, we may find that we need to be more relaxed about covering the syllabus. We need to address their learning needs, not our own predetermined agenda.’

How do you respond to this?

How do we meet individual needs? Differentiate by quantity?

When learners are successful, do you give extra work? Differentiate by task?

Do you give each learner a different activity? Do you allow learners to choose activities?

Differentiate by level of support? Do you give all learners are given the same task, then

offer different levels of support? Differentiate by outcome?

Do you use open activities that encourage a variety of possible outcomes and offer learners the opportunity to set themselves appropriate challenges?