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working memory overload - as it happens: where the learner is trying to calculate, but gets stuck, so uses an informal method, but gets stuck and so forth - so what looks from the outside as day dreaming or fake thinking may actually be overwhelmed thinking;
shame avoidance - the learner would rather give up before they begin and console themselves that they “didn’t try”, “you didn’t teach us” or “this won’t be useful in my adult life” rather than try and fail. This behaviour can be seen as a way of dealing with cumulative failure. If we make learning maths too stressful, then our learners will be primed for forgetting the uncomfortable feelings that the lesson induced, as well as any maths they may have learned during that lesson . See also (motivated forgetting see maths anxiety).
The first type of giving up is the easier to work with than the second, but both types are what timely practice was built to improve.
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timely practice repurposes the research on how experts learn to ensure that embedding learning is easier for low attaining maths learnersour cohort.
Experts use deliberate practice to build up complex chunks of skills and knowledge in their long-term memory.
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I call this a double whammy, because learners with smaller working memory capacities are doubly disadvantaged - and often go on to become low attaining learners. I would say the best thing we can do as teachers is to teach low attaining learners in a smaller working memory friendly manner.
(4) feedback (fixing incomplete/incorrect chunks) is best after a nights sleep
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Contrary to our expectations, feedback is better given after one sleep, than directly after an error. It seems that if we give feedback on the day of the error, we may not be as effectively triggering reconsolidation - see (2) above - that is we are not as effectively triggering the brain to change chunks in long-term memory. On the other hand, if we leave feedback for too many days, then feedback is not as effective as it could be either.
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The learner has built an incomplete chunk in long-term memory - despite timely practice layers being small and therefore easier to learn, sometimes the learner will need more support to build a chunk - the teacher, via feedback-dialogue, should work with the learner to find what is missing and help the learner fix it. See also (5) fading scaffolding, for more about this. We recommend assessing rather than marking of assignments, to assist with this. With marking, the teacher might write a note to the learner, showing the missing bits, but with feedback-dialogue, we help the learner add the missing bits to the chunk, ideally via questioning rather than telling.
The learner has not replaced/adapted an incorrect chunk built some time ago, with a new/adapted chunk in long-term memory. This is different from 1. in that the chunk to do the old incorrect method hasn’t been overwritten, despite perhaps a new chunk being built in the lesson. So here we are working on changing the trigger i.e. the learner choosing the new correct chunk, rather than the old incorrect one. The best way to do this, is to offer a reason why the old incorrect one is incorrect , that or inefficient which chimes with the learner’s understanding.
The learner is still reliant on some of the “unacknowledged scaffolding'' of the lesson e.g. placement of workings out on the page or use of a diagram etc. See (5) fading scaffolding for more about this.
The learner has misread the question or poorly applied their numeracy skills when answering the question. This is likely to be due to working memory overload - all learners, even the most able A level maths learners experience it. As they are learning and working through something new and hard, they are unable to accurately apply skills which are usually easy for them. I sometimes describe this effect to students as their brain isn’t very good at easy thinking and hard thinking at the same time. The best we can offer learners as they practise, is that they can look through their workings out for accuracy periodically. Sometimes I suggest they write “check for accuracy” on the answer line, as an aide memoire, for when they think they have solved the problem. We need to encourage learners to realise that making “silly mistakes” is often a sign of hard learning going on, not a sign that “they can’t even do the easy maths”.
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More about fading scaffolding is found in (4) feedback (fixing incomplete/incorrect chunks) is best after a nights sleep + how to fix incomplete and incorrect chunks, see above.
The difference between being able to answer questions in a lesson, where all the questions require the same, recently learned skill, and being able to answer the interleaved retrieval practice questions within the learners assignment is a little like the difference between being able to follow a recipe and being a creative chef. As teachers we are often unaware of how much scaffolding is in the classroom when we are teaching a topic e.g. notes on whiteboard, vocabulary fresh in learner’s minds etc. Almost all the practice questions that learners will do in the a maths lesson will be on the topic of the lesson, (except of course those in their timely practice assignment). In the lesson where teaching occurs, learners don’t need to use the triggers for their chunks in long-term memory, they just need to remember their learning of the lesson.
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“what diagram will I ask you to draw?”
“where on the page, would it be best to show your working workings out?”
When we ask questions like this we help nudge the learner to replace the external scaffolding of lessons with their own internal scaffolding - i.e. a better/bigger/more complete chunk in long term memory. It is often clear, that that is what we are doing e.g. as as soon as we say “what diagram”, we see the “aha” look and the learner wants us to go away and leave them to get on, they know what they are doing. The diagram, often already has a chunk attached to it, in the learner’s long term memory.
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We have to accept that selecting best learned later and hoping that “in class teaching and practice” in the next spiral of the curriculum, is unlikely to solve the problem: the learner could answer practice questions in the lesson they were taught, but can’t recall enough the next lesson. It is clear that the problem is not - being unable to apply the process , instead - rather the problem is being unable to recall to recall the process.
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In our development of this version of timely practice we have created many scaffold pair layers, one of which carries with it some of the scaffolding of the lesson. These make it easier for us to “reduce the amount of new” from one layer to the next. Here are 2 examples of scaffold pair layers.
 given - sign layers 3 and 4 |  given - sign layers 9 and 10 |
Not all layers, which have a scaffolded layer planned, are written yet. This is the main reason why some topics e.g. frequency table has gaps between some layers.
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In (5) fading scaffolding, an example of the need to
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to join 2 or more chunks together was given
e.g. to write 7% as a decimal, we are trying to get the learner to recall and join the chunk of how to write 7% as a fraction and the chunk that knows that the fraction 7/100 means 7 ÷ 100 and the chunk that knows how to divide a number (without a decimal point) by 100.
was given. I don’t think many teachers would count this as problem solving, most would classify this as merely requiring learners to use a number of skills to perform a standard problem.
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