News

Current News In this edition of the News you will find:   Teachers Are The Best Resource   Student's Cube Tube Video   Something New in Eric The Sheep   Choosing Teaching Craft   Get to Know a Cameo      ... Window Frames      ... Have A Hexagon Please feel free to distribute this information.

Email News Services If you would like to subscribe please send an email request to: doug@blackdouglas.com.au: In the subject line write Subscribe Maths. Add your name and preferred email address. Mathematics Centre eNews is published two or three times per term through the school year. Working with Mathematics Centre (PDF) will help you find your way around our site. Browsing Hint Use the View/Zoom options of your browser to 'move' the page closer or further away. Ctrl +, Ctrl - and Ctrl 0.

• Teachers Are The Best Resource

  Teachers are the best resource in a school community... This quote is from Task Centre Project Consultants' Newsletter, No.2, January 1994. Yep, thirty years ago. (See Link List below.) There is a direct, unbroken thread which links that two page printed and posted document to the eNews you are reading at the moment ... and in that time our opinion on this point has not changed in any way. In fact, you will find it restated in the list of attitudes on page 2 of any Maths With Attitude manual.

  Task Centre workshop day.

  Twenty years before Newsletter No. 2, January 1974 - yep, fifty years ago - Neville de Mestre returned to Australia with an idea generated by a visit to the Stapleford Mathematics Resource Centre, UK, during his 1973 study leave at Cambridge University. It took three more years, and the full-time assistance of teacher Bea Duncan, for the idea to be realised as a set of 100 tasks in a school room dedicated to inviting students to get involved in hands-on problem solving.

  ...we opened the doors to our first class of 8 year olds in March 1977. There were six teachers, three parents and 25 children in the room, and I spent the whole time keeping the teachers and parents away from the tasks that the children were attempting. It didn't take me long to realise that these tasks were for primary, secondary and adults too.

  This is how the first maths centre for 8 to 80 year olds was born - and it was good!
  From How Task Centres Began, (see Link List below).

  This was the first Task Centre in the world - a uniquely Australian concept - and it operated for 15 years before government support was finally withdrawn. It was visited by many teachers and students from many parts of the country, some of whom followed up by creating their own Task Centre. They used their own materials and tasks they had seen or could discover in books by Neville and Bea, or in other mathematics education sources.

  There is a direct, unbroken thread which links those first Task Centres to the eTask Package currently available to help teachers work together to build their own Task Library for flexible use in their schools.

  A 'homemade' task from the 80s. This is still in the eTasks as Task 68, Six Square Puzzle.

  A network of enthusiastic 'Task Centre teachers' grew from these early experiences and a body of classroom-based wisdom developed to integrate tasks in a variety of ways in addition to the original model. In 1984 - yep, forty years ago - Michael Richards was one of these teachers and in 1995 he wrote a Ten Year Retrospective view of his decade integrating tasks into his teaching. This is how it begins: Pre-Task Centre Teaching Prior to 1984 I had taught in the traditional mathematics manner. That is, I encouraged silence at all times; I explained mathematical concepts from the front of the class and with the aid of the blackboard to write examples of relevant problems;

  the students copied the examples, then tried to replicate my method on other problems listed in their text book. I taught in this way because I believed that my job was to pass on mathematical skills and standard mathematical applications to the students. I tried hard to explain things clearly and reasoned that if I could explain the maths ideas as simply as possible, and in a way that made sense to me, most students would be able to understand my explanations.

  Remembering the boredom of mathematics classes in my school days, when opportunities arose, I would try to 'make maths interesting'. These efforts took the form of collecting and using everyday examples of mathematics, organising 'maths games days' and offering an elective subject of geometric constructions.
  From A Ten Year Retrospective

  The next heading in this article is Maths Task Centres and their attraction to me in 1984. See Link List below.

  Curriculum Corporation was established at the beginning of the 90s by the Ministers of Education of Australia. With Charles Lovitt's leadership, its Mathematics Professional Services (formerly MCTP) took up the challenge to collect and distribute stories of excellent mathematics education. In 1992 Mathematics Professional Services turned to Task Centre teachers to collect their stories under the auspices of the Mathematics Task Centre Project. Designed to disseminate this wisdom to a new school, the first Task Centre Project workshop was held on July 1st 1992. That led to (a) developing and providing an initial set of tasks to get schools started, and (b) gathering and resourcing more consultants so more workshops could be run in more places.

  Over 100 schools were serviced through 1993 and about one third of those purchased the tasks with a workshop day. There were at least a dozen consultants across the country. Which brings us back to the quote above from the Consultant's Newsletter which continues with:

  ...and this project seems to have captured all the elements which bring together the ingenuity, organisation, team work and teaching experience of a staff.

  There is a direct, unbroken thread which links these experiences to the support Mathematics Centre currently offers teachers throughout the world in its collection and retelling of success stories from classrooms.
  Do you know any other mathematics education initiative with a fifty year influence?

  Digger deeper into the history through the Link List below:

  • Short version:
        Background section of What is a Task?
  • Medium version:
        Short version + History link on that page, then the Moments from History link.
  • Long version:
        Short version + History link on that page + all the A Sense of History page including links.
  • Research version:
        Long version + all the eNews issues at the bottom of the Current News page from October 2001 to the present.

• Student's Cube Tube Video

  The Year 9 student who produced this video titled it Multiplication with Poly Plug. It is appropriate for Years 5 - 9 (and probably other levels). She discovered the problem herself outside school, had it hanging around in her mind for three months or so, then one day started explaining it to her friend in algebra class. After school that day she arranged for the video to be filmed at home the next day.

  We are delighted to present this piece of self-directed learning which grew from playing with Poly Plug. It is full of multiplication, that's true, but it is also an algebra adventure involving seeking and seeing patterns, explaining the pattern, generalisation, triangle numbers and a quadratic function.

  You probably know about Triangle Numbers, but I think you will find at least one thing in this 10 minute video that you haven't seen before. See Link List below.

• Something New in Eric The Sheep

  The July 2010 eNews records Damian Howison's excitement when he looked at the contribution to the Eric The Sheep task cameo from Year 5 at St. Edmunds Junior School, UK. Interesting, because Damian teaches Years 7 - 12. The news provided a link to Eric, so anybody who read that edition was able to discover how student recording in Year 5, half a world away from Damian's school in Swan Hill, Australia, inspired this secondary teacher to see a new way of solving the problem. However, in the 14 years since Damian's contribution no one has been able to see it unless they happen to read that particular news edition. At the time I should have also added his inspiration to the Eric cameo. Better late than never, that has now been done. Even if you think you know Eric The Sheep back to front, you can return to that cameo, see Link List below, and find something new in Eric The Sheep.

  You don't baaa-ter with me. If I want to get to the front, it happens.

  Eric has always been a popular problem across primary school and junior and middle secondary years. This is reflected in the fact that as well as the St. Edmund's contribution it includes student work from a Year 1 in a USA school and a slide show report by two Year 7 girls from Hillston Central School, New South Wales.

• Choosing Teaching Craft

  Since the evolution of Mathematics Centre into its current form through 2010, with its logo first appearing in the July 2010 eNews, its published charter has been: All students can learn to work like a mathematician in classrooms engineered to fascinate, captivate and absorb learners. Long before that we recorded successful teaching craft strategies evidenced in classrooms as the checklist you see in the image. In workshops, this is used to review activities through the lens of learning features likely to help engineer this type of classroom. Post workshop, teachers are encouraged to use this checklist and the Working Mathematically page (see Link List below) as planning tools for their lesson sequences. This is long way from the pre-1984 preparation and execution of teaching described by Michael Richards above. Teachers often comment how useful it is to be reminded of the many strategies proven to be useful in developing quality mathematics learning. In part because the list helps them avoid missed opportunities. Perhaps you could use the Learning Features page together with this eNews edition as a mini-workshop in your next team time.

  See Link List below to print the PDF version.

  Each of the few activities mentioned in this eNews links to more information. Choose one, or perhaps separate into pairs and assign one to each pair, then dig deeper, review their potential against Learning Features and/or Working Mathematically, discuss, share, plan.

  For example the new video, which is only 10 minutes.

  • Clearly student ownership was critical in the learning displayed, but what other features are likely have contributed to the learning?
  • In what ways does she show she is learning to work like a mathematician?

  Similarly for:

  • Task 4, Window Frames
  • Task 28, Plate Triangles (the same mathematics as the video)
  • Task 45, Eric The Sheep
  • Task 53, Have A Hexagon
  • Task 68, Six Square Puzzle

• Get to Know a Cameo

  Task 4, Window Frames
  

  The task supplies a 0-99 number grid and several 'window frames'. Each frame is made of panes, some of which are clear. The pattern of clear panes is different in each window frame. Placing a frame on the grid selects a particular subset of numbers to explore. What can be found out? Do the same discoveries apply if the frame is applied to a different subset of numbers? Would the discoveries apply to any subset of numbers selected by the particular frame. Make and test hypotheses. That's the essence of the task. So much to discover ... and what happens if the grid changes shape? ... or becomes the 1 to 100 times tables chart?

  In the eTask Package this task is in the 'more work' set because it requires extra printing, one page of which is on clear plastic.

  Task 53, Have A Hexagon
  

  There are 18 different products that can be made by choosing a number from each of two cube dice. These have been placed into the 18 sections of three hexagons. Players choose a hexagon to be 'theirs'. Players take turns to roll the dice, evaluate the product and mark the appropriate cell, wherever it is on the hexagons, by placing a counter beside the product. Multiple counters may be placed if that's the way the dice fall over time. Each of the boards has six numbers and both players are using the same dice, so the game is fair. Right?? Fair meaning each board has an equal chance of being covered first.

  The investigation begins by testing the fairness of the way numbers have been assigned to the hexagons, and continues with the challenge of finding - and convincing someone else that you have found - a fairer way.

  In the eTask Package this task is in the 'easy to make' set because it only requires two dice, a few counters and printing.

Link List Consultants' Newsletter No. 2 How Task Centres Began Michael Richards' Retrospective What is a Task? A Sense of History eTask Package Six Square Puzzle Maths With Attitude Multiplication with Poly Plug: Student video Year 5 - 9 Poly Plug Eric The Sheep Learning Features Working Like a Mathematician Window Frames Have A Hexagon Maths At Home Task Library Task Cameo Library Task Cameo Content Finder Calculating Changes Calculating Changes Content Finder Calculating Changes Year Level Finder Working Mathematically with Infants Picture Puzzles Order Form Did you miss the Previous News? If so you missed information about: What Teachers Say Calculating Changes Activity ... Visual = Number Get to Know a Cameo ... Soma Cube 1, Magic Hexagon

Did You Know? You can Search Mathematics Centre. Our Site Map acts as a Table of Contents to help you find what you need in Mathematics Centre. You can find photos of every task using the Task Library. You can find tasks by content using the Task Cameo Content Finder. You can create your own Task Library in a professional learning context with the eTask Package. Calculating Changes offers Content Finder & Year Level Finder tools. You can find tasks coded by Year Level and Curriculum Strand in the Task Centre Catalogue. (PDF file) You can search for lessons by Year Level, Curriculum Strand, Lesson Features & Keyword at Maths300. You can connect Tasks to their Maths300 companion lesson using Tasks & Maths300. (PDF file) Excel version provided by Pymble Ladies' College also links each Task to its Maths With Attitude content strand. All these links, and more, appear in Working with Mathematics Centre. (PDF file)