Mathematics and AfL

Clare Lee | View as single page | Feedback/Impact

Assessment must be part of learning

Assessment must be part of learning because teaching is not the same as learning:

Consider the following extract adapted from Denvir and Brown (1986):

One student was assessed as having the following 'gaps' in her knowledge.

She does not know:

  • The numbers backwards from 20
  • Number bonds other than doubles
  • The answer when adding units to a decade number
  • The answer when adding ten to a two digit number
  • The answer when taking a ten away from a two digit number

Over two months the student's teacher planned and delivered specific teaching designed to address these 'gaps' and at the end of this time she was assessed again.

Surprisingly she could not demonstrate mastery of any of the skills that she had been specifically taught at the end of the two months. However the post test showed that she had mastered other skills that she did not demonstrate on the pre-test. For example she could now

  • Use counting up/back/down strategy for "take away"
  • Model two digit addition without re-grouping using base-ten apparatus
  • Model two digit subtraction without re-grouping using base-ten apparatus
  • Model two digit addition with re-grouping using base-ten apparatus
  • Bundle objects to make new groups of ten in order to facilitate enumeration of a collection that is partly grouped in tens and ones

Students do not learn what we teach, what they learn is unpredictable therefore assessment has to be a central part of any lesson and any planning for learning.


  • Denvir, B and Brown M (1986) Understanding of Number concepts in low attaining 7-9 year olds: Part i and Part ii,Educational Studies in Mathematics ,17, 15-36 and 143-164.