Thinking Differently with Extra Thoughts

Inspired By a Maths(?) Story

Some of the buzzy terms flying around education at the moment are things like ‘spaced practice’ and ‘interleaving’; having read some articles about how people have reordered their whole curriculum programmes to be both ‘spaced’ and ‘interleaved’ it put these concepts on a pedestal for me. I saw them as being unachievable given the constraints within which most practitioners work, myself included: I am given a calendar of what to teach and when by;  I plan week to week… okay, okay, more like day to day; I rush headlong from one topic into the next to keep up with my colleagues and where I ‘should be’. Working in this way doesn’t allow me to spiral the curriculum to give maximum benefit of re-consolidated knowledge to the pupils.


But then I read a book by Simon Singh over Christmas. A spot of light reading! It’s about a theorum suggested by Pierre De Fermat from a few hundred years ago which had baffled mathematicians for centuries. The story culminates in a British mathematician named Andrew Wiles combining parts of numerous different techniques in order to prove this most profound of problems.

It got me thinking about how we should, as teachers, combine specific pieces of information from educational research and cognitive science to create richer learning experiences in the classroom. Think in a more intertwined way to solve the problem. Start on the smaller scale to unravel the solution.

Spaced Practice

In a similar way to Andrew Wiles, considering how to include parts of mathematical strategies to solve a small part of a greater problem, I started thinking about how spaced practice fits in on this smaller scale.  Turns out, I was utilising spaced practice along with probably everyone else in the eduworld – I just hadn’t thought of it in this way!

In its simplest form, to facilitate spaced practice:

  1. Teach some new material
  2. Put some questions in a retrieval quiz in a following lesson
  3. Set as a homework
  4. Feature it again in a revision lesson and also in a topic test
  5. Then do more revision and some mock exams
  6. And finally revision for terminal exams.

This just seemed like normal good practice to me so I didn’t identify it as taking advantage of the benefits of spaced practice.


Desirable Difficulties

I read a while ago about desirable difficulties (DD) in this document and the overall idea of DD in a nutshell is – you design tasks that require higher order thinking (like Bloom mentioned) and make pupils think hard about the content. This leads to increased retention of the knowledge.

Some of the key techniques in creating DDs mentioned are: interleaving, spaced practice, testing and generation effects. Seeing as how you’re probably already doing spaced practice and testing, I’ll say no more about them!

The graphic below shows the perceived and actual effects of interleaving content with the latter approach being significantly more effective.



In an ideal world, the curriculum would be spiraled and organised for regular repetition of previously learned content throughout a whole specification or even across key stages – a true mastery model. However, as a teacher within a department where you are given a calendar with content to get through by certain points of the year in time for mock exams and end of year exams this seems beyond reasonable.

In the reading I had done up to this point on interleaving, again, I hadn’t fully realised the extent to which you can filter this approach down to individual topics, sequences of learning or even individual learning intentions. But then my new thought process kicked in.

For example, lets take teaching specific latent heat and specific heat capacity (separately but within the same topic). Eventually, pupils have shown good performance on guided practice of each type of calculation: you’ve taken them through how to convert units; change the subject of equations etc. Now set them a sheet of mixed problems for independent practice. It isn’t overcomplicated but often overlooked. This simple approach does several things:

  • Increases the intrinsic cognitive load of the task by forcing pupils to make decisions based on their existing knowledge. They must choose which equation to use, whether they need to convert units, change the subject, what units the answer should be in…
  • Interleaves the required knowledge which has been shown (links to Bjork work above) to improve long term retention of knowledge.
  • Increases the chance of transference of knowledge to the new task which should also increase the understanding of the deep structure of the questions: they may see that when changing the subject for either equation you end up with a similar structure. (Energy is always on top!)
  • May well lead to a success rate of around 80% which is Rosenshine’s guideline (fingers crossed!)

Again, this is something which you probably already do to some extent, maybe through homework tasks, but it’s relatively easy to take greater advantage of the effect of interleaving content. Just remember to incorporate it into your planning for review lessons. Take the time to make the impact.

Creating Desirable Difficulties: Because But So (BBS)

This is a suggestion I picked up from The Writing Revolution via Bob Pritchard on Twitter and I bloomin’ love it! It’s great for increasing intrinsic cognitive load as it forces pupils to consider material from different perspectives as well as working on developing their writing structure. It presents desirable difficulties through the generation effect and should therefore make the knowledge more memorable. As pupils are required to manipulate existing knowledge in different ways, it can generate new knowledge or at least new links between existing knowledge. Having read through some of Efrat Furst’s recent work it could also create stronger links between different knowledge in long term memory and reinforce memory traces.


Efrat’s work is a key influence on the way I am considering how different cognitive science developments impact on my practice.  An example of BBS is described below.

We had in previous lessons become familiar with the key language of genetics and variation and had also looked at single gene inheritance. This lesson was leading into learning about evolution by natural selection and linked these two big ideas together. Mutations are the key to evolution. This BBS followed a short video and a discussion about what mutations are and what their effects can be, which included a cavalcade of questions requiring mini whiteboard responses from pupils.

The pupils were given time to consider and write out their ideas for each sentence then we fed back and constructed meaningful sentences.


After this they did a quick exam question which by their nature tend to interleave content and they did rather well! I am also finding that more pupils attempt more questions having been exposed to previously interleaved content.

Avoiding Undesirable Difficulties

The first time I thought in this more intertwined way was probably when I first read about CLT and a thought popped into my brain: “I’m never doing a marketplace type activity ever again!”. Almost every aspect of this type of activity goes against recommendations from both CLT and Rosenshine. The difficulties created are extraneous and not germane to the process of learning.

Other activities I have decided to steer clear of are:

  • Anything where pupils get out of their seats and go and copy information from posters around the room. Many years ago I was told this was better for kinaesthetic learners…
  • Card sorts. Again, VAK is dead in the water, and the amount of time they take is just not worth it! Most of the cognitive load is organisational or involves them realising they’ve dropped one on the floor.

Thinking Differently

So remember, when you read about the next big thing in Educational Research or Cognitive Science consider if it already fits into your current practice. Could it help you solve a small problem without requiring any major overhauls? Take the time to stand back and look at your practice and appreciate that you are already doing a bloody good job, but maybe (just maybe) a small change could have a big impact.

If you’ve made it this far through this blog, thank you and well done! If you can make any further suggestions of activities which could either provide desirable difficulties of a cogent nature please do let me know. Equally if you want to bash some techniques from yesteryear also share your wisdom with me!

You can follow me on twitter @MrTSci409 and tag me into any pertinent posts!

Best wishes, happy new year and best of luck for the new term!


Extra Thoughts

Part of the reason why I am blogging is to learn. By either researching or then having my thoughts challenged enables me to develop so I welcome feedback. On this blog post I hadn’t had any feedback so I asked for some by tagging David Didau (bold move) and Sputnik Steve. David came through in his inimitable style in response to the section of the blog below.

I read a while ago about desirable difficulties (DD) in this document and the overall idea of DD in a nutshell is – you design tasks that require higher order thinking (like Bloom mentioned) and make pupils think hard about the content. This leads to increased retention of the knowledge.

didau reply

On the first point I agree. You need that initial learning to be accurate and precise, bringing in desirable difficulties at this point could muddy the waters and lead to information needing relearning rather than reconsolidating.

On the second, I have a conjecture.

The DDs should be mostly successful as the feedback provided on the task can correct any errors and then follow up tasks can test the new understanding. Failure can be an effective motivational tool when your students have a view that they can improve; they *learn* from their mistakes.

The notion of pupils being happy to engage with intrinsically difficult tasks and learn from failure (as opposed to the difficulty coming from the effort of reconstructing the neurological pathway) comes from DT Willingham’s Why Don’t Students Like School?. Willingham describes having a class of Felicia’s and Molly’s where the students have different ideas about the malleability of intelligence.

“Students who believe that intelligence can be improved with hard work get higher grades than students who believe that intelligence is an immutable trait.”

The implication of this is that those students who are challenged with higher level thinking skills will learn and remember more even if (maybe, especially if) they fail to some extent along the way.

Ultimately, you do want the result of your teaching to result in success for students and at some point you have to stop working on a concept and move on to new material. At this time you would obviously hope for pupils to be 100% successful before that pesky problem of forgetting kicks in. I think that the DD aspect of this can be more effective if it is a little more drawn out and actually involves some new learning, maybe just in terms of forming new connections between existing knowledge, within it as well as reconsolidating previously covered content.

Thank You

As I said at the beginning of this additional section I said that I blog to learn and this is absolutely true and I appreciate the time taken by David and also Dr Moruki and Efrat Furst in helping develop my understanding of this topic. Thank you and keep challenging!

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