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how to calculate the range + how to subtract,
interpreting a stem and leaf + using a key which requires place value adjustment,
term to term rule for sequences versus + counting on the missing numbers,
expand: multiply in algebra + simplify by addition/subtraction + formal algebraic notation,
pictograms: using scale factor + calculating multiples,
not following the teacher’s instructions: too many instructions - , hence some will get be missed out.
As much as possible we need to improve learners confidence to get their workings on to paper - to reduce working memory load - but we may be working against years of shame for using non-formal methods, so gently does it.
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Chunk-based theory says that chunks are built of two parts:
the trigger “use me I think I’ll be useful for a problem like this”
the rest of the chunk which holds the knowledge and skills.
Experts use chunks in place of working memory - hence they can appear to have super-human working memory capacities - in their field of expertise.
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Consolidation is the process whereby a brain state in active or working memory is stored in long-term memory. This process modifies synapses on the dendrites of neurones. After retrieval of the memory, a similar process, called reconsolidation occurs whereby the old memory is altered and replaced by the new memory. Multiple retrievals and reconsolidations may be needed to build an accurate chunk. It seems we are not prompted to reconsolidate
Both consolidation and reconsolidation happen during sleep, so we can’t possibly know what a learner has learned during a lesson. We must wait for at least one nights sleep, to find out what has become learning and what has not. It seems that if recall is too easy, reconsolidation won’t happen at all or make a perceivable change in long term memory. This fits with Bjork’s desirable difficulties. It seems that by its very definition reconsolidation can’t happen at the end of the lesson where the skill is taught, because the learner hasn’t had a sleep yet to consolidate their so hasn’t even consolidated the learning. |
(3) overcoming low attaining learners' double whammy
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There are number of general problems that feedback may need to overcome.
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,
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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 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, below 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”.
(5) fading scaffolding
More about points 1. and 3. fading scaffolding is found in (4) feedback is best after a nights sleep + how to fix incomplete and incorrect chunks above.
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read the question and decide which skills to apply and
recall the complete process they learned in a previous lesson,
so we may soon see it is not surprising that sometimes we will see occasions where teaching hasn’t become embedded learning (yet).
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get the learner to join 2 or more chunks together 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 also means 7 ÷ 100 and the chunk that knows how to divide a number (without a decimal point) by 100.
to add something new on to the end of an existing chunk e.g. to add on to the chunk for finding the median of an odd number of data items, the extra steps to find the median of an even number of data items.
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Hence, we are unlikely to fix the recall problem, with another lesson - whether the lesson is next term or next year - when we tell the learner what to do (unless, there are parts of the process that are not yet mastered).
We are however, much more likely to fix the recall problem, by a few quick feedback-dialogue sessions, in the next few lessons, especially if we see what the learner can already recall and then help them add a bit more of to the process to the end or join existing processes together.
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 given - sign layers 3 and 4 |  given - sign layers 9 and 10 |
At the moment, April November 2022, the app can’t automatically swap between scaffold pair layers - but we plan to do this in the future.
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it could be what many of us might see as too simple to be problem solving: answering a word problem, which we at timely practice classify as secret x sign, that requires the learner to realise that the problem will be solved by multiplication,
it could be a more complicated word problem: e.g. requiring both multiplication and addition, which I think most teachers would classify as problem solving,
it needn’t be a word problem e.g. the diagram below could provide simple or complex problems:
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it could be that the learner is told the diameter of the larger semi-circle and asked to find the diameter of the smaller semi-circles,
it could be the learner is told the diameter of the shape and asked to find the area of the shape,
it could be the learner is told the diameter of the shape and the price of 1 cm2 of gold leaf, and asked to find out the cost of covering the shape with gold leaf.
These problems are hardly novel, but I would say 2. and 3. require genuine problem solving skills: they require
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