# Optimal Time For Spacing Gaps (?)

This blog is linked to my previous blog on trying to apply spacing in a content heavy subject. In that blog I set out my plans to build in spacing with my Year 10 Science class by introducing lag/retrieval homeworks and spacing lessons. The homework is set some time after the topic is complete. The spacing lesson is where the topic is revisited (via tests/past paper questions etc) after another time gap. I know that spacing is effective but I had no hard evidence to guide me in deciding how long the gaps should be.

I included this table in my previous blog to give ideas for rough timings:

The problem with the table is that I am actually splitting up each topic (apart from topic 2) into an a and b so there are 15 mini-topics to think about lag homeworks and/or spacing lessons.Another problem was that the planned timings of the lag homeworks and spacing lessons was fairly arbitrary with a short(ish) gap between study and lag homework and a bigger gap between the homework and the spacing lesson and then the biggest gap to June for the exam.

I was encouraged to look at any academic paper that may give some insight into the optimum timings for spacing events. I read Spacing Effects in Learning, a Temporal Ridgeline of Optimal Retention by Cepeda et al. After a few reads I realised that for the first time I had something concrete to trial in terms of gaps between spacing events.

The paper describes an experiment where the gap between the initial study and the restudy (the Gap) was varied and the gap between the restudy and the final test (the RI) was also varied. The research looked to trial a number of different gaps with a number of different retention intervals. The gap + the RI = the total time between initial study and test.

This was different to other research that had taken place which looked at varying the gap against a constant RI. The research by Capeda et al looked to establish when was the optimum time to introduce a spacing event (the restudy) and did it change if the time from first study to test (the gap + the RI) increased. The team chose to test the optimal gap with RI lengths of 7, 35, 70 and 350 days.

The results were fascinating. The results were very much dependent on how long it was between initial study and test.

As expected, as the RI increased, the optimum gap before restudy increased. Interestingly, the experiment did not find some golden ratio between gap and RI. In fact,as the RI increased the ratio between the gap and the RI decreased. This means as the RI increases the optimum gap increases but not at the same rate. The experiment found that the following RIs had optimum gaps of (NB- these are based on interpolating the experimental data with cubic splines):

RI | Gap |

7 | 3 |

35 | 8 |

70 | 12 |

350 | 27 |

I put these into Excel and produced a graph which I think gives a starting point in looking at optimal gap to RI ratio.

For instance, If you finish a topic today and the test is in 60 days then (perhaps) your optimum gap before restudy would be 10 days which leaves an RI of roughly 50 days (a 1:5 ratio or gap being 20% of RI).

If your class finishes a topic today and the test is in 114 days then (perhaps) your optimum gap before restudy would be 14 days which leaves an RI of 100 days (a 7:50 ratio or gap being 14% of RI).

If your class finishes a topic today and the test is in 250 days then (perhaps) your optimum gap before restudy would be 21 days which leaves an RI of 230 days (gap being 9% of RI).

This graph is perhaps more “user friendly” showing time from initial study to test against gap to restudy:

The changing gap to RI ratio is interesting. It seems the restudy is the point in between which best balances the time from original study to the time of the retest. The fact that the gap stays small relative to the RI suggests strongly that the optimum spacing gap is very closely linked to the rate of forgetting. Even for very long RIs (350 days), the gap is only 27 days. It seems that it is preferable to have the restudy session within a shortish time of the original study despite the fact it gives a very long RI. This is surely because if the gap was any bigger too much of the original study material would have been forgotten and retrieval strength would be practically zero. It is better to keep a relatively short gap and trade off with a very long RI. I imagine a spacing session much later than the optimum gap would be more like a reteaching lesson rather than a restudy/recall lesson.

So hopefully, the above graph gives a starting point on when to introduce a spacing activity (a lag homework, a spacing lesson, a test etc).

**2 Spacing Events?**

What really got me thinking was could I use the data from the experiment to design optimum spacing gaps if I was going to introduce 2 spacing events. These would be my lag homework and the spacing lesson. After much deliberation I came up with the following premise:

If I could treat them as 2 separate gap and RIs (where a + b+ c = time from study to test) and so:

If I just look at the study and the lag homework and the spacing lesson I need to choose a gap and an RI that gives optimum recall for the spacing lesson.

If I then look at the lag homework and the spacing lesson and the exam I need to choose a gap and RI that gives optimum recall for the exam.

My leap of faith is that these spacing gaps work together to give optimum recall for the exam.

As an example- I finished topic 2 on Monday. I want pupil to have optimal recall for the heavy revision and exam practice that will start on June 1st (roughly). This means that from Monday 31st October there 212 days until June 1st. By using the above graph I have worked out my gaps of 5 days until the Lag Homework, an extra 18 days until the spacing homework and then leaving a 185 day gap until June 1st.

At first this final RI seems too big. It seems counter intuitive to think that the optimum 2 gaps would see both spacing activities take place within a month of study leaving a RI of 7 months. However, there is a real trade off here in terms of the rate of forgetting. The bigger the gap, the more a pupil will forget making the retrieval event far less effective. “One potential danger of waiting too long before reviewing information is that

students may forget much of what they have learned previously, and this forgetting may

offset any benefits that would have occurred due to spacing.” Carpenter et al, 2012.

Next steps: I have got rid of my pretty Microsoft word table (with all of the colours) and have replaced it with the table below:

Topic 1a and 1b have been completed on the above dates but the spacing homeworks went out a lot later than the “ideal” dates. This means that the spacing lesson will also be delayed past the “ideal dates” above. However I can run with the above dates for Topic 2 so I will have something to compare come June.

My intention is to record when I complete each topic and to then use the graph to calculate the best 3 gaps to maximise retention of knowledge for June 2017.

I am not certain that these timings will be the optimum. However, I am also conscious that I don’t want huge gaps between the events as I don’t want the spacing lesson to be a re-teaching lesson.

I am just going to see how it goes and evaluate at the end of the year.

The bottom line is that I think the spacing will be of benefit. Hopefully I am on the right track and working with (potentially) optimum gaps. We shall see.

Huge thanks to Dylan Wiliam for sending me the Cepeda et al article. It was massively appreciated.

Feedback is very welcome below.

### Trackbacks & Pingbacks

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Hi Damian,

As always an interesting blog and I hope your spacing proves a success.

Just wondering (perhaps you have thought and written about this too) – Do all topics require the same gap(s)? ie Some Physics topics seem to give students more of a challenge to understanding than others.

Would the gap need to be more/less/same for topics of (seemingly) varying conceptual difficulty?

(eg red shift compared to, say speed/time graphs)

Best wishes

Huw

Hi WHD, I hope you are well. Please read the (amazing) comment by Carolina. So much to think about.

Hwyl Huw,

Damian

Hi Damian,

thanks for this blog post. I promised that I would give you some feedback. So here I go.

– The optimal gap for a 35-day RI was 11 days for recall and the optimal lag for a 7-day RI was 1 day (this has been replicated in other studies, too, see Kuepper-Tetzel & Erdfelder, 2012, for example).

– It’s important to note that the retention interval is calculated from the end of practice to the time of the final test, not from the initial study session. You do this correctly in your figure and I see that you are imposing a specific ratio when you describe how the idea of optimal lag translates into a learning schedule (text below second graph). However, for teachers and students this kind of scheduling is rather ackward (although your interpretation is completely correct). In addition, and you come to this point later in your section about “2 Spacing Events”, teachers and students will usually engage in more than one revision session. Thus, I think for educational settings it is more helpful to look at how multiple revision sessions should be scheduled. This taps into the question whether gaps between one session and the other should stay constant over time, whether gaps should increase (expanding schedule) or decrease (contracting schedule) over time. If you are interested in this, check out a paper of mine that looked into that. We find that the optimal scheduling depends on the RI. I think that this kind of scheduling is easier to rationalise.

– You conceptualise your “2 Spacing Events” as spacing with two RIs, but it is probably more straight forward to conceptualise the homework and spacing lesson as two learning events that are separated by different gaps and the RI is the time between the last study opportunity and the final test.

– You state that “a spacing session much later than the optimum gap would be more like a reteaching lesson rather than a restudy/recall lesson.”. In principle that is correct. However, if this is the only mechanism driving the effect one would expect that there is one gap that is optimal no matter how long the RI is. That is, in fact, one of the theories that has been suggested. It says that an optimal gap should be long enough, so that information is actively and successfully retreived from memory, but not too long, so that it’s all forgotten. Thus, we aim for restudying not learning anew. Now, the puzzling thing about the optimal gap/RI interaction is that is goes against that in principle sensible explanation because a gap of 11 days is optimal for a test 35 days later, but detrimental for a test 7 days later. In my papers (Kuepper-Tetzel & Erdfelder, 2012 or Kuepper-Tetzel, 2014), I attempt to shed light into that aspect. My research basically shows that different mechanisms are responsible for the effects after long RIs compared to short RIs. It’s quite technical, but I found it so interesting that you started thinking about why the effect occurs that I thought you would appreciate this brief thought experiment.

– To answer the question the person before me posted: Research is still looking into that issue. You are absolutely right that we cannot expect that the optimal gap is the same for all kinds of material or even for different populations. I ran a study with 6th graders and looked at optimal lag and found that indeed the 1-day lag was optimal for vocab learning when the test occured 7 days later, but for a test 35 later it did not matter whether pupils restudied after 1 day or 10 days. So, more research is needed here.

Hope that helps a bit.

Thanks again for this great piece!

Carolina

Hi Carolina. Huge thanks for taking the time to read and give feedback. I will be searching and reading both your papers to gain more insight. This is such a fascinating (and important) area. I may write a longer comment after reading them (particularly if I have more questions). Thanks again for you feedback. It’s fantastic to get the input of a genuine expert 🙂 .

Damian

I have been reading around interleaving, spacing and retrieval for a few weeks now and this blog article as well as one other you have written has really caught my attention; This was a fascinating read!

I would love to know the research papers etc that you have used to find out about optimal spacing as this is something I would like to build into our new schemes of work but I would like to be more informed before starting this. Would it be possible to direct me towards the relevant places?

Hi Rob. Yes, I can do that. If you drop me a message or email I’ll send you some papers. You’ll find my contact details when you google my name.

Absolutely riveting. I will need to sit down and reread again. Have you a link to the capeda article?

Huge thanks for reading and commenting.

A link to the article can be found here:

Click to access Cepeda%20et%20al%202008_psychsci.pdf

Thanks again,

Damian

So what happened? Did you write a follow up post?