I was recently asked for some tasks to use with KS3/4 that would help teachers work in a more 'open way'. I decided that it is not so much the task but the way of working itself that is vital. The tasks themselves are what comes after the way of working has been established. Have a look at what I wrote and let me know what you think.

In terms of working in 'this way', I have found that there are a number of intermediary steps required before specific tasks will be of any use. For a start it is important that you are constantly working with your class on 'becoming mathematicians' this can be explicitly stated to students and perhaps discussed. How would a mathematician approach this task? What would a mathematician do that is different from a non-mathematician? These questions, if used consistently and given enough time, can change learners perspectives about what it means to 'do mathematics'.

Other important shifts in practice would include how resources and tasks are used. A task that has the potential to be open and exploratory and interesting for learners can easily be undermined should the teacher fall into the trap of 'telling'. As soon as we are arresting initial considerations, discussions, attempts and ideas and replacing them with 'the way to do it' we might as well not have bothered finding the task. Unfortunately this will mean quite a few lessons where learners are frustrated: if they are used to the teacher being the person who tells them what to do they are going to be annoyed and upset. Some structure towards this way of working is thus needed.

I have found that the easiest way to work like this with a class is to do it from day one. Obviously you don't currently have this luxury (but you soon will!) so this might mean with your current classes building in 10-15 minutes at the start of each task a time where learners are going to try and make sense of the task themselves. You might refuse to answer any questions until then. After this time you could ask the class for any observations: what do they think about the task? What approaches are they considering? What vocabulary do they not understand? This discussion in itself could last another 10-15 minutes. Eventually you might get to the point where the period of initial consideration could last most of the lesson with very little input from you.

Beyond this it is important to find opportunities to empower the learners. Instead of giving them 10 questions all the same, why not give them two and ask them to write their method and then invent 3 more of their own...that way they can answer them and set them for other learners. They could even share them on the board. You will be surprised: learners will often think of far more challenging examples than you would have set them. I really believe that Nrich has more than enough starting points for you to explore with your class but I would say before you use them try them yourself...they are often quite tricky and require some getting used to. Support during this period is not an issue: in fact it is probably vital: what is important is how, over time, this support fades away.

Two final thoughts:

1. There is no such thing as a bad resource, just a bad use of a resource.

2. Don't think with questioning it is as simple as open questions - good, closed questions - bad. The task 'write me a sum with the answer 12' will be a lot less interesting than 'write me a sum which includes at least one negative and at least one decimal and has the answer 12'.

## 2 comments:

Your post very much resonates with the way I think about maths education, and "becoming mathematicians" is definitely at the heart of what we are trying to do at NRICH. You've captured the essence of what I was trying to do at the start of the video clip in this problem: http://nrich.maths.org/2293&part=note

Thanks a lot for this video Alison, I am going to share this directly on the blog! I use this problem in my book: Big Ideas...

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