Integrating Tasks The photo reflects the original concept of integrating tasks by establishing a Task Centre Room devoted to practical hands-on problem solving in mathematics. Over more than three decades teachers have added many other ways to integrate tasks.

A task centre room - the original model.

Integrating tasks into the core of the curriculum is essential in order to get the best from the resource. This had been shown over and over again in schools from around the world. Typically integration begins in a small way, perhaps with a two or three week unit. Planning for success in this way develops enthusiasm in teachers and students which generates further planning, fresh approaches and, eventually, revision of the curriculum. Curriculum review using the Working Mathematically process, the process of learning to work like a mathematician, as a framework has been very useful to many schools. A young person learning to work like a mathematician might be compared with a young person learning to drive. The Learner Driver needs experience with a teacher who models how to drive well, and an invitation to practice the model for themselves. Similarly, a Learner Mathematician needs experience with a teacher who models how a mathematician works, and an invitation to apply the model for themselves. Tasks offer the invitation to students to work mathematically, and the richness for teachers to be able to build whole class investigations to model Working Mathematically. This page records some of the ways teachers have integrated these two uses.

Models & Structures A vital element of any successful curriculum planning is conscious, deliberate choice of teaching craft which encourages learning. Many teachers have found this Features Checklist helpful when planning. During the decades of Task Centre history, teachers have developed many models and structures for building curriculum around the three lives of a task. Some of these are: Maths With Attitude Mixed Media Model Replacement (3-Part) Unit Home/School Lending Puzzle Olympics Poster Problem Clinic Menu Maths Self-directed Maths Journey You are invited to continue this development by contributing structures, plans, models that are successful for you. Maths300 members can find more advice and examples related to constructing a Working Mathematically curriculum in their Curriculum Planning link.

Maths With Attitude

Mixed Media

• whole class lessons
• hands-on problem solving
• problem solving software
• skill practice worksheets (or text material)
• time to reflect on learning
• assessment opportunities

A vital element of the process is to reflect on what is learned and how it is learned before the final assessment of the learning. In general the structure is run for two weeks. The third week begins with a discussion lesson around the question: What do you know now that you didn't know two weeks ago?. Responses to this discussion guide teachers in rounding off the three week unit during the remaining sessions.

A Mixed Media unit can be constructed if there are tasks which relate to the topic and software that extends the topic. Check the Task Catalogue in the Documents link on the left to identify tasks for your content purpose, and Maths300 lessons and software which also relate. MWA Number & Computation Years 7 & 8 (see Resources), includes resources for 4 Mixed Media units constructed from these resources.

The Task Centre Project also markets an example of the model which is titled Points of View: Representing 3D Objects in 2D. You can find this kit in our Order Form - PDF file.

Replacement (3-Part) Unit

A Replacement Unit is structured around twenty hands-on tasks related to the strand being studied. These are listed on a menu. It also requires reproducible student worksheets to extend the tasks. The structure assumes that staff have arranged a Week Zero to familiarise themselves with the material and jointly plan how they will use it.

Week 1 - Introduction

• If this is the first time such an approach has been used it may be necessary to discuss the experiment with the students (...another step in our efforts to make learning mathematics a more successful experience for you...).
• In pairs, students select tasks and follow them through guided by the card. The menu is used to record the tasks tackled and journal entries can be used to record jottings as they work through the tasks.
• Teachers visit and interact with groups during the week - collecting informal assessment information and considering what the students' work suggests as the needs for the following week.

Week 2 - Formalisation

• Teacher-led lessons built on needs that have shown up in the previous week and also guided by the local curriculum objectives. These are whole class investigations which are often supported by Maths300 lesson plans. (See Web Sites link.)
• Given the requirements of Week 3, this second week will need to include a lesson on learning to write a maths report, if students have not had this experience.
• Assessment can be through short tests/quizzes or short-term homework assignments.

Week 3 - Investigations

• Students return to the menu and choose one task to explore for the week.
• They are guided deeper into the iceberg of the task using an Investigation Sheet.
• Assessment is based on an Investigation Report which becomes part of the student's Assessment Portfolio.
• Working in pairs but presenting separate reports is encouraged.

Replacement units have been successfully used as 'in-house' professional development programs masterminded by staff members. Units have also been used as the focus of district wide professional development with a particular focus on resolving issues of transition between primary and secondary schools.

Home/School Lending

Puzzle Olympics

Of course, you don't have to wait four years to use the idea again. Why not an Annual Mathlete Championship? Or adapting the idea to create an engaging parent night?

Poster Problem Clinic

Learn more about this teaching technique in our Poster Problem Clinic link.

Menu Maths

Choice. If students are to become the independent, autonomous learners we hope for them to be, we should start now. Students are capable of making their own choices about their learning. Moreover, they are enthusiastic about it.

Self-directed Maths Journey

Students are asked to choose their own activities within a limited, but challenging, mathematical landscape. It is just like being put into a broad, fenced environmental landscape and being given free reign to explore.

Each Self-directed Maths Journey (SMJ) is a loosely structured unit plan designed to encourage independent, self-directed mathematics learners. A feature is the development of mathematics in a language context - a model which helps teachers 'work smarter' by simultaneously achieving numeracy and literacy objectives.

Students keep a diary of their adventures and teachers encourage detailed entry in the diary by allowing sufficient time to write it. The diary has a dual purpose:

• In writing 'for an 'audience' students reprocess the work they have been doing and this helps to enhance learning.
• It provides a record that contributes to evaluation evidence.

The two week SMJ is prepared in the previous week, just as a journey into an unknown physical landscape is prepared beforehand. This occurs in two ways - by class exploration of problems which leave room for further exploration during the journey and by preparation of the diary.

Preparation of the Diary

In a mathematics session, introduce a problem (relevant to your curriculum objectives) that will need more than one session to explore its iceberg. Leave the investigation unfinished but with clear indication of the directions it can go. Explain that this investigation will be one of the activities to choose during next week's Self-directed Maths Journey.
(In the example below Bob's Buttons, Task 123, and Multo from Maths300 are used in this way.)

Follow up (in a language session?) with the concept of keeping a diary of the Self-directed Maths Journey. Collect examples of diaries from the library - literary diaries like 'Diary of Anne Frank', or professional diaries like that kept by Joseph Banks, the botanist on Captain Cook's explorations of Australia. Diaries/notebooks also feature in 'popular culture'. For example the father's diary is central to the plot in the film 'Indiana Jones and the Last Crusade', a movie well known to most students, and the film has several shots of the book showing text, sketches and maps. Note items like these as features of a diary and add others suggested by students such as the importance of dates and the possible inclusion of photographs. Encourage the use of the school's cameras to record significant mathematical moments. Consider also the possibility of an electronic diary if you are interested in achieving Information Technology outcomes in conjunction with mathematics and language.

Introduce the idea of a diary published for others, such as that of Joseph Banks, being prepared at a later time from notes taken at important moments. Perhaps use the image of a hiker travelling with a diary in their backpack and a notepad and pencil in their shirt pocket. The pad is used to record significant moments in the day and the diary is filled in later around the camp fire.

Provide 'provisions' for the SMJ:

• small spiral notepad (or equivalent)
• a more substantial book to use as the diary
• an outline of the mathematical landscape, such as the example below from MWA Number & Computation 5/6
• the Working Mathematically process page

Provide time to decorate and personalise the diary. The Working Mathematically process and the landscape page are placed in the front pages of the diary. Students are told that the next page is to be a Map Page and thereafter they record each day in text, drawing and photo as they wish.

The Map Page records each date and its activities in name only as a summary of the adventure. These items are arranged on the page as the student wishes and are linked with pathways and other landscape features in an imaginative way.

On The Journey

• Students work in pairs - it is usual to go on a journey with a companion - but keep separate diaries.
• It doesn't matter which order students tackle the activities, or which ones they tackle, or how many they tackle, or even if some activities are left started, but unfinished. What matters is that they demonstrate through their diary (and interview if you wish) how they have worked like a mathematician in each session.
• Some students may need help getting started because the range of choice may be daunting. In such cases, choose a hands-on task for them and sit down together to ask questions that will help them begin.
• Plan a compulsory teacher-led activity that students have to attend for a given number of sessions in the journey. These can be useful mini-tutorial times related to the problems, processes or skills of your chosen exploration area.
• Allow time every maths session to begin diary writing. Encourage students to work further on the diaries in their own time.
• Collect diaries regularly and annotate with encouraging comment and suggestions. Celebrate examples of student diary work that you wish to encourage in the group.

Following The SMJ

• Allow time to finalise diaries. Collect, read, comment and display.
• Ask students to prepare their own assessment of what they have learnt on the journey to add to any other assessment practice you use.

Self-directed Maths Journey II Mathematical Landscape Bob's Buttons: Search for a way to predict the pattern for any given pair of groups and left overs. The software will help your search. Multo: Search for the best way to arrange the numbers in the grid. The software will help your search. What's It Worth?: Make a puzzle card. What's It Worth?: Try someone else's puzzle card. What's It Worth?: Try some puzzles from the software. Screen capture and print the results for your diary. Tasks: 4 & 20 Blackbirds, Add The Pack, Bob's Buttons, Change, Doctor Dart, Making Fractions 2, Number Game, Peg & Tape Fractions, Pick A Box, Steps. From Text: Exercises... Compulsory: 2 Rod Mat Chats with your teacher. Place these items anywhere on your map page and as the unit progresses build the map of your mathematical journey.

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