chunk-basedTheory

(0) Introduction and links to the other teacher training topics

Chunk-based theory enables the teacher to understand how the teaching of the lesson (see plan teaching) is absorbed by the learner through the interaction of working memory slots and existing chunks in long term memory.
Chunk-based theory enables the teacher to recognise how a smaller working memory capacity or inaccurate or incomplete chunks or weak/non-existent triggers mean that the learning of the lesson isn’t fully retained and how retrieval practice and feedback (see assessment and feedback) might fix this … and that more practice in the lesson and/or later re-teaching is less unlikely to fix this.

1 (0) Introduction and links to the other teacher training topics
2 (1) How chunks in LTM can replace slots in WM + poor rememberers double whammy
3 (2) Build + Improve chunks/triggers in LTM
4 (3) 3 symptoms of working memory overload or could they be symptoms of chunk problems?
5 (4) Fading scaffolding
6 (5) Problem solving - combining chunks in novel ways

(1) How chunks in LTM can replace slots in WM + poor rememberers double whammy

LTM = long term memory, WM = working memory

If learners have a smaller working memory than their peers or if they have a shorter retention of new learning period than their peers then they are less likely to process the activities of the lesson and retain the learning of the lesson than their peers. Hence they may miss out on building accurate well triggered chunks in long term memory.

A chunk in long term memory can act as slots in working memory, so chunks can effectively increase the working memory capacity of learners. The trigger is part of the chunk which calls out “use me I’ll be useful for a problem like this” when learners think “How can I solve this?”

When learners, who didn’t build an accurate well triggered chunk in long term memory, return to learn more on the topic they can’t use the chunk, the chunk that their peers built in long term memory, which their peers use to reduce the working memory capacity to solve problems. Their peers follow up this new lesson by building an additional chunk to add to their existing chunk. After new learning our cohort, who often didn’t building accurate well triggered chunks when the topic was taught previously, may go on to

not build a chunk the next time the topic is taught or they
muddle their old partially built chunk, with the new learning and building an inaccurate or incomplete chunk.

I call this a double whammy

less likely to build a chunk,
being more reliant on the missing chunk to learn more.

Where high attaining learners can overcome the odd missing chunks, low attaining learners generally can not.

The best thing we can do as teachers is to teach low attaining learners in a memory friendly manner**

This is what timely practice was built to do.

** smaller working memory and/or a short retention friendly manner.

(2) Build + Improve chunks/triggers in LTM

timely practice repurposes the research on how experts learn to ensure that embedding learning is easier for our cohort.

Experts use deliberate practice to build up complex chunks of skills and knowledge in their long-term memory (LTM).

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.

It takes time and appropriate practice to build chunks in long-term memory.

Chunks with slots for variables are called templates.

Mental schema are another name for chunks or templates.

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

if we can easily recall our learning - hence overlearning is far less effective than retrieval practice - see retrievalPracticeTheory(4),
by activities which induce uncomfortable feelings - what we might have learned, is not laid down in long term memory - perhaps to preserve our self esteem.

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 sleep to find out what has become learning and what has not.

It seems that if recall is too easy, reconsolidation won’t happen. There will be no change in the duration of the recall-ability from 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 so hasn’t even consolidated the learning.

(3) 3 symptoms of working memory overload or could they be symptoms of chunk problems?

There are signs of learners with small working memory capacities which we can glean from observation over time: https://thepsychologist.bps.org.uk/volume-21/edition-5/working-memory-classroom

There are 3 signs of working memory overload which we can witness as they happen - these can happen to any learners - even those with average or above average working memory capacities:

muddling methods,
missing steps and
giving up.

Each of these symptoms can be considered as a building chunk problem e.g.

muddling methods - could be weak/absent triggers or inaccurate chunks,
missing steps - could be incomplete chunks,
giving up - could be weak/absent triggers or due to missing/inaccurate/incomplete chunks.

Let’s look at each of these in terms of maths learning.

muddling methods, very popular methods to muddle in the maths classroom are

calculating area versus perimeter,
median versus mode versus mean versus range,
column methods for addition versus subtraction.

The first two may be more because we usually teach them at the same time, rather than because they are naturally muddled. The third example of muddling column methods, comes I think, from the fact that all standard methods - have high working memory needs. I would say that column methods for addition and subtraction, long multiplication and division are paper saving but working memory heavy.

We are more likely to witness muddling methods when the learner is trying to recall learning, rather than when engaged in new learning. The other two symptoms missing steps and giving up may be witnessed during learning or when recalling learning.

missing steps: often happens when chunks in long-term memory are incomplete or when the working memory is overloaded by applying 2 methods together e.g.

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 + 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 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.

giving up: there are 2 kinds of giving up we may witness

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 (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.

(4) Fading scaffolding

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 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.

Once learners begin doing retrieval practice questions in their timely practice assignment, they have to

read the question and decide which skills to apply and
recall the complete process they learned in a previous lesson,

so it is not surprising that sometimes we will see occasions where teaching hasn’t become embedded learning (yet).

To help the learner recall the scaffolding of the lesson for themselves, we can use prompts to trigger the chunk e.g.

“what diagram will I ask you to draw?”
“where on the page, would it be best to show 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 now know what they are doing. The diagram, often already has a chunk attached to it in the learner’s long term memory.

To help the learner recall all the steps of a process, is slightly different, we aren’t trying to get the learner to recall a fully finished chunk, rather we might be trying to

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 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.

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 - rather the problem is being unable to recall the process.

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.
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 to the process or join existing processes together.

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.

givenSUBsign layers 3 and 4

givenSUBsign 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. MMMRQseparate has gaps between some layers. Please use https://timelypractice.atlassian.net/wiki/spaces/CKB/pages/3271688201 to request layers which you need.

(5) Problem solving - combining chunks in novel ways

In (4) fading scaffolding, an example of the need 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.

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.

Problem solving, requires more

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 secretXsign, 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:

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

the chunk for what diameter/radius mean and/or how to work out diameter from radius or v.v.
the chunk to work out the the area of a circle,
and combining these chunks in novel ways.

What we know from research on cumulative practice is that learners are much more likely to be able to solve problems, if they have mastered all the pre requisites. So timely practice provides a layer circle(8), to answer example question 1. above. I doubt that such a question will be asked in a GCSE paper, but the layer provides consolidation of the meaning of radius and diameter. Mastery of this layer and mastery of shape skills YC layer 6, how to find the area of a circle, might make solving problems like 2. within the learners grasp. Whereas I think, most maths teachers, with experience of teaching maths learners below the lower quartile, would be doubtful if such learners would be able to solve problems like 2. and 3. in a lesson, but certainly would not expect them to be able to solve such problems weeks after the lesson.

The timely practice way to teach problem solving, is through cumulative practice.

Disclaimer Many low attaining learners, come to timely practice late in their schooling. Such learners are unlikely to be able to solve problems like 2. and 3. because they simply run out of time before they take their GCSE.