Principles of Engelmann's Direct Instruction: Review

This post is part of a series where I go in to detail on some of the main aspects of Direct Instruction as laid out by Siegfried Engelmann in this book.

Below are links to the other posts in this series. Scroll past them to read the article.

• Atomisation
• Overtisation
• Expansion and Context Shaping
• Cognitive load
• Review
• Lesson structure and schemes of work
• Speed principle
• Difficulty and Motivation
• Defining range/scope
• Categories for different types of knowledge
• Instruction for basic types of knowledge
• Instruction for linked types of knowledge
• Instruction for routines
• Instruction for problem solving techniques
• "Real world" maths
• Prompts and scaffolding
• Correcting mistakes
• My take on the strengths and weaknesses of Direct Instruction

Review

According to Direct Instruction, only 15% of each session should be on new content, with the rest dedicated to review. This seems miniscule to me and I have not managed <40% let alone 15% whilst trying it last term. However, I have massively upped the amount of review that I now plan for in my lessons. This has given me much more scope for the reminding and interleaving of topics and it seems to have made a positive impact on student confidence and grades.

Types of review

• Reteach: In the follow-up lesson from initial instruction, reteach the component with a set of examples. This is made feasible as instructions now take <1 minute (see atomisation).
• Blocked practice: Over the next few lessons, practice the skill in a set of questions on this topic only. This may start prompted, with worked examples or some scaffolding, but these prompts should fade until students can perform on the questions without prompts.
• Question discrimination: Where there is another skill whose set-up looks highly similar to the skill just learnt (say worded LCM questions and worded HCF questions), teach how to differentiate between the two and then present a random set of questions on the two topics. Note that to save time, you may get students to only perform the discrimination and perhaps the first step or two of the working.
• Cumulative review/Interleaving: A review of up to 6 topics. These topics will change between each review session, allowing students to refresh their memory on a wide range of skills. The topics should include:
• The two most recently taught topics
• One topic that is highly similar in set-up to the most recent topic
• One topic that students have struggled with in the past (and has been re-taught)
• Two other topics not reviewed recently

In order to keep track of which topics have been reviewed recently, I use an excel spreadsheet (I - initial instruction, R - review, S - reviewed but struggled with):

Building to cumulative review

Also mentioned in DI is a step-by-step approach for building up to the full cumulative review. I have found this particularly helpful with lower-ability sets. Before I have avoided doing unprompted cumulative reviews with these classes as I knew that students would not be able to remember the topics (indeed they often forget everything from the lesson on the day before!).

Steps to build to cumulative review:

1. Prompted, blocked questions
2. Unprompted, blocked questions
3. Questions alternated between the new topic and a mix of highly different, secure topics
4. Continue number 3, but add more and more questions in between each question on the new topic
5. Full cumulative review (after teaching discrimination with highly similar topics)

The idea is to do two or three of these in a single activity, slowly building up the complexity as students become more comfortable. At first you may do 1-2, then 1-2-3, then 2-3, then 3-4, then 4-5, then only 5 (or you may build it up much faster or slower, depending on the performance of the class).

DI also recommends avoiding moving on to new topics whilst students are still struggling with the cumulative review.

Example of question discrimination

I find SSDD problems to be a great place to start thinking about which topics are similar to the one taught. For some classes, I know that I can give them some SSDD questions immediately after initial instruction and they will be fine with just this. However, for many students, particularly with English as a foreign language, I find it useful to first teach the discrimination as a correlated feature before they work up to the SSDD problems themselves. So with pythagoras for example:

1. First define the correlation: "I know that I can use pythagoras because I can make a right-angled triangle where I know two sides"
2. Now show various example questions, some on pythagoras and some on similar-looking topics (like trig). The aim is not to answer the questions, but to decide when pythagoras is applicable. Demonstrate the first few before students have to answer.
3. The answer is either:
• "Yes" Why? "Because I can make a right-angled triangle where I know two sides"
• "No" Why? "Because I cannot make a right-angled triangle"
• "No" Why? "Because I do not know two sides"
4. Practice this until they are firm.

Notice here that I defined it as "When can I use pythagoras?" rather than "When should I use pythagoras?". Otherwise the correlation would become "I know that I should use pythagoras because I can make a right angled triangle where I know two sides and I want to work out the third side". This is a further example of atomisation - a way of splitting up the "When should I..." into more easily digestible components - to facilitate high success rate of initial instruction.

Therefore a final instruction plan would be to teach "When can I..." then "When should I..." before finally actually answering SSDD type problems.

Practicalities and Addressing Concerns

This may seem like it is going to slow down the teaching of new topics drastically. This will be addressed in the next section on "lesson structure". I have found some slow-down, but it is not drastic. This effect may also reduce over time as students are (hopefully) more likely to remember the topics from last year when learning new topics which build on them in the next.

DI recommends choral response for most of their activities. I think this only really works with classes of up to 10 students. Any more than this and it is hard to hear what everyone says and to make sure everyone is taking part. I like to do these reviews on mini-whiteboards, as this allows me to quickly assess everyone and to give instant feedback on misconceptions.

It is important to keep a high pace during these activities, so with longer, more complex procedures, I may ask students: "What's the first step?" or "What's the next step in the working shown?"