Wednesday, 23 January 2019

miniMATHS - 2. Big Bigger Biggest

This is my favourite task. If I was in pre-k, I think I could have spent hours with sticks or rocks, lining them up in order of length. Actually, I probably did when I was.

The big idea behind this task is prompted by something I heard Nora Newcombe say at a conference last year. (Nora is a significant voice in mathematics education and research and has written heaps)  She said that her research had found that, while a sense of number was not something that babies are born with, they do seem to possess an innate sense of "magnitude" - something being "more than" something else.

So I was interested to include a task where students can develop this skill, looking at objects and arranging them based on an attribute such as length or area. This task also provides an opportunity to reverse the process, to look at small, smaller and smallest. 

It is not an accident that this task has used the nominative, comparative and superlative. This gives important links to grammar and language development in an informal context.

This task is linked to the second outcome from the Early Years Learning Framework:

Children are connected with and contribute to their world.

A big idea linked to this outcome is "change" - and this can be explored through the task by developing groups of objects that grow in a certain direction - by length, height, mass, area or in some other way. Children can see how they can add new objects to their sequence to make it grow. 

Once again, if anyone gives this one a go and has any feedback, please let me know. I would love to hear about it.

And here's the link to the website: 

Tuesday, 22 January 2019

miniMATHS - 1. How many leaves?

from the "miniMATHS - Maths Inqiries in Nature" booklet

The tasks are organised based on the Early Years Learning Framework (EYLF). I linked each task to one of the five outcomes and put them in numerical order.

Outcome 1 - Children have a strong sense of identity
Task 1 - How many leaves?

The task is simple to set up. Draw a square in the dirt. See how many leaves you need to fill it up.

It is measuring area using informal units.

But you can take this to interesting places:

- move the leaves around in different arrangements to see if the number you need stays the same
- try using different types of leaves
- try using different sized shapes to fill up
- even try using the children themselves to fill up big spaces

One of the important ideas we want to experience is that "area is the space inside". And we can measure it.

from the "miniMATHS - Maths Inqiries in Nature" booklet

One of the important ideas presented in the EYLF outcome #1 relates to perspective. The "How many leaves?" task provides opportunities for students to explore the area of the square in many different ways and to understand that different people will find different solutions.

"Comparison" is another important concept that this task highlights, finding the area of a shape and comparing materials and strategies to complete it.

This task is ideal for small group interaction and is firmly based in the Nature Play pedagogy, using natural materials in a natural setting. Students can play with the idea and modify it to pursue their own questions and interests.

I would be interested in getting feedback from teachers who try out this task in their own schools. I would be particularly interested in hearing what the students have to say. 

Let me know.


Here's the miniMATHS website:

Monday, 21 January 2019

miniMATHS - Maths in Nature Inquiries

The Background

In 2018, my good friend Sam Hardwicke told me about the ACT Government Nature Play grants and suggested I should have a look at putting something in. I submitted an application on behalf of the Canberra Maths Association. We proposed to:

- write 10 inquiries/tasks/lessons/resources to be used outside in the natural environment
- run 10 workshops with preschools to share these resources

We were successful in our application and got the grant. A group of about 10 interested teachers from all levels of education, from early childhood, primary, secondary and tertiary, got together at the CMA conference in August and put together ideas for the 10 tasks. It was a productive time. I went away with pages of notes that I wrote up as the miniMATHS program.

The 10 tasks we came up with were:

1. How many leaves? - using informal units to measure area
2. Big, bigger, biggest - ordering by length
3. Same, same, different - identifying common features
4. One more - you make a number of objects, I'll make one more than you have
5. Shadows - moving objects to make new shadows
6. Stacking - building a pile of objects
7. Make a star - building a radial pattern
8. Does it float? - playing with floating and sinking
9. Rolling - looking at objects that roll
10. Repeat my pattern - if I make a pattern, can you extend it?

These 10 tasks were shaped into a book. I wanted some sort of printed product that teachers could physically carry with them into the bush, or at least outside into the playground. So some of the grant went into the printing of a book for every preschool in Canberra.

The 10 tasks have also been uploaded as a website that is available to anyone, not just ACT teachers: 

Over the next week or so, I will post a bit more detail about each of the 10 tasks. Maybe you will find them useful. I would be keen to hear any feedback.

And any Canberra teachers - keep an eye out for the miniMATHS workshops rolling out over January and February.


Wednesday, 12 September 2018

Adding 5

I was interested in exploring how we might represent the addition operation as a pattern. We had been playing with the addition algorithm and looking at adding numbers up to 4 digits.

So I took it way back and asked how we might make a pattern to represent adding 5.

And here is what happened:

I was underwhelmed. Surely we could come up with more than simple lines getting bigger by 5 each time. And was it a coincidence that just about every student had represented adding 5 in exactly the same way?

So, I drew a long breath and asked our favourite question:

"Can you do it a different way?"

And thankfully the answer was a resounding, "Yes!"

Here is what our next attempts looked like:

Several representations looked at groups of 5 being stacked up on top of each other. An interesting idea - take it into another dimension - but similar to the idea of parallel lines.

Two different students looked at representing the idea of adding 5 as an array. 

Then we had 2 who make a circular pattern. 

And also a radial pattern.

Then we had a few interesting ideas. Here, the student has decided to start at 3 (the central group of light blue lids) and then adding groups of 5 at each end. Her pattern went 3, 8, 13, 18...

This was a rather unusual idea. I can see the 5 blue lids. I can see several rows that have 5 yellow lids. But I could also see lots with 6 as well. What was going on?

"Well, you can start at any lid, and then count 5 in any direction. And then keep going."

Well, that certainly took it to places I wasn't expecting.

And then we had this one:

So, this student decided to reinvent numbers, place value, the counting system - everything.

Each group of lids represents a number in the counting by 5s pattern (5, 10, 15, 20, 25 etc) but the number of lids is not relevant. Each group has a unique arrangement, demonstrating an understanding that all numbers are unique and represent unique values. 

So much more interesting than a series of parallel lines.

Like it. Well done, Year 2.

Saturday, 8 September 2018

AMSI 2018 Excellence in Teaching Award

I was honoured yesterday by the Australian Mathematical Sciences Institute (AMSI) along with 9 other outstanding Australian teachers and received an "Excellence in Teaching" award. 

Image may contain: one or more people

This is me with BHP Principal, Inclusion and Diversity Fiona Vines.

The Canberra Times, our local newspaper, did a very sympathetic write up about me, though I'm not sure about the "rockstar" bit:

I would like to thank everyone who has supported me in my mathematical journey, starting with my inspirational and extremely patient wife, my family, my colleagues, you - the readers of this blog - and ultimately my students who challenge me to think clearly and to be creative every day.



Tuesday, 21 August 2018

Nets of Cubes

We are exploring polyhedra in Year 2 this week. Yesterday we had a great time playing with shadows and looking at what could be made from a selection of different objects.

Today we wondered what a cube would look like if you "unfolded" it - laying out each face flat on the ground.

The kids, perceptive as ever, thought they knew how to do this. With little prompting, they headed off with paper and rulers to make some nets.

Once everyone had made a net, I asked them to bring them back to the group and share them. Every student had produced a net that looked like this:

Every student - except one. His net looked like this:

Time for some provocative teacher action. Was it possible that there would be more than one way to make the net of a cube? Is it really true? Are there more ways out there that we haven't found yet? Could we possibly explore and see what we might find?

The kids leapt into it. All except one student, who refused to believe there might be other ways. He was dogmatic - there could only be two ways - the two ways we had already found.

And then the other students started to produce new ways to unfold the cube. Here are a few examples:

It only took ten minutes and we already had about 8 different nets for the cube.

And in the process, we also discovered something else really interesting - there are some "nets" made up of 6 squares that wouldn't fold up into a cube. Here are a few of those:

Interesting learning for Year 2 students. Because by exploring the arrangements that wouldn't work, they were able to come up with some "rules" for their nets:

1. It has to have 6 squares

2. If it is based around a line of 4, you need one square off the the right of the line and another one of to the left.

Here is what the classroom floor looked like after 25 minutes of exploring:

We were not convinced that we had found all of them - in fact I knew that we hadn't.

So it was music to my ears when one girl asked, "Can we keep doing this at home tonight?"

Taking action. 

I wonder what we will see in the morning.

Thursday, 16 August 2018

400 000

Data from the blog - cracked 400 000 views yesterday, thanks to some enthusiastic students at ACU Canberra looking at some of the work my kids had done - thanks people.

Looking forward to the next 400 000.

PS - Something happened about 18th March 2016. That's the big spike. Lots of traffic came from France - not sure why. 
A PYP event? Maths conference? Cyber hacker?