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Principles

Tasks are not games - they are the starting points of investigations. All tasks in the collection have been well trialed 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  Continuing Use


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

Principles of Continuing Use

Tasks can be far more to the mathematics curriculum than a resource used once in a while. They are a vital component of a curriculum built around students learning to work like a mathematician.

Mining the depths of the mathematical and pedagogical richness built into these tasks does not happen by accident. It relies on clear and committed personal and departmental planning. What can we learn from successful schools about the ongoing core use of tasks?

The following seem to be the key elements in building continuing success:

Working with tasks
Framework
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.

Document
Feature the use of tasks 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 can select a task from the shelf 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.

Induct
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 the tasks and the principles and practice behind their use. Introduce them to this web site.

Communicate
Keep the framework and the documentation in front of the school population. Perhaps the most important way to do this is to look for and celebrate student work. 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 and relaxed but purposeful 'maths nights'. Maths displays in hallways can be very powerful.

Assess
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.

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

Revitalise
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.

And you don't have to do it all yourself. 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.

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