The Forgetting Curve

It is the case in many schools that each lesson is expected to have a learning objective which involves extending learners’ current knowledge or understanding. Such a policy is understandable, given the immense amount of content teachers and learners are required to cover during Key Stages 3/4. These policies push Heads of Department to maintain a fast learning pace. Once retention has been ‘confirmed’ through an end of topic test (or similar), the logic of this approach is that new content should be covered: the quicker the pace, the more time to revise, the higher the grades.

The forgetting curve, however, is a psychological concept introduced by Hermann Ebbinghaus, which asks serious questions of this approach.?

What Is the Forgetting Curve?

The forgetting curve demonstrates how memory retention declines over time when knowledge is not reinforced. After learning something new, we forget a significant portion within hours, and after a few days, what remains can often be negligible. This rapid decay is slowed when learners revisit material, especially through active recall or application in new contexts. The act of recalling information strengthens neural pathways, making it easier to retrieve the same information again in the future.

A question I often ask is, what is the relative value of relational understanding as opposed to procedural understanding??

Procedural knowledge is often (if not always) necessary to establish a relational understanding. However, if a learner remains confined to a procedural level of fluency, the forgetting curve suggests that their retained knowledge will asymptotically decline. In the short term, procedural learning can hold similar value to relational understanding, as it may enable learners to achieve similarly high marks in topic tests. Over time, however, the long-term value of relational understanding becomes evident.

This raises an important question about the purpose and effectiveness of short-term, single-topic tests:

What is the Information Value of Short Term Topic Tests??

As per the graph above, a significant proportion of the knowledge demonstrated by learners in topic tests is shortly afterwards forgotten, and lost before they next encounter a higher stakes summative assessment. As such, I would claim that the information recorded within the shared drives of maths departments is possibly of low value. Yes, it serves to rank learners reasonably effectively, but as per previous blog posts, I would argue that this is a net negative to most learning environments.?

How might short term testing carry higher information value?

First let us consider another critical stage of learning: how Year 11 students consolidate knowledge during revision periods. In my experience significant progress can be made during this period, and the forgetting curve is a useful model to explain why.?

The repeated exposure to classic exam questions - mean from a grouped frequency table, compound interest calculations, show that a given recurring decimal is equal to a given fraction - these are consolidated in a manner consistent with the graph above. This is particularly so, when the questions involved have only limited scope for adaptation. For example, it is harder to create an extension question for reverse percentages as the method for each question is usually very similar, whereas for similar solids where the solution can involve exact values (surds and pi), a wide array of equations with different methods to solve, ratios or percentages could be thrown in…for these questions it is much easier to turn them into extension questions, and vary them in significant ways. As such learners’ forgetting curves may not show such prompt improvement for these more difficult topics as for other more predictable topics.??

There is a huge opportunity, however, to revisit previously taught concepts within topic tests. I am open to persuasion on the breakdown of prior knowledge to recently taught content, but I nevertheless strongly endorse the principle that prior knowledge should constitute a significant proportion of each topic test. The prior knowledge being assessed could focus on the key concepts - prime factorisation, linear equations, quadratic equations, laws of indices, fractions etc. - consolidating them over repeated iterations to facilitate future learning.???

Repeated exposure to concepts resets the forgetting curve, and each time the exponential decay of retention is significantly slowed. This process allows for long term retention, but as per the second paragraph in this post the repeated exposure to concepts is particularly valuable when it occurs within new and different contexts. This brings us onto a matter that should be considered in coordination with assessment design.??????

The Role of Sequenced Schemes of Work:

Effective recap does not happen by accident.?

A well-sequenced curriculum avoids the pitfall of compartmentalised knowledge, where students treat topics as isolated entities. Instead, it allows learners to strengthen their neural pathways for each concept. In all honesty, I do not consider this point worthy of explanation: a coherent scheme of work is simply essential. Whilst many schemes of work evolve over time, there is usually reason to adapt them to pedagogical research, ensuring they are both coherent and flexible.

There is one final closely related point:

Designing Lessons which Interweave Prior Knowledge:

It is a common practice of accomplished practitioners to regularly dip into prior knowledge. This could be quick-fire quizzes at the start or end of lessons, or just dropping questions into worksheets. It could, however, involve subtle and skilled interweaving of topics. The point, however, is that you cannot expect all teachers to be accomplished practitioners. There is a solution to this which is being worked toward by a number of multi-academy trusts and a few notable others. This solution is to carefully resource schools with lessons aligned to a (well-sequenced) scheme of work, but again to do this to a high standard requires a significant amount of time from (probably more than one) very skilled practitioners.?

It is simply not sensible, not realistic, nor fair to assume that teachers will spend the necessary time to make such lessons for every class they teach, and redesign them for new schemes of work if and when they move to a new school. The forthcoming curriculum and assessment review would be advised to address this obvious shortcoming.?

Another blog post, coming soon.

George Bowman

Founder, Maths Advance.

https://mathsadvance.co.uk/

[email protected]