Tasks and Their Place in Mathematics Teaching and Learning - Part 1

By Back, Jenni; Foster, Colin et al. | Mathematics Teaching, January 2013 | Go to article overview

Tasks and Their Place in Mathematics Teaching and Learning - Part 1


Back, Jenni, Foster, Colin, Tomalin, Jo, Mason, John, Swan, Malcolm, Watson, Anne, Mathematics Teaching


Jenni Back, Colin Foster, Jo Tomalin, John Mason, Malcolm Swan, Anne Watson consider the format of tasks and what changes have the potential to optimise the outcomes for both teacher and learner. You may want to read part 1 in MT231 before continuing.

Every summer, John Mason, Malcolm Swan and Anne Watson run a residential four day workshop called the Institute of Mathematics Pedagogy. Up to 25 people, teachers, educators, and researchers meet and work on a theme about teaching and learning mathematics. Part 2 [Part 1 was published in MT231 November 2012] continues to follow the theme 'ïnkering with Tasks'. The group worked together to consider how tasks might best be presented to optimise the learning opportunities and outcomes for all learners.

Tinkering with Tasks

This article follows on from the earlier exploration in Part 1 concerning the place of tasks in teaching mathematics, and draws on the work of the Institute of Mathematics Pedagogy held in Oxford in July 2011. We spent a great deal of time at the meeting looking at why and how we might adjust, develop, restrict, and open tasks and this article presents this to you.

As Colin said:

I came to the Institute thinking that tasks are one of the most important elements of what happens in the mathematics classroom. I still think that, but would qualify it by saying that how a task is used is much more important to me than the precise details of the task itself. I have seen mathematics teachers 'mine' great lessons out of what had appeared to me to be pretty uninspiring material, by using it to provoke discussion and inviting learners to critique and change it.

Why tinker?

There are a range of reasons we identified for 'tinkering' with tasks and the phrase captures some of the sense of playfulness and fiddling that goes with the activity of adapting resources to use with students in the classroom.

The group suggested the following reasons for such 'tinkerings' to make the task:

* more accessible

* deeper/richer

* include a surprise

* include more variety

* open up opportunities

* access different maths

Colin commented on the process of preparing to work with a specific task in the classroom:

'When looking at a potential task to use in the classroom it is nice to anticipate problems that learners might have yet not necessarily to try to eliminate them, but work on ways of supporting learners through the difficulties. For me, a task can only ever be a starting point, and soon after offering it to learners I find them doing things that I had not anticipated. I often find myself wondering whether I should 'bring them back to the task', like a politician who is failing to answer the question, but then why should I prioritise my agenda over what the learner is finding more interesting? I think I am growing to trust learners more to take what they need from a task. Human nutrition is immensely complicated, yet most of us believe that if we eat a sensible amount of a wide variety of foods, our bodies will naturally take the nutrients they need in the appropriate amounts. To try to plan for every vitamin, for example by giving each one separately, would be impossibly complex, and mirrors for me what happens when micro-learning objectives assume central importance in the classroom. If I offer learners a rich variety of mathematical experiences, perhaps I should trust them to take what they need from each in the quantities that they can handle at that time?'

Genres

Malcolm introduced us to five different genres of tasks that he has identified:

* Evaluating mathematical statements, where students are presented with an assertion that they have to exemplify or refute providing justifications and proofs. Always/sometimes/ never true activities are of this type.

* Interpreting multiple representations, where students interpret and translate between different forms of equivalent information. …

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