Provocation #1: Snails in the Garden

With more than 1000 species of snails in Australia, there are always some nearby - usually in your letter box or on your home grown veges!

In this provocation we look closely at the geometric, measurement and spatial reasoning concepts embedded in a fascination with snail shells...

Early observations

A group of 4 year olds are very interested in snails sliding across the ground. They are touching the snails' shells and watching what happens. This causes a great delight as the snail retreats. The educator watches the children's reactions and dispositions. The children are leaning in to look closely. One of the children picks up the snail and looks at the shell closely. This non-verbal interaction is informative.

Taking a closer look

Building on the childrens' fascination and desire to look closely, we see this as an opportunity to collect some of the snails in a bug catcher so the children can go inside and use magnifying glasses. This closer look provides an opportunity to notice unique aspects of the snail. Once again, we would be watching the children's gestures and and listening to the language they are using to describe what they see, asking them:

what do you notice
what do you wonder?

We would now prompt them to focus their analysis on descriptions of the shell in order to promote some mathematical thinking.

Analysing the information

In these observations children may generate language related to the shape of the shell, for example a"circle that gets bigger" and a "line". This language connects to the mathematics concepts of geometry, measurement and spatial reasoning. It would suggest to us an opportunity to inquire into spirals.

Swirl by Swirl

Planning with intentionality, we would build on the children's prior knowledge by reading Swirl by Swirl: Spirals in Nature by Joyce Sidman (Harper Collins, 2018). This book is available in hard cover but if that is not accessible, readings of it can be found on the internet. As you can see by the front cover, the snail shell is represented, creating a link to what the children have just experienced.

Building mathematical vocabulary

The language and pictures in this text encourage children to consider a spiral in many forms: a merino sheep's horns, the cross section of a nautilus shell, and the web of a spider. It also describes the actions of a spiral, for example the unfolding of a plant, the curling of an animal's body, and how it grows from small to bigger. It also connects the structure of a spiral with its purpose in nature, i.e strength, protection and efficiency.

Focusing our mathematical content knowledge - what is a spiral?

Through observation, discussion and action (including gestures) our intention here is to start focusing children's attention on the definition mathematicians use to describe a spiral. This is where our own professional wondering is important - what is a spiral?

The Brittanica dictionary defines a spiral as:

A circular curving line that goes around a central point while getting closer to or farther away from it (www.brittanica.com).

Identifying the specific terms used to describe spirals informs the planning of intentional mathematical opportunities associated with this concept. This mathematical content knowledge is combined with our practice knowledge - a combination that is referred to as pedagogical content knowledge or PCK (Shulman, 1987).

Embodied Learning to promote connections

We would be looking for opportunities to deepen children's understanding of the connection between the 1-dimensional line and its 2 or 3-dimensional (2D or 3D) spiralling image/object generated by its curve. Asking children to consider how they would make a spiral with the whole group would encourage connections between these dimensions. Using their whole bodies and working together, children may join hands to make their spiral - this would be the 1-dimensional line. To make the spiral they need to use spatial orientation and reasoning skills to form the curve from a central point. Here we would prompt children to think how they made the spiral, and if they could unfurl their spiral then curl it back up again? Taking photographs of their spiral and discussing these would assist the connection between what they see, what they constructed and how they made it. Taking and viewing video of this experience would reinforce the movement or action of a spiral and the children's role in this.

A little bit the same, a little bit different

Building on these experiences, we suggest other modes of connection to the measurement (length is 1D), geometric (1D, 2D and 3D) and spatial reasoning (visualising, perspective) concepts developed so far. This may include rolling playdo and forming it into a spiral. Given this opportunity, children would probably create the line of playdo first then curl it. Similarly, providing the opportunity to create spirals using pipecleaners - perhaps winding them around their fingers, and/or using a range of natural materials to create spirals would to build this conceptual understanding. Linking these experiences to those that are contextually relevant and part of children's everyday lives, like cooking (bread scrolls) and eating food that looks beautiful (that spiral shape) will strengthen their relevance. Going on a spiral hunt could be fun! This would be an interesting culminating activity to see if the children are using the appropriate mathematical language and applying the underlying conceptual understanding, i.e. being able to tell the difference between a circle and a spiral.

Playdo picture - https://lifeovercs.com/easy-homemade-play-dough-recipe-for-kids/

Unedited, unfiltered made-from-scratch c

Planning these experiences - connection to the EYLF2.0

We recognise that learning experiences achieve outcomes across those outlined in the Early Years Learning Framework 2.0 (AGDE, 2022).

In terms of the content and processes in these learning experiences, we will focus on Outcome 4: Children are confident and involved learners.

This outcome outlines the holistic nature of children’s learning, including experiences that “combine children’s sensory perceptions, body movement, actions, thinking and emotions" (p. 50).

The Key Components of this outcome include the development of learning and thinking skills and processes such as problem solving, inquiry, experimentation, hypothesising, investigating and reasoning. They focus on opportunities for children to transfer and adapt what they have learned from one context to another. Educators are encouraged to promote mathematical language, and recognise children's mathematical understandings so they can build on these.

These goals fit well with the experiences described above.

PLANNING

The five components of the EYLF2.0 planning cycle which inform out thinking about children's experiences are Observe, Assess, Plan, Implement and Evaluate.

Representing the initial spiral experience would look like this:

OBSERVE - Listen/collect information

Engage with children's curiosity about spirals - looking at snails in the garden.

ASSESS - Analyse/interpret learning

Listen to, and watch for, the multimodal languages the children use to describe spirals and where we see them.

PLAN - Design

Planning with intentionality, incorporating children's prior knowledge, including enriching this experience via the picture book “Swirl by Swirl” and incorporate embodied learning to explore the concepts of measurement, geometry and spatial reasoning.

IMPLEMENT - Enact

Read Swirl by Swirl, focusing on a connection to the mathematical language used to describe spirals and their purpose in nature.

Made a spiral using our bodies, and generate connections to multimodal representations.

EVALUATE - Critically evaluate

What worked well and why? How can I further extend this concept of spirals and the related big ideas? What is the evidence of learning, in relation to the intention of the experience(s)

A little cliffhanger, or provocation to ponder...

We stand on the shoulder of giants to incorporate a plot device made famous by writer Thomas Hardy who left one of his characters literally hanging off a cliff at the end of a chapter in 1873!

If we peel an orange or apple from top to bottom in one length, would we consider that a spiral?

Why? Why not?

References:

Australian Government Department of Education [AGDE] (2022). Belonging, Being and Becoming: The Early Years Learning Framework for Australia (V2.0). Australian Government Department of Education for the Ministerial Council. https://www.acecqa.gov.au/sites/default/files/2023-01/EYLF-2022-V2.0.pdf

Shulman, L. (1987). Knowledge and Teaching: Foundations of the New Reform. Harvard Educational Review, 57, 1-22. http://dx.doi.org/10.17763/haer.57.1.j463w79r56455411

Sidman, J. (2018). Swirl by swirl: Spirals in nature. Harper Collins

https://www.britannica.com/dictionary/spiral