Unit rationale, description and aim

To become a generalist primary teacher with a primary school curriculum specialisation in mathematics, pre-service teachers must possess expert content knowledge.

This unit focuses on geometry and measurement but also considers the importance of proof in mathematics. Consideration of the basic need for measurement will lead into a discussion of Euclidean geometry. The need for proof to justify mathematical statements will be considered. This unit will also introduce some non-Euclidean geometrical ideas including spherical geometry and a brief introduction to topology.

The aim of this unit is to develop the mathematical content knowledge of pre-service teachers.

2025 10

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  • Term Mode
  • Semester 1Online Unscheduled

Prerequisites

NMBR140 Introduction to Mathematical Thinking or NMBR141 Number Development in Mathematics

Learning outcomes

To successfully complete this unit you will be able to demonstrate you have achieved the learning outcomes (LO) detailed in the below table.

Each outcome is informed by a number of graduate capabilities (GC) to ensure your work in this, and every unit, is part of a larger goal of graduating from ACU with the attributes of insight, empathy, imagination and impact.

Explore the graduate capabilities.

Explain the historical and cultural development of...

Learning Outcome 01

Explain the historical and cultural development of geometry and measurement and their contribution to society (APST 2.1)
Relevant Graduate Capabilities: GC2, GC5, GC11, GC12

Demonstrate an understanding of geometry including...

Learning Outcome 02

Demonstrate an understanding of geometry including Euclidean geometry as a logical system (APST 2.1)
Relevant Graduate Capabilities: GC1, GC3, GC7, GC11

Demonstrate an understanding of dynamic geometric ...

Learning Outcome 03

Demonstrate an understanding of dynamic geometric systems and the use of technology (APST 2.1)
Relevant Graduate Capabilities: GC2, GC3, GC7, GC10

Use analytic and Euclidean geometry and geometrica...

Learning Outcome 04

Use analytic and Euclidean geometry and geometrical ideas to solve problems (APST 2.1)
Relevant Graduate Capabilities: GC1, GC2, GC3, GC8

Demonstrate an understanding of foundations of non...

Learning Outcome 05

Demonstrate an understanding of foundations of non-Euclidean geometry and topology (APST 2.1).
Relevant Graduate Capabilities: GC1, GC2, GC7, GC8, GC11, GC12

Content

In all topics the effective use of technology will be key, allowing students to focus on the understanding, rather than the mechanics of each particular topic.

Topics covered will include:

Quantifying the world

  • What can we measure and what can’t we and why we bother: Mensuration to include perimeter, area, volume and angle
  • From measurement to geometry, the development of measurement systems and measurement devices (Historical and cultural development of mathematics within geometry and measurement)
  • Measuring the world: Analytic geometry

Describing the world

  • Proof not opinion: Euclidean geometry, basic premises, theorems and deductive proof
  • Pretty pictures: Properties and construction of families of 2D figures and 3D solids including the Platonic solids
  • Transformation geometry to include rotation, reflection and translation of 2D figures and 3D solids. Symmetries and pattern

Describing all possible worlds

  • The world we live on and the worlds we don’t: Non-Euclidean geometries
  • Forgetting measurement: Topology

Assessment strategy and rationale

The assessment tasks for this unit have been designed to contribute to high quality student learning by both helping students learn (assessment for learning), and by measuring explicit evidence of their learning (assessment of learning). Assessments have been developed to meet the unit learning outcomes and develop graduate attributes consistent with University assessment requirements. The assessment tasks provide multiple opportunities (presentation, problem solving and examination) in different ways (visual, verbal and written) for students to demonstrate:

Knowledge of content

Application of mathematics in real world contexts

Development, use and communication of appropriate mathematical language

Minimum Achievement Standards

The assessment tasks for this unit are designed to demonstrate achievement of each learning outcome.

In order to pass this unit, students are required to complete all required assessment tasks as per the Assessment Policy and gain an overall pass mark.

Electronic Submission, Marking and Return

Assessment tasks are submitted electronically whenever possible. Marking will include a moderation process. Assessment returns will occur within the 3 week period as per the Assessment Policy. 

Overview of assessments

Assessment Task 1: Early Skills Assessment Early...

Assessment Task 1: Early Skills Assessment

Early skills test or assignment, designed to allow students to demonstrate what they have learned.

Weighting

20%

Learning Outcomes LO2, LO3, LO4

Assessment Task 2: Learning from Others Investig...

Assessment Task 2: Learning from Others

Investigate how the mathematics of geometry AND shape was developed and used within an indigenous culture to solve a particular problem or problems. Discuss whether the use of mathematics has changed over time within the chosen culture.  

Weighting

40%

Learning Outcomes LO1, LO2, LO4

Assessment Task 3: Final Examination : Written te...

Assessment Task 3: Final Examination:

Written test covering the skills and concepts from the unit

Weighting

40%

Learning Outcomes LO1, LO2, LO3, LO4, LO5

Learning and teaching strategy and rationale

Teaching and learning organisation can take several forms. This could include intensive weekend classes supported by web-based tools, Intensive one week winter or summer schools supported by web-based tools or weekly face-to-face classes during semester.

Students may be expected to participate in online discussion and sharing via eLearning. Class resources will be available via eLearning as will access to relevant web links.

This is a 10-credit point unit and has been designed to ensure that the time needed to complete the required volume of learning to the requisite standard is approximately 150 hours in total across the semester. To achieve a passing standard in this unit, students will find it helpful to engage in the full range of learning activities and assessments utilised in this unit, as described in the learning and teaching strategy and the assessment strategy. The learning and teaching and assessment strategies include a range of approaches to support your learning such as reading, reflection, discussion, webinars, podcasts, video etc.

Duration

This unit includes 4 contact hours per week for 12 weeks, comprising 2 hours of lectures and 2 of tutorials.

This unit will normally include the equivalent of 24 hours of lectures together with 24 hours attendance mode tutorials.

150 hours in total with a normal expectation of 48 hours of directed study and the total contact hours should not exceed 48 hours.

AUSTRALIAN PROFESSIONAL STANDARDS FOR TEACHERS - GRADUATE LEVEL

On successful completion of this unit, pre-service teachers should be able to:

AUSTRALIAN PROFESSIONAL STANDARDS FOR TEACHERS - GRADUATE LEVEL

2.1 Demonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area.

Representative texts and references

Required text(s)

Australian Curriculum https://www.australiancurriculum.edu.au/

Australian Curriculum, Assessment and Reporting Authority (ACARA) www.acara.edu.au

McLeod, G. et al (2019). Introduction to Mathematical Thinking. Custom Edition. Pearson

Australian Curriculum Mathematics. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/

Relevant state and territory Mathematics curriculum documents

Recommended references

Bellos, A. (2010). Alex’s adventures in numberland: Dispatches from the wonderful world of mathematics. London, England: Bloomsbury.

Bellos, A. (2015). Alex through the looking glass: How life reflects numbers, and numbers reflect life. London: Bloomsbury

Craine, T. (Ed.) (2009). Understanding geometry for a changing world. Reston, VA: NCTM.

Joseph, G. G. (2011). The crest of the peacock: Non-European roots of mathematics (3rd ed.). Princeton, NJ: Princeton University Press.

Nelson, R. D. (Ed.). (2008). The Penguin dictionary of mathematics. London: Penguin UK.

Robson, E., & Stedall, J. (Eds.). (2009). The Oxford handbook of the history of mathematics. Oxford: Oxford University Press.

Sutton, D. (2007). Islamic design: A genius for geometry. Wooden Books.

Wells, D.G. (1991). The Penguin dictionary of curious and interesting geometry (3rd ed.). London: Penguin.

Locations
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