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What teachers said about the tasks they set
| Mathematical learning purpose | Task/tool/resource types | Motivational/engagement | Contradictory comments |
|---|---|---|---|
| Learn how to tackle complex tasks | Structured multistage tasks, maybe with redundant information. Talk about methods; reflect on methods | They need help to step out of the comfort zone; it gives a 'buzz' to have achieved something hard 'Resilient mathematicians' make lots of mistakes |
Low attaining students need more structure They are not used to doing such tasks |
| Promote thinking Play with concepts from a variety of directions Develop generalities |
Complex tasks; exploratory tasks with identifiable focus; tasks that require a mathematical generalisation Tasks everyone can get started with Tasks that encourage open, divergent, thinking |
Include everyone's ideas, work with others, get involved, experiment Get a sense of key ideas Take ownership because they have figured things out for themselves Understand connections because they have made them |
Takes too long, 20 mins to get started on open-ended work They don't like to experiment |
| Consolidate 'basic' skills Work reflectively on own Develop memory and adaptation |
One-stage tasks Mental maths Typical textbook exercises Students present a mini maths lesson Use them in context of something harder |
Feel secure Feel expert |
Cannot recall when I last used a textbook Need to rewrite textbook questions as they are too dense |
| Introduce new ideas based on familiar mathematical knowledge Challenge and extend existing ideas |
Challenging questions Show some contradictions and ask 'what now?' New mathematical contexts for old ideas Can you make a...? |
Feel good about being able to use what they already know They get excited when I show them that what they have worked out sometimes turns up on tests, or in later years |
I have to simplify things for them |
| Memory, fluency, speed accuracy | Rehearsal/repetitive tasks Pub quiz; bingo; team games |
Everyone can be included | Have to provide easy ways to remember |
| Let me know what they can do Adapt knowledge |
Here is the answer, what could the question be? Give me an example of... Tell me what you know already about... |
Puts them in control; lets them know you care about what they already know | I give little tests often to find out what they know |
| Compare multiple ways to do things Express ideas Expose contradictions |
Compare methods and approaches Whole class discussions Debates: who thinks this, who thinks that, why? |
Pair work, team work, valuing all ideas, include lots of students Become more confident with expressing ideas, and more able to take risks Use board to display range of ideas |
I give one way to do things or they get confused. Group dynamics are a problem |
| Make connections and see what maths means | Use maths questions arising from other subjects Use maths questions arising from artefacts from outside school, e.g. shops, newspapers, games Ask for reasons |
Gives me insight into their lives Connects with who they are outside the classroom |
|
| Words, writing and language | Focus specifically in writing and recording what you think - use writing frames Repeat forms of language, e.g. 'if I ... would it ...?' and '...because ...' 'why...?' Wordsearch technical terms; "Give me maths words beginning with (letter)" |
It is easier to record because you need to than report because you have to | |
| Learning how to do test questions | Reading question and writing answers | Success in tests (we hope) | Need help with reading |
