Bloomin’ Mathematics

 (checked & updated October 2016)

It seemed that everywhere I looked today I kept finding Kathy Schrock’s ‘Bloomin’ Google‘ where she has categorised Google tools according to Bloom’s revised taxonomy. Her blog post explains its origins.

My Digital Tools blog has information on Bloom’s taxonomy, in particular the digital version of the taxonomy which accounts for the new technologies and the processes and actions associated with them.

Thinking about the different levels of the taxonomy is useful when planning questions for students. So often questions relate only to the lower order thinking skills.

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.

blooms-questions
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).
probing-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!

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.

Underground Mathematics
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?