Friday, 25 January 2019

miniMATHS - 4. One More

Task 4 - One More.

Seems like a very simple task.

You make a line of objects.

You partner makes a similar line - then adds one more.

Seems simple because it is simple. But it is also the beginnings of some very significant mathematics. 

- One to one correspondence (I make a line, you make a line) is the starting point for counting and giving a value to a collection of objects.
- "Adding one more" builds the idea of how numbers grow, how to build a sequence that increase by regular steps, how to think about addition.
- This is also pre-algebra: x, x+1....
- And we are learning about more than and less than.

Similar to Task 2 and 3, this task focuses on EYLF Outcome 2, "Children are connected with and contribute to their world."

One of the big ideas that is raised in this task is the idea of equality. In a mathematical sense, we are talking about the balance between two values. In a broader sense, we can take this conversation to include equality between people.

Equal shares is an important lesson in childhood. We can use this maths task to springboard into a discussion of how we should live with each other. From this, we can also develop strategies for dealing with inequality. 

Check out the miniMaths website:

Thursday, 24 January 2019

miniMATHS - 3. Same Same Different

This task - Same Same Different - is a fun game that children can play in many different contexts. It asks children to collect a set of three objects, two of which have a common feature that is absent in the third object. It is easy to see the potential for individual variation. And it also encourages children to think and to explain their thinking.

The suggested variations take the task into new places. "Same Same Same" asks the children to find common features in all three of their objects. "Different Different Different" turns the task upside down, requiring the children to identify differences between each of their objects.

And how is this task mathematical? Isn't it just a matching game? Well, at it's heart, this task is framing up some elementary concepts of algebra - finding common values, identifying sameness and difference, using logic and reasoning. These concepts are also important in numerical operations such as addition, subtraction, multiplication and division.

One aspect of the EYLF Outcome 2 looks at finding similarities and differences between people. Sound familiar? Isn't this the overt purpose of this task, finding same and different? This task can provide an ideal opportunity to promote conversations about diversity and individual differences. 

In the context of play, children can be encouraged to consider deep concepts and to start thinking about their own place in the world. Their connection with and contribution to the world is significant and should be nurtured through positive learning experiences such as this.

The miniMaths website can be found here: 

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.