In a post on Cognitive Science in the Classroom, I mentioned Knowledge Organisers, or to be more precise I mentioned Kris Boulton’s “When shouldn’t I use knowledge organisers?”. Kris has written on why they are less applicable to maths. Certainly, I have not used knowledge oranisers for Mathematics myself with one exception, I have used William Emeny’s Angle Facts; as Kris Boulton says in his article, “Maths is super-dense with concepts, and processes, but really only very few facts.” Noting topics where students do need to know more facts, he includes angle facts.
When I have used Will’s angle facts, I have adapted it so some content is missing, particularly the section on basic angle facts, students can be given just the diagrams for example and asked to recall the basic angle facts. I have also asked students to recall as many basic angle facts before they see the list as in the organiser, so using it following retrieval practice or as a retrieval exercise.
As noted in this post on Knowledge Organisers from Durrington Research School, it is not about the knowledge organisers themselves but how they are used for planning, teaching and testing. Note the example shared of a Maths Knowledge Organiser, Year 10 Expressions, Foundation. I like the fact that key vocabulary is included here, the few key facts needed and of course by far the largest section – key concepts with examples.
To quote the Durrington blog, “Maths are using their range of knowledge organisers to support homework tasks. Firstly, the students can access their maths knowledge organisers are any time using our online system Connect. This means that students have scaffolding in place for when they are working outside of the classroom. Furthermore, every fortnight the maths team set a homework that is based on retrieval quizzing. The students are required to use the knowledge organisers to find the answers to upcoming quizzes and then actually sit the quiz in class on the due date for the homework. Students who score less than 12 out of 15 are then supported in making flashcards on the questions, again gaining the information from the knowledge organiser, and use these to retest until they are successful. This strategy demonstrates how knowledge organisers can be used to support learning through the testing effect.
NonExamples.com – Jonathan Hall
If I want definitions, characteristics and examples (clarified with the use of non examples), then I could return to the Frayer model. (See Frayer Models.)
Reading further on Knowledge Organisers, I do recommend this collection of blog posts and articles from St Mary’s Catholic Academy, on Retrieval Practice which includes the use of Knowledge Organisers. Once again, the emphasis is, quite rightly, on how they can be used fro rerieval practice.
Searching for Mathematic Knowledge Organisers, I have come across some resources I wish to explore further, such as the Henry Box School on Knowledge Organisers where the school are sharing Knowledge Organisers for each subject, recognising the support parents can offer. On TES, GCSE Maths 1-9 Knowledge Organisers is a (free) set of 50 files, described as “A full set of Knowledge Organisers containing the facts, definitions, formulae etc. that students need to know for the new GCSE Maths specification, broken down into individual units. On each Knowledge Organiser, content shaded in grey is for Higher Tier only.
Can be used for homeworks, revision, starters, plenaries or any other ways you might find useful.”
The files have been created in Word, I like the 3 column format which includes, Topic/Skill, Definitions/Tips and importantly, Examples.
I will return to this topic as I have further resources I wish to explore….
…and I want to ask my students what they think.
Autograph is also excellent for illustrating the Newton Raphson method – something which will be very useful in teaching Numerical Methods for A Level.
I have often mentioned the excellent 
Noting the popularity of 
A nice little starter from Transum, 
