Unit rationale, description and aim

At a time of rapid ongoing change as a result of globalisation, internationalisation and the continuing development of information communication technologies, the ability of educators and allied professionals to empower young people to develop substantive understanding of mathematics as a language to use in solving problems, making connections and communicating ideas in real life is of critical importance. In this unit, within the Mathematics specialisation of the Graduate Certificate in Education and the Master of Education, students will develop mathematical content and pedagogical knowledge for the teaching of geometry, measurement, and trigonometry in the middle years of schooling (Years 5-9). This unit reflects current mathematical pedagogies, such as inquiry-based learning, with a particular emphasis on investigation. Approaches include the effective use of digital technologies and manipulatives. Forms of argumentation and proof are highlighted. Deductive and inductive reasoning are used to solve problems and carry out investigations based upon geometry and measurement. Therefore, the aim of this unit is equip students with advanced knowledge, integrated understanding and expert skills in mathematical content and pedagogical knowledge for the teaching of geometry and measurement in the middle years of schooling.

2025 10

Campus offering

No unit offerings are currently available for this unit.

Prerequisites

Nil

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.

Appraise the historical and cultural development o...

Learning Outcome 01

Appraise the historical and cultural development of geometry and measurement and their contribution to society (APST 2.4)
Relevant Graduate Capabilities: GC1, GC5, GC6

Apply theories and research informing children’s m...

Learning Outcome 02

Apply theories and research informing children’s mathematical learning and children’s development of mathematical concepts and processes in Measurement and Geometry as required by Australian Curriculum: Mathematics (ACARA) and other relevant curriculum documents for the middle years (APST 1.2, 2.1, 2.2, 2.5)
Relevant Graduate Capabilities: GC2, GC7, GC12

Explain geometry including Euclidean geometry as a...

Learning Outcome 03

Explain geometry including Euclidean geometry as a logical system (APST 2.1)
Relevant Graduate Capabilities: GC1, GC2, GC4

Use technologies and resources that will enhance u...

Learning Outcome 04

Use technologies and resources that will enhance understanding of geometry, trigonometry, and measurement (APST 1.2, 2.1)
Relevant Graduate Capabilities: GC8, GC9, GC10

Articulate the developmental sequence for teaching...

Learning Outcome 05

Articulate the developmental sequence for teaching the measurement of mass, time, capacity, length, perimeter, area, surface area and volume (APST 1.2, 2.5, 3.3)
Relevant Graduate Capabilities: GC2, GC4, GC12

Examine dynamic geometric systems and an ability t...

Learning Outcome 06

Examine dynamic geometric systems and an ability to discuss the impact of technology (e.g., GeoGebra) on mathematics learning in geometry as well as pose challenging problems and apply geometry, trigonometry, and measurement to solve mathematical and real-world problems) (APST 2.1, 2.5, 2.6, 3.3)
Relevant Graduate Capabilities: GC1, GC8, GC10

Analyse student difficulties and misconceptions an...

Learning Outcome 07

Analyse student difficulties and misconceptions and errors in learning geometry and measurement concepts in the middle years (APST 1.2, 5.1)
Relevant Graduate Capabilities: GC2, GC7, GC11

Content

Topics covered will give consideration to mathematical content knowledge (MCK) and pedagogical content knowledge (PCK) and associated teaching methods, and include:

  • Historical and cultural development of mathematics within geometry and measurement
  • Euclidean geometry, basic premises, theorems and deductive proof
  • 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
  • Mensuration to include perimeter, area, volume, and angle
  • Pedagogical aspects of teaching and learning geometry, trigonometry and measurement through inquiry-based learning including problem posing, investigative approaches, dynamic geometry systems and manipulatives
  • Diagnosing and remediating common student misconceptions and difficulties in geometry and measurement.

Assessment strategy and rationale

In order to successfully complete this unit, postgraduate students need to complete and submit three graded assessment tasks. The assessment strategy used allows students to demonstrate their knowledge and skill related to geometry and measurement. The first task is a mathematic investigation; the second is a clinical interview related to misconceptions in measure or geometry; the third task focuses on the historical and cultural development of geometry.

Overview of assessments

Assessment Task 1: Investigation Extended mathema...

Assessment Task 1: Investigation

Extended mathematical investigations (e.g. angle sum of triangles on curved surfaces) with reflection on impact of task on future teaching of the associated content

Weighting

30%

Learning Outcomes LO4, LO5

Assessment Task 2: Interview Conduct a clinical s...

Assessment Task 2: Interview

Conduct a clinical student interview highlighting common misconceptions in measurement or geometry and critique your findings against the research literature

Weighting

20%

Learning Outcomes LO2, LO5, LO7

Assessment Task 3: Written Assignment An assignme...

Assessment Task 3: Written Assignment

An assignment highlighting the historical and cultural development of geometry and/or measurement and focusing on problem posing, investigation, and problem solution (e.g., students pose and solve two problems highlighting a cultural use of mathematics and chose and solve two historical problems (one each from measurement, geometry/trigonometry). One task should be an investigative task. Use the four tasks as a basis for a unit, to be shared with colleagues, highlighting the historical and cultural development of mathematics using teaching strategies to develop and implement engaging learning.

Weighting

50%

Learning Outcomes LO1, LO2, LO3, LO4, LO5, LO6

Learning and teaching strategy and rationale

This unit is offered in multi-mode Engagement for learning is the key driver in the delivery of this curriculum, therefore an active learning approach is utilised to support students in their exploration and demonstration of achievement of the unit’s identified learning outcomes. A range of strategies will be used to support active learning and may include: lectures, tutorials, workshops and seminars; synchronous and/or asynchronous digital engagement in reading/library tasks and presentations, learning activities, discussion forums and consultation as mediated through the Canvas site. Other modes of delivery may include webinars and presentations.

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, workshops, and assignments etc.

AUSTRALIAN PROFESSIONAL STANDARDS FOR TEACHERS

On successful completion of this unit, students should have gained evidence towards the following standards: 

Standards/Attributes/Criteria

1.2      Understand how students learn (Highly Accomplished) 

2.1      Content and teaching strategies of the teaching area (Highly Accomplished) 

2.4       Understand and respect Aboriginal and Torres Strait Islander people to promote reconciliation between Indigenous and non-Indigenous (Highly Accomplished)

2.5      Literacy and numeracy strategies (Highly Accomplished) 

2.6       Information and communication technology (ICT) (Highly Accomplished)

3.3      Use teaching strategies (Highly Accomplished) 

5.1       Assess student learning (Highly Accomplished)

Representative texts and references

Representative texts and references

Duatepe-Paksu, A., Lymen, E., & Pakmak, G.S. (2012). How well elementary teachers identify parallelogram? Journal of Educational Studies, 38(4), 415-418.

Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. Journal of Mathematical Behavior, 31(1), 60-72.

Fujita, T., Kondo, Y., Kumakura, H., &  Kunimune, S. (2017). Students’ geometric thinking with cube representations: Assessment framework and empirical evidence. Journal of Mathematical Behavior, 46, 96-111.

Miller, S.M. (2018 online). An analysis of the form and content of quadrilateral definitions composed by novice pre-service teachers. Journal of Mathematical Behavior, 31.

Stillman, G. (2013). Problem finding and problem posing for mathematical modeling. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modeling: From theory to practice. Series on mathematics education Vol. 8. Singapore: World Scientific.

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