Year

2024

Credit points

10

Campus offering

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  • Semester 2Multi-mode, Multi-mode Indigenous

Prerequisites

Nil

Incompatible

EDMA241 Mathematics Education 1: Curriculum, Pedagogy and Assessment , EDMA262 Mathematics: Learning and Teaching 1

Unit rationale, description and aim

Mathematics education has grown to become a recognised and significant research area in education. Its theories are based on analysis of the structure of mathematical tasks, the psychology of teaching and learning, and an understanding of the effect of social context on learning. Research on expertise in teaching mathematics has shown that teachers of all year levels require general pedagogical knowledge, specific mathematics pedagogical–content knowledge, and mathematics subject–matter knowledge. All three of these knowledge areas are important in this unit.

In this unit, pre–service teachers develop an understanding of the importance of mathematical knowledge for teaching and how to address the requirements of the Australian Curriculum: Mathematics, and learner needs.

Approaches to learning and teaching mathematics that are effective and respectful of children’s and students’ background and culture will be emphasised. The role of manipulatives (concrete and virtual), digital technologies, language, representations, and mental processes in developing children’s and students’ conceptual understanding and skills will be explored. Methods of assessment will be considered to identify children’s and students’ mathematical understanding and to inform planning and teaching.

This unit aims to provide an introduction to early childhood (prior to school) and primary school mathematics education and will specifically focus on aspects of planning, teaching, and assessing the Number, Algebra , Measurement, and Space (geometry) strands of the Australian Mathematics Curriculum, underpinned by a clear understanding of relevant subject–matter knowledge and current theories of learning and their impact on mathematics teaching.

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
LO1Describe what it means to learn, know and teach mathematics and how mathematics is a powerful tool in making sense of the world (APST 2.1, 2.3, 2.5; ACECQA B1, B2, B3)GC1, GC2, GC9, GC11
LO2Explain the importance of mathematical beliefs, and developing confidence, resilience and positive attitudes to mathematics (APST 1.2, 1.3, 4.1; ACECQA A1, A6)GC1, GC2, GC3, GC9, GC11
LO3Demonstrate personal mathematical knowledge for teaching, and understanding of the development of mathematical concepts, skills and thinking strategies and processes (APST 2.1; ACECQA A1, A6, E2)GC1, GC2, GC3, GC7
LO4Apply appropriate approaches to teaching mathematics that cater for children and primary students across a full range of abilities and diverse learning needs, particularly the use of formative, summative and diagnostic assessment data (APST 1.2, 1.3, 1.5, 2.3, 2.5, 3.2, 3.3, 5.1, 5.4; ACECQA A1, A6, B1, B2, B3, C4, E3)GC2, GC9, GC11
LO5Apply theories and research about children and primary students' development of mathematical concepts and proficiencies to design learning sequences and learning experiences to support student’s mathematical learning of Number and Algebra (restricted to Whole Number including number and place value and four operations and financial mathematics), Measurement (units of measurements) and Space (Geometry) (shape, location and transformation), as outlined in relevant pedagogical and curriculum documents (APST 1.2, 1.5, 2.1, 2.3, 2.5, 2.6, 3.2, 3.3, 3.4; ACECQA A1, A6, B1, B2, B3, C1, C4)GC1, GC2, GC9, GC11

AUSTRALIAN PROFESSIONAL STANDARDS FOR TEACHERS - GRADUATE LEVEL

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

1.2 Demonstrate knowledge and understanding of research into how students learn and the implications for teaching.

1.3 Demonstrate knowledge of teaching strategies that are responsive to the learning strengths and needs of students from diverse linguistic, cultural, religious and socioeconomic backgrounds.

1.5 Demonstrate knowledge and understanding of strategies for differentiating teaching to meet the specific learning needs of students across the full range of abilities.

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

2.3 Use curriculum, assessment and reporting knowledge to design learning sequences and lesson plans.

2.5 Know and understand literacy and numeracy teaching strategies and their application in teaching areas.

2.6 Implement teaching strategies for using ICT to expand curriculum learning opportunities for students.

3.2 Plan lesson sequences using knowledge of student learning, content and effective teaching strategies.

3.3 Include a range of teaching strategies.

3.4 Demonstrate knowledge of a range of resources, including ICT, that engage students in their learning.

4.1 Identify strategies to support inclusive student participation and engagement in classroom activities.

5.1 Demonstrate understanding of assessment strategies, including informal and formal, diagnostic, formative and summative approaches to assess student learning.

5.4 Demonstrate the capacity to interpret student assessment data to evaluate student learning and modify teaching practice.

ACECQA CURRICULUM SPECIFICATIONS

On successful completion of this unit, pre-service teachers should have developed the following specific knowledge:

A. Child development and care

A1. Learning, development and care

A6. Diversity, difference and inclusivity

B. Education and curriculum studies

B1. Early Years Learning Framework

B2. The Australian curriculum

B3. Numeracy, science and technology

C. Early childhood pedagogies

C1. Alternative pedagogies and curriculum approaches

C4. Teaching methods and strategies

E. History and philosophy of early childhood

E2. Contemporary theories and practice

Content

Topics will include:

  • Mathematical knowledge for teaching
  • Mathematical content and proficiencies as detailed in the Early Years Learning Framework and the Australian Curriculum: Mathematics and other state and national documents
  • Identification of the key ideas, principles and misconceptions in number, algebra, measurement and space.
  • Assessment practices including interviews and open-ended tasks, that inform the learning and teaching of mathematics
  • Theories of learning that support the teaching of mathematics, with emphasis on those that support conceptual understanding and procedural fluency
  • Influence of the teacher on student learning
  • Typical pathways/trajectories/frameworks in children’s and students' mathematical learning, early years to late primary years, and its application to the design of learning experiences that are appropriate to child and student needs
  • Design of learning experiences/tasks and lessons which incorporate the use of manipulatives, words and symbols, students’ interests and digital technology
  • Plan, implementation and management of mathematical learning experiences for individual, group and whole class teaching and learning.

Mathematics content basis for the teaching in this unit will be Number (restricted to Whole Number including number and place value, four operations and financial mathematics), Algebra, Measurement (units of measurements) and Space (shape geometry, location and transformation) as required in early learning and primary school spaces. This will include pre-service teacher reflection on and enhancement of their personal mathematical knowledge for teaching.

Learning and teaching strategy and rationale

The learning and teaching strategy for this unit is based on a socioconstructivist approach that recognises that learning builds on pre-existing understandings and is shaped by a learner’s sociocultural context. Pre-service teachers should expect to participate in a range of the following: seminar presentations, group discussions, , self-directed study activities and assessment tasks. Participation in appropriate educational settings may be required, in particular learning experiences/tasks expected on early learning and/or classroom placement.

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. The learning and teaching and assessment strategies include a range of approaches to support learning such as reading, reflection, discussion, webinars, podcasts, video etc.  It is expected that students attend all classes on campus if they are enrolled as an on-campus student.

The unit is hosted on a Learning Management System (LMS) site with resources and online links, announcements, and a discussion board to post questions and reflections that promote connection between content and educational experiences.

 

Mode of delivery: This unit may be offered in different modes to cater to the learning needs and preferences of a range of participants.

On Campus

Most learning activities or classes are delivered at a scheduled time, on campus, to enable in-person interactions. Activities will appear in a student’s timetable.

Multi-mode

Learning activities are delivered through a planned mix of online and in-person classes, which may include full-day sessions and/or placements, to enable interaction. Activities that require attendance will appear in a student’s timetable.

Online unscheduled

Learning activities are accessible anytime, anywhere. These units are normally delivered fully online and will not appear in a student’s timetable. 

Online scheduled

All learning activities are held online, at scheduled times, and will require some attendance to enable online interaction. Activities will appear in a student’s timetable.

ACU Online 

In ACU Online mode, this unit is delivered asynchronously, fully online using an active, guided learning approach. Pre-service teachers are encouraged to contribute to asynchronous weekly discussions and receive regular and timely feedback on their learning.  

Technology Enhanced Learning

Technology use will be modelled by the teaching team to reflect the nature of technology in primary schools.

Assessment strategy and rationale

A range of assessment procedures are used to meet the unit learning outcomes and develop graduate attributes and professional standards and criteria consistent with University assessment requirements.

The three assessment tasks and their weightings are designed to allow pre-service teachers to progressively demonstrate achievement against the course learning outcomes by demonstrating academic and professional standards.

The Mathematics CPA unit will focus on developing understanding of, and skills across the professional knowledge, practice and engagement needed to meet expectations of the Graduate Attributes and the Australian Professional Standards for Teachers: Graduate level.

Through completing Task 1, pre-service teachers will have the opportunity consider the big ideas in the teaching and learning of Space (geometry mathematics). The second task builds on the learning of mathematics and focuses on using data and evidence of a child's/student's Number learning to inform planning of learning experiences/tasks to build on a child's/students’ knowledge.  In Task 3, pre-service teachers will demonstrate the use of curriculum documents to create a sequence of learning activities and associated resources that enhance student understanding and proficiencies in Measurement. These assessment tasks model the ‘real world’ of early learning and classrooms and the teaching responsibilities required to teach effectively in those spaces. These assessments also engage pre-service teachers in diverse forms of communication including a teaching and learning guide, an achievement report and planning/programming documentation, and a video presentation for classroom use.

The three assessment tasks are sequenced to allow feedback and progressive development of content knowledge and skills to prepare pre-service teachers for mathematics content and pedagogical knowledge units in the sequence of mathematics and numeracy units.

Minimum Achievement Standards

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

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

Overview of assessments

Brief Description of Kind and Purpose of Assessment TasksWeightingLearning Outcomes

Assessment Task 1: Teaching and Learning Guide: Space (Geometry)

Critically reflect and develop a teaching and learning guide that draws together understandings from the lectures, tutorial/workshop activities and prescribed readings. The journal entry demonstrates critical reflection and growing understanding of:

  • Key ideas about the content area of Space (geometry)
  • Students’ misconceptions and difficulties when learning the content area,
  • Teaching strategies, learning experiences/tasks and resources to best support the learning of children and students,
  • The curriculum progression related to the content area of Space (Geometry)
  • Articulation of implications for future practice.
  • <

20%

LO1, LO3, LO4

Assessment Task 2: Data-informed Planning in Number

Interpret data, collected through the use of a mathematics assessment interview, concerning a child/student achievement in Number.

Report on and analyse the child’s/student’s responses accurately in respect to the interview questions. Form judgments about their mathematical development with reference to a theoretical framework and curriculum progression. Summarise the data and judgements about the child’s/student’s achievement in a report suitable for reading by an in-service teacher. Include research guided recommendations for the child’s/student’s future Number learning and use insights from data analysis to design a subsequent teaching and learning plan including a variety of resources (may include ICT, manipulatives, games and task cards) for the child/student, assuming that their child’s/student’s peers will also benefit from the learning programmed in that teaching and learning plan.

40%

LO1, LO2, LO3, LO4, LO5

Assessment Task 3: Teaching and Learning Measurement Presentation

Develop a digital presentation (e.g., PowerPoint, pod/vodcast, video, blog, webpage) that:

  • Demonstrates the mathematical content knowledge (MCK) required for teaching Measurement in the early or primary years and related proficiencies addressed in the unit
  • Shows a carefully constructed sequence of teaching and learning activities, including the teaching resources (at its most basic in the form of a lesson plan) that demonstrate application of MCK and pedagogical content knowledge (PCK) to effectively teach Measurement concepts and/or skills associated with one measurement attribute (e.g., length, capacity, mass, etc.).
  • <

40%

LO1, LO3, LO4, LO5

Representative texts and references

Required text(s)

Van de Walle, J., Karp, K., Bay-Williams, J., & Bass, A. (2019). Primary and middle years mathematics (1st Australian ed.). Pearson.

Australian Curriculum: Mathematics. https://v9.australiancurriculum.edu.au

Early Years Learning Framework: Belonging, Being & Becoming (v. 2.0): https://www.acecqa.gov.au/sites/default/files/2023-01/EYLF-2022-V2.0.pdf

Relevant state and territory Mathematics curriculum documents.

Recommended references

Baker, P., Callingham, R., & Muir, T. (2023). Primary mathematics: Integrating theory with practice (4th ed.). Cambridge.

Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.

Boaler, J. (2016). Mathematical mindsets. Jossey-Bass.

Booker, G., Bond, D., & Seah, R. (2020). Teaching primary mathematics (6th ed.). Pearson Australia.

Clarke, D. (2005). Written algorithms in the primary years: Undoing the good work? In M. Coupland, J. Anderson, & T. Spencer (Eds.). Making mathematics vital (Proceedings of the 20th biennial conference of the Australian Association of Mathematics Teachers). AAMT, pp. 93-98.

Department of Education and Training of Western Australia. (2004). First steps in mathematics: Number. Rigby Harcourt Education.

Haylock, D. & Manning, R. (2019). Mathematics explained for primary teachers (Australian ed.). Sage Publications.

Haylock, D., & Cockburn, A. D. (2017). Understanding mathematics for young children (5th ed.). Sage Publications.

Knaus, M., & Featherstone, S. (2015). Maths is all around you: Developing mathematical concepts in the early years. Bloomsbury Publishing.

MacDonald, A. (2018). Mathematics in early childhood education. Oxford.

McIntosh, A., & Dole, S. (2004). Mental computation: A strategies approach. Department of Education, Tasmania.

Reys, R. E., Rogers, A., Bennett, S., Cooke, A., Robson, K., Ewing B., & West, J. (2022). Helping children learn mathematics (4th ed.). John Wiley & Sons Australia.

Rowland, T., Turner, F., Thwaites, A., & Huckstep, P. (2009) Developing primary mathematics teaching: Reflecting on practice with the knowledge quartet. Sage publications.

Siemon, D., Warren, E., Beswick, K., Faragher, R., Miller, J., Horne, M., Jazby, D., Breed, M., Clark, J., & Brady, K. (2021). Teaching mathematics: Foundations to middle years (3rd ed.). Oxford University Press.

Note: A number of seminal texts are included due to their relevance to the learning in the unit.

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