Mastery of the curriculum requires that all pupils:
•use mathematical concepts, facts & procedures appropriately, flexibly & fluently;
•recall key number facts with speed and accuracy and use them to calculate and work out unknown facts;
•have sufficient depth of knowledge & understanding to reason & explain mathematical concepts & procedures & use them to solve a variety of problems.
The best ongoing, formative assessment should be an integral part of teaching, concerning what pupils know, understand and can do. Tasks and activities may be presented orally, using equipment and/or as part of a group activity as well as written. The encouragement of discussion, debate and the sharing of ideas and strategies (between teacher and pupils, and between pupils themselves) will often support assessment and teaching and learning.
Pupils can really understand a concept, idea or technique (are expected) if they can:
•describe it in their own words;
•represent it in a variety of ways (e.g. use concrete materials, pictures & symbols)
•explain it to someone else;
•make up their own examples (and non-examples) of it;
•see connections between it and other facts or ideas;
•recognise it in new situations and contexts;
•make use of it in various ways, including in new situations.
Pupils are working at mastery with greater depth are able to:
•solve problems of greater complexity (i.e. where the approach is not immediately
obvious), demonstrating creativity and imagination;
•independently explore & investigate mathematical contexts & structures, communicate results clearly & systematically explain & generalise.
Assessment prompts/tasks: Tasks could be used for pupils who grasp concepts rapidly, but these and deepening prompts (such as those in the challenge diagram) should also be used with the whole class where appropriate, giving all children the opportunity to think and reason more deeply. NCETM Assessment materials, Assessment examples in the Ready to Progress materials, reasoning prompts (like Odd One Out or Spot the Mistake) and investigations such as those on Nrich can provide rich opportunities for assessment.
Ready to progress Materials