*“If it be not now, yet it will come: the readiness is all.” – Hamlet*

**Spaced Repetition**

The idea of progressively lengthening the periods between testing / review is common, relatively common sense and borne out by experience. It’s been used in the design of foreign language programmes, for example. Items can be reviewed once a week, then once a fortnight, then once per month. What constitutes the best schedule is the subject of debate, as you might expect in the world of educational research, but there appears to be a consensus that gradually lengthening the gap improves retention. It is not necessary to be familiar with the neurological / cognitive literature to take advantage of this.

**SAFMEDS**

SAFMEDS is a technology developed by the Precision Teaching movement, initially based on flashcards and now due out in app form. SAFMEDS is a self-explanatory acronym which stands for Say All Fast Minute Every Day Shuffled. You time how many of the words / items the student can identify correctly in a minute and chart this. All the items are presented and “shuffled” i.e. in a random order. However, you can also ensure that all the items are reviewed and allow the time to be the factor that changes. This makes sure that all the items are practised. You can also graph progress to enable more visual analysis and to help motivate the student.

NB Precision Teaching uses a “celeration chart” which is semi-logarithmic – the y-axis (for learning) is on a log scale, the x-axis is arithmetic (for time). If you like that sort of thing, it’s a work of beauty. It charts the student’s acceleration, not just corrects / incorrects. In this view, acceleration equals the rate of learning of the particular (clearly defined) learning objective. You can read more about the celeration chart here.

**Cumulative Review**

Like spaced repetition, cumulative review allows for increasing time gaps between revisiting items. However, it can be very sophisticated. A carefully planned curriculum will revisit skills to ensure that they are systematically combined with other skills to deepen and broaden learning. Note that ‘learning’ here does not just mean ‘understanding’: it means what the student can do – recall, re-organise, explain, analyse, synthesise, evaluate.

So, for example, at a simple level we can teach students to manipulate subject-predicate placement using conjunctions. Then we study independent and dependent clauses. Next we revisit subject-predicate manipulation, and then combine that with what we learned about clauses. When we then move on to paragraph writing, we will apply the skills we have used beforehand to deploy sentence structures for emphasis of meaning and rhetorical effect. Cumulative review allows the teacher and the student to check that skills have been mastered and maintained before combining them with further learning.

The rider here is that unless we have a very carefully designed curriculum we will end up with steps out of order, or make the steps too large for students to really master before they move on. While curriculum design needs to contain both fluency building and cumulative review, the most important thing, and perhaps the hardest for teachers to do, is to conduct a rigorous, logical analysis of what it is we want our students to learn. Partly because of time, partly because we love to be creative, and occasionally because we are so thrilled with our own inventiveness, our planning is often more intuitive than we realise. Logic requires a deep level of detail that takes considerable time.

The curricula of Zig Engelmann and his colleagues in the Direct Instruction movement are highly sophisticated examples of logical analysis. There is much more to say on this topic, but for now let this suffice: if, when you read a Direct Instruction programme, you say to yourself “but this is so simple”, then you have proven Engelmann’s genius.

Reblogged this on The Echo Chamber.

I use Englemann’s maths materials with my own kids and you are right, after a while you realise just how carefully crafted they are.The chance of an individual teacher or even a school managing to craft a course of study to be as effective are minimal but most teachers have no idea that they should even be attempting to use the principles you outline and have not seen anything like Englemann’s materials. I was showing a DI book to a maths teacher friend the other day and was amused to see that he tried to find how a topic was taught by looking for a contents page with chapters. I had to explain how the instruction gradually builds knowledge and undertanding, never allowing the student to forget what has been learnt.