How can you choose what to teach?

The more efficient the instructional sequence, the greater the benefit to students and this is of particular importance for students who have lagged behind their peers because, if they are to catch up, they will need to learn more in less time. But how can such a goal be achieved? Lessons need to be focused, purposive and communication needs to be clear. However, even if these conditions are met, this will not guarantee that learning will be maximised.

Generativity

DI programmes teach to the general case and teaching can be said to be ‘generative’ if it enables a learner to respond appropriately to untaught situations. In this sense, generativity is very similar to the ideas of transfer and flexible knowledge. For example, if reading instruction enables student to read untaught words, it can be said to be generative. Teaching students that the grapheme ph is a spelling for the /f/ sound can be said to be a generative approach if students can then decode untaught words that contain this grapheme.

Teaching number families in basic arithmetic is also a generative approach. For example, in addition and subtraction, 2, 3 and 5 is a number family because it can produce four basic facts: 2+3=5, 3+2=5, 5-2=3 and 5-3=2. Instead of asking students to memorise these four facts, students can learn one number family alongside the relations necessary to produce the four facts. This approach is far more efficient as it has a lower memorisation load whilst also teaching students relations that can be transferred to other number families.

Teaching students to manipulate the components of a sentence is also a generative strategy and is a much more efficient approach than learning how to copy and apply single example sentences.

Most content domains are so large and complex that it is impossible to teach everything that they encompass. There are far too many possible combinations of content, responses and contexts to teach them all individually. Because of this, we need to teach to the general case, but how can this be done?

Content Analysis

The purpose of content analysis is to identify generalizable relations within a domain and arrange the content in such a way that learning becomes as efficient as possible. Efficiency here means maximizing the amount of learning within a given time and the goal is to produce the most learning from the least amount of teaching.

A content domain is synonymous with the topic that is being learned, examples of which include computer programming, writing analytical essays, mathematics or molecular chemistry. For every possible content domain, there will be multiple ways of conducting content analysis and deciding what to teach and some ways will be more generative than others. For example, in the content domain of spelling, teachers could decide to produce word lists for students to learn based around topic themes or commonly misspelled words; however, such decisions could be problematic as they are not generalizable. Alternatively, words could be grouped and taught according to phonic or morphographic content therefore producing a highly generative approach to spelling instruction.

Content analysis is the base upon which all other pillars of curriculum design stand. Every other part of curriculum design (creating explanations, sequencing examples etc) will depend upon the content analysis. If the content analysis isn’t up to scratch, the generativity of instruction will be minimal irrespective of how well the other aspects have been designed.

So if it is so important, how do we do it properly?

The process of content analysis should involve a cycle of logical and empirical analyses:

The process should begin through logical analysis where teachers generate possible methods of organizing the content. These should then be logically compared before being empirically tested.

Here’s what this might look like in English:

Imagine you want to teach students how to write compelling pieces of persuasive writing.

Step 1: Engage and Generate

You would start by reading research into effective writing instruction, perhaps choosing to read The Handbook of Writing Research

The handbook explains how emulating model texts and teaching students how to structure their writing can be effective approaches. So, you come up with a few possible approaches:

  1. Teaching classical speech structure (Exordium, Narratio, Divisio, Probatio, Peroration)
  2. Asking students to emulate that brilliant article that you found
  3. Teaching a different persuasive structure

Step 2: Logically Compare

By logically compare all three approaches, it quickly becomes apparent that approach b is not optimal. While the article is brilliantly polemic, it does not contain a transferable structure that students can use and, despite the fact that the prose is captivating, sardonic and nuanced, its complexity will preclude all but the most able students from aping its inimitable style. While students may benefit in other ways from reading the article, it will not be the best choice here. As a result, you logically infer that a or c may be more suitable, both containing malleable structures that could be used in a wide range of relevant contexts and tasks.

Here are some possible questions you could ask while comparing approaches:

  1. Is the approach clear enough for all students to understand?
  2. Can you create and sequence sufficient examples and non-examples in order to refine and develop students’ mental representations of what you are teaching?
  3. Can the approach be practiced so that students build fluency?
  4. Does the approach allow space for creativity: is it a straightjacket or a springboard for success?
  5. Is the approach applicable to the full range of relevant contexts that student will encounter? 

Step 3: Empirically Test

Once you have finished deciding which one you will use, you will need to test whether it is efficient and generative. Just because an approach is logically generative does not mean that it will necessarily be empirically generative.

For a test to truly assess generativity, it must involve untaught content. With structuring persuasive writing, you could use Language Paper 2 Question 5 tasks that students have not encountered before so that you can see whether they can apply the approach that has been taught. To make the test as valid and rigorous as possible, you should choose an outlier style of question where the topic and task are maximally dissimilar to what is usually asked for: does the approach work with writing letters? What about topic X? You should also pay close attention to the output of the weakest students and use them as your guide as to whether the approach is successful.

Directly examining the domain

Reading research can be very helpful when beginning content analysis but so can analyzing the domain itself. Wherever possible, content should be chosen for its utility and whatever subject you teach, there will be some big ideas or concepts that can be applied to different units and topics, some even crossing traditional subject boundaries. As an example, the idea of convection can be applied widely in science and geography:

If you are interested, many of the ideas in this blog post are based upon ‘Features of Direct Instruction: Content Analysis’ Behaviour Analysis and Practice 2021. Thanks to @JonOwenDI who posted a link to the paper on twitter.

I would highly recommend Jon’s blog which has some fascinating posts about DI and curriculum design.

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Checking for Understanding

CFU is really important in the I stage and the We stage of  a lesson. Students should be able to do independent practice (You stage) with minimal support and for this to happen, you need to use CFU properly.

The table below gives an overview of the different stages of the I-We-You continuum as well as how it matches ideas from Cognitive Load Theory and Rosenshine’s Principles of Instruction.

I stage

You will either be explaining information or demonstrating a skill or process. CFU is important here to ensure that kids understand what you are doing.

Here is an overview of what this might look like when reading a text:

Here is an overview of what this might look like when you are modelling:

We Stage (Guided Practice)

Here is an overview of guided practice:

Features of Guided Practice:

  1. High Frequency of Questions and Overt Student Practice
  • Teachers should ask questions that are directly relevant to the new content or skill, ensuring that they choose the correct category of questions: procedural questions for processes and skill; declarative questions for content and knowledge.
  • Practice activities should be ‘overt’ in that it should be simple for the teacher to ascertain whether the student is performing correctly or not. Written work is ideal here as the teacher can move around the class to check all student responses.
  • Teachers should regularly check for understanding. This could be through oral questions or through checking written work as students are completing it.
  • If it is clear that a student or students do not understand something, the teacher should offer a repeated or additional explanation or relevant feedback as necessary
  • If it is clear that lots of students do not understand, it may be necessary to stop the guided practice and then reteach the whole class.

2) Ask lots of questions and check the responses of all students

Asking questions is an important part of teaching but if questions are to be useful, we need to think about why we are asking them. Questions can be asked to check understanding, to push students to develop or improve their answer, to consider alternative viewpoints or to help them make links between ideas. Questions also provide pupils with vital practice on what is being taught.

Most of the time it is far more efficient to teach stuff, then ask students questions about what you have taught.  Beginning with eliciting questions like ‘Who knows what The Great Chain of Being is?’  or ‘What do you think ‘hubris’ means?’ before teaching them anything is probably not that useful. The worst example of this is ‘guess what’s in my head’ where a teacher asks a question with a specific answer in mind, hoping to elicit that specific answer from the class. This guessing game can go on for ages and is almost certainly a waste of time.

What should be the focus of Questioning?

Successful teachers ask more useful questions to as many students as possible. Their questions will focus on declarative knowledge (the content that is being taught) as well as procedural knowledge (the processes that students need to follow if they are to complete tasks properly.)

Let’s have a look at some examples:

Declarative Questions:

  1. What is the subject of the first sentence?
  2. What is the noun form of ‘benevolence’?
  3. If the audience knows something that the character does not, what is this technique called?
  4. Why does Macbeth want to kill Duncan?
  5. Who is responsible for Macbeth’s demise?

Procedural Questions:

  1. How did you find the answer to that question?
  2. What are the 5 steps you should follow when answering the examination question?
  3. Explain how to write an analytical introduction
  4. What you should include in your first paragraph and why it is important?
  5. How do you know that?

Asking procedural questions is really important. Not only does it provide additional practice as students are asked to explain how they have done something, but it allows other students to understand the process that the student used to complete the task.

Here are some useful strategies:

Using Mini-White Boards

Mini-white boards are ideal for checking an entire class’ answers at once. They are especially useful for lower order, closed and factual questions, their size prohibiting answers that are anything more than a few sentences.

Cold Call

This technique helps to ensure that all students are engaged and thinking about what you have asked. Assuming you have taught them what they need in order to answer the question, this can be an equitable and appropriate means of ensuring everyone thinks of an answer, an outcome that is more difficult to achieve with traditional ‘hands up’ style questioning.

Let’s have a look at an example.

Teacher: How do you know that Ozymandias was arrogant?

The teacher should then pause, allowing everyone the opportunity to think of answer

Teacher: Abimbola……………what do you think?

Choral Response

Asking an entire class to respond at the same time means that everyone answers the question. This allows for far more practice as well as providing the teacher with more comprehensive information about whether their students have understood. Choral response questions are ideally suited to lower order, closed and factual questions. For this approach to be successful, students need to respond at the same time. If some students are faster than others, the slower students can just copy the answer they hear instead of thinking for themselves. If you are thinking that this approach sounds weird or won’t work with teenagers, you may be pleasantly surprised: typically, they enjoy choral response, especially if the teacher is enthusiastic.

Let’s have a look at an example:

Teacher: Which rhetorical technique involves three ideas in succession?

The teacher then needs to give a cue: clicking fingers, saying ‘Go’, or dropping a raised arm all work well.

Whole class: Tricolon


Building Flexible Knowledge

I have written before about ‘The Instructional Hierarchy’, a framework that splits learning into five stages:

  1. Acquisition
  2. Fluency
  3. Retention
  4. Generalisation
  5. Adaptation

This blog will demonstrate how a multi-lesson instructional sequence can be used to ensure that students are able to generalise. Such an approach can help students develop the flexibility of their knowledge so that they can transfer and apply what they have learned to a good range of relevant contexts.

If you want a more detailed explanation of how to teach appositives, this blog might be of interest.

Stage 1: Acquisition

One of the key points about acquisition is to begin with lots of model sentences, explaining, labelling and questioning the key points.

In the example below, students were asked to complete sentences 2, 4 and 5. I then asked them to write 3 more appositive sentences about these topics:

  1. Gothic Literature
  2. Asia
  3. Summer

Before they started, I gave lots of oral examples and made sure they knew a synonym for each topic (genre/continent/season etc) so that they had the knowledge required to write the sentence: the synonym would be used as the noun in the appositive phrase: The largest continent, Asia is also the most populous.

Stage 2: Fluency and Stage 3: Retention

In this second lesson, I went over the example sentences (1-5 in the example) with students, ensuring that initial teaching spanned 2 lessons. I then asked them to write their own (they were not allowed to copy mine). I gave them 3 minutes to do this. Most were able to finish in this time.

Stage 3 Generalisation and Stage 4 Adaptation.

After they had done a few lessons of timed fluency practice with simple descriptive appositives, I introduced these examples in order to demonstrate how these constructions can be adapted and used as part of extended analytical writing. I then chose some pieces of evidence from a non-fiction text we had recently read about giraffes and asked the students to complete short analytical paragraphs about each piece, following the same sentence constructions.

The next lesson involved this:

In this lesson, students began by completing 5 appositive sentences. Some sentences required retrieval of the content we are currently learning (Romantic Poetry), others didn’t. We then went over the two examples at the bottom, further reinforcing the fact that these constructions lend themselves well to analysis too.

I then asked students to help me complete these:

  1. The persona wears ‘clothes of death’
  2. The child is described as a ‘thing’
  3. The church makes a ‘heaven of our misery’
  4. Blake lists ‘God and his priest and King’

In the next lesson, we then widened the application even further by asking them to practice a reduced form of an analytical introduction, a useful approach to beginning essays. At this stage, I want the year 8s to be able to write a short version of this important essay component; in year 9, they will develop this into something that is far closer to what they will eventually be expected to include in their GCSE essays.

TGoL here is The Garden of Love by William Blake. We had previously read and analysed the poem in detail and come up with a list of 6 big ideas that the poem could involve and I asked students to write versions of the model, choosing the ideas that they liked the most and could explain convincingly.

All of the previous instructional examples involve restrictive drills; the next step was to get students to apply what they had learned to extended writing.

This was the next step:

The plan demonstrates the link between the mini-analytical introduction and the two subsequent paragraphs. I wrote this start of a model live under the camera so that students knew what to do (apologies about the squiggly crossing out-that should read ‘title/name’). At this stage, students are prompted to include what they have previously practiced to fluency in restrictive drills. (see “3+ analytical appositives” in the example above)

This example sequence moves quite quickly through the stages of learning and this is testament to the speed at which this particular class learn. Other classes may need much more practice and the instructional sequence would span many more lessons.