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increasing the likelihood that teaching becomes embedded learning for low prior attaining and under achieving learners.

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The vast majority of learners who can be described as low prior attaining or under achieving (“our cohort”) 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' “our cohort’s” progress significantly acceleratesaccelerate.

(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 insufficiently 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).

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titleavoiding pitfall: learners often subvert the pre access process

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 “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?

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titleavoiding pitfall: teachers (and sometimes learners) are overly optimistic that teaching and fluent practice in the lesson will result in efficient learning

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 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.

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  • 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 our cohort - who no matter what the standard was, have learned that they won’t meet that standard - that when they use timely practice we are in the business of assessing them to help them learn better. (We probably won’t be able to avoid summative testing entirely.)

  • 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”

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titleteach like a revision program or like cramming?

An effective revision program uses these key behaviours

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.

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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 question in 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.

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titleAssessment is about improving future learning, whereas marking may have different purposes

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 do 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.

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titleTop Tip 2: only write the assessment outcome: don't give value judgements, don't give hints, don't correct working, don't try and find where or why errors were made

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 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 embedding enabling the learner to embed the learning.

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titleTop Tip 3: if the assessment outcome is feedback on blank, position the asterisk** so that the learner can see it, but preserve almost all of the answer space.

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

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The teacher may want to display the following

Phase 1 top tips (using timely practice for pre assess only)

Phase 2 top tips (using timely practice for teaching and retrieval practice and possibly pre assess)

on the whiteboard/a poster for

  • the learners and

  • to share with teaching assistants and other adults visiting the classroom.

Info

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. write page 2, Q7 at the end of last lesson’s assignment

  • is there a question that you think is best learned later? - if so - find a similar question in your new assignment and 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. page 1, Q3 at the end of your new assignment, to remind yourself to return to the question,

  • if you are stuck, look to see is the question in the learned and remembered? section - this means it's a pre assess question - you can miss it out and write bell or draw the bell symbol (best learned later),

  • if you need help on questions in the timely practice section, 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, instead the app will give you another practice question sooner (so you are much more likely to be able to answer a similar question independently and accurately in your next assignment,

  • is there a question in the timely practice section 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 your peers/your teacher/other adults 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!

Discourage learners from Discourage learners from working out a score for their assessed assignment (its not written in the poster 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.

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Examples of feedback-dialogue are given within the questions for this layer (ask if you would like this training).

(7)

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sometimes best learned later may result in more embedded learning than

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feedback

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In Assess t.p. the decision between feedback 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.

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titleTop Tips for deciding between a feedback assessment outcome and best learned later
  • 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 https://timelypractice.atlassian.net/wiki/spaces/CKB/pages/3110699106/Best+practice#(10)-schedule-a-cool-down-before-each-holiday
    • feedback - this is issue can be in part dealt with by us of a cool down period, see (10) below

(8) use the assessment for learning data to plan who learns what …

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 expandLinear the teacher may need to look at the learners skills in the topic simplify simplifyPQ (x/÷)

Teaching up to 3 different layers will usually provide sufficient differentiation for the learners without undue complexity for the teacher.

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Training on how to do this is found in https://timelypractice.atlassian.net/wiki/spaces/CKB/pages/3110699127/Using+timely+practice#(5)-Get-started%3A-when-can-the-teacher-use-Plan-Teaching-within-the-app%3F (5) above

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titleWhy doesn’t timely practice collect complete assessment for learning data on each learner in each topic?

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.

Mainly 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 more more 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

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Usually the teacher’s best use of the timely practice assignment episode is giving feedback rather than teaching (as described in https://timelypractice.atlassian.net/wiki/spaces/CKB/pages/3110699106/Best+practice#(5) -schedule-a-%E2%80%9Ctimely-practice-assignment%E2%80%9D-episode-every-lessonabove). However 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 “for the next 3 minutes: begin your (silent) do now: look at your assessed assignment and begin your new assignment”.

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titleMore sophisticated teach-learn options are not necessary

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 https://timelypractice.atlassian.net/wiki/spaces/CKB/pages/3110699106/Best+practice#(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

https://timelypractice.atlassian.net/wiki/spaces/CKB/pages/3110699106/Best+practice#

scheme of learning is to

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.

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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.

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titleHere are some examples of 5 minute fillers
  • 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 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.

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titleHow long should a cool down before a holiday be?

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

The purposes of a cooldown are

  1. to avoid wasting teaching time: e.g. a newly taught layer will need more than a week of timely practice before it is likely to be remembered for 2 weeks. Hence continue with timely practice until directly before a holiday, but without any new teaching during the cooldown period will make better use of learning time (use the rest of lesson time to do activities which aren’t learning new maths content - see suggestions below).

  2. to embed learning prior learning so that it can be recalled, without recourse to feedback, after the holiday. If layers become overdue during a holiday, and can’t be asked, then the learner is less likely to be able to recall this learning after the holiday. By allocating some cooldown lessons before the holiday (for which the teacher creates assignments with e.g. 30% more questions), fewer layers are likely to become overdue during the holiday. (Since, with more Increasing the number of retrieval practice questions, means layers are more likely to be asked shortly after closer to when they are “ready” - rather than closer to when they become “overdue” Retrieval Practice Theory).

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titleSuggestions of before a holiday activities
  • 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).

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titlePoorly spaced lessons can be mitigated by similar strategies to those for cooldown

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.

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