News

2025 News In this edition of the News you will find: February 2025   The Year of Free Mathematics Centre What does free mean? Why this way? Pass it on April 2025   Seeds Have Begun To Scatter First responders Future firsts New to Mathematics Centre Video ... Maths on a Mat: 3 Generations Web Papers ... Two papers about teaching craft Rotagrams ... Discover their new home Antonio's teaching craft June 2025   Seek and Ye Shall Find Notre Dame Leads The Way Threading: a Learning Feature Worth Considering What is Threading? Evidence for Threading Beginning to explore Threading Your Links Will Break September 2025   Freeing Up Maths Education FMC Travels The World Learning From Last Century Algebra through geometry: the Geoff Giles way Which Resources Are Free in FMC?

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. Please feel free to distribute this information.

February 2025

The Year of Free Mathematics Centre

On or before December 1st this year, depending on interest, Mathematics Centre will be turned off.

From February 2025 the complete Mathematics Centre site and all digital resources are freely available. You only have to ask. If that's all you need to know, go to the Order Form now. If you want to know more, read on.

What Does Free Mean?

It means it's a gift. You receive free, the complete Mathematics Centre site to store on any computer or server, whether or not the storage device is publicly available on the internet, and all digital resources. Poly Plug and Rotagrams will still need to be purchased. The Order Form has all the details for both Free Mathematics Centre and the purchasable materials.

Free Mathematics Centre is provided to be freely used, shared, reproduced or distributed in perpetuity.

Changes have already been made to the live site to redesign the Professional Development link to focus on an extensive range of unique free DIY Professional Learning programmes. Also Calculating Changes has been modified to allow free access to the Members section. That's 75 new number sense activities (K-8) that most teachers have never seen before.

As detailed on the Order Form Free Mathematics Centre is an all or nothing gift. The whole is greater than its parts.

• The web site is rich on its own, but without the resources, which originally grew from teacher-expressed need, it offers much less practical, day to day classroom assistance.
• The resources without the web site are useful but without the web site do not have the extensive documented classroom-based, teacher-contributed wisdom which brings insight to their use.

Consequently, individual items are not available separately.

A small word of caution:
When you get your copy of Free Mathematics Centre, don't mess with the structure, for you know not what you do and it will break.

Why This Way?

Fifty-five years ago to the month, at Orbost High School, I taught my first mathematics lesson as a qualified maths teacher. As far as my grandchildren are concerned, I'm not sure about anyone else, I haven't yet taught my last.

However, over the past year or two I have come to realise there is an outside chance I might fall off the face of the earth sooner rather than later and I began wondering what would happen to all the wonderful collected stories, rich with classroom wisdom and, often surprising, mathematical content, held in trust in Mathematics Centre if I did.

Mathematics Centre exists to:

• encourage debate about teaching craft that fascinates, captivates and absorbs students in the process of learning to work like a mathematician.
• provide unique resources supporting teachers to build Working Mathematically classrooms.

This is a charter which teachers have shown, over more than 30 years, to be sufficiently flexible as a core curriculum planning and execution framework - in several countries and within the demands of many official curriculum documents - to produce quality learning, teaching satisfaction and success beyond what is normally expected or experienced.

As you weave through Mathematics Centre note the teacher names, the range of schools and where they are in the world. It won't take you long to find evidence to validate that claim. If you're one of those contributing teachers reading this, put your hand up now.  : )

I could turn the site off right now and get on with my next fifty-five years, but how would that support the teachers who use it right now (presumably at least some of the 2,000 or so subscribers to this eNews), or honour the 'share so all can grow' attitude of the hundreds of teachers who have contributed to the evolution of Mathematics Centre? I decided instead that I had to try to pass it on.

Pass It On

In early 2024 I approached the Mathematical Association of Victoria, wondering if they would accept the Mathematics Centre site and the business aspects of its resources as a gift. MAV was enthusiastic at first. Discussions and questions were rolling along positively, but at the end of the year I was informed that the decision was no thank you. Curiously that change of mind occurred after a claim from the Australian Association of Mathematics Teachers to some form of intellectual property right in the those few Mathematics Centre tasks from which some Maths300 lessons have grown. A claim that has been made by others in the past, then withdrawn.

No one owns the concept of hands-on problem solving tasks, no one owns the problems on which each task is based and no one owns the names of the problems. All this is part of the history and world of mathematics education. A history that is well documented on Mathematics Centre back to March 1977 and includes the pre-history that led to that moment.

It is only possible to copyright the layout, wording or format of any representation of the problems involved in a task. Anyone can take the same problem and create their own educational form of it, but no one can copy another's layout, wording or format in doing so.

When the discussions with MAV ended I was asked Could you gift it to someone else?. My immediate thought was there wasn't any other suitable organisation. However, with a little more thought the path became clear. What came from teachers, schools and the broader world of mathematics education could be offered back to teachers, schools and the broader world of mathematics education, but spectacularly enriched by the decades of input from others and the curation of Mathematics Centre.

Freely offered, easy to obtain, and with the invitation to keep passing it on to others. Sharing so all can grow. ... And then I could turn off the site.

Your copy of Free Mathematics Centre is waiting. Use the Order Form ... or contact me to make an appointment to come to our Bayswater North office with your USB. We could have a cuppa and a chat while the computer does the copying.

Keep smiling,
Doug.

If you love something set it free; ... Often attributed to Richard Bach, author of Jonathan Livingstone Seagull, but there is some doubt about the original. Look up the rest of the quote for yourself.

April 2025

Seeds Have Begun To Scatter

Free Mathematics Centre - a gift to you of this entire web site and all of its digital resources - has begun to spread around the world since the gift was announced on February 17th.

I would love to receive a copy. I have used your tasks regularly throughout my classes and always enjoy the challenges and thought-provoking discussion they promote.
...Ted, Western Australia

If you haven't read the original announcement above, best to do that now for background.

First Responders

Antonio Sánchez was the first person in the world to contact about accepting the gift of Mathematics Centre. Hello, I am a teacher from a small town in Spain (Murchante). I was browsing the internet and was intrigued by the "Maths with Attitude" papers. I didn't know that the resources had been made freely available to everyone until I clicked on the link to order form. ... I was wondering if there was any possibility of getting the content of the Mathematics Centre site from Spain. Teachers from outside Australia need to make contact first because postage varies from country to country. I wrote back to Antonio and explained the process. Within a day he had sent the appropriate amount by PayPal and the first Free Mathematics Centre USB in the world was on its way, arriving, as you can see in his photo, on the 6th of March. Read below about Antonio's fascinating approach to teaching. The first FMC to a southern hemisphere teacher went to Mitch Howard in New Zealand.

You might remember coming to Lincoln High School about 16 years ago? It was a great day and I know the people who were there still remember it fondly as a source of inspiration. ... I'm interested in the 'year of Free Mathematics Centre'.

A quick call a day or so later with card details and Mitch's copy of FMC was on its way to his current school.

The first Australian to receive a copy was Dr Paul Swan in Perth.

I hate the idea of good ideas being lost.

His copy was sent off at the same time as he was heading to South Australia to run professional development sessions. True to his word he told teachers about FMC and some have responded since. A few days later he included information about FMC in his newsletter and that has resulted in more sent off around Australia and overseas.

Thanks Paul. You help is very much appreciated by myself and the teachers receiving their copy.

Following these three there have been copies sent to USA, Denmark, Canada, UK, Netherlands and Sweden as well as several across Australia.

The opportunity to receive your copy remains open. Read the original announcement above then follow the directions on the order form. The process of entrusting Mathematics Centre to one teacher who passes it on to two more will ensure that this collection of classroom success stories is always available to teachers of future generations. There's a potential growth function involved here too. Virus mathematics put to good use.

Future Firsts

Which will be the first maths teachers association ... the first teacher training institution ... the first school system ... the first education department to include Free Mathematics Centre on their web site. Does it have potential to enrich debate about what makes great mathematics teaching and learning?

Comments such as those below, extracted from recent emails, suggest that there are many teachers who feel learning to work like a mathematician in fascinating, captivating and absorbing classrooms has currency within a wide range of official curriculum now and into the future.

• I happened upon your site by sheer luck. Your work here is amazing! There are so many great tasks. I look forward to using them. I teach special ed mild/moderate disabilities grades 3-5. Lots of the infant activities will be great to start and I think I can move them to some of the older activities as we go. (Alma, USA)
   
• I can't thank you enough for your amazing resources! I have been using them with my own children and recently have been running a homeschool math/science workshop and have been sharing the activities with even more children! (Johanna, Australia)
   
• The children do well in maths but their understanding of spatial reasoning is not as good as their understanding of other areas. I want to put together a sequence of learning for us to try and thought the resources you have could be useful. (Christine, UK)
   
• I've loved all of your workshops I attended over the years and have used so many of your activities with my high school classes. And Maths at Home was a life saver in 2020. (Ann, Australia)
   
• I am a relatively newly qualified maths teacher in Denmark, and yesterday I came across your wonderful collection of various math exercises for school children. (Hans, Denmark)
   
• Thank you for your generosity. This is very helpful especially to a newly certified teacher who wanted to encourage more thinking and less rote memorization. (Kamille, Canada)
   
• I am a math coach at an elementary school in North Carolina. I learned of your retirement from Dr. Paul Swan's email newsletter. Over the years I've used and shared many activities from your Task Centre. Your work has been far-reaching, and SO appreciated! (Alisan, USA)
   
• I love your article on Explicit teaching! (Margarita, Australia)
   
• My kids all attended a school that used your resources a lot. (Matt, New Zealand)
   
• (Thanks) ... for the training you delivered to a school I worked in some 15 or so years ago. Today, I still draw on that experience, and the subsequent experiences shared with the students as we rolled out the Maths Task Centres. It has shaped my practice and my personal values along with it. (Lizzy, Australia)
   
• We met about 20 years ago at a UK maths conference... I shared several reports (through Mathematics Centre) on lessons using the Maths Tasks. Since then, I'm back in the US, I have a PHD in maths education, and I'm working with gifted students in 6 schools as well as teaching at the local university. Throughout this time, I have used many of the task cameos with my students and also pointed my university students towards the activities as great examples of getting students involved in hands-on, brains-on learning. (Matt, USA)
   
• Thank you so much for sharing. I am a pre-service teacher, so I'm sure these resources will be very helpful for years to come! (Christine, Australia)

New to Mathematics Centre

Filmed at the 2024 December Conference of The Mathematical Association of Victoria, Eleni Pilafas, Matt Skoss and Doug Williams introduce teachers to the possibilities of whole body involvement in learning mathematics, using a variety of content at a variety of year levels. The finale involves the teachers acting out the working processes of a computer sifting a set of numbers into order from highest to lowest. This video is now available for staff discussion and workshopping on Cube Tube.

New Web Papers

Two papers added in the last month. Access them from the Web Papers section Index.
Both address:

• the value and importance of investing in teacher professional development.
• consciously choosing teaching craft from a broad palette of proven learning features.

Inquiry into Effective Strategies for Teacher Professional Learning
Text of a presentation and support papers presented to a 2008 Victorian Parliamentary Inquiry which argues that teachers are the best resource we have. It includes suggestions from teachers about what makes professional development effective.

Explicit Teaching: Opportunity or Opportunity Lost?
Originally published in the October 2024 edition of eNews, this article highlights how the technique of Explicit Teaching needs to find its place as one choice among a broad palette of proven learning features.

New Home for Rotagrams

The new world supplier for Rotagrams is now:      Objective Learning Materials      Contact John Lawton ... 0438 199 228 / jlawton@mathomat.com.au This information is included in our Order Form and Resources list. Designed by renown Scottish educator Geoff Giles in the 1970s, a Rotagram is used to explore the concept of angle and develop and explore various angle theorems, without the use of a protractor. The focus is on angle as a geometric entity, rather than its measurability. Read a little more about Rotagrams in Resources / Rotagrams. Your copy of Free Mathematics Centre includes all the classroom materials listed here.

We are delighted that this remarkable learning tool will not be lost to mathematics education when Mathematics Centre closes. Even better, John's current Ph D study in Mathematics Education focuses on teaching and learning geometry and already includes a section on Rotagrams.

Antonio's Teaching Craft

Currently teaching in primary school, Antonio has ... "spent about 20 years trying to bring manipulative and comprehensive experiences to the classroom and trying to generate a love of mathematics.".

At Murchante school they video all their maths lessons. Antonio straps his mobile to his chest and forgets about it as the lesson progresses. Why?
The videos:

• "help the kids revise or see how we learnt stuff."
• "show the families what we're up to in class. Since our maths teaching's a bit out there compared to what they're used to, the vids keep everyone happy. And the grandparents love seeing their grandkids in action, ha!"
• "are great for us teachers in our training workshops."

"I also run arithmetic workshops for the folks, so if we send home some homework, they don't try to force their old-school ways on the kids."

The 'go to' concrete material at every level of the school is Cuisenaire Rods. Caleb Gattegno would be very impressed. "We use Cuisenaire rods from Year 1 to Year 6 for just about everything - numbers, sums, geometry, stats, you name it."

In many of their videos you see large boxes of them on every table. You also see other materials. You see many other teaching craft choices in action too. I don't understand Spanish, but I do understand classroom and some of the things I saw were:

• Children working in groups.
• Vigorous and enthusiastic mathematical discussion.
• Children confident to move around the room to share their work with colleagues and teachers.
• Use of words and drawings, not just symbols and equations.
• An atmosphere of encouragement, respect and purpose that aims to include all children and build self-esteem and group interaction.

It's a classroom experience - an every day classroom experience - created by deliberate teaching craft choices. An atmosphere that could never be achieved by focusing on explicit teaching.

And it is successful. "...after our good results in the diagnostic tests, the government rang me up the other day asking if I want to be a maths advisor.".

It is absolutely worth looking at the EscuelaMurchante Channel. There are 245 classroom lessons arranged in playlists for Years 6 through to 1. What do you see?

Keep smiling,
Doug.

June 2025

Seek and Ye Shall Find

Great news!

One question left unanswered when Free Mathematics Centre (FMC) was created in February was whether or not the Search box at the top of of its home page would work after the live Mathematics Centre site is turned off later in the year. Further investigation confirmed that it would not. So, no current live site - no answers to searches from FMC.

However, our wonderful new colleague Antonio Sánchez, the first person in the world to receive a copy of FMC, has a background in programming and offered to write a new search function unique to FMC.

Enter a search word or exact phrase in the Search Box and Antonio's search function responds in milliseconds in a new tab showing all the on site references to that word or phrase; just as in this image of a search on 'Pythagoras'. Antonio's work is outstanding. He has produced a super quick, attractive, comprehensive and accurate search function for FMC that operates through your browser whether or not your computer is online. All those who have received FMC after April 28th have this function included. And all earlier adopters, those before April 28th, have been sent the necessary upgrade files. (If you are one of these people and you did not receive these files around May 5th, please contact doug@blackdouglas.com.au.) It's almost worth getting a copy of FMC just to be blown away by this facility. See Order Form.

Search, chase the response links, learn; a truly adventurous way to extend your pedagogical and mathematical knowledge.

Notre Dame Leads The Way

In the April issue we asked who would be the Future Firsts.

Now we know that the first teacher training institution in the world to make Free Mathematics Centre part of their curriculum is The University of Notre Dame Australia, Fremantle. Lorraine Day and Shyam Drury ...already use the MTC in one of our courses and can now look to expand that repertoire.

In this instance MTC (Mathematics Task Centre) means a physical copy of the hands-on tasks in the Task Library ...for students to explore..

FMC has been mounted so students can access it with one click after log in and the link is available to undergraduate and postgraduate students and alumni.

From your copy of FMC you can build your own Task Library over time. FMC includes all the print materials, organisational advice, video support and workshop leader's materials to framework on-going, self-directed professional development around learning to work like a mathematician in fascinating, captivating, absorbing classrooms, while simultaneously building a Task Library task by task.

UND is the first teacher training institution, so which will be the first:

• maths teachers association
• school system
• education department

to encourage teachers to investigate a world of alternatives to text-based learning by making Free Mathematics Centre readily available.

While we are mentioning firsts, the first copy of FMC in China has gone to Dulwich College, Shanghai, an International Baccalaureate school.

Threading: a Learning Feature Worth Considering

The Calculating Changes division of Mathematics Centre is dedicated to engineering 'aha' moments in number. The intent is to enhance children's number sense beyond what is normally expected for their age. This aim has been achieved in a wide range of primary school educational settings. Some of the evidence for this claim has always been available in the Free Tour section of Calculating Changes. However with the announcement of Free Mathematics Centre in February (see link at top of page), came public access to the Members section which contains a great deal more evidence - most of it classroom based; a smaller amount research based.

• Calculating Changes gateway.

For most teachers, the teaching craft feature (pedagogical strategy if you prefer) referred to as Threading will be new. It is however critical to the successful use of the 70+ activities which have become available since FMC. If you teach K - 6 (8) and would like your children to do even better in their number work, feel free to explore Calculating Changes in more depth. The following few paragraphs provide context and support for your adventure.

• You will find Threading concisely explained in the In Brief link on the gateway page.

What is Threading?
Threading is a teaching craft strategy created, explored, extended and integrated into classroom curriculum by scores of teachers (and some parents) who were involved in various long term professional development from around 1996/7 to around 2015. (A little of this work was also extended through the development of Maths At Home in lockdowns.) The two major systems which were (independently) involved were the Tasmanian Aboriginal Education Unit and the Canberra Goulburn Catholic Education Office. Other individual schools around the country have been involved at various times and sessions related to this work have often been run at conferences. In fact, that is how professional development opportunities were generated for many of those other schools.

Evidence for Threading
Evidence for the claim that Threading contributes significantly to enhancing children's number sense is in the 100+ easily accessible activity stories gathered from classrooms, and presented as teaching notes with commentary. You will discover that all come from teacher involvement in professional development which inspired their creator/developers to want to work with their children in a different way.

Beginning to explore Threading

If you only have time to look at one of these activity stories then this one captures not only the mechanics of the content and pedagogical choices involved, but the passion, wonder and developing self-images of the children and, more importantly, their teacher. Poly Plug, Proportion & Percent You will note that the teacher is named. An equivalent acknowledgement is recorded in almost every one of the 100+ stories. Not all of the activities involve threading. A few are in the form of investigations, thereby drawing on pedagogy more prevalent in other divisions of

14 out of 25 turned over. What happens if another student joins in?

Mathematics Centre, such as the Mathematics Task Centre. It was natural for Calculating Changes teachers to make connections with these investigations because all of the work, stories, professional development programs, research, classroom resources, Cube Tube videos and anything else within Mathematics Centre, including Calculating Changes, has been created and nurtured within an assumption that

school mathematics is learning to work like a mathematician in fascinating, captivating and absorbing classrooms.

Over time, working in this professional development environment led to the development of Working Mathematically with Infants, a resource document combining threading and investigations into 60 weeks of planned, sequenced and integrated activity-based core learning over 60 weeks from K to Year 2. This document is now freely available through Free Mathematics Centre.

• WMI background and sample material

Working Mathematically with Infants can be used in any system in parallel with any official curriculum document.

It's worth noting that the development of WMI was in large part stimulated by infant teachers asking where's our curriculum support when they realised that a sequenced, documented program was available for Years 3 to 10 through Maths With Attitude.

Research supports the claim that Threading, when learned, practised and nurtured through on-going professional development does enhance children's number sense. The Calculator Aware Number (CAN) research in England was one starting point for Calculating Changes all those decades ago. It is outlined in the Background link on the gateway page. The success of CAN was recreated through Deakin University's calculator project some years later.

Also the Tasmania Aboriginal Education Unit did its own research within its Changing Places project and a brief summary can be found in the Evaluations link on the gateway page. It should be noted that this was a complex project with the intent of changing the situation for Indigenous students in both language and mathematics simultaneously and it included teachers, parents, elders and Indigenous community members as participants. Many of the stories from this project are included in Calculating Changes and evidence for the success of threading is included within those, as shown above in Poly Plug, Proportion and Percent. However in terms of the overall Changing Places research it can only be claimed that Threading was a contributing teaching strategy to the project's success.

As has been mentioned to researchers in the past, there is room for more dedicated research into the value of Threading.

Happy exploring. The most fruitful way will be with your children and in the company of colleagues who are also interested in enhancing children's number sense beyond what is normally expected for their age.

Your Links Will Break

• Do you manage a web site with includes links to Mathematics Centre?
• Do you have links to Mathematics Centre bookmarked in your browser?
• Do you have links to Mathematics Centre activities or other support pages embedded in curriculum documents through your server?

These links will all break when Mathematics Centre is turned off on December 1st.

You can fix this before it happens. Obtain a copy of Free Mathematics Centre (see order form below). Mount it...

• ... on your web server within, or parallel to, your site
• ... in your personal computer
• ... on your school/institution server

and edit your links.

Converting links from the current live Mathematics Centre site to links within your copy of Free Mathematics Centre is easy. For example, the current external link to Poly Plug, Proportion & Percent is:

https://www.mathematicscentre.com/calchange/members/memb_act/proport.htm

This part of the pathway:

https://www.mathematicscentre.com/

is the path from any computer through the web and into the current Mathematics Centre top level. The rest of the pathway leads down into the Mathematics Centre folders to reach the required file shown at the end of the path.

When your copy of FMC is appropriately mounted, the pathway to Poly Plug, Proportion & Percent will be:

../calchange/members/memb_act/proport.htm

where the two dots (..) means the internal pathway to and through your computer or server to reach your Free Mathematics Centre top level. You are simply substituting one entry path for another. The substitution will be the same for every link because the structure within Free Mathematics Centre is identical to the structure of the current live Mathematics Centre site.

What an advantage to FMC schools, institutions and teachers!

Your on-line curriculum documents actively linked to explanations, discussions, evaluations, teaching craft models, activities, videos, investigations and more that support achieving the objectives of the systemic documents through the lens of learning to work like a mathematician.

Keep smiling,
Doug.

September 2025

Freeing Up Maths Education

In their May e-News, the Association of Teachers of Mathematics (ATM) UK included a paragraph informing readers about the Free Mathematics Centre opportunity. The paragraph included a link to this background information which I was invited to prepare for their web site. Looking back this makes ATM the first mathematics teachers' association we know of to mention FMC in their communications. There is so much in Free Mathematics Centre to support teachers of every school level. It's wonderful that ATM Council recognised that this opportunity would help teachers continue to strive for best practice learning. If your local association hasn't mentioned it in their news, perhaps they don't know about it.

in the news in UK

on the web in Sweden

In Sweden, just before this September update, Sveriges Matematiklärarförening (SMaL), the Swedish maths teachers' association, announced that it has made Free Mathematics Centre available through its web site. The first maths teachers' association to do this. Their commitment to supporting members is clear. We are so happy you decided to share FMC to all of us!. The SMaL Board organised for a copy of FMC to be zipped and uploaded to Dropbox, Then they created a menu item Mattegömmor – Mathematics Task Centre on their home page which leads to a few

introductory paragraphs and the Dropbox link. Please visit this article. The text is in Swedish but you can copy and paste it into Google translate and in less than 10 seconds you will have a very good understanding of what has been written.

The only word the translator had any problem with was Mattegömmor, which it resolves as Math or Math Hides. This anomaly isn't surprising when you know that Mattegömmor is a composite Swedish word created by teacher Barbro Anselmsson near the end of last century to represent the hands-on mathematics tasks as ...a place where mathematics is hidden.

We are immensely grateful for SMaL's generous support in helping to fulfil the objective of widely sharing the classroom wisdom embedded in FMC. Over decades many Swedish teachers have contributed stories to FMC. These will now be available for generations to come.

In mid-March Hans received his copy of Free Mathematics Centre. Our work was completely new to him so he spent time exploring. Then in the last week of August we received a message telling us the school had given ...a green light for a set of 25 poly-plugs. They were in the mail a couple of days later. Hans teaches Year 1 - 4 children and is head of maths. He has ...a focus on tactile math activities to help the kids getting a better understanding and added I've already placed your site at the school's own intranet. And offered it to others.

shared with colleagues in Denmark

Have you considered the possible benefits for your school if Free Mathematics Centre, with all its digital resources, was included on your school's intranet? See below for a list of everything included in Free Mathematics Centre.

FMC Travels The World

Since the June update FMC flash drives have been sent overseas to South Africa, El Salvador and Sweden and in Australia to teachers QLD, NSW, ACT, VIC, TAS and WA.

One of these was to Elizabeth Rademaker a home education parent in Queensland. In early August she wrote:

...it's just been really bugging me recently that there's no centralised website for your average aussie teacher to go find rich maths tasks. I went searching and found yours, and was so excited until I realised I couldn't easily access any of the maths tasks.

She went on to explain that while searching through the site, which she tells me was several hours,

My children kept rushing over as I would say 'oh that's a good one'. And then we'd have fun trying to solve the problem. I especially liked figuring out the kangaroo hopping task. I hadn't come across it before, and it has such a beautiful solution. Plus, I liked reading through all of the history of the tasks and your thoughts on maths teaching.

Elizabeth went on to ask whether the eTask Package is included in Free Mathematics Centre (FMC) and enquire further about Poly Plug. Before the end of August she had her copy of FMC, which does include the complete eTask Pack, and her 'class set' of 4 Poly Plug.

...the mail arrived today. We've all had fun making patterns out of the poly plugs, and I look forward to using them for the actual maths tasks.

...And yes, I have home schooling friends who I'm going to share it with too.

If you are looking for pathways through the 30 years of classroom stories recorded in Mathematics Centre, two good starting points are:

• Big Picture, which acts as a Table of Contents for the major divisions.
• Site Map, which acts as an index of links to details within the major divisions.

There are many other ways in too. Whether you are using the current live site, or a copy of FMC, feel free to contact me for navigation suggestions related to your particular interest.

Learning From Last Century

My last MAV Annual Conference workshop was last December (2024) and it was entirely built around the concept of Algebra Through Geometry created last century by renown Scottish educator Geoff Giles, Stirling University. I think Geoff, now deceased, would have been the first to nod to the ancient Greek mathematicians for conceiving algebra through their geometry, but Geoff's development was, and is, for the classroom. No algebra student ever again needs to ask:

I don't get it Miss. What's x?

Have any of your students asked that this year? Then consider the following extracts from my workshop slides. The full slide show is available for anyone to use in their own staff workshop or broader professional learning session. However, by design, slides are intended to be viewed in steps, so if you want to more fully experience the mathematical surprises waiting below, pause to ponder after each yellow rectangle before scrolling on.

• Before you begin it would be useful to print this Algebra Through Geometry Recording Sheet.

Algebra Through Geometry: the Geoff Giles way

Antonio knew exactly how to calculate the area of the boomerang shape.
He showed Carmen how he did it and she agreed he was correct.

All the learning from here involves TakTiles, which are 'jigsaw puzzle' pieces based on X and Y (TakTiles were designed by Geoff too.) I had my 10 copies printed and laminated in less than half an hour at a commercial office megastore, then spent a little over an hour cutting out the pieces. 10 sets for a workshop with up to 20 participants.

When you know how to calculate the area of the boomerang shape, if you are curious about where this approach might go, visit Task 71, Algebra Through Geometry. This cameo includes: Teaching notes Slide show to support teacher workshops ...perhaps whole class lessons too? Recording sheet Print Master for Tak Tiles Investigation Guides digging deeper and deeper into text book algebra through images And it's all free right now. But by the 2025 Annual Conference, neither this material, nor any part of Mathematics Centre will be available live through the current site. Mathematics Centre will be removed from the web on December 1st. See below to find out what will be available and how to obtain your copy.

Which Resources Are Free in FMC?

Free Mathematics Centre is the entire Mathematics Centre site and these digital resources. You only pay for the USB, the packaging and postage. This Order Form has more detail about ordering.

• eTask Package
• Working Mathematically with Infants (K - 2)
• Maths With Attitude eManuals (3 - 10)
• Picture Puzzles
• Professor Morris Puzzles
• Menu Maths @ Café Conundrum
• Poly Plug Game Pack
• Maths300 ETuTE

Find a description of each item in the Resources link.

Keep smiling,
Doug.

Link List Order Form (PDF)

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)