planTeaching

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, but 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.

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.

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,

• use of 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 an effective 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.

Why? The teacher, learners and the timely practice app go to a deal of trouble to find learners' firm learning foundations and to make sure all the layers the learners already know are added into the learners' retrieval practice pool - to make sure they keep all of their learning fresh. We don’t want to undo all this hard work by adding new layers which may not be built on firm learning foundations.

The carefully curated retrieval practice pool ensures that learners can “get on with their timely practice assignment” whilst the teacher has time to give feedback. If we allow “barely better than a guess” layers to be added to the retrieval practice pool, the learners who arguably will benefit from timely practice the most

• perhaps the learners are absent often,

• perhaps they take longer to answer their questions because they struggle to read with meaning,

• perhaps they take longer to answer their questions because of very inefficient 4 operation strategies,

will need too much feedback and will therefore get the least from timely practice.

A learner’s column in the Plan Teaching topic dashboard

• which has some mid grey and darker blue-grey squares - indicates that pre assess is not complete;

• which only shows light grey squares - indicates that the app does not intend to pre assess the topic (judging all the layers too hard);

• which shows a mix of white and light grey squares - indicates the app thinks the learner could learn layers from the topic, but has not learned any yet;

• the (often fuzzy) line between the shades of blue (perhaps mixed with light grey) in the lower part of the column and the white (usually mixed in with light grey) in the upper part of the column is the (often fuzzy) “goldilocks” point where teaching should begin.

In a class where there is a wide spread of attainment this is very likely. e.g. a low attaining learner may only “already know” fewer than 30 layers whereas a learner at about GCSE grade 4 is likely to “already know” well over 100 layers. The learner who knows more will need to answer questions on far more layers in order for the app to find the sweet spot to begin teaching each topic.

Once some learners no longer have pre assess questions to answer, the teacher should make good use of lesson time for the lowest attaining learners. Consider creating slightly longer timely practice assignments so that:

• learners who haven’t finished pre assess yet, will finish more quickly;

• there will be time to teach learners who have finished pre assess an extra topic, whilst their peers answer further pre assess questions.

The learners who have finished pre-assess can learn a layer from “the class topic” and an additional layer from one or even two other topics per lesson, whilst the learners who are still doing pre assess do longer assignments. The teacher should make good use of the time when the majority of learners are doing long pre-assess assignments, which don’t require feedback-dialogue, to spend time with the lowest attaining learners - this time, well spent - will increase the motivation of the lowest attaining learners and be a chance to fix some fundamental gaps, which will make it easier to teach the whole class in the future.

The topics the learners who have already finished pre-assess can be drawn from all topic theme, but the teachers would be advised

• to teach 10bond, base10add and sequenceMultiple if they are not fully mastered;

• to avoid teaching extra layers on a topic within 6 weeks of when the topic is scheduled to be taught to the whole class (so that the extra layer will be well embedded, before the teacher comes to teach the topic to the whole class);

• to begin to teach numberX10etc and at least 3 of the 4 operations (multiply or divide may be missed out);

• to fill in fundamental learning gaps such coordinate, fractionINTRO, orderFDP, place0value99, place100value9999, proportionalGraph, proportionOFhalf, rulerANDscale and sequenceT2T;

• to use the early layers of some topics to fix other topics e.g. stemLeaf, correctTOnearest and decimalFraction to improve place value and inequality to improve understanding of negative number;

• to teach some layers, such as simplifySD (sum/difference), simplifyPQ (product/quotient) and solve10bond, which may help learners to overcome any fear of algebra that they might have. It will also to enable the lowest attaining learners to shine when the whole class begins to learn the topic together (It can be a really good “sales technique” for retrieval practice, when the lowest attaining learners can do more than their peers because “we learned it last half term with timely practice”) - especially when it is clear that these learners can learn also easily learn the another slightly harder layer on their firm learning foundations).

• a timely practice assignment episode + T-L on topic A + P-L on topic A + + T-L on topic B + P-L on topic B

• a timely practice assignment episode + T-L on topic A + P-L on topic A

  • + a teach-learn episode on topic B in one lesson

  • + a practise-learn worksheet on topic B in the next lesson

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 new learning than by learning at a pace that works for them … and remember it’s not OK to hold some learners back, because other learners take more time to learn (or are absent more often).

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,

• telling groups of learners that they can ignore what you are going to teach for the next few minutes - it's better than the many other 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. Most of our cohort learners have had many years experience in “playing along” and pretending they understand what is being taught, when they only understand part of what is taught.

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 are not the same. 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”.

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

• 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. after a little whole class teaching with proportionalFormulaNC 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 at a flip chart, whilst other learners are doing their practise-learn worksheets. By organising a few learners to hand out the correct practise-learn worksheets, 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.

• 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.

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

Use the good practice of activating the learners in the class to be teachers:

• 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.

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

• 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

• there are also some whole class activities which aren’t in timely practice (yet).

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 solve - 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 Taught” 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 Taught” Thursday’s topics alongside Tuesday’s after Tuesday’s lesson.

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.