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Unit rationale, description and aim

According to the Alice Springs (Mparntwe) Education Declaration (2019), “Every student must develop strong literacy and numeracy skills in their earliest years of schooling”. To become an effective teacher, educators must possess deep content knowledge to model, investigate explore and discuss mathematics using a variety of approaches which will provide learners with the foundation for successful lifelong learning.

This unit uses a direct instruction pedagogy to support pre-service teachers to gain a deep learning of important mathematical content knowledge needed for teaching mathematics to students from birth to twelve years of age. The mathematical focus areas include number and algebra, measurement and space, and chance and data, as reflected in the Australian Curriculum: Mathematics. The learning is underpinned by a mathematical modelling process; examples of the application of mathematics in the real world; cross-curriculum capabilities; relevant historical and cultural examples of the content, including Aboriginal and Torres Strait Islander ways of knowing; and problem-solving techniques. The content and assessment in this unit embed this understanding in authentic contexts and meaningful representational tasks. 

The aim of this unit is to provide pre-service teachers with a deep understanding of the foundational mathematics content knowledge required to make pedagogical decisions about students and their learning.

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.

Learning Outcome NumberLearning Outcome DescriptionRelevant Graduate Capabilities
LO1Demonstrate enhanced understanding of mathematics including the correct use of terms, notation and common errors in thinkingGC1, GC3, GC7
LO2Explore and apply a variety of problem-solving strategies and computational approaches to solving mathematical problemsGC1, GC2, GC3, GC7, GC8, GC9, GC11, GC12
LO3Explain the structure inherent in various mathematical systems and undertake mathematical modelling to develop expertise in the field of mathematicsGC1, GC2, GC7, GC8, GC9, GC11, GC12
LO4Describe the historical and cultural development of number, measurement and spaceGC1, GC2, GC5, GC6, GC9, GC11, GC12

ACECQA Curriculum Specifications

In connection to the learning outcomes, on successful completion of this unit, pre-service teachers should have developed the following industry specific knowledge based on the Australian Children's Education and Care Quality Authority (ACECQA) standards:

Industry StandardRelating toRelevant Learning Outcome

Numeracy, science and technology


Alternative pedagogies and curriculum approaches

LO1, LO2

Teaching methods and strategies


Historical and comparative perspectives


Contemporary theories and practice



LO1, LO4

Australian Professional Standards for Teachers - Graduate Level

In connection to the learning outcomes, on successful completion of this unit, pre-service teachers should have developed the following industry specific knowledge based on the Australian Professional Standards for Teachers - Graduate Level standards:

Industry StandardRelating toRelevant Learning Outcome
APST(GA)2.1Demonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area.LO1, LO2, LO3, LO4


Topics will be selected from:

  • Number Systems: 
  • Natural numbers and counting
  • Whole numbers, integers, fractions
  • Properties of numbers: base 10 system, multiples, factors, primes, number patterns
  • Basic operations: addition, subtraction, multiplication and division
  • Patterns and Algebra
  • Space
  • Two-dimensional and three-dimensional space: classification and properties
  • Angles
  •  Position
  • Measurement 
  • Length, time, area, volume and capacity
  • Metric and other measurement systems
  • Accuracy of measurement
  • Estimation
  • Chance and Probability
  • Data and Statistics
  • Problem solving and computational strategies
  • Mathematical modelling
  • Mathematics in other cultures
  • History of Mathematics
  • Mathematics as empowerment. 

Learning and teaching strategy and rationale

Learning and teaching will take place through a combination of self-directed studies including lecture-type content, video clips, academic readings, weekly tasks, and reflection on learning experiences, and two hours per week contact hours.  

Teaching and learning strategies are designed to be flexible and promote self-regulated and guided learning, underpinned by adult learning principles, and will include:  

  • Lecture-type content online to enhance mathematical content knowledge;  
  • Tutorial/workshop activities to engage in learning through active collaboration;  
  • Reading schedule and recommendations which involve directed reading as well as self-directed study suggestions;  
  • Discussion Forum online postings and responses designed to encourage peer learning.  
  • Webinars and podcasts for lecturer and student communication 

 This unit uses a Learning Management System (LMS) for the provision of lecture and tutorial content, required and/or further readings, and other unit material. Recorded lectures will be made available to students through this system. 

Assessment strategy and rationale

The assessment tasks and their weightings are designed to allow pre-service teachers to progressively demonstrate achievement against the unit learning outcomes. Assessment task 1 incorporates a diagnostic test which will enable students to develop a learning plan to build their current knowledge to meet the mathematical understanding and knowledge expectations for teaching in primary and/or early childhood settings. Assessment task 2 allows students to demonstrate a range of problem-solving strategies and their knowledge of mathematics by solving a range of problems and the development of mathematical investigations. The final assessment task is an examination assessing the learning outcomes and content that is taught and practised throughout the unit. These three types of assessments involve a variety of tasks to challenge students’ learning and enable differentiation of achievement and be equitable and ethical. 

Minimum Achievement Standards

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

In order to pass this unit, students are required to submit all assessment tasks, meet the learning outcomes of the unit and achieve a minimum overall passing grade of 50%.

Overview of assessments

Brief Description of Kind and Purpose of Assessment TasksWeightingLearning OutcomesGraduate CapabilitiesStandards

Assessment Task 1: Knowledge test and development of a learning plan 

To demonstrate mathematical knowledge and understanding and develop a learning plan to meet the content knowledge requirements for teaching mathematics in primary and/or early childhood settings.


LO1, LO2GC1, GC2, GC3, GC7, GC8, GC9, GC11, GC12ACECQA -C1, ACECQA -C4, ACECQA -F5, APST(GA)2.1

Assessment Task 2: Problem-Solving Folio 

To demonstrate an understanding of the deep learning and knowledge required in each of the content areas, pre-service teachers are required to: 

  • solve a range of problems 
  • reflect on the mathematical thinking and reasoning strategies used in the solution process 
  • Develop a mathematical investigation dealing with a real-world context 



Assessment Task 3: Written examination 

To demonstrate independent understanding of key mathematical content and problem-solving skills undertaken in the unit. 



Representative texts and references

Required text(s)

Oxford University Press UK (2020). Oxford Student’s Mathematics Dictionary. Oxford, UK: Oxford University Press.

Recommended texts

Bassarear, T. (2020). Mathematics for elementary school teachers (7th ed.). Boston, MA: Houghton Mifflin.

Billstein, R., Libeskind, S., & Lott, J. W. (2016). A problem solving approach to mathematics (12th ed.). Boston, MA: Pearson Addison Wesley.

Brady, K., & Winn, T. (2017). Maths skills for success at university. South Melbourne, Vic: Oxford University Press.

Clarke, D. M. (1996). The case of the mystery bone: A unit of work on measurement for grades 5 to 8. North Ryde, NSW: The Mathematical Association of New South Wales.

De Klerk, J. (2019). Illustrated maths dictionary (5th ed.). South Melbourne, Vic: Pearson Education.

Haylock, D. (2019). Mathematics explained for primary teachers (6th ed.). London: Sage Publications.

Thiel, O., & Perry, B. (2019). Innovative approaches in early childhood mathematics. New York, NY: Routledge.

Waite, S. (2017). Children learning outside the classroom: From birth to eleven. London: Sage.

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