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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.
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Avoiding pitfalls: Learners with smaller working memories are vulnerable to a double whammy
Learners with smaller working memories are more dependant on using chunks from long term memory memory capacities are less likely to build chunks in long-term memory after the lesson than their peers.However, learners
Learners with smaller working memories are less likely to build chunks in long term memory 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.
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| title | teach like a revision program or like cramming? |
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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 |
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| title | Research please follow the links below if your are curious to know more |
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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. |
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The following layers describe in more detail how the teacher can apply increasing interval retrieval practice, adjusted by feedback to help the learner to build chunks in long-term memory through regular timely practice during most maths lessons. |
(3) learners (not teachers) mark the learners' practise-learn worksheets
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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 the nights sleep after the lesson, we will need to ask this question a little later,
learners may learn the skills they were taught without fully completing the practise-learn assignment.
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| title | Top 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 |
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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). 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, not 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: this may lead to so the teacher may not needing 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. |
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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 feedback-not-allowed code written beside the question? 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.
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| title | Top tips for deciding between a feedback assessment outcome and best learned later |
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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 the a cool down period, see (10) below
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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 , limiting the teaching on a topic to a maximum of 3 different layers, 1 to 4 different layers are enough i.e. provides sufficient differentiation for the learners , but without undue complexity for the teacher.
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| title | Detailed look at a small group (of very different learner's that a tutor must teach) |
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Here a tutor has a challenge of teaching 4 very different learners, who have “weird and unexpected” strengths and weaknesses. Topic | | Ava | Baz | Charlie | Dylan |
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Topic | | Ava | Baz | Charlie | Dylan |
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Level of Learner | Detail | 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. | Global target | N/A | Find and fill in some glaring gaps. | Fill in gaps and improve | 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. | multiple |  | Teach layer 6 | Teach layer 6 | Teach layer 6 | Teach layer 2 (we want to get him feeling positive and successful) | factor |  | 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. | decimal fraction |  | Teach layer 8 or 9 Layer 8 is a scaffold of 9 - so err on the side of caution, while the teacher gets to know the class. | Teach layer 8 or 9 Layer 8 is a scaffold of 9 - so err on the side of caution, while the teacher gets to know the class. | Teach layer 3 | Teach layer 1 | fraction +/- The 3 different layers 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 layer 6 rather than layer 5. | Image Removed | Teach layer 6 | Teach layer 6 NB not layer 5 as it relies on fractionINTRO 9 as can learn layer 6 with Ava this term and next term layer 5 with Charlieseparately. |  Image Added | Teach layer 6 | Teach layer 5 | Teach layer 4 | Teach layer 1 | fraction INTRO |  | Teach layer 11 | Teach layer 5 Get Baz and Dylan to teach each other? | Teach layer 7 | Teach layer 6 Get Baz and Dylan to teach each other? |
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Future improvements - allow the teacher to see when a layer has all its pre requisites from other topics.
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| title | Why doesn’t timely practice collect full information on each learner in each topic? |
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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 relatively frequently 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 lots of learning gaps/who rush asking 2 questions on a layer is very necessary - as for up to 40% 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 helpful 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). Our auto pre assess process is on our plans to improve soon. 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 ely likely to be able to recall the learning of each lesson, until the next lesson, when the retrieval practice will begin to embed the learning deeply into long term memory. |
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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 and simple).
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| title | It's OK to teach the whole class a topic together, even though learners will then move on to practise different layers: |
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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. |
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| title | Here are some examples of 5 minute fillers |
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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) these : 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 in 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. |
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| title | Suggestions of before a holiday activities |
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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)
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