Thinking about the different levels of Bloom’s Taxonomy taxonomy is useful when planning questions for students. Even if you are not convinced by Bloom’s Taxonomy we are all convinced of the need to question our students in a way that challenges them makes them think hard – more than just simple recall type questions.
Nrich has a small number of articles on Bloom’s taxonomy, this by Jennifer Piggott showing the heirarchy of thinking skills together with skills and question cues and 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.
Lindsey Shorser has written a short paper on the interpretation of Bloom’s taxonomy for Mathematics.
A very useful resource is this 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. I have tried many of these in the classroom, they really make students think and encourage a deep understanding. 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.
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 provides probing questions. (No levels any more – but still some great questions).
Focused Assessment Level 4 Focused Assessment Level 5 Focused Assessment Level 6
Focused Assessment Level 7 Focused Assessment Level 8
Diagnostic Questions – brilliant diagnostic questions – use this with your classes and find out what your students know – or are in a muddle with! (See all Diagnostic Questions posts and Craig Barton’s own blog). In particular see this post with links to the excellent examination questions collection.
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.
Corbettmaths 5-a-day. This is a wonderful resource with more than enough questions at different levels to keep you busy all year round with a variety of ages. I print the questions for students and hand them out as they come into the room so they can get straight to work. I find that using the Windows snipping tool I can easily fit two sets on an A4 landscape page making them economical to print or copy; this is a size that can easily be stuck into exercise books. See this post for more information.
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.
Alternatively try Here’s the diagram – what’s the question, see also Algebra Snippets where students are shown a diagram or just part of a question and must decide what the question is – good for vocabulary and examination terminology.
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 resources.
For questions to really get your older students thinking, try these resources.
For younger students try Andrew Jeffrey’s lovely free gift ‘What’s the same, what’s different?
The Kangaroo Maths site offers extensive resources, now updated – a shift to assessing without levels. Check the Assessment section and note in particular the “Build-a-Mathematician Progress Tracker Sheets. Referencing the old levels, but still with many useful questions, Levelopaedias provide exemplification and probing questions for each of the assessment criteria except ‘Using and Applying’. See also the ‘Convinced’ package which is a resource package based on the assessment criteria from Levels 4 to 8. The levels are no longer relevant but the questions are still good questions! Each set of questions includes a self assessment for students.
Various nrich resources such as the excellent curriculum mapping documents which link topics to nrich problems and an article by Jennifer Piggott which addresses the use of NRICH resources to support assessment of progress.
Exemplification examples: these illustrate what pupils should be able to do within a particular strand of objectives by the end of each year.
CIMT have diagnostic tests available for the Year 7, 8 and 9 resources, also Revision tests available for GCSE. Most resources from CIMT are freely available, just a few, like these tests require a password.
See for example the Year 7 Course Material page and note the Diagnostic Tests available for each section.