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: This booklet of sample questions has been created as part of a project funded by the NCETM on Questioning the use of Bloom’s Taxonomy.

Blooms Questions NCETM

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.

For more always / sometimes / never and also some true/false questions use CIMT’s excellent Mathematical Proof. 

See also: Rich Tasks and the Questions page.

For many Proof resources – see Proof – 2021.

11 comments on “Rich Questions in Mathematics

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  3. I did quite enjoy the Brighton booklet, but wanted to scream when I saw the desk layout. Move the tables! Don’t have the teacher as focus of the classroom, then the teacher will move about. Scrap teacher’s desks!

    • Colin thank you for all your valuable observations. I do like that Brighton & Hove project – there are some excellent ideas there – I think reflecting on the way we use questioning in the classroom is very important.

      Talking to some of my Year 10 students on this subject recently, they said there was a need for questioning at all levels from the simple recall type questions – because they do need that for exams, to the questions demanding higher order thinking to help them make connections and apply their knowledge.

      • I totally agree about the simple questions, and like to start a lesson with a quick recap of the previous lesson, including simple recall questions. (My multiple-choice versions are somewhat popular on TES.) At the end I like the learners to share what they have learnt. As for the teacher’s desk – I was doing research for an MPhil nearly twenty years ago at a newly created CTC (you might have to google that, you youngster). They had no teacher’s desks, and were very soon at the top, or second, in exam results tables. That an a Mac at every elbow…

  4. I’ve spent an interesting couple of hours ploughing through this lot, and thanks for pointing me to them. Much is useful, but I am at the point where I think there is far too little hands-on and creativity in the classroom and in the minds of teachers. This is all written stuff, possibly to be presented audibly, but nothing practical. Where’s the kinesthetic learning? A couple of examples: for all manner of division and factor type questions I have jars of pebbles – Barbara and Derek Ball wrote whole chapters on the number 42 – what can we do with 42 pebbles? And for shape and space, I have a simple net of a 3,4,5 triangular prism – cut it out, make it up, and pose your own questions. I’ll describe it one day, the fun and mathematics it generates.
    I’ll be back…!

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  6. A very useful topic to have raised, and I’ll be looking at the resources you recommend during the coming days. Personally I never answer a question, and haven’t done for years and years, and always reply to a question with another question. What I fear is that it takes a great deal of confidence to build questioning skills, and a very sound subject knowledge, but anything that helps us get away from closed questions, in both spoken and written form, is good. I had a wonderful ‘questioning’ lesson on Friday, albeit with a very small group, but I hope to get round to sharing it on blog this week. And I think I’ll just reiterate – closed written questions aren’t much different to spoken ones.

    • I agree Colin it does indeed take time and confidence to build questioning skills. I also often respond to questions with another question and always let my students know they can do that to!

  7. Thanks for this fab collection on rish tasks and in particular rich questions. I also love ATM ‘Thinkers’ which is a great resource for questions to encourage deeper thinking and understanding!

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