- Professional Learning 2008/9
Our first Maths on the Move session for Semester 2 will be Learning to Work Like a Mathematician for staff of Moana Primary School, South Australia, on July 25th. With this MOTM booking and others related to Maths With Attitude, Task Centre Packages or Working Mathematically Curriculum Packs the diary is pretty full for Term 3, but there are still spaces in Term 4 for those who get in soon.
Maths on the Move offers a tried and tested library of 2 six day workshops and 15 one day workshops which all contribute to shifting your curriculum, at every year level, towards students learning to work like a mathematician.
Plan ahead to be involved, and especially consider the proven value of professional learning extended over time. Use either of the six day workshop sequences (one for primary and one for secondary), or consult with us to build your own extended course using a selection of one day programs. (See Link List below.)
Discussions with district, state and system leaders about these programs is especially welcome. We have considerable experience working in large scale co-ordinated programs and can offer evidence of their success.
- MAV Matters 1
The Mathematical Association of Victoria (MAV) and the Mathematics Task
Centre have been working together since 1996. At that time, Andy Wain, who
was leading teacher in a task centre at Rosebud Secondary College, suggested
to us that there should be a task centre site on the web, and, almost
simultaneously, the MAV asked us about including quality problem solving
experiences on its fledgling web site. We brought the two together and Andy
volunteered to manage what became known as the Problem Solving Task Centre (PSTC)
section of the MAV site. Later Andy spent some years as the MAV web master.
Since 1996, the MAV has expanded and so have we, including developing our
own Mathematics Task Centre site. Both organisations have always worked
together comfortably because both :
- work to support teachers through professional learning
- believe that mathematics education is about learning to work like a mathematician (Working Mathematically), not just practising the skills of a mathematician.
Recently Ian Lowe, MAV Professional Officer, approached us with a view to
rationalising the task centre information which, as a consequence of
history, is currently spread over both sites. Basically we want to make it
easy for teachers all over the world to visit one place and find all they
want to know about tasks, using tasks and professional learning related to
tasks. Changes will begin to happen soon. Much of what is currently on the
MAV site will find a new home here and the MAV will redesign its site to
provide links to the Mathematics Centre.
- MAV Matters 2
Continuing co-operation between Mathematics Task Centre and MAV has led
to considerable benefits for their members. Victoria has a state curriculum
(VELS) with a strong Working Mathematically dimension. Our Maths With
Attitude kits provide resources, planning documents and suggested teaching
craft to fulfil most of the requirements of this strand (and many of the
other objectives of the official curriculum) from Years 3 to 10. It just
simply made sense for the MAV to add some of its own resources to Maths With
Attitude and develop a complete set of syllabus documents addressing every
requirement of the curriculum.
So Victorian teachers can now access Working Mathematically in VELS: a
Maths With Attitude approach, and all the support resources including MWA,
from their professional association and be confident of addressing every
requirement of the state curriculum. (See the Link List below). And not a text book needed anywhere from Year 3 to Year 10!
If any other professional associations would like to offer a similar
service to their members, either Ian or I would welcome the opportunity to talk.
- New Tasks
Three exciting new tasks have just been released. That makes a total of 238. Our catalogue has been updated to include these and they have also been added to the Enhancing Maths With Attitude link.
Last October, Per Berggren, Trädgårdsstadsskolan Sweden, showed us a report by one of his Year 9 students into this problem. It wasn't a task at the time, Per had used it as a whole class investigation, but Helena's exploration of square and triangle number patterns within the stars convinced us it should be. Star Numbers satisfies all the key principles of selecting a task and can be tackled by both primary and secondary students. As always the card represents the tip of an investigation iceberg. For example, extension challenges could be:
- If I tell you any size Star Number, can you tell me the number of plugs to make it?
- If I tell you the number of plugs I have, can you tell me the largest Star Number I could make?
We have had to invent a new piece of equipment for this task. A Trisquare may look like a simple shape (perhaps that's its charm), but it leads into an amazing range of mathematical content. So much in fact that we have had to create two Trisquare-based tasks to capture just some of it. This task moves in the direction of perimeter and area after a challenge based around the mathematician's twin questions: How many are there? How do you know you have found them all? Iceberg questions for this task include:
- Can you find a 2 (or 4) Trisquare shape to represent every perimeter between the shortest and the longest?
- You are going to tile a floor with Trisquares. How would you lay them out? Is there more than one way?
Perhaps you have begun to sense a connection between Trisquares and Sphinx. Indeed, Trisquares do 'grow' in the same sense as Sphinxes, ie: 4 Trisquares make a Trisquare just like 4 Sphinxes make a Sphinx. Perhaps students have discovered this themselves while exploring 4-Trisquare shapes on the previous card. This task explores the growth pattern which develops from this special construction. The visual pattern that develops is matched by a numerical pattern and students begin to realise that if length increases by a factor of n, then area increases by a factor of n2. An iceberg investigation is:
- Jenny also showed she could make Size 5, 6, & 7 Trisquares. How many pieces would she need in each case, and how did she do it?
- Trisquares: Class Sets
The new Trisquares tasks are an invitation for students to work like a mathematician. Each one contains enough equipment for two students to investigate these problems. However, every task has three lives and the second of these lives is as a whole class investigation. If you would like to investigate in this way (and thereby model what it means to work like a mathematician) you will need more Trisquares.
Trisquares are now available as a set of 6 panels (108 Trisquares) for $88, plus freight.
Based on a class of 25, that's 4 per student to begin the investigation(s) and a few spares. Students grow Trisquares by combining with other students. Trisquares have been added to our Price List, see Link List below, and can be ordered using your school purchase order faxed to 03 9727 4644.
And the third life of a task? Each task is the tip of an iceberg and the third life kicks in when you write an Investigation Guide to lead students beyond the card and into that broader investigation. When using tasks as an invitation, Investigation Guides help to manage your support time because students have something relevant to continue with when they come to the end of the card. Guides can also be used in whole class investigations.
- New Maths300 Lessons
Our sister project Maths300 has released two new lessons. They have also been added to our Enhancing Maths With Attitude page.
Birth Year Puzzle
This popular puzzle offers many advantages. It shows the mathematical investigative process, has huge opportunity to practise basic skills, can develop creativity, offers 'point-of-need' opportunity for teachers and caters for mixed ability classes. The challenge is to use the four digits of your Birth Year in that order, and with any legitimate mathematical operations, to generate all the numbers from 0 to 100.
Tables For 25
This lesson explores the iceberg of Task 235. Working in groups, a context familiar to all students, is the focus of the lesson. Mr. Edwards begins his class of 25 by asking them to organise into groups of 5 at each table, with at least two boys in each group. How the table arrangements work out will depend on how many boys there are in the class altogether, which is what opens the door to a broad investigation and a personal project for each student.
- MacMurphy Strategy
During a workshop, Chris MacDonald and Joel Murphy (MacKillop College, Swan Hill) were working with Task 57, Two Squares. The task leads students towards discovering the rule for finding the difference between two squares. The task is spatially based, but Chris and Joel extended the number aspect of it and found a way to derive the rule by developing organised data and breaking the analysis of it into smaller parts. In other words, they worked like mathematicians. Their work has been recorded in the Task Cameo for Two Squares. See Link List below for the Task Cameo and for the Working Mathematically Process.
Also, while on Task Cameos, a couple of other thoughts from workshops have been added to the cameo for Task 12, Matching Cards. See Link List below.
- Tasks of the Month
Two new cameos this month.
- Six Square Puzzle helps to develop spatial perception and logical reasoning. It offers only a selection from the many found in literature and builds them into a theme by using the same starting point in each case.
- Tricubes is a challenge in 3D spatial perception for both students and teachers. It gives sufficient information for its solution through the isometric drawings, but a considerable amount of reasoning is needed to correctly interpret the diagrams.
Click a photo to access its cameo, or access all current cameos through the Link List below.
- Site Improvements
Have you noticed any? We hope so. There has been a lot of background work this month to try to make the site easier to use. You may notice little things as you explore, but two key items are:
- Navigation Bar has been redesigned so Task Cameos are easier to find.
- Site Map link (new last issue) is now available from every page with a Navigation Bar, which means it is never much more than one click away.
- Did you miss the May/June News?
If so you missed information about:
- Iceberg Information about four Tasks of the Month (Tasks 64 - 67)
- Announcement of our new site map
- Maths Mat in Sweden
- Maths300 in Cambodia
- National Maths Day at MacKillop College
- ...and more
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