1. Teaching Space & Geometry K-6
This workshop provides training for teachers in the teaching of the Space and Geometry strand of the K–6 Mathematics syllabus and is linked to the DET numeracy resource on CD, Teaching Space and Geometry K–6.
Why is this strand of the syllabus called Space and Geometry? What is the difference between space and geometry?
Students working in space, explore, visualise and investigate the features of geometric figures. Whereas, students working on geometry, use reasoning to study and generalise more abstractly, the properties of geometric figures.
Previously in NSW, space was taught in the K-6 syllabus and geometry in 7-10 syllabus. The current NSW Mathematics K-6 syllabus shows a progression between space and geometry.
Hopefully, as we progress through this workshop, the progression of concepts from space to geometry will become clearer.
Chris Francis and Bernard Tola - Space & Geometry K-6

2. Features and properties
Feature: a generally observable attribute of an object or shape.
Property: an attribute of an object or shape, the identification of which requires mathematical knowledge.
The progression of learning in the Mathematics K-6 syllabus makes a distinction between the features and the properties of shapes and objects.
Examples 2D
Feature: a rectangle has four sides.
Property: a rectangle has opposite sides of equal length. 3D
Feature: a rectangular prism has faces that are rectangles.
Property: a possible section of a rectangular prism is a pentagon.
Chris Francis and Bernard Tola - Space & Geometry K-6

3. Features and properties
Discuss what are features and what are properties of a triangle.
Activity
Have the participants discuss the question from the slide with a partner, then share with the whole group.
Examples
Feature: a triangle has three angles.
Property: the sum of the angles of a triangle is 180 degrees.
Chris Francis and Bernard Tola - Space & Geometry K-6

4. Features and properties
Where are features and where are properties a focus for teaching in the syllabus?
Activity
Provide participants with a photocopy of the relevant pages from the Mathematics K-6 syllabus.
Organise the participants into pairs.
Have the participants highlight on their sheets where a focus on features and a focus on properties occurs in the syllabus
Participants discuss their responses in small groups.
Discuss responses as a whole group.
Chris Francis and Bernard Tola - Space & Geometry K-6

5. Features and properties
The learning progresses from:
identifying and describing features, to
manipulating features of objects and shapes, to
applying properties.
The learning progression will be elaborated upon later in the workshop as it underpins the content within the CD resource.
Chris Francis and Bernard Tola - Space & Geometry K-6

6. Teaching Space & Geometry K-6 resource
The CD resource aims to:
deepen teacher and student understanding of the features and properties of geometrical figures
strengthen the teaching of space & geometry through pedagogical discussion.
The resource aims to deepen an understanding of Space & Geometry by going beyond counting, naming and classifying shapes and objects to using features and properties in working mathematically processes.
It aims to strengthen visualisation skills by moving away from presenting prototypical images. Students construct and manipulate shapes and objects, embed and disembed shapes and predict and discuss transformations.
Chris Francis and Bernard Tola - Space & Geometry K-6

7. Investigating a lesson
ES1 Unit: Discovering shapes
These activities will assist students to identify and match two-dimensional shapes.
Lesson one: Sorting two–dimensional shapes
Lesson two: Make it like mine
Lesson three: Find a face
Briefly guide the participants through the components of the CD.
Go to Stage 2, Exploring quadrilaterals, Lesson 2
View video
Explain the purpose, outcomes, key concept.
Activity
Provide the participants with a copy of lesson three: Find a face. ( lesson outline only).
Provide the participants with paper.
In groups have the participants:
Read and discuss the lesson
As a group, record the lesson purpose and outcomes including the Working Mathematically outcomes.
Have some of the participants share their responses
Go to ES1 – Discovering shapes and show lesson three, Find a face
Chris Francis and Bernard Tola - Space & Geometry K-6

8. Lessons high in metalanguage:
have high levels of talk about language and how it works
point out how words can have different meaning in different contexts.
Go to professional discussion for Find a face.
A common misunderstanding is that metalanguage refers to vocabulary, particularly the KLA-specific vocabulary of mathematics or to a list of words.
Examples of metalanguage are:
Discussing the meaning of the word difference in mathematics and in everyday life.
Discussing the role of prepositions in a word problem.
Discussing the text features of mathematics word problems. E.g. In a mathematics word problem, the question comes at the end of the text.
Activity
Have the participants read through the description of metalanguage on the slide.
Chris Francis and Bernard Tola - Space & Geometry K-6

9. Professional discussion
How is metalanguage different from simply using mathematical terms?
Identify the use of metalanguage during this lesson.
Are there other key points where the lesson would benefit from a discussion or commentary on aspects of language?
Briefly show the questions from the professional discussion.
If time, share one or two responses to the questions.
Chris Francis and Bernard Tola - Space & Geometry K-6

10. The progression focus builds upon research on the development of spatial thinking and geometric knowledge.
Lessons within the CD resource are aligned to the linked components of the progression focus .
The five linked components are not independent of one another. Each component shows a progression of learning.
The developmental levels typically fit in with particular stages:
ES1/Stg1 – Identifying and describing features
Stg1/Stg2 – Manipulating features of objects and shapes
Stg2/Stg3 – Applying properties.
However, not strictly so:
For example, when teaching about reflex angles, Stg3 (SG3.2b), the teacher would initially need to teach at the identifying and describing features development level. The progression for developing knowledge of reflex angles may begin with recognising and describing examples and non-examples (language/visual imagery). Then move to developing students’ dynamic imagery, e.g. visualising the angle arms opening/closing and describing what happens to the angle. Then to identifying properties of angles, e.g. a reflex angle is an angle between 180° and 360°.
Chris Francis and Bernard Tola - Space & Geometry K-6