Rich Questions in Mathematics

 See also: Rich Tasks and the Questions page updated, 2016.

Ofsted (The UK Office for Standards in Education, inspect and regulate services which care for children and young people, and those providing education and skills for learners of all ages) as part of their judgement on the quality of teaching quite rightly include ‘the extent to which teachers’ questioning and use of discussion promote learning’. Research has shown that often teachers’ questions are closed questions which require only lower order thinking skills from students. There are some excellent resources available to help teachers think about the types of questions they can use to support students’ learning. 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.This includes many practical suggestions for the classroom and concludes with a self analysis.

The project includes the use of Bloom’s Taxonomy as an aid to thinking about the level of challenge / thinking required for a question. One of the consistently popular posts on this blog is Bloomin’ Mathematics which has links to several resources on Bloom’s Taxonomy. Of particular interest here on questions is an excellent resource: a booklet of sample questions which has been created as part of a project funded by the NCETM on Questioning the use of Bloom’s Taxonomy (scroll down the page for the final report).

For further questions which require higher order thinking skills see the Levelopaedia from Kangaroo Maths which has numerous probing questions and also the focused assessment materials which make it clear what students should be able to do and give probing questions. Whilst we happily don’t have levels any more these remain great questions.
Focused Assessment Level 4   Focused Assessment Level 5   Focused Assessment Level 6
Focused Assessment Level 7   Focused Assessment Level 8

Diagnostic Questions - Algebra
Diagnostic Questions – 
brilliant diagnostic questions – use this with your classes and find out what your students know – or are in a muddle with!

Further Resources:

Multiple Choice questions can really help expose misconceptions as mentioned above, there are many other sources too and note Daisy Christodoulou’s comments on the use of Multiple Choice questions.

Hosted by the National STEM Centre I do like Susan Wall’s Thinking Questionsopen–ended questions which should certainly make your students do just that – really think.

Nrich have some excellent advice on questioning, see Working Effectively with All Learners which offers questions and prompts to encourage discussion and Using Questioning to Stimulate Mathematical Thinking.

See Dylan Wiliam’s paper on Rich Questioning.

Always / Sometimes / Never questions and scroll right down to ‘Convincing and providing’ for question sets and solutions. For more always / sometimes / never and also some true / false questions use CIMT’s excellent Mathematical Proof. There are many such resources on TES – try some of these resources. See this post for further Proof resurces. For younger students try Andrew Jeffrey’s lovely free gift ‘What’s the same, what’s different?

 See also: Rich Tasks and the Questions page.