Tag Archives: intervention

What I think about…learning

Moving schools and with more than an eye on headship is sure to get you reflecting.  The following posts are what I think about various things, in no particular order.  First was displays.  Next up – learning.

Asking teachers what learning is surely throws up disagreements of varying degree from polite dispute to outright warfare.  What makes sense to me is that learning is a change in long term memory.  Too often, children don’t manage to transfer concepts from working memory to long term memory and without that internalisation, we cannot say that they have learned.  All we can say is that they have done some work.  Now that work might well have been good, but teachers and leaders need to be aware of the difference between short term performance and long term internalisation.

Performance vs learning and the importance of desirable difficulties

The key paradox is that to improve long term retention, learning has to be made more difficult in the short term even to the extent of being unsuccessful.  We remember what we think about and learning happens when we have to think hard about content.  If children are thinking about things other than what we have intended for them to learn (a distracting context, for example) then that’s what they’ll remember.  If they haven’t had to think too hard, they may well produce some decent work but the thinking behind it is less likely to be retained.  So what does this mean?  Units of work and individual lessons need to be planned around what it is that children will be thinking about.  Each decision about what the teacher will do and what the children will do needs to be justified with that question mind and amended accordingly.  We all get better at what we habitually do – we become more efficient – so if we require children to be able to remember knowledge, procedures and concepts, we must give them ample opportunities to practise remembering those things.  The efficacy of the testing effect has robust evidence and seems to work because testing (either yourself or a teacher posing questions) triggers memory retrieval and that retrieval strengthens memories.  Flash cards are a perfect example of this in action.

What’s important is that this testing is low stakes – no grade, no mark at the end of it, just practice in remembering and feedback on responses.  Feedback can take two forms.  Firstly the feedback can be from teacher to child and is as simple as telling the child what they were good at and what they misunderstood, then correcting those misconceptions.  Secondly, feedback can be from child to teacher and involves the teacher using the information to plan what to do next to develop understanding further.

Low stakes testing is a desirable difficulty – one way of making learning difficult (but not too difficult) so that children have to think hard.  Other desirable difficulties apply more to curriculum design:

  • Interleaving (switching between topics)
  • Spacing (leaving some time between sessions on a particular topic)
  • Variation (making things slightly unpredictable to capture attention)

By presenting content to children little and often, with increasingly longer spaces in between, teachers can instill the habit of continual revision rather than only revising when some sort of exam is approaching.  As such, concepts are internalised and retained rather than forgotten.  Robert Bjork’s research on desirable difficulties can be found here:

Knowledge

The idea of knowledge can be divisive.  Recalling knowledge is often described as lower order thinking and many are keen, quite rightly, to get children to do higher order thinking. This can be dangerous because knowledge is necessary but not sufficient.  Higher order thinking skills rely on a sound basis of knowledge and memory so teachers must ensure that these aspects are fully developed before expecting success in higher order thinking.  Knowledge needs to be internalised too.  It’s not enough to be able to Google it.  The more a child knows, the easier it is to assimilate new knowledge because more connections can be made:

Knowledge

Scaffolding

Children are more alike than different in how they learn.  Attempting to teach to a child’s perceived learning style is nonsense.  Everyone, no matter what we are learning, requires three things: knowledge, practice, and feedback on how we’re doing.  It is of course true that children come to a lesson with varying levels of prior knowledge and to a certain extent have different needs in order to be successful.  Teachers may have (and many, I’m sure, still do) differentiated tasks three, four or more ways – an unnecessary burden on time and a practice that reinforces inconsistency of expectations, particularly of the perceived ‘lower ability’ children.   For those children that are behind their peers, if they are not supported to keep up with age related expectations, they will be perennially behind and will never catch up:

Keeping up Differentiation

If we only cater for their next small step in development, we’re failing them.  Instead, all children should be expected to think and work at age related expectations.  Teachers should scaffold tasks appropriately so that all can work at that expectation and we do not have a situation where ‘that’ table are doing something completely different.

Scaffolding

For children that grasp concepts quickly (not our ‘most able’ children – heavy lies the crown…), teachers provide opportunities to deepen their understanding before acceleration into subsequent year groups’ content.  Undoubtedly, there are a small number of exceptions to this.  There are some children that have a lot of catching up to do before we can even think of getting them to keep up with age related expectations.  But if they are removed from lessons to carry out this catch up work, then everything will always be new to them – they’ll miss seeing and hearing how children are expected to think and work.  It is much better to precisely teach, and get them to practise, the basics that are not yet internalised in short bursts and often so that they remain with their peers as much as possible, experiencing what they experience but having the support needed to catch up.  This could be basics such as handwriting and number bonds, for example, and teachers should work closely with parents where there is a need to catch up to set short term, focused homework until the basics internalised.

Intervening

When children misunderstand something, when the work in their books is not to the standard expected, is a crucial time.  Paramedics talk of the golden hour – one hour after an accident – where if the right treatment is given, the chances of recovery are significantly higher.  With children’s learning, if we leave misconceptions to embed or even thrive, we’re failing them.  Even if we mark their books and write some wonderful advice for them to look at and act upon the next day or the day after, we leave holes, holes which children can slip through.  When there is a need, we should intervene on the day so that children are ready for the next day’s lesson and are keeping up.  This of course requires flexible and creative used of TAs and non-class based staff but from experience, it works. Interventions focus on the work done that day.  For some children, pre-teaching may be more beneficial.  Before the school day starts, they are shown the main content of the day’s lesson and carry out a couple of practice examples so that when it comes to the lesson later on, they have some prior knowledge which will improve their chances of success in that lesson.  This concept is in contrast to pre-planned, twelve week intervention programmes where children are removed from other lessons for significant periods of time.

Learning is complex and relies on many interrelating and often unpredictable conditions.  That said, there is much that we can control and doing so greatly increases the likelihood that what we intend to learn is learned – really learned.

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Hassan’s internal number line

Hassan is a wonderful boy. He’s polite and has a great group of friends. But Hassan started Year 6 working significantly below his peers. His school history is of sustained underachievement with very little progress. He did not have an internalised number line with which to think about numbers, to the point where he could not reliably say which number out of two was biggest.

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This post is an account of an intervention carried out by a teaching assistant. It is one of the most successful interventions I have seen and has resulted in vast improvements in Hassan’s ability to think about numbers. Here’s what happened:

These number cards were prepared: 53, 67, 54, 35, 76, 45

Two of the cards were presented to Hassan and, with the use of Numicon or dienes blocks or arrow cards, the teaching assistant modelled explaining which was the bigger number. Hassan picked this up fairly quickly, but to help him to retain this procedural knowledge, it was repeated little and often over the course of a few days.

A third card was added and the teaching assistant again modelled, using appropriate concrete equipment, how to order them. When he could consistently order three numbers, a further card was added until he could deal with ordering six cards. Using those six cards, the teaching assistant made seven different sequences:

53, 67, 54, 35, 76, 45

67, 35, 76, 54, 53, 45

76, 35, 67, 53, 45, 54

45, 53, 35, 76, 67, 54

54, 45, 76, 53, 35, 67

53, 54, 35, 76, 45, 67

45, 76, 54, 67, 53, 35

The cards were presented to Hassan in these orders, one set at a time, and Hassan was asked to order them. At first, with this slight change in task, he would place the numbers in fairly random order for each sequence. After completing each sequence, the teaching assistant ordered them with him, using concrete models when necessary. When Hassan was asked to read out the order, if he was incorrect, he often didn’t notice. However, when the sequence was read aloud to him, he could hear the error and would correct it.

This was repeated over several days for short periods of time. Sometimes this was in maths lessons and at other times it was not. The seven different sequences would be laid out in a straight line and he would pull the cards out and order them. As the days progressed, he could very quickly pick out card 35 and put it furthest left and also card 76 and put that furthest right – the smallest and greatest numbers. However the other cards in between were never placed consistently in order.

After a week of doing these sequences once or twice a day, he could order every sequence in the correct order. A new set of numbers was introduced: 12, 27, 45, 54, 59, 72

Hassan was very good at picking out the biggest and smallest numbers. The numbers in between were still more difficult for him. The teaching assistant modelled looking at the tens and units columns and this prompted him to order them correctly.

The cards were then mixed up, with more numbers being added one at a time to see if he could order them again. His confidence was growing and once he was happy with the order he had put them in, he was asked to read the numbers out to see if he could spot any errors himself. He often did and corrected them without the teaching assistant needing to intervene.

After a few days starting with six or more cards, he could reliably order them correctly every time. Next, some three digit numbers were added to make twelve cards overall. He was quickly able to deal with this progression. He was then given cards with multiples of ten to see if he could slot them into the correct places. He struggled a little with cards 10 and 20 but he placed multiples of ten more than twenty in the right places every time. If he needed to, he referred to a tape measure to check.

Once he was confident in ordering these numbers and could do it correctly every time, two numbers from the sequence were chosen. He was asked: ‘What are the smallest and biggest numbers that could go in the gap?’ This proved to be quite tricky for him and he would often say the number before the smallest card. This took him around a minute to process each time, and many answers were guesses. The teaching assistant modelled looking at a tape measure to find the two numbers (53 & 59). He then could see, using the tape, which numbers would come after 53 and before 59, and therefore the biggest and smallest that could go in the gap.

From here, Hassan is now working on adding and subtracting one digit numbers and multiples of ten from numbers in his card sets, with increasing success. Soon, the goal is that he can add and subtract any two digit number from any other.

Why this intervention worked, when other have failed

Spacing and interleaving

Regular short sessions, interspersed with other topics in maths lessons, with varied lengths of time in between those sessions has given Hassan time to internalise patterns of numbers and procedural knowledge for dealing with them.

Building knowledge of the number system

The more he practised recalling facts about numbers and procedures for how to think about them, the more successful he became. Each nugget of internalised knowledge enabled further memory development until he had internalised the basic number system.

Deliberate practice to mastery

The moment that Hassan understood and was successful did not signal the end of the intervention. It will continue until he never makes a mistake, even when tasks are altered.

Making links between ideas

Any new concepts were introduced alongside concepts that Hassan was familiar with.

Detailed dialogue between teacher and teaching assistant

Using video and observing ‘live’, the teacher and assistant talked about the nuances of the decisions that Hassan made to tweak tasks and feedback. This precise tailoring resulted in explanations, tasks and feedback which were accurately matched to Hassan’s needs.

This intervention was put in place because Hassan was working significantly below his peers at number. It was clear that he had not internalised a number line at the beginning of the year, but this shows that he now has. He will need more practice to cement his understanding but the progress that he has made has been good. We did not work on this with him for a week before the Christmas holiday. He had just over two weeks off school over Christmas and when he returned to school after the holiday, he could still deal with the number tasks accurately. Next, we are looking to see if the results are replicable with other children.

Details about the child have been changed to preserve anonymity.

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Filed under Maths