Why formative assessment matters: the power of prior knowledge

“The most important single factor influencing learning is what the learner already knows. Ascertain this and teach him accordingly.”

(Ausubel, 1968 in Wiliam, 2016)

The memory of a chess master is both astonishing and limited. Masters can take in and remember game situations at a glance; novices remember the positions of just a handful of pieces. Yet masters’ memories are no better than those of novices when chess pieces are placed at random. Simon and Chase (1973) suggest that as a chess player examines a game, they either encounter a known pattern, or they add an unfamiliar pattern to their memory. During a decade of study, experts learn up to 50,000 ‘chunks’: each chunk being the positions of several pieces. Skill in chess is the development of increasingly complicated mental models, or schema, comprising thousands of positions.

Learning – in chess or any other domain – is the addition of new chunks to these schemata, and the creation of new links between these chunks. Adding new chunks provides crucial building blocks: we need to know words, events, dates and multiplication facts. Chunks do not accumulate like piles of junk however; as we learn, our schemata are reshaped: we make connections between words, ideas and concepts. Individual chunks – Hamlet’s responses to Ophelia, to Rosencrantz and Guildenstern, to the ghost of his father – can be encapsulated in one chunk: Hamlet’s character. Adding chunks, creating new links and encapsulating chunks allows us to think in increasingly complex ways: we can compare Hamlet’s character with Othello’s without needing to remind ourselves of each of Hamlet’s actions first. This, Alfred North Whitehead argued, is how civilisation advances, through:

“extending the number of important operations which we can perform without thinking about them.”

Students’ existing schemata are therefore critical to what they learn. If students’ schemata include the 44 phonemes in English, we can ask them to read any word; if our students have a vocabulary which encompasses 90-95% of a text, they are likely to be able to comprehend it (Hirsch, 2006). Prior knowledge dictates what and how we can teach. Students ability to make sense of the Reformation will depend on their familiarity with Tudor monarchs, Christian worship and Sixteenth Century Europe; our awareness of their prior knowledge will guide us to identify which aspects of their schemata to activate, to build upon or to seek to correct.

What of skill? Skill itself – that is, winning chess games – is the response to the patterns we recognise and recall: “The patterns that masters perceive will suggest good moves to them (Simon and Chase, 1973).” This begins to seem a skill (rather than the conscious application of knowledge) when a chess expert comes, through practice, to recognise a pattern “quickly and unconsciously, and the plausible move comes almost automatically.” (Often we attach characteristics to such behaviour, describing an attack as ‘bold’, and losing track of the critical role which knowledge has played in making these choices, which seem bold, possible.) To apply this to an example in schools, skill in solving maths problems means correctly identifying the operations to perform (from memory of similar problems) and performing those operations (from memory of how to perform them).

Ignorance of students’ prior knowledge leaves us fumbling in the dark. Without it, we cannot choose where to pitch a lesson, identify who will need help or evaluate who has learned anything new: our plans and responses will be insensitive to the differing needs of students familiar with the Reformation, those needing a brief reminder and those fresh to the topic entirely. Ausubel’s line is particularly helpful because ascertaining what students know and teaching them accordingly can be done at the start of a unit, the start of a lesson, or in the middle of one. What students know and have learned will continue to affect what they can learn. Formative assessment matters because it focuses our attention on students’ prior knowledge and provides us with the techniques to bring this knowledge to light.