Arguing for change

This topic is particularly suitable for people who line manage a maths department.

(1) teach a small bite on firm foundations - embed that learning - then repeat

We call this smaller working memory friendly teaching


  1. Teaching a small bite on firm learning foundations means learners are more likely to retain the learning of the lesson until the next lesson.

  2. Using increasing interval retrieval practice can extend the durability of the recall-ability of the small bite from the next lesson to many months at which point …

  3. … the small bite is very likely to be firm foundations for future learning, so we can now repeat the process on another, small bite of learning.

  1. Teaching too large a bite or several small but similar bites or teaching on insecure learning foundations - means that although we are likely to see success of our teaching within the lesson - we are more likely to see the learner can’t independently recall and accurately apply the learning of the lesson the next lesson. i.e. not all teaching has become learning during the night after the lesson.

  2. If the learner can independently recall and accurately apply the learning of the lesson the next lesson, they will forget that learning - or not be able to recall that learning - if they do not use the learning within a suitable time frame.

  3. If we can successfully embedded a small bite of learning, if we don’t repeat this process sufficiently frequently - by teaching a little more on the the topic several times a year - learners will still fall behind their peers who can learn larger bites at one time.

More detail

The steps in the summary guide us to the most efficient process:

  1. Teach an appropriate grain size - for low attaining learners this is a small bite - but which bite? The timely practice app can help the teacher identify suitable next bites to teach and provide suitable teaching and learning resources and teacher training to give a very high chance of success.

  2. Embed the learning using increasing interval retrieval practice and respond to the need for feedback. The timely practice app schedules the retrieval practice, the teacher provides the feedback within a time in the lesson allocated for this, whilst all the other learners in the class are productively engaged in embedding learning.

  3. Spiral through the curriculum at a faster pace, whilst ensuring steps 1. and 2. are applied.

Sufficient research on all of these aspects will be introduced throughout this - the explaining and training course - but here are links to the key research for the curious:

(2) 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

  • 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, but for the next few practices will, almost certainly, appear less fluent.

Quick summary

A little overlearning is useful, but don’t waste lesson time with more, instead use the “saved” lesson time to embed the learning of previous lessons or teach more.

Culturally we have learned that fluency is a proxy for deciding if learning has happened - and its hard to shake - but by watching learning happen with retrieval practice, especially with learners who find learning hard, hopefully you will become convinced. Of course lack of fluency can also be an indication that we are teaching too much or too hard.

Good luck lesson observers in deciding if teaching is becoming learning!

Research feel free to read about Rohrer and Taylor's experiments which were designed to find the relative efficacy of overlearning and retrieval practice when teaching a new maths skill.

(3) utility of embedding learning methods

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

Increasing interval retrieval practice combines both distributed practice + practice testing i.e.

  • several practices on a topic spaced over time each with a practice question + attempt to recall + feedback triple

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

Although medium utility 1 is similar to the high utility methods because it is essentially a practice question + attempt to recall + feedback, interleaving doesn’t wait for a night sleep between teaching and attempt to recall.

The medium utility methods 2. and 3. encourage the learner to consolidate and reconsolidate existing and new learning in their memory, whereas all the low utility methods do not.

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: Rereading text, which has already been read


Medium utility

  1. Interleaved practice: Make flash cards use all the practice questions in one session, shuffle these flash cards them share them out to use in different subsequent sessions.

  2. Elaborative interrogation: Make flash cards “Explain why …” written as the question

  3. Self explanation**: Make up a table with attributes as row headings and old and new information as column headings, etc

Low utility

  1. Rather than highlighting text, the learner makes up flash cards with questions on one side and answers on the other

  2. Imagery**: draw the image on the question side of flash card + image and detail on the other

  3. Mnemonic**: write out the leading letters vertically on the question side + the completed mnemonic on the answer side

  4. Write out the headings of the summarisation** on the question side of a flash card

  5. Rather than re reading text, make up flash cards

NB Write the answer on the reverse of the flash card or write the book and page number the answer can be found.

** Write cards so the question side can covered with thin paper which is written on - so cards can be reused

(4) why most learners don’t need the proposed interventions


Doing some assessment for learning, prior to planning teaching, is far more effective than doing none, however it can be complex to do, record and use. These complexities mean that for most learners minimal - and on the hoof - assessment for learning is the best use of the teacher's time.

Common obstacles are:

  • insufficient detail - as national curriculum statements are so broad,

  • insufficient detail  - as it would take "too much" time and effort to pre assess in finer detail,

  • insufficient detail  - as too much detail is at best unwieldy for the teacher to use effectively,

  • not accurate  - as learners tend to forget what they have learned over time - e.g. assessment in May of year 6 will not be accurate by September of year 7,

  • not accurate - as ensuring learners don't copy is hard within a class room situation,

  • not accurate - as a small variation in the way a question is asked can mean the difference between a learner being able and not able to answer a question.

Hence in our opinion although RAG recording of exam performance may be better than nothing, they are not a good use of the teacher's time.

More highly attaining learners can often manage to learn and fill in, or steer around, learning gaps as they learn new skills. So teachers of more highly attaining learners can often fill learning gaps they discover, as and when they discover them.

Lessons can fail to be effective because of unexpected gaps in learning. We know that good assessment for learning can improve learning outcomes, so for low attaining learners - who, by definition, need more help to learn - assessment for learning is far more likely be worth a bit more effort.


Once the teacher has spent time re-establishing pre-requisites skills, in order to teach something harder, both the department and the teacher want to "get on and make the most of it". Part of why schools use a teach-each-topic-once-a-year SOL is that it avoids “wasting teaching time revising” and means the teacher needs to do less differentiation and they can teach from a common beginning point.

but isn’t this another way of saying that teachers are encouraged by the SOL to teach in a way that avoids noticing forgetting?

Teaching a "large bite or several small bites” rather than a "small bite" will be a more efficient use of time providing most of the learners retain most of the new learning. Sweller’s research says that teaching better becomes learning if the teacher teaches the correct grain size.

The more a learner knows and the larger their working memory capacity is, the more new learning they are likely to be able to learn from a topic at a time.

The less a learner knows and the smaller their working memory capacity is, the smaller the amount of new learning the learner is likely to be able to learn from each topic at a time.

By learn we mean: learn within the lesson and retain after the lesson.

An annual scheme of learning makes learning harder for low attaining learners, as they often have "nearly but not quite remembered the pre requisites" before they are asked to use those pre requisites, not just for the next step of learning, but also for one or two steps after that. With a teach-each-topic-once-a-year scheme of learning we are asking the lowest attaining learners to follow the learning style which works for the highest attaining learners. Thinking of sport, it is like asking a swimmer with arm bands to follow the training regimen of member of the swimming team.


High attaining learners can usually easily remember the learning of the lesson for up to 5 weeks - so homework and end of unit tests, work well as unacknowledged retrieval practice.

Learners at the median can usually remember the learning of lessons for about 1 week - so homework and end of unit tests, works reasonably well as retrieval practice - although most of these learners will need to do some out of class revision to “do as well as they can”. Weekly quizzes followed by perhaps fortnightly tests - which include increasing interval retrieval practice on prior learning - are likely to work even better. 

Learners at or below the lower quartile can usually remember the learning of the lesson for a few days - so homework and testing are far less likely to make well timed retrieval practice. Additionally even if testing and homework is scheduled every few days, and this does extend the durability of the recall-ability of new learning, it is likely to extend the learning for no more than an additional fortnight.

So unless we use additional strategies - such as increasing interval retrieval practice, which timely practice uses - we can’t legitimately complain when low attaining learners can’t remember what we taught them last week/month/term/year.

(5) motivation is an outcome of success

Culturally - especially with the rise of neoliberalism - many people believe that increasing motivation gives rise to greater success. 

Mihaly Cziksentmihalyi's contribution to understanding learning - pointing out that motivation is the outcome of success, rather than what is commonly believed: learners must provide motivation before than they can be successful - is to my mind so simple, and yet so powerful.

Flow – The Psychology of optimal experience, Mihaly Cziksentmihalyi, Harper, 1990

  1. High stakes, summative testing reduces motivation of low attaining learners. Getting tough?

  2. We are wasting schooling time when we test learners on skills we know they won’t know yet. Assessment for learning is far too powerful learning tool to be used merely to find out if learning has happened. (see 0:49)

  3. We reduce the probability of feedback being successful, if we give too much feedback at one time.

  4. When we assess and give feedback and a mark or grade - learners focus on the mark or grade, not the feedback. Inside the black box

timely practice was written to 

  1. Reduce the need for testing, we make assessment for learning low stakes and we reduce the need for future pre assess by tracking how new learning is embedding, that is we do assessment of learning, that is assessment of retrieval practice. During the pre assess process we encourage the teacher to explain to the learner its purpose is to find out what the learner knows and what the teacher should teach next, not to judge the learner.

  2. We want learners to get over 80% of their timely practice retrieval practice questions correct - so feedback requirements are low and so feedback is likely to be successful - so, sometimes we need to reduce the number of layers which are regularly requiring feedback.

  3. However we encourage teachers to discourage learners from giving themselves a score on their retrieval practice assignments.

(6) teaching strategies which give greatest benefit to the hardest to teach learners

Learners with ALN and SEN and learners living with poverty and trauma, usually find learning harder than peers. These learners benefit most from teaching strategies

  • which reduce the working memory load of the lesson,

  • which teach on firm learning foundations,

  • which help the learner to embed the learning of the lesson into long term memory

  • which lead to success, which leads to increased motivation.