A traditional pre assess process which asks all the learners the same questions at the same time - whether they answer within a test, selecting from multiple choice options or using mini white boards - makes many learners uncomfortable. “Our cohort” are often especially uncomfortable, so they often undermine its effectiveness by quietly not engaging, copying or otherwise avoiding answering, perhaps by claiming they know everything or nothing or perhaps by asking - when will I use this in life?

People are not naturally good judges of what they have learned, so rather than finding out if teaching has become learning, by asking learners if they know something or by assessing them at the end of the lesson, it would be better to assess by questioning at least one sleep after teaching.

Research by Bjork tells us that, until we learn more about our own learning, we are often seduced into thinking

• that finding practice easy means we are learning well

• that finding practice hard means we are not learning well.

In fact almost the opposite is true. Fluency of practice is not an indicator of learning taking place, it's when we struggle to practice (Bjork calls it desirable difficulty) that we embed learning better i.e. it's easier for us to recall for longer. Once learners, learn about learning, over time, they will overcome this misconception.

Every time we help ensure a learner create a chunk in long term memory from the learning of the lesson - when they otherwise would create no chunk or create an imperfect chunk - we are ensuring the learner will make more progress when they otherwise would.

An effective revision program uses these key behaviours

• pre assess: the learner decides what they need to learn,

• a more tightly spiralled curriculum: the learner splits up what they will revise into smaller blocks and space these out over their revision program,

• retrieval practice, self-assessment and feedback-when-necessary: to ensure that the learner fully retains all their learning, the learner reviews frequently what they have learned and gets help if necessary.

If we think about teaching following an annual scheme of learning it is much more like cramming than a good revision program since

• pre assess: may not be done at all or may not be done in sufficient detail or may be difficult for the teacher to use,

• all the teaching on a topic: is done within a short period of time and only once a year,

• practice questions: are done within a short period of time.

However it is not surprising we teach like "cramming" - as it is easier for the teacher - and it works for most learners

With timely practice the teacher can teach learners with a wide spread of attainment like a revision program rather than like cramming.

Suppose the "big" bite of teaching on a topic with blocked teaching could be split into 3 small "bites" and let's suppose the learners might judge them as: "OK", "hard" and "very hard". With blocked teaching a teacher might find that a few "more able" learners in the class learn and retain all of the "big" bite, but most learners will not. Instead with a more tightly spiralled  scheme of learning, the teacher can teach

the "OK" bite in term 1,

the "hard" bite in term 2 and

the "very hard" bite in term 3.

However, since the learners master the "OK" bite during term 1, through their timely practice, when the teacher returns to teach the "hard" bite in term 2, the learners will find the "hard" bite much easier to learn. So now the learners will judge that bite as "OK" and by term 3 the "very hard" bite will also be "OK" for the learners to learn - as through retrieval practice with timely practice - they will have mastered both the "OK" and "hard" bites.

So by spacing out the teaching of a topic most of the class can learn and retain what the teacher was previously expecting only the more able in the class to learn.

1. Mastery learning: ensuring that learners can use and apply pre-requisite skills to a high standard before learning new work. Mastery Learning is associated with an additional five months’ progress over the course of a school year compared to traditional approaches.

2. Chunk-based learning: this branch of theory came about from studying how experts practise and structure their learning. We are all limited to 4 ± 1 slots in our working memory. However if we can form a process into a chunk in long term memory, we reduce the number of slots required in working memory. The chunk replaces some of the working memory requirements. The chunk makes it easier to decide which process to use, remember the order of the steps of the process and makes it easier to apply the process. The power of chunks is that we can create chunks of chunks etc. Chunk-based theory strongly recommends a number of teaching-learning strategies including a spiral-curriculum and deliberate practice.

3. Cumulative practice: for what we consider higher order skills, such as generalising and problem solving, research suggests that when learners are using two different pieces of knowledge/skills/methods to learn a third, the learners are most successful if both the two existing pieces of knowledge/skills/methods are more strongly embedded before the third is learned. 

... taken together imply that it is better, for the low attaining learner, to come back to topics more frequently, but learn less new work each time.  

timely practice doesn't use either of the standard ways to solve the mastery learning problem - what to do when some learners in the class have learned and some have not yet learned - instead we use an efficient process where the learners who are finding a topic harder, get more practice and feedback with their teacher - so nearly all learners are ready to learn the next bite in a few months time.

The timely practice app ensures that the practice done within timely practice assignments is deliberate practice. timely practice enables learners to improve their skills by practice and the teacher to use feedback and scaffolding to help the learner when required.

The following sections describe in more detail

• how the teacher can apply increasing interval retrieval practice, adjusted by feedback to help the learner to build chunks in long-term memory through regular timely practice during most maths lessons

• the most effective ways to teach new learning in the rest of the lesson.

The purpose of marking may be thought to be

• To make sure there are no remaining written errors on the page: the reason might be that then the learner can revise from their exercise books. This is not a good use of time, because we want learning to be improved soon, rather than hope learners will return and revise at a later date.

• To give hints or clues or model answers to help the learner. However the teacher must guess what the learner was thinking/ not thinking when the learner made their error(s). This is not a good use of time because often the teacher will guess wrong, or the learner won’t read, or understand if they even read what the teacher has written.

• The teacher gives value judgements in the hope of changing learners effort/motivation in lessons. This is not a good use of time, because value judgements, even positive ones, may decrease rather than increase the likelihood of learners learning from suggestions and the learners motivation.

• A repetition of all or part of the original teaching. This is not a good use of time, because if the teaching of the lesson, didn’t lead to embedded learning, the teachers explanation - which is necessarily less detailed and can’t involve assessment for learning, as the lesson could - is less likely to lead to embedded learning.

Although each outcome of marking may sometimes be effective, the probability that any of these will be effective at embedding learning is low, and the cost to the teacher is high.

This saves the teacher a little time for each question

_{The only exception to this rule, is for example, if the learner makes an error in a complex multistage word problem, the teacher might want to write down the numerical answer (on the learner's page, or on the teacher’s lesson plan page) to save the teacher having to work out the answer to check the learner's correction.}

If the assessment outcome is a tick or best learned later or reset: there is no need for feedback in the next lesson.

If the assessment outcome is feedback on attempt or feedback on blank: then we expect the learner to try and self correct or get peer to peer help or initiate a feedback-dialogue with the teacher, within the rules of the classroom.

By assessing and where necessary, engaging in personalised feedback dialogue in the lesson, we gain multiple advantages:

1. The teacher is replacing the time and effort they would spend on marking, non-directed time, with only the possibility that they may need to spend directed time, inside of lesson time, on feedback. The teacher need not feel guilty, as not marking + giving feedback in the lesson (if necessary), helps the learner learn better.

2. The non-directed time spent by the teacher will be less - today - because this kind of assessment is far quicker than marking, and will be less - in the future - because feedback is far more likely to be successful and so similar questions will be asked less frequently and answered more accurately.

3. The learner has a chance to self correct or self reflect or get peer-to-peer help: so the teacher may not need to spend lesson time giving feedback or failing that, the learner has time to read the question again and will be primed to adjust their chunk or mental schema (Kornell et al 2009) during the feedback-dialogue.

4. With in-lesson feedback-dialogue the learner is far more likely to engage with the teacher than they are likely to engage with the teacher's marking.

5. Without marking by the teacher, the teacher and learner can start the feedback-dialogue from a common place.

6. With in lesson feedback-dialogue the teacher has a chance to learn about learner's past thinking and/or influence the learner's future thinking, more effectively than with marking.

7. Feedback-dialogue makes excellent, non threatening, feedback for the teacher on fine detail ways to improve future teaching. It allows the teacher to gain decades worth of high quality teaching experience within a much shorter span of time.

8. Feedback-dialogue provides an opportunity for the teacher to help the learner to better deal with the emotions brought up by errors e.g. to move on from self-criticism or making excuses or blaming others and to help the learner reflect about their question reading or process or problem solving skills i.e. help the learner grow a growth mindset.

9. Feedback-dialogue is likely to increase the learner's motivation whereas marking is likely to decrease it.

10. Sometimes during feedback-dialogue the teacher and/or learner will realise that the layer is best learned later - and this is also a productive use of the teachers and learners time - because now they can stop putting their time and effort into making this layer stick and instead put their efforts in to embedding other layers which are far more likely to stick. After all we can’t expect to go from a place where most teaching is forgotten to a place where absolutely all teaching becomes embedded learning. Surely a process where almost all teaching becomes embedded learning should satisfy us - there is no shortage of other layers to teach - before returning, to see if this layer will stick in a few months time.

The main disadvantage (such as it is) is that there is very little in the way of an easy to follow paper trail of the efforts the teacher has put in. There is the record that feedback dialogue has been requested, and possibly the corrected workings by the learner. In future assignments we usually see the learner being able to answer correctly similar questions and there is the record of the subsequent progress on the layer within the timely practice app. If the teacher must be checked up on, then the “checker-upper” must do the work to find out if the teaching is successful or not. This counterposes with a marking trail - where the teacher is doing the work of demonstrating that they have tried - but cannot possibly demonstrate that they have been successful - in enabling the learner to embed the learning.

Not giving hints etc will pay dividends, as the answer space can be used to answer the question

• by the learner and teacher to model answering if the learner gets peer-to-peer help or feedback-dialogue with the teacher

• by the learner if the learner can actually do the question - perhaps they just didn’t see it, they got distracted, they were having “an off-day” etc

** or other symbol used to show that the answer is not fully correct but that the teacher wishes the learner to try and self correct/get peer help/get feedback

Even though many questions will take the teacher "next to no time" to work out the correct answer, the teacher should use the answers provided by the app, because 

• the small bits of extra time to read the question and work out the correct answer add up,

• it distracts the teacher from the assessment task - i.e. how well is this learner able to apply their learning - it is harder, and therefore takes fractionally longer, for the teacher to switch back and forth between doing maths and assessing maths.

The primary task is embedding learning and the secondary task is giving feedback.

Every time we help a learner fix a chunk in long term memory - when they otherwise would be left having learned no chunk or an imperfect chunk - we are ensuring the learner will make more progress when they otherwise would.

• use the layer history to decide, how frequently has the learner needed feedback? - usually 2 feedbacks in a row is enough, this isn’t available yet

• if the feedback isn’t going well, the teacher and learner are likely to remember the previous feedback-dialogue and they should both be honest about whether the feedback is working,

• does the learner still have some motivation for the feedback process?

• the more feedback assessments per assignment, the less likely each is to result in embedded learning - usually 3 feedbacks per assignment is enough,

• the decision to give feedback or decide a layer is best learned later needs to made within the context

  • e.g. the number of learners in the class/group - a tutor with fewer learners in their group, might give choose feedback whereas a teacher with a larger class might choose best learned later,

  • e.g. the amount of time until the next school holiday - if there is only 2 days before a 2 week holiday, then the learner is unlikely to retain the benefits of feedback - this is issue can be in part dealt with by us of a cool down period, see (10) below

We ask questions on a few key layers of a topic - which gives us a broad brush stroke picture of the learner’s skills and learning gaps - which are at an appropriate level for the learner. We know that quite often asking one question on a layer is insufficient to find if a layer is secure or not, so we always ask a second question if the learner seems to know the first. The assessment of the key layers is then used to gather more assessment for learning data in finer detail.

We don’t ask up to 2 questions on each layer from each topic because

• it would take too long: so we rule out some key layers that we consider too easy or too hard (based on the Level for Learner the teacher inputs into the app),

• it would be too traumatic for learners: so we try and remove layers which we think would be too hard for each learner based on the responses to earlier questions. Hence the teacher can say to the class “Everybody will get some too easy, some OK and some too hard questions in their learned and remembered section, this is to help the app find out for the teacher, what to teach you soon”

Also because

• there is little point in assessing a scaffolded layer, which can’t be understood, until after being taught.

See auto pre assess for more detailed information

The teach-learn part of most lessons rarely holds low prior attainment learners back, but trying to practise too much or too hard in the practise-learn part of the lesson or failing to make efforts to embed new learning regularly does.

In whole class teaching, learners with low prior attainment can often answer questions from harder layers, but

• being able to answer in the scaffolded situation of whole class teaching, following on from reminders about their current learning and after a small bite of new learning, and

• being able to retain and answer such questions later is more difficult. It’s easy to be deceived that learning performance results in embedded learning. One timely practice experienced teacher describes this effect as “hurrah, they’ve got”, the teacher will want to move on, but recommends not doing this instead “just stop”.

See (1) teach on firm learning foundations (above) and remember the subsequent layer isn’t on firm learning foundations.

The teachers task with a timely practice scheme of learning is to

• (2) teach 1 layer per learner, per topic, per curriculum spiral (above) and

• (5) schedule a timely practice assignment episode every lesson (above)

so that new learning quickly embeds. There is usually sufficient time within an academic year to spiral through most of the topics within the scheme of learning several times.

Getting practise-learn and retrieval practice “more right” will lead to large learning gains, without the more sophisticated options suggested below.

It’s likely that whenever we teach a topic we have learners at different places on the ladder to mastery of the topic.

Thinking about the learners with the lowest prior attainment of the topic

• should we expect them to learn the most? - of course not,

• should we expect them to learn, several previous years of schooling on the topic, in a few minutes? - of course not.

Thinking about the learners with the highest prior attainment of the topic

• should we expect them to learn the least? - of course not,

• should we prioritise their needs over all of their peers? - of course not.

Hence acknowledging that some learners will spend a few minutes of some lessons “being quiet and allowing the teacher to teach other learners something that is too easy/too hard for you to learn right now” is better than pretending that all teaching will be both accessible and learned by all learners.

• There is some value in reviewing skills already mastered on a topic - it primes learners to more readily hang the new harder learning on the easier already existing chunks.

• There is some value in telling groups of learners that they can ignore what you are going to teach for the next few minutes - it's better than the above alternatives.

• Often we won’t have to come out and explicitly say “ignore me now”, generally we will find our learners do their best to join in (or appear to join in) with whole class teaching, whether they “get it” or not.

Other more sophisticated planning is possible, please read on from the next expand boxes.

• With mini white boards/scraps of paper and large felts: ask learners to work out 1 or 2 or all of a few questions (each from a different layer) shown on the whiteboard e.g. 50% of £26 = … and/or 75% of £26 = … and/or 5% of £26 = …

• With a no hands up policy, after a sufficient pause, direct questions to specific learners e.g. with a layer 3 practice question, ask a learner who is learning layer 3 now, but with a how/why question on layer 3 question ask a learner who is learning layer 5.

• When teaching layer 1 of a topic to a few learners when the rest of the class has already mastered it (and possibly higher layers too): introduce the topic, ask some learners to “have a go at the review questions on your desk aiming for accuracy, whilst I work with a small group. Then we’ll come back together, in a few minutes, to see who has been 100% accurate”. This stops the masked-fidget from learners who “already know” when the teacher is teaching slowly to those who are being introduced to the topic, yet learners who “already know” the skill are still primed for learning harder layers from the topic.

• Learners who only needed to learn the easiest layer being taught from a topic might be directed “If I’ve given you a practise-learn worksheet, you can ignore me and do the worksheet, while I teach everyone else something new-for-them” and then quickly follow up with “OK, if you don’t have a practise-learn worksheet I want your full attention now”

• Another alternative, e.g. with solve is to model “the hardest skill” {begin the problem} and then explain that “the next bit most of you can do” {intermediate stage} and finally “everybody can now solve this part” {final stage}.

• Another alternative e.g. with proportionalFormulaNC after a little whole class teaching is to issue some learners with calculators or times table grids saying “what I’ll be teaching now has harder numeracy skills, but not harder mathematical skills, so some of you are allowed to use a calculator and some a times table grid.”

• Teach several similar layers together as a whole class, e.g. layers 2 to 4, but if one or two learners are learning an outlier harder skill e.g. layer 7, then teach them at their desks or a flip chart, whilst other learners are doing their practise-learn worksheets. This can be done by organising a few learners to hand out the correct practise-learn worksheets to most learners, whilst you get the learners learning the harder layer together and reading the teach-learn questions you plan to use. Then once every learner has started their practise-learn worksheets, teach the small group the harder skill.

• Obviously, if you have teaching assistants, you can teach 2 or more groups exactly what they need to learn simultaneously.

Some of these include the good practice of activating the learners in the class to be teachers:

• Interleave teach-learn and practise-learn episodes within a lesson, so some learners might be (re)doing a practise-learn worksheet on a layer 1, (a layer which they’ve already learned), whilst the teacher teaches layer 1, using the teach-learn questions to a small group. Then the teacher switches the focus of their attention: some learners learn new harder layers and those that have just learned layer 1 now do the practise-learn worksheet.

• Get the one learner who needs to learn layer 5, to teach the one learner who needs to learn layer 1, while you teach the other learners layer 3. Teaching will advantage the learner who needs to learn layer 5 as long as the teacher makes sure they have enough time to teach layer 5 later in the lesson.

• “I’ve partnered you in pairs, one of you is good at layer 3 but can’t do layer 4 (and vice versa) … see if you can find out who has already learned each skill, and use the teach-learn questions I’ve given you to teach each other the missing skill”

When the teacher knows exactly which skill to teach to each learner, in advance of the lesson, the teacher can find many ways to make better use of lesson time.

I’ve not had the class control skills to say “Tuck your practise-learn worksheet under your planner, but don’t begin it, until I say you can”, but you might be one of those super-teachers, and may be able to use this method to good effect.

• some maths puzzles or patterns to find within a times table grid written on e.g. a flip chart

• create a second “catch-up” timely practice assignment (which will have questions on more embedded layers, which are unlikely to need feedback: to do this create a second assignment, the catch up one, directly after creating an assignment for a lesson - the urgent question will have gone into the first assignment, so the second one will contain non-urgent questions). The “catch up” assignments, can be completed “any when within the next week” without causing the problem that retrieval practice questions will be asked too late, and so can be used as a filler activity,

• ask learners to annotate recently learned questions with think aloud speech and thought bubbles (either questions the learner is really confident they know, or questions the learner has recently had feedback on),

• ask learners to pair up and test each other on some times-table facts they are learning (perhaps have an envelope for each learner with a few flash cards in),

• ask learners to draw a cartoon of a given maths word,

which can be used by learners who finish earlier than their peers do.

Before a half term holiday: 2 lessons to 1 week

Before 2 week holidays: 1 to 1.5 weeks

Before the summer holiday: 2 to 3 weeks

• a whole class project which uses a mix of maths skills e.g. maths and Islamic art, group problem solving, nRich activities, what would you do with $177 billion dollars? (Jeff Bezos' wealth at the time of writing this), maths investigations, shape puzzles or

• school required activities such as tests or the school requirement for learners to set themselves targets for maths etc or

• whole class project which uses fewer/no maths skills e.g. history of mathematics, women mathematicians, mathematics of colonialism, wealth and income distribution, or

• review timely practice for the past term/year: learners compare their timely practice assignments from a term/year ago and now (teachers have reported to us that this results in impressive motivation gains), or

• learners annotate recently learned questions with think aloud speech and thought bubbles.

The teacher can also reserve, topics to teach just prior to a slightly shorter cool down period:

• e.g. topics which may be easy to learn, but time consuming to develop accuracy such as frequencyGraphs or stemLeaf,

• e.g. topics which are quick to review e.g. simplify or solvingReady (it’s quick to review these skills, one question from each layer is usually sufficient review).

Teachers may find that most learners don’t remember what they learned on Thursday, by the following Tuesday (after a long-maths-weekend). Rather than wasting time giving lots of feedback every Tuesday, use this knowledge to adjust lesson planning and homework.

• e.g. create a short homework assignment dated Saturday,

• e.g. teach fewer topics on Thursday and create a longer timely practice assignment for Thursday,

• e.g. don’t “Edit Teaching” of Thursday’s topics directly after Thursday’s lesson - instead allocate lesson time on Tuesday for learners to redo their practise-learn worksheet from Thursday and/or redo some teach-learn practise questions with the whole class and then “Edit Teaching” of Thursday’s topics after Tuesday’s lesson.