The timely practice app was designed to allow the teacher to far more easily apply research backed, best practice, to make teaching more likely to become embedded learning for low attaining and under achieving learners. In the main it isn’t that teachers don’t know what works, its that without a tool like timely practice, best practice is too time consuming for teachers to apply.
The vast majority of learners who can be described as low attaining or under achieving have smaller working memory capacity than their peers. However this is not the main reason that they are not achieving as well as their peers. Their main problem is being educated in a system set up for those with average and above average working memories. Having a smaller working memory capacity per se, is far less of a problem. With timely practice we have consistently demonstrated that: once the teacher starts to teach in a smaller working memory friendly way, the teacher will see that previously low attaining and under achieving learners' progress significantly accelerates.
(1) teach on firm learning foundations
Effective pre assess, finding out what learners "already know" means we can make best use of lesson time.
We won't teach learners what they "already know", nor attempt to teach them work for which they don't have sufficiently firm learning foundations; instead we can teach in the "sweet spot" between. So teaching and learning become more efficient, i.e. we can increase the output (retained learning) per hour (of lesson time).
With timely practice, teachers only need to pre assess a topic once, before they teach the topic for the first time. Next time the teacher spirals around to teach the topic, the teacher will be able to see in fine detail what the learners know and don't know yet from the assessment of retrieval practice data the app collects.
Of course it is no good collecting robust assessment for learning data, unless the teacher uses it to better plan teaching.
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. Low attaining learners are often especially uncomfortable, so they often undermine its effectiveness by quietly not engaging, copying or otherwise avoiding answering, perhaps by claiming it is a waste of time because 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 something 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.
timely practice ensures that
pre assess and retrieval practice are "low stakes". Learners, over time, learn their assessment is formative (to help their learning) not summative (to judge them against a standard). We need to teach most low attaining learners - who no matter what the standard was, have learned that they won’t meet that standard - that we are in the business of assessing them to help them learn better.
it may take some time for learners to begin to feel comfortable, what the teacher can do to help is keep sticking with the message: “I’m finding out what will be easiest and most valuable to teach next” and “I’m finding out how well you can recall recent learning, so that you can recall it more easily in the future”
How do we pre assess? - we use a trial and improvement process - please read this if you are curious to know more about how this works.
How do we schedule retrieval practice? - please read this about how we do it in the app and this if you want to know about the research.
At the moment we only do a 2 round pre assess - ideally in some circumstances, some learners will do a third round. We hope, in the future, to
ask fewer unnecessary questions on scaffolding layers within the pre assess process.
use A.I. based on our data analysis to decide what, if anything, to ask in the third round.
(2) teach 1 layer per topic per curriculum spiral
Summary: Learners are more likely to be able to build an accurate chunk in long term memory, during the night after the lesson, if we teach them one small bite - a timely practice layer - rather than if we teach them a “too large for the learner” bite i.e. several layers. Since the teaching and subsequent practice of a layer takes between 10 to 30 minutes, often there will be time to teach more than one topic per lesson, so the class will more quickly spiral through the curriculum, each time teaching a small bite more on firm learning foundations.
Avoiding pitfalls: Learners with smaller working memories are vulnerable to a double whammy
Learners with smaller working memory capacities are less likely to build chunks in long-term memory after the lesson than their peers.
Learners with smaller working memory capacities are more dependent on chunks than their peers to process the content of lessons.
Every time we help ensure a learner creates 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.
If you are not convinced about limiting what the amount taught per topic per spiral - why not just give it a go - with a class of learners who you don’t expect to retain most of what you are expected to teach them and see how it works out?
In our development of timely practice and our training of teachers we have found that changing from an annual to a more tightly spiralled scheme of learning is the hardest of the changes for teachers to take on. We accept that some schools would prefer to use timely practice without doing this - however our experience is that this significantly dilutes learning gain. For these schools we offer trials where they can measure and compare gains in embedded learning.
An effective revision program uses these key behaviours
pre assess: the learner decides what they need to learn,
Efficient process: Some learners will more quickly master what they have recently learned in a topic than others, but by using retrieval practice and waiting until the next spiral of the curriculum before teaching another layer on the topic
the learners who are finding a topic harder, get more practice (and if necessary feedback with their teacher),
so (in almost all cases) learners are ready to learn another layer of learning when the class returns to learn more on the topic in the next spiral of the curriculum,
when the teacher returns to teach the topic in the next curriculum spiral, they can see which learners are ready to learn a new layer and which are not. The teacher may be able to apply what they learned from the feedback process during the previous spiral, to help all learners, but especially those learners who didn’t master a layer in the previous teaching spiral.
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.
We hope, in the future, to use A.I. based on our data analysis to find if and when the rule
teach only one layer per topic per curriculum spiral
can be broken without loss of progress.
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.
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.
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 timely practice to help the learner build a chunk or add to an existing chunk in long term memory, so each learner can learn a little more from a topic, spiral by spiral.
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.
(3) learners (not teachers) mark the learners' practise-learn worksheets
The practise-learn worksheets are made with cut-off answers, because
Learners will learn better by doing this self assessment, and will have the opportunity to get help if they make mistakes during the lesson.
Teachers should not use their non-contact time assessing the learners' practice questions on the topics of the lesson. That is not a good way to find out if teaching has become learning, although the teacher may spot check during the lesson, to check that the learners are self assessing their work.
We know that
end of lesson assessment cannot tell us what we want to know - “has teaching become learning?” - because learning will only be embedded in long term memory in during sleep the night after the lesson - so we will need to ask an assessment question at least one day later
learners may learn the skills they were taught without fully completing the practise-learn assignment.
The first time we can find out - “has teaching become learning?”, i.e. has teaching resulted in the desired change in the long-term memory of each learner - is by asking a retrieval practice question on the skill the next maths lesson. The timely practice app will schedule this for the next assignment. All the teacher needs to do is tell the app which learners were absent, and therefore shouldn’t be assessed on the topics taught that lesson.
(4) assess (don’t mark) the timely practice assignments
Assessment is about improving future learning, whereas marking may have the following purposes:
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.
The teacher guesses what the learner was thinking/ not thinking when the learner made their error(s) and give hints or clues or model answers to help the learner. 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 do 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 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.
If the teacher does need to do feedback-dialogue in the classroom then
the teacher replaces marking - which is non-directed time work - with feedback in the classroom - which is directed time work,
the learner is more likely to improve their learning,
the necessity for the teacher to guess what is going on in the learner’s head is reduced or avoided and
more of the responsibility for improving future learning can be given to the learner.
The assessment outcome for each question should be communicated to the learner and the app. The most efficient way to do this is
This saves the teacher a little time for each question
Teacher’s may find suppressing their urge/habits to write more a little difficult at first - but stick with it - not only will it reduce the teacher work load in non-directed time, it will also
make retrieval practice more effective at embedding learning.
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 learners correction.
If the assessment outcome is a tick or best learned later or run-out-of-time: 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:
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.
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.
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;
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.
Without marking by the teacher, the teacher and learner can start the feedback-dialogue from a common place.
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.
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.
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.
Feedback-dialogue is likely to increase the learner's motivation whereas marking is likely to decrease it.
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 embedding 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.
(5) get the most from each timely practice assignment episode
Return the most recently assessed assignment to the learners, along with their new assignment.
The teacher may want to show or adapt the following and display it on the whiteboard/card for learners, while the teacher trains the class on how to get the most from this episode of the lesson.
A poster is a helpful device to share with teaching assistants and other adults visiting the classroom: we need to see what the learner can do independently.
Top tips for learners doing their timely practice assignments
Look at your assessed assignment and see all the questions you got correct - by doing this you embed this learning more deeply.
Look at each question which has an asterisk, * , assessment outcome and decide:
can you answer it now, perhaps you missed the question out by mistake?
can you see an “oops” in your workings out? if so, you may circle it or fix it,
did you “mis-copy” some of the numbers from the question? if so, you can circle the errors or fix them,
do you need some feedback-dialogue with a teacher in the room? + does that teacher need to be a paid teacher?, if so, get help or make it easy to find the question for when its your turn for help e.g. draw a dark line down the edge of the question or write page 2, Q7, fold over the corner of the page etc
is there a question that you think is best learned later?, if so, wait until you find a similar question in your new assignment, when you can write the bell symbol instead of an answer.
Begin answering questions in your new assignment
are there any questions you need to have feedback from last assignment before you answer? - write e.g. Q4 at the end of your assignment, so that you will remind yourself to return to the question,
if you are stuck, look to see - is the question in the learned? section- this means its a pre assess question, so just miss it out and write bell or draw the bell symbol (best learned later),
if you need help on other questions, it’s ok to ask for help - your teacher will write the feedback symbol beside the answer line - this will mean you get help when you need it, but the app won’t think you could easily answer, and instead will give you another practice question sooner, and so you are much more likely to be able to answer independently and accurately next time,
is there a question that you think is best learned later? if so, tell your teacher by writing the bell symbol instead of an answer - although if you do this too often, your teacher won’t always listen to you!
you are allowed to ask teachers to read words or sentences to you - and they won’t use the feedback symbol.
Teachers and teaching assistants expect you to answer each question independently, if you don’t answer your questions independently then you won’t make progress. Please don’t try and “sneak extra help” from teaching assistants - they will record the feedback symbol beside the answer line and your teacher will know!
FYI At the moment it isn’t easy for the teacher to tell to the app, after feedback between the teacher and the learner, that a layer is best learned later for the leaner. So for now it's easier to to tell the app when assessing an assignment.
Discourage learners from working out their score (its not written in the card above, because that might be counterproductive). It is better to concentrate on feedback, and judge oneself on progress. We know that when a learner gets only feedback, they pay better attention to the feedback than when they get a score and feedback.
(6) get the most from feedback-dialogue
Feedback should be done after some teaching has become embedded learning, so sometimes reteaching - especially after a long gap between lessons - will be more efficient than giving feedback. If the long gap between lessons can be foreseen, then a cool down period can be planned within the SOL.
Remember the layer has already been taught and successfully practised in the lesson, so feedback must be something more e.g.
help the learner add the bit they have forgotten of a skill or process, to the bit that they have remembered of the skill or process,
if accuracy is an issue - help the learner to check though their workings out - with the ultimate goal that the learner begins to be able to do this for themselves,
adapt the learner's past thinking to influence the learner's future thinking,
use the opportunity to train the learner to figure out what strategy or knowledge will ensure the learner can solve similar problems in the future,
sometimes feedback gives the teacher and or learner the opportunity to realise that the layer is best learned later.
Additionally, the process of feedback-dialogue, makes excellent, non threatening, feedback for the teacher on the fine details for future teaching.
Examples of feedback-dialogue are given within the questions for this layer.
(7) sometimes best learned later is more appropriate than feedback
The decision between feedback on attempt and best learned later, can be complex as we are deciding on the best use of the teacher’s and learner’s lesson time. The question isn’t about just whether the teacher and learner can use the feedback process to “get the learner to be able to ask similar questions in the layer” but also about balancing the cost in lesson time allocated and the cost to the learner’s limited supply of motivation.
In a nutshell the question is
Will the learner, in the next week or two, “need too much help” to embed this learning?
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
the decision to give feedback or decide a layer is best learned later needs to made within the context 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
In the future we will use A.I. to give teachers “our best guess” + make it easier for the teacher to tell the app, after a feedback attempt, that the layer is best learned later.
(8) plan which layer to teach each learner from a topic using AfL data
Usually the teacher will only need to consider the progress on topic of the topic they plan to teach, to decide which layer to teach each learner. However sometimes the teacher may need to look at the progress of topic of another topic e.g. for the topic expand linear the teacher may need to look at the learners skills in the topic simplify x/÷
Usually teaching 1 to 4 different layers will provide sufficient differentiation for the learners without making undue complexity for the teacher.
Here a tutor has a challenge of teaching 4 very different learners, who have “weird and unexpected” strengths and weaknesses.
Level of Learner
Ava’s teacher has no real idea of grade learner would gain if she took her GCSE exam tomorrow (she is new to the school).
Baz, would gain a grade, which would almost certainly be below grade 4 if he took his GCSE exam tomorrow.
Charlie might gain a grade 1 if she took her GCSE exam tomorrow.
Dylan is not expected to get any grade if he took his GCSE exam tomorrow.
Find and fill in some glaring gaps.
Fill in gaps and improve
his ability to read questions with meaning,
Charlie has some unexpected strengths, so here the task is to find out why she has so many weak areas, as well as build on her strengths.
Dylan, is one of the weakest learners in the school, so may well have been taught “too hard” in most his maths lessons - so err on the side of easy and see how learning embeds.
Teach layer 6
Teach layer 6
Teach layer 6
Teach layer 2 (we want to get him feeling positive and successful)
Teach layer 6
Doesn’t need to learn - teach BIDMAS layer 4, while the other learners, learn factor skills
Teach layer 6
Teach layer 1
BIDMAS - could be taught as an extension layer in the second half of a lesson - or see teaching suggestion given when planning teaching of the topic factor
Ava doesn’t know this, and her assessment on multiple and factor indicate she would be better learning other skills.
Baz can learn layer 4 while the others learn more factor skills
A surprise that Charlie knows this - her numeracy skills are higher than expected.
This topic will be too hard for Dylan. Due to his low level for learner, he wasn’t even asked questions form this layer. The teacher might teach him some 4 operation skills, which the rest of the learners already know.
Teach layer 8
Teach layer 8
Teach layer 3
Teach layer 1
Layers 1, 4 and 6 all rely on labelling a fraction line - so shouldn’t be too difficult for the teacher - layer 5 isn’t like this, so teach Baz separately.
Mainly because it would take too long and it would be too traumatic for many learners - who have low self esteem in terms of their maths learning.
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 - but only questions 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. (For learners with lots of learning gaps/who rush when answering questions - asking 2 questions on a layer is very necessary - as for up to half of their layers, we will find one question answered correctly and a second not).
Using the information on key layers we ask a question on layers, we call them interesting layers, we think teachers will find this information interesting in order to plan their teaching.
There are some layers which we don’t ask questions on - usually these are layers which include considerable timely practice scaffolding - so the learner is unlikely to have met these type of questions before. After teaching the layer, the scaffolding will be very helpful to the learner, but before teaching the scaffolding is likely to be confusing.
However the data the app collects will provide much better data than the teacher can expect to when using one or two pre assess questions at the start of the lesson because
we significantly reduce the likelihood of copying,
answering a question on an assignment is much less stressful than answering a question in a class, where some learners will feel they will be “shown up” so teachers are less likely to see a false negative,
we ask 2 questions on any layer on different days so teachers are less likely to see a false positive,
the app collects all the data in an easy to visualise way - so that planning is easy for the teacher and so every learner is likely to be able to learn what they are taught
… and we also ensure that the teacher is unlikely to teach too much to each learner on a topic, so each learner is likely to be able to recall the learning of each lesson, the next lesson, when the retrieval practice will begin to embed the learning deeply into long term memory.
(9) plan the teaching and learning activities of the lesson
timely practice + T-L on topic A + P-L on topic A + T-L on topic B + P-L on topic B
timely practice + whole class project
the timely practice episode
Usually the teacher’s best use of the timely practice episode is giving feedback rather than teaching. But the teacher can interleave timely practice with teaching e.g. if only one learner must learn layer 6 and all the other learners layer 2 or 3, the teacher might teach layer 6 to the learner, whilst the rest of the class “begin your silent do now: looking at your assessed assignment and beginning your new assignment, for the next 3 minutes”.
teach-learn (T-L) episodes
Always make use of the fact that each layer is quick to teach and learn (because all the pre-requisite skills are mastered), so keep whole class sessions short (i.e. KISS keep it simple and short).
as reviewing skills already mastered on a topic primes the learner to more easily be able to hang the new harder learning on the easier already existing chunks,
telling groups of learners that they can ignore what you are going to teach now, isn’t exactly ideal - but it is better than teaching too hard and muddling what the learner has just learned.
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. In my opinion this leads to too often: shoving too many bites of learning down each learner's throat, with the outcome that many low attaining learners only partially digest the learning of the lesson and too easily muddle methods, miss skills and give up: the classic signs of working memory overload.
There are a number of ways the teacher can use the advantage of knowing exactly what learners already know on a topic.
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 about a layer 3 question, perhaps ask a learner who has mastered layer 3 and 4 and is learning layer 5 now.
When teaching layer 1 of a topic to a few learners e.g probability tree (1), 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 a review question on their desk - aiming for accuracy “whilst I work with a small group. Then we’ll come back together, in a little while, to see who has been 100% accurate” This stops the “masked (or perhaps not so masked) fidget” from learners that already know something, which the teacher is teaching too slowly, and it reviews the skill so the learners who already knew the skill, are 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”
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 allocated practise-learn, has started their practise-learn worksheets, teach the small group the harder skill.
if you have teaching assistants, you can teach 2 or more groups exactly what they need to learn at the same time
Remember it is completely OK to teach e.g. layer 1, layer 3 (and layer 4 which is the same as layer 3, but without the scaffolding) and layer 5 in the same session one after the other.
It's not so much that the teach-learn part of most lessons have been a problem for low attaining learners, it's the practising part which often lets low attaining learners down. So getting practise-learn and retrieval practice “more right” will lead to large learning gains, without the more sophisticated options suggested above.
practise-learn (P-L) episodes
It's not OK to get learners to practise several new practise-learn worksheets on the same topic, as almost always this will lead to muddling methods and greater need for feedback later.
It’s OK to teach some learners 2 topics in one lesson, and others only 1 topic. Remember learners are more likely to be left further behind, by consistently failing to embed learning, than by learning at the pace that works for them.
It’s essential that learners follow up the teach-learn on a layer with their teacher, with independently answering their practise-learn questions, but sometimes the practise-learn questions from the second topic may be need to be deferred until the next lesson, in which case defer adding the layer as taught until the next lesson too.
There are a number of ways the teacher can use the advantage of knowing exactly what learners already know on a topic, and exactly what each leaner should learn next.
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, with a small group (who have not yet mastered layer 1). 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”
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 it to good effect. 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.
To help get the class together again e.g. to move on to teach a second topic - have some activities which can fill about 5 minutes of time, but which won’t move the learner on in learning the topics that are being taught in the lesson.
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 will be full of non-urgent questions) the “catch up” assignments, can be completed “any when within the next week” without causing the problem that the retrieval practice questions will be asked too late, and so can be used as filler activities,
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.
(10) schedule a cool down before each holiday
A cool down with timely practice involves some maths lessons where timely practice assignments are done, but no new layers are taught.
Before a half term holiday: 1 or 2 lessons
Before the 2 week holidays: almost a week
Before the 6 week holiday: ideally 2 weeks
The purposes of a cool down are
to embed learning, which may be otherwise asked too late, as it will become overdue within the holiday period - hence often the teacher will create longer or catch up assignments
not to waste time teaching, what we can be almost certain will be forgotten - hence using the rest of lesson time to do activities which aren’t learning new maths content
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 requirement for learners to set themselves targets for maths 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
stick with a timely practice theme: 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), 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 e.g. stem and leaf diagrams,
e.g. topics which are quick to review e.g. simplify (so the skills can be easily reviewed after the holiday, if learners forget their skills)
(11) grow a growth mindset
Facilitate learners to grow a growth mind set by helping learners to deal with the emotions of getting answers wrong / being unable to solve problems, in a way that promotes good learning behaviours in the future.
With timely practice learners get to see how feedback and further practice helps them to master layers, which they have previously had difficulty learning. Over time, and sometimes through feedback-dialogue, the learner begins to have confidence that their attainment is improving and that they will always be able to learn, even if they find leaning a little hard at first.