retrievalPracticeTheory

(0) Introduction and links to the other teacher training topics

Our cohort are learners in the long tail of underachievement, they are learners who would be expected to gain below a grade 5 at GCSE, they just aren’t learning very well and they continue to fall further and further behind their peers. They often don’t deeply embedding the learning of each lesson instead they quickly forget what they learn. This is a depressing picture for teachers, learners and government.

However the good news is that more sophisticated lesson planning (see plan teaching), together with allocating more lesson time to smart retrieval practice and feedback, can dramatically increase the proportion (and absolute amount) of teaching which becomes deeply embedded learning.

(1) Ebbinghaus' forgetting curve

We have a cultural misunderstanding of learning within schooling - that learning is either secure or not.

However what we assess as secure within a few days/weeks of teaching may very well not be secure after a term/year/or more.

As people we know that e.g. some of what we learned in our degree or the names of our peers when we were in year 7, will be forgotten or partially forgotten without use, but as teachers and schools we prefer not to think of teaching and learning as so ephemeral. As with most progress, we must acknowledge and attempt to understand the root cause of a problem, before we can begin to solve our problem: for our cohort too much maths teaching becomes forgetting.

Ebbinghaus did a lot of work on learning and forgetting, his central thesis was

If we learn something and don’t use it, we will forget it.

We - over a century later - often think of this in graph form.

Learners retain the learning of a lesson, for very different durations.

In the graph below we see the curves of learners who will forget

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Not all low attaining learners forget within a week - but many do, not all high attaining learners retain new-learning for over a month - but many do. Improving learners' recall of learning will help many learners to improve their attainment.

Looking at the forgetting curves in the graph above - we suggest that learners who forget:

• within 2 days, within 3 days and within a week are ideal for timely practice - we call these learners our cohort - as they will gain the most benefit from timely practice,

• between 1 and 4 weeks although these learners will benefit from timely practice, they may gain almost as much from whole class retrieval practice,

• over 4 weeks - these are typically high attaining learners, who homework and end-of-unit tests etc works well for. However, most “top sets” in year 7 and 8 will contain a few learners who will benefit from retrieval practice and without a retrieval practice program may well be in middle or even lower middle sets by year 11.

(2) After success - increase the interval between one practice and the next

After a question is assessed with a tick within the app

• the app updates the depth of learning - the duration which the app knows the learner can independently recall and accurately apply the learning of the lesson for

• the app calculates the earliest date the layer should be asked again - the ready date - this is the duration of wait which will stretch the learner’s recall-ability of the learning of the layer

• the app calculates the latest date the layer should be asked again - the overdue date - after this duration of wait we think the learner is in danger of forgetting

Each question asked is from the layer, and we assume that success on any question indicates some level of mastery on all similar questions within the layer.

With successful retrieval practice we are improving the recall of the faster forgetter (e.g forgets within 2 days), with a few retrieval practice questions (e.g. 5 retrieval practice questions) until they can remember as the best rememberers do (e.g. for over 4 weeks)

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Over time, the fastest forgetter with retrieval practice can remember for longer than the best rememberer without retrieval practice. After a few more retrieval practice questions the interval (the wait between one practice and the next) will become several years. Often layers no longer need to be practised, because harder layers cover the same learning or because the next practice is due when the learner would be in year 14.

(3) After failure - give feedback and decrease the interval between one practice and the next

After a learner has attempted a retrieval practice question and doesn’t get it completely correct

• sometimes the layer proves to be best learned later so feedback is not required,

• sometimes the layer was asked very late (e.g. after a long weekend or holiday), so whole class/small group re-teaching might be more appropriate than feedback,

• usually giving feedback-dialogue and reducing the interval between one practice and the next is the best way to better embed learning.

The app doesn’t need to know the reason why the learner couldn’t independently and accurately answer the question - but the teacher may like to bear in mind possible reasons - see chunk-based theory - as they give feedback.

Here are some graphs, to show how the timely practice app adjusts the interval between practices as a response to

• correct - shown by a ✔︎ and

• feedback - shown by a * assessment outcomes:

Remember this section is about errors and feedback, many learners need no feedback on most of the layers they learn.

More about questions that need feedback after they are asked very late

Since most classes don’t have maths lessons 7 days a week, the app can only do its best. When a layer is asked very late, sometimes feedback is required, sometimes revising or reteaching is required. The pitfalls to avoid are:

• giving whole class teaching on a layer, which is in all the learners' assignments, and then assessing the question in the assignment as if the learner has not had help. To avoid this, get the class to complete their assignment + then collect the assignments in + then do whole class/small group revising or reteaching.

• reteaching or revising before learners have had a chance to retrieve - after all some learners may be able to retrieve. If we let learners try first, we have either stretched the recall-ability of that learning if they can retrieve or we have primed the learners for learning if they can not.

Sometimes we may be able to predict that most learners won’t be able to recall learning e.g. from the last maths lesson before a half term holiday, to the first maths lesson after the holiday. The teacher may prefer to

• do a cool down (retrieval practice assignment + project based learning for a number of days before the holiday) or

• only add the learning (of the last maths lessons before the holiday) “as taught” after revising or reteaching on the first maths lesson after the holiday.

Rest assured, even the most low attaining learners e.g. year 8 learners who couldn’t (yet) work out 43 + 10, manage to learn with imperfect lesson spacing. That said the lowest attaining learners could benefit from extra short practice assignments within the week and/or for homework if family/mentor/teacher support is available and this can fill the gaps created by poorly spaced lessons.

Once we can see learning slipping away to forgetting - by our assessment of retrieval practice - we can begin to find ways to reduce this.

(4) Retrieval practice trumps overlearning

After the teacher teaches and the learner practises a new skill learned in a lesson, and the learner appears to have “got it” then if we schedule extra practice

• within the same lesson - this is called overlearning,

• on a subsequent day - this is called retrieval practice.

A little overlearning is good - we need to make sure the learner hasn’t just had a lucky guess or question - but after a little overlearning: if we schedule extra practice which is

• additional overlearning - the learner may well become more fluent, but won’t be prompted to embed the learning more deeply,

• well timed retrieval practice - the learner will embed the learning more deeply, and although for the next few practices the learner will appear less fluent, the learning will stick.

(5) The utility of various embedding learning strategies

Dunlosky, Rawson, Marsh, Nathan, and Willingham, spent time investigating the efficacy of 10 common methods used for revision.

Here is a summary of their findings

High utility

1. Distributed Practice: practice questions on a topic in several sessions over time rather than all at one time

2. Practice Testing: self testing or past exam questions done in a low stakes manner

Medium utility

1. Interleaved Practice: a schedule of practice that mixes a few different kinds of problems during a single study period

2. Elaborative interrogation: thinking about “why”

3. Self-explanation: linking new information to known information

Low utility

1. Highlighting: highlighting or underlining whilst reading

2. Imagery: formal mental images while reading

3. Keyword mnemonic: use of acronyms to assist learning

4. Summarisation: Writing summaries

5. Rereading: Reading text, which has already been read