Memory and the primary mathematics classroom
As we prepare for the start of a new academic year I feel it's worth considering how we can adapt our planning to take note of some of what we know about long-term memory, in order that learning over time takes precedence over all else for it is indeed the only true measure of much of what we do.
For the purposes of this piece I intend to use the long/medium term planning developed by the White Rose Maths Hub as the skeleton on which to hang my ideas. This, I hope, will allow for consideration of the main points without the distraction of contemplating curriculum coverage/design at this particular point in time.
...repetition of material and spaced practice helps to consolidate and prevent pupils from forgetting...
In my experience, a typical lesson will feature some form of independent 'application', an attempt to consolidate the knowledge imparted during the preceding minutes and an opportunity for formative assessment. This often features questions directly related to the content of the lesson, yet as Daisy Christodoulou so eloquently points out when referencing the work of Roher and Taylor, '...repetition of material and spaced practice helps to consolidate and prevent pupils from forgetting.' (Making Good Progress? 2016)
"studying material once and testing three times leads to much better retention than studying three times and testing once"
As such we must consider exactly what we want our pupils to practise and when we want them to do so in equal measure. Research would suggest that cramming en masse, applying only that which has been featured in the lesson, has less impact on progress/learning over time than spacing and interleaving. Indeed there appears to be sufficient evidence to confidently assert that "studying material once and testing three times leads to much better retention than studying three times and testing once" (Psychology, 2016) Meaning the focus of any independent session should also really focus on what has been taught/learned during the preceding days, weeks, months and even years.
Now, it is not my intention, nor within my capability, to impart everything we know about memory within the confines of a single post and I am far from an authority on the subject. However, the wealth of information available to us, in my view, has never been greater and my aim is to explore how the ideas outlined can transfer into the primary mathematics classroom.
If we look at the proposed overview for Year 3 (above) we see a clear representation of what is to be covered and the suggested time frame for each block. While keen to avoid sweeping generalisations, in my experience this would typically mean the vast majority, if not all, of the mathematics taking place during Weeks 5 and 6 would safely fall under the umbrella of 'Statistics'.
Yet, from what I have come to understand, we can vastly improve the chances our pupils will retain what has been covered in the preceding 16 weeks by spacing the opportunities to recall the information/knowledge and allowing sufficient time for pupils to forget (counter-intuitive as it may be) as this is said to have a significant impact on changes to long-term memory. So yes, there will be lots of statistical analysis during Weeks 5 and 6 but any independent sessions will be littered with remnants of lessons gone by.
That being said - what would a typical practice session activity look like?
With little regard for style or presentation I decided that our understanding of memory could potentially manifest in the classroom in a similar fashion to the document linked above. It begins with some questions on statistics, perhaps that which has been covered during the day's lesson. If a high quality text book is being used then I would always consider what they have provided for each lesson and my own questions linked to the additional knowledge I want pupils to recall. However, in this instance, as my focus is memory and not text books, I have created my own questions linked to the hypothetical lesson.
Hopefully that's pretty straightforward. I've considered some of the potential misconceptions and provided opportunity for the pupils to practise what I hope they will have taken on board during the lesson. I then follow this up with links to lessons gone by...
....Here you can see the bottom of the page and instead of further statistical analysis I've asked the pupils to jump back as far as 12 weeks into their memory banks in the hope that it will result in a strengthening of memories which were partially formed 3 months earlier.
In theory, if such independent sessions were to take on this form over an extended period of time, were crafted carefully with prior learning in mind and always considerate of potential misconceptions, then the difference made to what our pupils retain in the long-term may indeed be immeasurable.
I'm not for a minute saying that this is by any means a perfect example and, while naturally reticent about blogging in the first place, my aim is to offer this up for discussion in order that our shared understanding may grow. I hope that I have interpreted what I have discussed as accurately as possible but, like many others, I reserve the right to be wrong and subsequently grow through participation in the community of online teachers. My initial thoughts are perhaps this is too simplistic. I look forward to finding out.
Christodoulou, D. (2016) Making Good Progress?.
Didau, D. and Rose, N. (2016) What every teacher needs to know about psychology.
White Rose Maths Hub Year 3 Scheme of Learn 2.0