Insights from DI part 7: Instructional Formats

This is the seventh post looking at how ideas from Engelmann’s DI can be applied to the everyday classroom. The first six can be found here: one, two, three, four, five, six

Like the last post, this one will examine The Components of Direct Instruction by Cathy L. Watkins and Timothy A. Slocum, an article from The Journal Of Direct Instruction and an extract from Introduction to Direct Instruction. The paper can be found here: https://www.nifdi.org/research/journal-of-di/volume-3-no-2-summer-2003/449-the-components-of-direct-instruction/file

Instructional Formats

Once you have decided upon what you will teach (choosing high utility, generalizable concepts that allow students to ‘further develop their expertise’ in a subject), and have devised sequences of clear communication, the next step is to decide upon the instructional format which ‘specifies the way that teachers will present each example, explanations that they will give, questions that they will ask, and corrections that they will use’. Broadly, teaching should be massively structured, explicit and supported at the beginning in order to ‘ensure a high level of success when strategies are initially introduced’. As student proficiency increases, this support will be faded out ‘so that students learn to apply the skills independently’, preventing them from becoming reliant on teacher assistance. Sequences of learning and practice should  move along a continuum from restricted to freer practice, the intention being that student understanding moves from being inflexible to flexible.

Lets have a look at an example from the article which uses these items:

If students were learning to read ‘VCe’ words like the ones in the table above (words that, due to the addition of an ‘e’ at the end, cause a long vowel sound) and were trying to discriminate these from ‘VC’ words like rat and not where the vowel sound is short, then an initial, highly supported instructional sequence may look like this:

Detailed and explicit, the sequence breaks what seems initially to be a simplistic concept into five logical, sequential steps. Each step potentially provides accurate information to the teachers not only about whether a student is proficient, but if they are not, what specific remedial work or additional teaching that may be required in order to address their lack of understanding. If a student fails step 2, perhaps they cannot recognise or do not understand the concept of ‘e’ and may require more practice distinguishing between letters of the alphabet. If students are correct on step 2, but incorrect on step 3, perhaps they require more practice with learning and saying the rule that is explained in step 1.

Later on in a sequence of learning, instructional formats may look like this:

Compared to format 1, these are far less detailed and involve far fewer steps, the assumption being that students are proficient enough to cope with reduced teacher support and instruction.

How does this apply to the everyday classroom?

Following this idea, I wrote here about how items that are taught should move from narrow to wider tasks, probably beginning with massed practice and moving towards spaced practice where students are increasingly expected to apply the knowledge in wider, less structured applications like paragraphs and essays.

Here is an example from teaching students to select and punctuate quotations (the assumption being that this is a new skill that they currently cannot do properly):

Format 1: (heavily supported and broken into sequential steps)

Text extract from Telephone Conversation by Wole Soyinka (a poem from a year 7 unit).

 “ARE YOU DARK? OR VERY LIGHT?” Revelation came.

“You mean–like plain or milk chocolate?”

Her accent was clinical, crushing in its light

Impersonality. Rapidly, wave-length adjusted,

I chose. “West African sepia”–and as afterthought,

“Down in my passport.” Silence for spectroscopic

Flight of fancy, till truthfulness clanged her accent

Hard on the mouthpiece. “WHAT’S THAT?”

Instructional Format:

1) Teacher: Here’s a rule: evidence should start and end with quotation marks.

2) Teacher: what’s the rule? Students: evidence should start and end with quotation marks.

2) Teacher: In the last line, underline the words that tell us that the landlady doesn’t understand what the poet is saying.

3) Teacher: say the words Students: WHAT’S THAT?’

4) Teacher: Did she say something or ask something? Students: Ask something

5) Teacher: How do you know? Students: There’s a question mark

6) Teacher: This is how you start: The Landlady asks QUOTATION MARKS

7) Teacher: what comes after the quotation marks? Students: What’s that?

9) Teacher: What is the rule about quotation marks? Students: evidence should start and end with quotation marks.

8) Teacher: what comes after the last word? Students: quotation marks

9) Teacher: How do you know? Students: because evidence should start and end with quotation marks.

Although this sequence is imperfect and certainly violates some of Engelmann’s rigorous principles, I have included it to demonstrate the necessity of breaking down communications into logical, sequential steps as well as to highlight the importance of explicit, teacher directed instruction in the early stage of a sequence of learning. The use of evidence seems like a simple skill to an expert, but it actually requires multiple tiny steps. Each step, in the absence of explicit teaching, guidance and support, is a potential source of confusion and a hindrance for a novice student.

Like the examples from the article, later instructional formats would gradually fade out some if not all of the steps within the earlier sequence, making the process less overt, eventually resulting in the expectation that students apply this important skill in extended writing without any teacher direction or support at all.

As experts we are prone to expert induced blindness: it is hard for us to remember that the processes, skills and abilities which we have automatized to the point of accurate and effortless fluency contain multiple steps which require explicit teaching if students are to reach a similar level of proficiency. Engelmann talks about the idea of dysteachia, the notion that student failure is almost always the result of ineffective teaching, and I think that many students struggle because we often fail to see just how far we need to break a process or concept down when teaching. I will explore this idea more in the next post.

The goal is that ‘by the completion of the instructional program the students’ performance is independent, widely generalized, and applied to various contexts and situations.’ What students could only initially achieve with massive and detailed support, they should eventually be able to do independently, making adaptations and generalisations and succeeding across a range of different and novel problem scenarios.

Next post: Insights from DI part 8: The 6 ‘shifts’ of task design

 

 

 

Insights from DI part 6: Five Principles for Sequencing and Ordering Examples.

This is the sixth post looking at how ideas from Engelmann’s DI can be applied to the everyday classroom. The first five can be found here: one, two, three, four, five

Like the last post, this one will examine The Components of Direct Instruction by Cathy L. Watkins and Timothy A. Slocum, an article from The Journal Of Direct Instruction and an extract from Introduction to Direct Instruction. The paper can be found here.

Direct Instruction teaches ‘generalizable strategies that students can use to solve a wide range of problems’. Instead of teaching a ‘set of discrete specific cases’, it teaches the ‘general case’ and the teaching ‘clearly communicates one and only one meaning and enables students to exhibit generalized responding.’

The authors of the article explain that ‘In order to teach a general case, it is necessary to show students a set of items that includes examples and non-examples arranged so that similarities and differences are readily apparent. Irrelevant aspects of the teaching must be held constant to minimize confusion, and relevant aspects must be carefully manipulated to demonstrate important differences.’

Although the theory behind the sequencing and ordering of examples is incredibly detailed and varies according to the nature of the concept being taught, there are five overarching, general principles that should be followed in order to ensure that communication is clear.

1) The Wording Principle

The idea of ‘faultless communication’ is a key tenet of DI and I touched on this idea here. The wording principle dictates that we should use the same wording for all items in a sequence and, by precluding variance in the language used, we can minimise potential confusion and unnecessary distraction for students. While tiny or even substantial differences in wording may seem trivial to the teacher, they may have catastrophic effects for novice learners. In DI sequences, teacher scripts detail exactly what is communicated, ensuring that this principle is adhered to. This table demonstrates how it is applied in maths.

Scripted lessons are controversial: many people abhor the idea, perceiving them to be dehumanising, dystopian and robotic. This, however, is a clear straw man. If you accept the idea that large parts of the act of teaching involve communication between a teacher and students, then it is self-evident that the clarity of this communication will either hinder or enable learning. Although I am not advocating creating scripted lessons for all aspects of teaching, there are clear benefits to creating communication sequences that are as unambiguous as possible.

How might this apply to the everyday classroom?

a) It may be worthwhile agreeing upon and standardising definitions for different concepts within a department.

b) When teaching concepts, try writing down what you expect to say to see if you are being consistent with the words that you use. Are you using several synonyms for one concept? Are you explaining an idea using unnecessarily technical language? Is all of the communication necessary? Is your explanation meandering and protracted?

c) Try to ensure that communications are not contradicted by later examples. If you define a verb as ‘an action word’, then this is problematic because many verbs have more than one word ( I am eating toast/The boys have been watching the news). If you are interested in the idea of creating communication sequences that avoid complication, ambiguity and contradiction, The Rubric for Identifying Authentic Direct Instruction Programs provides examples of flawed sequences of communication and suggestions for how they could be improved.

2) The Setup Principle

According to this principle, ‘Examples and non-examples selected for initial teaching of a concept should share the greatest possible number of irrelevant features’. This means that examples and non-examples should vary in only one way with all other aspects and features held constant. By doing this, you create a situation where interpretations and inferences are controlled, ensuring that ‘only one interpretation is possible’. Figure 2.2 demonstrates this idea:

The items in the left column differ in only one way, meaning that a student could only logically infer one meaning of ‘on’. On the right, there are numerous variables between the example and the non-example. A novice learner could logically infer that ‘on’ means any of these things:

a) ‘on’ means rectangular

b) ‘on’ means things with corners

c) ‘on’ means horizontal

d) ‘on’ means light grey.

Because a student could make any of these inferences, the setup principle has been violated and the presentation would be considered unnecessarily ambiguous.

In Theory of Instruction, Engelmann talks about ‘stipulation’. This is the idea that ‘the presentation implies that all features of these examples are necessary to the label. The result is that if the learner is presented with variations in any features, the learner will not treat the example in the same way’. After studying multiple examples that follow the left column of Figure 2.2, there may be a danger that a student will infer that ‘on’ only refers to rectangular objects. To prevent this, subsequent sequences would follow where the setup is changed, perhaps by using different shapes or objects or surfaces, demonstrating that ‘on’ is a wide ranging concept.

How might this apply to teaching English?

I have begun experimenting with creating sequences of examples and non-examples in order to teach grammar and specific sentence constructions. Students seem to be responding well to this approach, although I am certain that there are numerous tweaks and improvements that need to be made if the sequences are to fully conform to Engelmann’s rigorous theory.

Here are some examples from teaching present participles:

The first column contains only one variable between the example and non-example, meaning that a learner can only make one logical inference about the meaning of ‘present participle.’ In the second column, there are numerous variables between the example and non-example. Although there may be many more inferences, a learner could logically infer that ‘present participle’ means:

a) The inclusion of the word ‘Enfield’.

b) A sentence that is in the present tense.

c) A sentence that is in the active voice.

3) The Difference Principle

Carefully choosing non-examples is a crucial factor in helping students understand the ‘limits or boundaries of a concept’. To understand what something is, it is helpful to comprehend what it is not. Figure 2.3 demonstrates this idea:

The column on the left provides far more accurate and precise information as to the ‘point at which an example is no longer horizontal’ because both example and non-example are highly similar. The difference in orientation is only several degrees. On the right, the examples do not provide clear information as to the delineation between horizontal and not-horizontal, the difference of orientation spanning 90 degrees. For the difference principle to be most effective, examples and non-examples should be juxtaposed consecutively, making ‘the similarities and differences most obvious.’

How might this apply to the teaching English?

Here are some examples from teaching participial phrases:In the left hand column, the non-example is a gerund phrase (the subject of the verb ‘was’). Gerund phrases are often confused with participle phrases and the juxtaposition of these two examples demonstrates why that is: they are incredibly similar. The non-example here is helpful as it gives precise information as to the delineation between ‘present participle’ and ‘not present participle’. In the right hand column, the non-example is massively different, making it harder for a student to ascertain the boundaries of the concept being taught.

Like with the setup principle, to avoid stipulation (the idea where a student thinks that the examples in a sequence encapsulate the full range of the concept and that other, different examples will therefore fall outside of it), subsequent sequences would follow where the examples are changed, perhaps by using different sentence constructions or subject matter, demonstrating that ‘present participle’ is a wide ranging concept.

4) The Sameness Principle

In order to demonstrate the range and scope of a concept, we should juxtapose maximally different examples. If we were trying to teach the concept of ‘dog’, then we should choose examples that represent the widest possible variety of dogs. Let’s look at an example:

Although we could debate whether there are more strikingly different examples of dogs that we could use, these three have been chosen because, despite all being dogs, they are massively different. If we had merely shown different breeds of terrier, then a student may infer that any future examples that are not terriers would fall outside of the concept of ‘dog’: again, this is what Engelmann refers to as ‘stipulation’.

How does this apply to teaching English?

Here are some example from teaching participial phrases:

The right hand column only demonstrates a tiny range of possible examples of the concept. If we had merely shown these examples, then a student may infer that any differing future examples fall outside of the concept of ‘present participle’. They may logically infer that present participle sentences:

a) Always contain two words.

b) Always begin with a word that ends in ‘ing.’

c) Always precede the subject of a sentence.

d) Always begin a sentence.

d) Always contain the word ‘gossip’.

The left hand column demonstrates a far wider range of examples. I have deliberately inserted an example that includes a quotation as this is how students will most frequently apply these constructions. The second example begins with an adverb, preventing students from inferring the misrule that all present participle phrases begin with an ‘ing’ word. The third example has the phrase at the end of a sentence, demonstrating that these constructions are not always used at the beginning. A full sequence would contain many more maximally different examples, further broadening the scope of the concept.

5) The Testing Principle

After demonstrating several examples and non-examples, ‘to test for acquisition, we should juxtapose new, untaught examples and non-examples in random order’.  Figure 2.5 demonstrates this idea:

In order to ensure that that we are receive accurate information about a student’s understanding of a concept, we need to create tests that do not follow a predictable pattern.

All of these five principles are presented here as separate guidelines. Creating sequences of communication through examples and non-examples often requires multiple sets of juxtaposed examples and non-examples, which helps to avoid misrules and faulty inferences, ensuring that students not only learn the precise point when something stops being a concept (like the horizontal line and the line that is ever so slightly slanted), but also that they learn that a concept can contain innumerable varieties and differences yet still have the same label (like a Chihuahua and an Irish wolfhound: massively different, but still dogs.)

Next post: Insights from DI part 7: Instructional Formats

Insights from DI Part 5: Teaching Generalisable, High-utility Content

This is the fifth post looking at how ideas from Engelmann’s DI can be applied to the everyday classroom. The first four can be found here: one, two, three, four.

While the last four posts have primarily taken ideas from Successful and Confident Students with Direct Instruction, a recent book where Engelmann explains an overview of his approach, this post will examine The Components of Direct Instruction by Cathy L. Watkins and Timothy A. Slocum, an article from The Journal Of Direct Instruction and an extract from Introduction to Direct Instruction. The paper can be found here.

1) ‘The goal of Direct Instruction is to teach generalised skills: thus the first step in developing a Direct Instruction program is analysis of the content and identification of concepts, rules, strategies, and ‘big ideas’ (i.e. those concepts that provide strategies that students can use to further develop their expertise in a subject matter)…to enable them to exhibit generalised performance to the widest possible range of examples and situations. p.76

Lesson time is finite and one of the most important decisions when designing curricula is to consider the utility and importance of what is being taught. According to DI theory, we should design curricula by ‘identifying central organizing ideas and generalizable strategies that enable student to learn more in less time’. Although a wide curriculum that exposes students to myriad ideas, concepts and knowledge may seem optimal, if students merely experience the content at the expense of any real attempt to master or retain it, is it worthwhile? If a concept takes a long time to teach, yet its utility is limited to one specific unit or section of a curriculum, is it worth teaching and could the curriculum time be used for something that is more ‘generalizable’? If students are regularly taught concepts that they will never be expected to use in later lessons or applications, is this a good use of lesson time?

While all bits of knowledge are useful, some bits of knowledge are more useful than others.

Here are some things that I would consider to be high utility ‘concepts, rules, strategies, and ‘big ideas’ in English. These ideas, skills and concepts can be applied across units, years, and key stages, as well as helping students to ‘further develop their expertise in a subject.’

Specific sentence constructions

Explicitly teaching specific sentence styles and grammatical constructions to students can help them to broaden their range of expression, moving them from functional and simplistic written communication to sophisticated, nuanced and complex writing. Teaching phrases (participles, appositives and absolutes) is one high utility strategy because they can be used with all of ‘The Big Three’ genres of writing that we focus on (analysis, rhetoric and description). If you teach the component parts of a sentence, then they can be combined, manipulated and generalised by students into an immense number of combinations. To draw an analogy, Spelling Through Morphographs-one of the DI spelling programmes-teaches 750 morphographs that can be combined into 12,000 to 15,000 different words. This is far more efficient that teaching spelling through lists of individual words. This table illustrates the efficiency of teaching morphographs to students:

 

 

When teaching vocabulary we use vocabulary tables and deliberately list all relevant forms of the words, allowing students to explore morphology and affixes. As a result of this, students are beginning to make generalisations.

While morphographs are the building blocks of words, phrases are some of the building blocks of sentences and can be combined in lots of different ways when writing. Here are a few examples of how these sub components can be combined:

Choosing sentence styles that are high-utility is important and if students are to master them, they will need extended, distributed and varied practice, ideally spread across texts, units and years. Students begin to learn these structures in year 7, deconstructing worked examples that exemplify how they are applied within analytical paragraphs as well as practicing creating the structures themselves.

Here is a possible overview of a sequence for teaching present participle phrases, moving along a continuum from inflexible to flexible knowledge  and gradually fading out teacher support. This sequence would span many lessons and perhaps weeks of school time:

1. Students identify the specific structures within examples of isolated sentences. Following Engelmann’s theory, students should be presented with examples that demonstrate the full scope of the concept. Crucially, they should also see examples that are minimally different and, by treating them differently, be made aware of the limits of the concept. These non-examples will often elucidate common misconceptions. Engelmann’s theory behind sequencing and ordering examples in order to induce student understanding is fascinating and I am slowly working on creating sequences to teach specific sentence styles.
2. Students finish half-completed sentences or combine sentences. See this post for an overview of sentence combining.
3.  Students create sentences in response to a specific task:

EXAMPLES:

Write three present participle sentences about Macbeth’s ‘Is this a dagger soliloquy’ 

Write three present participle sentences that describe the picture.

4. You could then ask them to attempt smaller pieces of writing, perhaps just a paragraph, where they can apply the structure in a freer context, perhaps combining it with other concepts and skills.

EXAMPLES:

London: How is the omnipresence of suffering presented in the poem?

• Participial phrase

• 3 quotations

• ‘denounce’ ‘indignant’ ‘marginalised’

 

5. After students have become proficient at the specific structures in isolated, scaffolded contexts, they should then be expected to apply these component skills in wider writing. This can be achieved by regularly drawing attention to the specific structures within worked examples as well as including the structures within the success criteria for a piece of writing.

Vocabulary to be used in analysis

Instead of only teaching the vocabulary that you encounter within a text, teach the vocabulary required when responding to a text. Although it will be useful to teach some of the words within a text as they will be integral to comprehension and analysis, other words may be so recondite, anachronistic or genre specific that their utility is limited. Focussing on Tier 2 words-vocabulary that spans contexts and domains-is one way of promoting generalisations. See this post for more information.

A generalised analytical framework:

We have developed an analytical framework that can be used across texts and different tasks. Tentatively called ‘The 6 Skills’ (I am still unsure if these 6 are sufficiently distinct or whether they comprehensively encapsulate analysis!), our intention is to promote a generalizable strategy when responding to texts. Unlike vocabulary, contextual information, interpretation, authorial intention and explaining the effect of techniques (all potential examples of declarative knowledge in English), it is an attempt to formalise the procedural knowledge required when writing analytically. We are heavily indebted to the great work of many other teachers here!

PEE/PEEL and other similar frameworks were problematic and restrictive, resulting in clunky, predictable and overly formulaic paragraphs. Invariably, iterations of these abbreviations and acronyms also have fixed orders, placing evidence in the middle, one of the problematic inferences being that each train of thought contains only one quotation. Interesting analytical writing does not follow a predictable, sequential order. Finally, PEE also precludes embedded quotations, due to the unnatural scaffolding of sentence stems like ‘My evidence for this is….’.

Here is an annotated worked example that exemplifies our generalizable framework:

As well as exemplifying the 6 skills, the screen shot also demonstrates the utility of teaching phrases and how they can be used to create dense and linguistically sophisticated analysis.

Unlike PEE/PEEL, there is no fixed, consecutive order for how these skills are deployed and applied, meaning that student responses are not as formulaic and rigid. Although students will study worked examples that contain most if not all of these skills from the beginning of year 7, they will practice the skills individually and cumulatively, slowly building students up to being able to use all 6. See this post  for an outline of how to create focussed and cumulative practice activities.

A future post will look at this framework in more detail, explaining how it can be broken into constituent parts and deliberately practiced. I am aware that there are multiple potential flaws with this framework, not least regarding the amorphous nature of some of the skills, particularly those regarding the use of evidence.

Next Post: Insights from DI part 6– Five principles for sequencing and ordering examples