News

May 2022 In this edition of the News you will find:   Developing & Sustaining Corporate Memory   Free Play to Start the Day   Get to Know a Cameo      ... Mirror Patterns 2      ... Area Of A Triangle Please feel free to distribute this information.

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• Developing & Sustaining Corporate Memory

  Samantha Pinkerton, St. Aloysius College, Tasmania, was clearly looking forward to receiving her eTask and Maths With Attitude order when she contacted us recently.

  I am really excited to be working with your brilliant resources again after using them at MLC in WA for many years ... The team is very excited to implement them as part of our new programs next year and we plan on using a few for practice this year.

  Samantha and the team are beginning a curriculum shift.
  They can identify features of their current curriculum and have a shared vision of the features they want to move towards.
  Their curriculum is currently    here    and they want to shift to    --->    here.

  Curriculum shift is something we have all been involved in - often with great enthusiasm. We discuss, research what other schools have done, experiment with what we are reaching for, plan, make a case for administrative support, execute, evolve and refine. There's success, often informed by student attitude change and teachers feeling more satisfied with what's happening in the classroom.

  Many of us have also experienced curriculum shift decline, or even disappearance. Three, five, or seven years down the track there is little or no evidence of the success and enthusiasm that was.

  • We used to do it like that but...
  • Yeah we tried that a few years ago. I don't know where the stuff is now.

  We can list many reasons for the falling away, but what's the point. New official requirements, leadership changes, new school-wide thrusts, staff moving on, funding decline and more are always going to be part of the quicksand foundations of education. They are largely external and more or less need to be lived with. It could be that the more difficult problem is the default corporate memory of mathematics education.

  When the external forces impress and successful curriculum shift is wobbling, is the corporate memory of the recent demonstrated successes, or does it default to 'how maths used to be taught'?

  Our short article Sustaining Curriculum Shift (see Link List below) continues this introduction with guidance gathered from schools successfully shifting towards a mathematics education focus of learning to work like a mathematician. It is written in the context of exploring the pedagogical and content richness of a Task Library. Its principles may also applicable to other visions.

• Free Play to Start the Day

  The colour, texture and 'poppiness' of Poly Plug are so inviting that children just want to start fiddling with them. There is never any problem with children thinking of something to do with the resource, but what will you do with what they do with their Poly Plug? Free Play is a Calculating Changes activity which supports teachers to think on their feet when children say Look what we made.. The example below is from this Year 3 class. The questions listed are some that could be asked about the children's creation, but they weren't all asked by the teacher of this class. The same activity could be used at any primary level and the questions you ask will depend on which level and the children with whom you are working.

  Possible Questions/Challenges

  How many plugs in each row? Count by fives for me. How many plugs altogether? Teach your calculator to count by fives. Does it get the same answer? Suppose you both made a board like this. How many plugs would there be altogether? Suppose everyone in the room made a board like yours. How many plugs would there be altogether? How many blue plugs would there be in the room? How many yellow ones? Can you check your answer another way? Suppose the board is worth $1. How much is one row of plugs worth? How much are the yellow plugs worth? How much are the blue plugs worth?

  • Do you notice that the rows are all equal. Tell me how many equal parts are made by the rows. Tell me the fraction name for one row of the Poly Plug board.
  • What fraction of your Poly Plug board is blue? ... yellow?
  • Write me an equation about two fifths and three fifths.
  • If four people made boards exactly like yours and put them together, what percentage of the plugs would be blue? ... yellow?

  Free Play is a recommended activity in Working Mathematically with Infants (see Link List below). Calculating Changes Members can access the full text of the activity through Link List below. Others can explore more activities from the Calculating Changes Free Tour in Link List below.

• Get to Know a Cameo

  Task 159, Mirror Patterns 2
  

  This intriguing task is so clearly spatial and non-threatening to start with. All the students are asked to do is figure out where to place the mirrors to make the requested polygons. However this invitation to trial and improve immediately throws up the geometry of symmetry, properties of polygons, investigation of angles and transformation experiences. Partners are talking maths almost instantly. Before long it becomes clear that a key variable is the angle between the mirrors and that opens the door to measurement, number patterns, algebraic generalisation and more. The easy to state, easy to start nature of the task and the depth of its content is what gives it a place in any curriculum from Year 4 to Year 10.

  The cameo clearly explains the deeper mathematics and is enriched by an Investigation Guide and photographic prompt sheet contributed by Damian Howison, St. Mary MacKillop College, Swan Hill.

  In the eTask Package this task is in the 'more work' set because you need to hunt out two small identical mirrors (ask the science teacher perhaps) and a protractor and print, laminate and trim two extra sheets.

  Task 187, Area Of A Triangle
  

  Students play with the pieces in colour sets to make three triangles. Then they measure lengths and choose their own way to calculate the area of the triangles. They don't need to know a formula in advance, however, the Challenge does encourage them to discover such a rule for themselves. It is designed to help students discover that the area of a triangle is the same as the area of a related rectangle. Then to discover how the two shapes are related. A formula may or may not emerge, but it is common for students from upper primary onwards to be able to demonstrate and vocalise the interconnection.

  The cameo links to an 11 second Cube Tube video from a Year 5 student who demonstrates that this claim is true. The link also supplies an Investigation Guide based on the video that leads students towards discovering the triangle/rectangle relationship.

  In the eTask Package this task is in the 'special' set because it needs three different shaped, colour-coded triangles dissected in a particular way. The necessary files are supplied but will the user decide to make the triangles from laminated card, or from crafted wood like the ones in the photo?

Link List Sustaining Curriculum Shift Working Like A Mathematician eTask Package Maths With Attitude eManuals Free Play (Members) Calculating Changes Free Tour Working Mathematically with Infants Mirror Patterns 2 Area Of A Triangle Task Library Task Cameo Content Finder Calculating Changes Content Finder Calculating Changes Year Level Finder Order Form Did you miss the Previous News? If so you missed information about: A School Without Tasks... Learning From Homeschooling Calculating Changes Unit Plans Working With Mathematics Centre Get to Know a Cameo ... Same Or Different, Two Squares

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)