Coherence

connected steps

Key Messages:

  • Small connected steps are easier to take.

  • Focusing on one key point each lesson allows for deep and sustainable learning.

  • Certain images, techniques and concepts are important pre-cursors to later ideas. Getting the sequencing of these right is an important skill in planning and teaching for mastery.

  • When introducing new ideas, it is important to make connections with earlier ones that have already been understood.

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When something has been deeply understood and mastered, it can and should be used in the next steps of learning.

The Secondary PD material is based around:

  • six broad mathematical themes

  • a number of core concepts within each theme

  • a set of ‘knowledge, skills and understanding’ statements within each core concept

  • a collection of focused key ideas within each statement of knowledge, skills and understanding.

This detailed breakdown will help you to map out a coherent learning journey for students and a related teaching programme.

1. The structure of the number system

1. The structure of the number system

2. Operating on number

2. Operating on number

3. Multiplicative reasoning

3. Multiplicative reasoning

4. Sequences and graphs

4. Sequences and graphs

5. Statistics and probability

5. Statistics and probability

6. Geometry

6. Geometry

SHAPING THE YEAR 7 CURRICULUM: BUILDING ON YEAR 6 Ready-to-use training materials, ideal for use in planning effective curriculum transition from primary
SHAPING THE YEAR 7 CURRICULUM: BUILDING ON YEAR 6 Ready-to-use training materials, ideal for use in planning effective curriculum transition from primary

Atomisation

Atomisation is the process of breaking down a topic into its sub-tasks.

 

“Atomisation is a process in which teachers can collaboratively identify the specific and detailed knowledge that pupils must know to be academically successful.

Teaching all the sub-tasks of a concept and sequencing it in a logical sequence prevents pupils from being cognitively overloaded because each sub-task taught is being used or covered in future learning. In the teaching process, pupils will have committed prior knowledge in their long term memory so any future learning will occupy space in their limited working memory.”      

http://conceptionofthegood.co.uk/?p=702

 

The cost of atomisation is a valid one. The initial stages of teaching a concept take more time to cover the content. If we explicitly teach more sub-tasks than we would normally then we would have more time available to teach the rest of the curriculum. However, by not explicitly teaching all the sub-tasks of a concept it will result in the following consequences:

  1. Reduce the probability of a child learning parts of a concept on the first attempt
  2. Undermine a child’s ability to access future learning

Atomisation avoids these inadvertent consequences by:

  1. Guaranteeing a greater likelihood a pupil will learn the sub-task on the first attempt
  2. Increasing the probability of success when learning future content or more complex applications of the concept
  3. Saving time in the future which would be inevitably spent re-teaching
  4. Revealing sub-tasks that need to be taught that are usually overlooked in the curriculum.

http://www.mrbartonmaths.com/blog/naveen-rizvi-part-1-scripted-lessons-examples-and-social-media/

 

Further reading:

http://mrreddy.com/blog/2014/03/design-your-own-mastery-curriculum-in-maths/

https://themathsechochamber.wordpress.com/2018/01/23/atomisation-compound-shapes-kris-boulton/

http://conceptionofthegood.co.uk/?p=660

Reflect, Expect, Check, Explain – Craig Barton, page 151