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The Great Teaching Toolkit Evidence Review, June 2020 is an important read and part of an ongoing project. See my page Great teaching toolkit Evidence review for further links and resources. See also Exploration and Investigation with Technology.
Another worthwhile read is the earlier: What makes great teaching? Review of the underpinning research.
Robert Coe, Cesare Aloisi, Steve Higgins and Lee Elliot Major
October 2014. And have a look at these comments from Year 9 on good maths teachers!
Rosenshine’s Principles of Instruction
For the slides from my London Maths session, see:
Rosenshine’s Principles in the Mathematics Classroom | Mathematics, Learning and Technology
Rosenshine’s Principles of Instruction provides a very valuable list of research strategies teachers should know about and I believe it is well worth asking ourselves if we are incorporating these strategies regularly into our lessons. This UNESCO pamphlet on the Principles offers further reading and for a very clear summary of these principles of instruction, see olicav.com, Oliver Caviglioli’s wonderful resources including poster summaries of educational ideas. Scroll through the Poster collection for Rosenshine’s Principles of Instruction – Tom Sherrington has turned the ten strategies into a more powerful poster, chunked into four stages of a lesson.
Links to resources:
Research in 100 Words from Chris Moyse who descibes this series as “Simple summaries for busy teachers”. Also from Chris, his favourite research articles in one collection.
Further links and resources.
See these pages Great teaching toolkit Evidence review and Exploration and Investigation with Technology.
- Good Maths Teachers… student comments
- The Maths Teacher – David Smith
- White Rose Secondary Resources – scroll down for the complete secondary small steps document
- Andy Lutwyche – Building Blocks (all the individual resources are free)
- The Standards Unit
- Maths4All – includes the CIMT Interactive resources and text chapters
- nonexamples.com
- Frayer Models Knowledge Organisers – Mathematics
- Maths White Board
- Purposeful Maths (Factorising Single Brackets)
- BerwickMaths
- CIMT
- Math Whiteboard
- The Maths Teacher
- Adding Integers – GeoGebra
- PhET simulations (Equality Explorer)
- Wisweb Applets HTML5 (includes Standards Unit Software)
- Calculators and Tools including Quadratic Formula Calculator and Solver
- Math Open Reference including Constructions demonstrations.
- Increasingly Difficult Questions
- GeoGebra for Edexcel GCSE Higher Geogebra – Adding Integers
- GeoGebra – Rotations
- Desmos Classroom Activities
- CrashMATHS
- Worked Examples – A Level
- Integration – Desmos and WolframAlpha
- AQA Specimen Paper example – Desmos
- MEI Student Tasks
- Teachit Maths – The Shape of the Quadratic Function
- Knowledge Organisers
- Underground Mathematics and Review Questions
- Circle Theorems – GeoGebra
- Edexcel Guide to GeoGebra for AS and A Level Mathematics
Questioning
On Nrich, see this by Jenni Way on using questioning to stimulate mathematical thinking, with an addendum also which includes ideas for questions to use for student investigation. Not just for Maths but applicable to any subject I’d recommend very highly the Brighton and Hove Assessment for Learning project – Questions worth asking.
- Desmos Tasks for GCSE and A Level
- MEI Desmos Tasks for GCSE
- IDEMS International eCampus – Maths Bridging Course GCSE to A Level
- Transum Mathematics
- Spot the Mistake
- Quizlet
- Quizlet – verified GCSE Mathematics Resources
Review
- Retrieval Practice – this page has numerous links to resources
- Mathsbot
- Transum Refreshing Revision
- Berwick Maths Low Stakes Quizzes
Practice
- Goal Free Problems
- Here’s the diagram, what’s the question?
- Increasingly Difficult Questions
- Nrich article on Etudes – Colin Foster
- Colin Foster – Mathematical Etudes
- Examination Board Teaching Resources
- Open Middle
- Underground Mathematics series of pages
- Retrieval Practice – Two Things
From Craig Barton see Tes Maths: Lesson planning in mathematics, Secondary Maths resource highlights for students in secondary school. Craig has selected resources from the Tes Maths community that he has found invaluable when planning maths lessons. As the article states, we should think of our lessons as part of a sequence not a single unit. we need to think about where we want our students to get to, what sort of problems do we want them to be able to solve. Craig has grouped his chosen 12 resources into 3 categories, Worked Examples, Atomisation and Variety of activities.
Thinking also about observing lessons I have been reading various articles and blogs and came across David Didau’s ‘Where Lesson Observations Go Wrong’. Many of David’s comments really struck a chord with me, particularly his comment ‘no one knows my kids in my classroom like I do‘. That is so true; I think we would all like to think that any observer coming into our lesson has that in mind. If I observe a lesson in any capacity I want the teacher to know that I appreciate how well they know their students. Note David’s updates since writing that post: Ofsted has stopped grading individual lessons and his most recent post on the subject. I do like David’s suggested questions (reproduced below – thank you David) for observation feedback – questions like this make for a good conversation between the observer and class teacher. If I have planned my lesson properly, thinking about all the aspects mentioned in the five minute plan above then I should easily be able to answer these questions and in fact be glad to be asked them. The questions emphasize quite rightly that this is but one lesson in a sequence of lessons and only a tiny snapshot of my interaction with that class.
.
- Where does this lesson fit into your sequence of teaching?
- What have students had to learn in order to get to this point?
- What did they already know?
- How will you develop what students have done so far?
- How might the next lesson be adapted in light of what happened this lesson?
- How do you know if students are making progress?
- Why did you make the decision you made today?
- Is there anything you might do differently?.
These questions are useful for reflection – have an imaginary conversation with yourself even if you are not being observed. Actually come to think of it – isn’t that best of all – to get really good at observing ourselves?!
And always keep Professor Robert Coe’s poor proxies for learning in mind.
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