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
Cognitive Load Theory
The basic idea of Cognitive Load Theory is that everyone has an inherent limit to how much information can be stored in your working memory at one time, therefore students will struggle to grasp concepts when their working memories are overloaded with data.Though Direct Instruction does not reference Cognitive Load Theory directly, it still has a lot to say about ways to reduce the cognitive load for students, particularly during initial instruction.
Reduce clutter
Remove all elements of a problem that are non-essential to the skill, allowing students to infer what is essential/non-essential to the concept. This means changing this question:
Abby, Charles and David share out 32 sweets in the ratio 2:5:9. How many more sweets does David get than Charles?
in to this question:
Share 32 in the ratio 2:5:9
This also means removing non-essential elements from diagrams and avoiding the use of 'real-life' pictures or situations (more on this in the "real-world" maths section)
The wording/setup principle
Every example and practice problem that students do during the initial instruction should have the exact same setup, right down to the wording and the font of each question. In practice, along with the "single dimension transformations" discussed below, this looks a lot like Craig Barton's Variation Theory problems:
Single dimension transformations
As seen in the problem set above, only a single aspect of the question changes from problem to problem. This reduces cognitive load as there is a single aspect to concentrate on between questions. Craig Barton points to other benefits:By holding constant as much as possible and varying one element, we can direct students’ attention to that element that has varied. Any change (or lack of) in the answer may then be attributed to the change in the element. Moreover, because each question or example is related to the one that preceded it, students are able to form expectations as to what the answer will be. I call this process reflect, expect, check. This can lead to significant moments of revelation and discussion when these expectations are not realised, compelling students to think more deeply about the processes involved, instead of just cruising through an exercise on autopilot.
Atomisation
Discussed in more detail here, atomisation, or the splitting of skills down to their component parts, also means that students are learning a single concept at a time. This means there is less information that needs to be stored in their working memory at any one moment.Addressing concerns
- Students won't be able to generalise to similar questions which are worded differently.
- This is taught as a separate skill during expansion activities
- Students won't be able to repeat the process when a questions is not preceded by several highly similar questions
- This is also taught separately during review and context shaping activities.
- So no context? No treasure hunts, code-breakers, funny pictures practical demos or anything?! Won't students find maths incredibly boring?
- Most models for motivation put a high emphasis on 'perceived ability to succeed' as a main contributor to overall motivation. Atomisation is a fantastic tool for facilitating regular and obvious successful progress. I have found my students have enjoyed my lessons much more this year because they can 'feel' the progress they are making.
- All of those activities are possible to fit in to a Direct Instruction program, and should only be strictly avoided during the initial instruction phase. Because each component is small, each initial instruction phase should only take a few minutes. This frees up time to do the code breaker/treasure hunt as an expansion or review activity in a future lesson.
In the Direct Instruction model, the aim of initial instruction is to teach the central concept only, whilst avoid the learning of misrules. Separating the concept, question identification and recall and teaching them as separate skills is a further tool for reducing cognitive load.
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