NMBR542 - Geometry and Measurement in Mathematics

Year

Credit points

Campus offering

Prerequisites

Nil

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.

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.

On successful completion of this unit, students should be able to:

LO1 - explain, in some detail, the historical and cultural development of geometry and measurement and their contribution to society (GA4, GA5, GA8; APST 2.1)

LO2 - demonstrate an understanding of geometry including Euclidean geometry as a logical system (GA4, GA5; APST 2.1)

LO3 - demonstrate an understanding of dynamic geometric systems and the use of technology (GA5, GA10; APST 2.1)

LO4 - use analytic and Euclidean geometry and geometrical ideas to solve multi-step problems (GA4, GA5, GA6; APST 2.1)

LO5 - demonstrate an understanding of the foundations of non-Euclidean geometry and topology (GA5, GA8, GA10; APST 2.1).

Graduate attributes

GA4 - think critically and reflectively 

GA5 - demonstrate values, knowledge, skills and attitudes appropriate to the discipline and/or profession 

GA6 - solve problems in a variety of settings taking local and international perspectives into account

GA8 - locate, organise, analyse, synthesise and evaluate information 

GA10 - utilise information and communication and other relevant technologies effectively.

AUSTRALIAN PROFESSIONAL STANDARDS FOR TEACHERS - GRADUATE LEVEL

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

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

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. 

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

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.

Nicol, C., et al. (2019). Living Culturally Responsive Mathematics Education with/in Indigenous Communities Brill|Sense.

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.