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Tasks are not games - they are the starting points of investigations. All tasks in the collection have been well trialled in the classroom; some for as much as two decades. They are fun, but that is not a sufficient condition for including them in the collection.

This page describes the principles behind choosing and using tasks, managing tasks in the classroom and maintaining a healthy place for them in the curriculum.

Red Square  Choosing & Using Tasks

Red Square  Daily Management

Red Square  Sustaining Curriculum Shift

Task 2, Cars in a Garage

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Choosing & Using Tasks

Selecting or creating a good task and then making best educational use of it is based on these principles:
  • The task is intrinsically motivating.
  • The task provides hands-on materials to support its solution
  • The intellectual challenge is likely to result in a first level of success in 15 - 20 minutes.
  • The problem on the card is the tip of an iceberg; the beginning of a deeper investigation.
  • The task has three lives:
    • as an invitation for two students to work like a mathematician
    • as a whole class investigation to model how a mathematician works
    • as a deeper investigation led by an Investigation Guide.
  • The task can be used to illustrate the process of Working Mathematically
Task 166, Sphinx, has been made available in full detail to illustrate these features. You are invited to investigate it to learn more about the project. But be warned ... you might get hooked!

Also, the Iceberg Information about Task 184, Reverse, extensively embeds the text in the context of learning to work like a mathematician, and each Task Cameo suggests both iceberg questions and how the task could be converted to a whole class investigation.

Principles of Daily Management

Task can be used in many ways, organisational structures and unit plans. Explore some suggestions in our Integrating Tasks link. However in whichever way they are used, a key to success is training students to:

C... ount the materials as soon as they open the bag or box and again when packing up.
R... ead through the whole card to make sure it's all clear.
T... ry what's on the card using the Working Mathematically process as a guide.
R... ecord important information in an informal personal maths journal.
A... sk anytime - first your partner, then a classmate, then the teacher.

You might like to make a chart to display this routine for students.

For yourself, remember to pack up 10 minutes before the end of the session:
  • 5 minutes to check and collect material
  • 5 minutes to share and reflect on problems tackled today

Sustaining Curriculum Shift

School mathematics is about students learning to work like a mathematician in fascinating, captivating and absorbing classrooms.

Tasks are a vital component of this learning because they are rich in both content and pedagogical opportunity. But, just putting tasks in front of students is not a solution for anything.

Mining the depths of their richness takes effort. Teachers, students, school leaders and the school community may all need to reconsider their views about mathematics education.

Working with tasks

Such curriculum shift relies on clear, committed personal and departmental planning and the continuing support of school leaders, particularly in providing on-going time for collaborative planning and funding for professional learning and resources. The effort and time involved in shifting to an evolving Working Mathematically curriculum needs to be nurtured and nourished to be sustained.

  • What can we learn from successful schools about continuing, purposeful core use of a Task Library?

The following seem to be the key elements:

Accept and publish a framework for your teaching. Know why you choose to use tasks as part of the curriculum and why you choose your particular model(s) for using them. Are your students learning to work like a mathematician or just trying to reproduce the skills of a mathematician?

Ensure that the administration, kids and parents are clear about your curriculum's purpose. By default, requiring students to purchase a text book is a statement of your framework. An alternative begins when everyone recognises that these tasks contribute to learning to work like a mathematician because they represent an invitation to work on a problem ... and trying to solve interesting problems is a mathematician's work.

Tasks have three lives. Feature the use of tasks in all ways in the written syllabus material. Reinforce the framework and make the 'when and how' of use clear.

Build on the metaphor that a collection of tasks is as important to numeracy as a collection of books is to literacy.

  • A student (usually pairs of students) can select a task from the shelves to explore, extend and enjoy for themselves.
  • Equally a teacher can select the same task from the shelves to use with the class for all to explore, extend and enjoy together.
One learns to love literature/problem solving through a balance of both invitation and modelling.

In-coming teachers (...and students and parents) need to know why and how you are using tasks. Make time to work with them on understanding tasks and the principles and practice behind their use. Introduce them to the Mathematics Centre site.

One way to do this is by integrating Maths At Home activities into the curriculum, perhaps as part of a homework programme. Several of the activities include investigations from the Task Library. All of the activities are explicit in their focus on the Working Mathematically framework.

Keep the framework and documentation in front of the school population.

  • Learning to work like a mathematician is beyond just learning mathematics. It is learning mathematics in the context of how all mathematics content developed. The context of interesting problems. Refer to, and use the language of, the Working Mathematically page as often as possible with each other, students, school community and school leaders.

    How might a mathematician start this problem?
    What questions might a mathematician ask now?
    What maths skills do we have in our toolbox that might be useful here?
    Which strategies in our strategy toolbox could we try?

Look for and celebrate student success. For example, our Sphinx Album celebrates the work of many students and teachers, and you will find more in our Recording & Publishing Album.

  • Consider using:

    ...the school newsletter and/or web site,
    ...relaxed but purposeful 'maths nights',
    ...maths displays in hallways and public areas,
    ...a borrowing system for tasks to encourage Maths Around The Kitchen Table.

Don't just talk about the Working Mathematically principles detailed in your framework. Build in appropriate assessment to show how kids are in fact learning to work like a mathematician. See models, methods, tools and examples in our extensive Assessment page.

Build in-house and external professional development into your regular professional learning program. Show each other kids' work. Play with some tasks together.

Make a feature of new tasks added to your collection and familiar tasks extended, or developed into whole class lesson explorations. For example, Task 116 Who Owns The Monkey? is in our collection because it was included in one school's collection after a pupil found it in a magazine. Change displays you put up last term.

Visit other schools with a similar approach. Have a coffee, take a tour, share some teaching, have a chat.

Over time these actions become integral to the way mathematics education is seen in the school. A new corporate memory begins to develop - a memory that mathematics education is learning to work like a mathematician, rather than the more common default of just doing maths.

And you don't have to do it all yourself.
Re-inventing the wheel is inefficient.
Maths With Attitude kits are a collection of years of teachers' work designed to support you with framework, structure, content, assessment and professional learning in a week by week program. In fact 25 weeks of unit plans for a Working Mathematically curriculum for each and every year level from 3 to 10.

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More from the Mathematics Task Centre