Year

2024

Credit points

10

Campus offering

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Prerequisites

EDMA500 Foundations of Mathematics and Numeracy Curriculum and Pedagogy for Children

Incompatible

EDMA685 Mathematics Education 2

Unit rationale, description and aim

The Australian Curriculum: Mathematics aims to ensure that students are confident, creative users and communicators of mathematics, able to apply mathematics in their work and lives, Pre-service teachers must develop effective instructional and assessment strategies in mathematics to facilitate these aims for learners in early childhood and primary contexts.

This unit provides opportunities for pre-service teachers to consider issues and strategies in planning, implementing and monitoring learning experiences in early childhood and primary school mathematics, with a focus on further Number and Algebra and Probability and Statistics. Drawing on contemporary research, national and state curriculum documents and initiatives, pre-service teachers will explore theories of learning mathematics and effective teaching and learning strategies that enhance students’ understandings of mathematical content and proficiencies.

This unit will promote cognitive skills to analyse and synthesise a range of learning experiences and teaching approaches. A range of formal and informal assessment strategies will be examined with an emphasis on using student data to inform and differentiate teaching, and report on student achievement. Pre-service teachers will further develop theoretical frameworks of numeracy education and quality pedagogy for planning, teaching and assessment in mathematics and numeracy across other learning areas, focusing on the content areas of rational number, algebra and algebraic thinking, probability, and statistics as prescribed in national and state curricula.

The aim of this unit is to further develop per-service teachers’ understanding of theoretical principles and practices of mathematics education and to extend the application of contemporary pedagogy of early childhood and primary school 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.

Learning Outcome NumberLearning Outcome DescriptionRelevant Graduate Capabilities
LO1Critically discuss a range of issues related to contemporary mathematics teaching and learning, and communicate this analysis effectively, drawing on relevant research, the Early Years learning Framework, the Australian Curriculum: Mathematics and other state and national curriculum documents (APST 1.2, 2.5, 3.6; ACECQA A8, B1, B2, B3)GC1, GC2, GC7, GC9, GC10, GC11, GC12
LO2Evaluate student learning and implement extended learning sequences and teaching strategies, including the ethical use of digital technologies, that cater for the diverse needs of learners of different abilities and backgrounds, with appropriate assessment and moderation, constructive and timely feedback and reporting practices for sharing understandings of progress with students and stakeholders (APST 1.3, 1.4, 1.5, 1.6, 2.2, 2.3, 2.4, 2.5, 2.6, 3.2, 3.3, 3.4, 4.5, 5.1, 5.2, 5.3, 5.4, 5.5; ACECQA C1, C2, C4, C5, D3)GC1, GC2, GC5, GC9, GC10, GC11
LO3Critique and synthesise the specialised mathematical knowledge for teaching through informed research, required for primary school student acquisition of mathematical understanding, fluency, problem solving and reasoning in Number and Algebra, Statistics and Probability to inform planning for mathematics teaching with students of varying abilities, referenced to the Australian Curriculum: Mathematics and other relevant mathematics curriculum documents (APST 1.1, 2.1, 2.2, 2.3, 3.1, 3.2; ACECQA B1, B2, B3, C1, C2, C4, C5)GC1, GC2, GC7, GC9, GC10, GC11
LO4Enact and apply professional confidence and competence in the specialised mathematical knowledge for teaching (mathematical skills, concepts and processes) relating to Number and Algebra, Statistics and Probability to engage early childhood and primary students in their learning and to evaluate the effectiveness of teaching programs (APST 2.1, 3.4, 3.6, 6.2, 7.4; ACECQA A8, B1, B2, B3, C1, C2, C4, C5)GC1, GC2, GC3, GC6, GC7, GC11, GC12

AUSTRALIAN PROFESSIONAL STANDARDS FOR TEACHERS - GRADUATE LEVEL

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

1.1 Demonstrate knowledge and understanding of physical, social and intellectual development and characteristics of students and how these may affect learning.

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.

1.4 Demonstrate broad knowledge and understanding of the impact of culture, cultural identity and linguistic background on the education of students from Aboriginal and Torres Strait Islander 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.

1.6 Demonstrate broad knowledge and understanding of legislative requirements and teaching strategies that support participation and learning of students with disability.

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

2.2 Organise content into an effective learning and teaching sequence.

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

2.4 Demonstrate broad knowledge of, understanding of, and respect for Aboriginal and Torres Strait Islander histories, cultures and languages.

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.

3.1 Set learning goals that provide achievable challenges for students of varying abilities and characteristics.

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.

3.6 Demonstrate broad knowledge of strategies that can be used to evaluate teaching programs to improve student learning.

4.5 Demonstrate an understanding of the relevant issues and the strategies available to support the safe, responsible and ethical use of ICT in learning and teaching.

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

5.2 Demonstrate an understanding of the purpose of providing timely and appropriate feedback to students about their learning.

5.3 Demonstrate understanding of assessment moderation and its application to support consistent and comparable judgements of student learning.

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

5.5 Demonstrate an understanding of a range of strategies for reporting to students and parents/carers and the purpose of keeping accurate and reliable records of student achievement.

6.2 Understand the relevant and appropriate sources of professional learning for teachers.

7.4 Understand the role of external professionals and community representatives in broadening teachers’ professional knowledge and 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

A8. transitions and continuity of learning (including transition to school)

B. Education and curriculum studies

B1. Early Years Learning Framework

B2. the Australian curriculum

B3. numeracy, science and technology

C. Teaching pedagogies

C1. alternative pedagogies and curriculum approaches

C2. play based pedagogies

C4. teaching methods and strategies

C5. children with diverse needs and backgrounds

D. Family and community contexts

D3. Aboriginal and Torres Strait Islander perspectives

Content

Topics will include:

  • Rational number, algebraic thinking, and probability and statistics will form the mathematical content basis of this unit.
  • Research informed approaches to successful mathematics learning that are responsive to the strengths and needs of students from diverse linguistic, cultural, religious and socioeconomic backgrounds. 
  • The role of mathematical investigation and open tasks for constructing mathematical knowledge and orchestrating mathematical discourse, reasoning, argumentation, and proof.
  • Effective resources that support and enhance the teaching and learning of mathematics (e.g., manipulatives, digital technologies, and visual representations)
  • Assessment practices to guide learning teaching of mathematics: (e.g., informal and formal, including diagnostics approaches to formative and summative assessment of cognitive and affective learning).
  • Recording and tracking of student learning – interpretation and analysis of student data; moderation of student learning outcomes against class, state and national norms
  • Reporting of student learning outcomes to parents/carers and other stakeholders – types of reports; strategies for engaging parents
  • Issues regarding national testing programs, e.g., NAPLAN
  • Approaches for different levels planning for mathematics teaching, e.g., yearly, term, daily, whole school to year level
  • Incorporating the mathematical content and proficiencies
  • Integrating the mathematical content strands to facilitate connections across dimensions of mathematics
  • Effective contexts for mathematics learning (e.g., children’s literature, real life contexts, games, problem solving and investigations)
  • Identifying opportunities to use Numeracy across the curriculum, and ways that numeracy teaching strategies can be applied to other areas of the curriculum
  • Powerful pedagogical actions in mathematics (e.g. creating powerful learning environments, grouping practices, scaffolding learning, attending to literacy demands, promoting productive discourse and collaborative argumentation, questioning and prompting), selecting tasks and models that promote deep learning and knowing and using pedagogical knowledge.
  • Current national, state, and territory initiatives in mathematics education, as well as professional bodies and organisations that support teacher professional learning in mathematics 

Learning and teaching strategy and rationale

Engagement for learning is the key driver in the delivery of this curriculum which is offered in on-campus mode. A range of teaching and learning strategies are employed to reflect contemporary mathematics and numeracy learning pedagogies as can be applied in early childhood and primary contexts. These include interactive learning experiences; student-led discussions and group work; directed hands-on learning activities; real-world problem-solving; and the integration of digital technologies as a pedagogical tool for accessing, sharing and learning in mathematics. These experiences are facilitated through lectures, seminars, tutorials and self-directed reading/activity guides and study resources. The on-campus learning experiences are supported by online learning strategies, including synchronous and/or asynchronous digital engagement in reading/library tasks, learning activities, and discussion forums as mediated through the Learning Management System unit site.

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.

Technology Enhanced Learning

Technology use will be modelled by the teaching team to reflect the nature of technology in early childhood settings and primary schools. Student online platforms will include the Learning Management System, Online materials will be available in advance and as post-learning material. The announcements platform will serve as the main communication platform for all students. The use of forums will be made available if required. 

Face-to-face/Online Learning support

Students enrolled in both face to face and online learning modes are required to regularly log into the Learning Management System site to access recorded lectures and important announcements, to communicate with other students and lecturers, and to submit assessments and access feedback and grades. Students who are enrolled in either face to face or online learning will have equal access to support from the lecturer in charge and tutors.

Additional equipment requirements for online learning:

  • Reliable broadband access is recommended.
  • Headset with microphone to listen to podcasts, view videos and interact in synchronous classes.


ACU Online

This unit uses an active learning approach to support students in the exploration of knowledge essential to the discipline. Students are provided with choice and variety in how they learn. Students are encouraged to contribute to asynchronous weekly discussions. Active learning opportunities provide students with opportunities to practice and apply their learning in situations similar to their future professions. Activities encourage students to bring their own examples to demonstrate understanding, application and engage constructively with their peers. Students receive regular and timely feedback on their learning, which includes information on their progress.

Assessment strategy and rationale

The assessment tasks and their weightings allow pre-service teachers to progressively demonstrate achievement against the course learning outcomes by demonstrating academic and professional standards. The assessment in curriculum and pedagogy units focuses on applying content knowledge and skills to the design and implementation of curriculum, pedagogy and assessment. In this unit, the assessment focuses on pedagogies for developing mathematics and numeracy in advanced concepts of Number and Algebra and in Probability and Statistics. The three tasks are sequenced to allow feedback and progressive development in understanding requirements, including teacher knowledge for teaching mathematics in early childhood and primary school settings.

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 demonstrate achievement of learning outcomes by submitting all assessment tasks and obtaining a combined score of at least 50%. Assessment in this unit includes a Critical Task: Assessment Task 2 Designing a research-informed Sequence of Learning. This task is core to the demonstration of a number of Australian Professional Teacher Standards. Pre-service teachers must demonstrate mastery of every summative standard listed in the learning outcomes and attain a score of at least 50% in Task 2 in order to pass this unit.

Electronic Submission, Marking and Return

All relevant assessment items will be submitted electronically via the Learning Management System site. Marking will include a moderation process. Assessment returns will occur within the 3 week period as per the Assessment Policy. 

Overview of assessments

Brief Description of Kind and Purpose of Assessment TasksWeightingLearning Outcomes

Assessment Task 1

Case Study Analysis

You will be assigned a case study (note: other students from your class will be assigned the same case study). Each case study will include details of a learner; their recent learning experiences in mathematics, and their diagnostic assessment and related data about their understanding of rational number. Individually, review and analyse the assessment data. 

Identify:

  • Curriculum links (content and proficiencies assessed)
  • Learner strengths
  • Learner needs

Compare your findings with a case study partner to arrive at a consistent judgement.  Individually, in a concise report suitable for another teacher, describe your learner’s mathematical knowledge and misconceptions displayed, using examples from the assessment data. Include a description of the moderation process undertaken to arrive at the final assessment of the learner. Referring to the learner’s report, propose recommendations for future learning posed as learning goals and formulate feedback for the student.

The report content should demonstrate alignment to the research literature and ACARA F-6 Mathematics curriculum or equivalent. Also identify sections of the report which are suitable for inclusion in a parent/carer report on student achievement.

In response to the report, choose an open-ended task that would extend that student’s understanding of rational number. Present task details and design a task-specific assessment rubric that a teacher could use to assess student learning.

30%

LO1, LO2, LO3

Assessment Task 2

Designing a research-informed Sequence of Learning

Critical Task

Critically review and synthesise the research literature related to the learning pathway (from Birth to 12 years) of a mathematics concept (select a concept from rational number, algebra, or statistics and probability), including key skills and strategies, possible student misconceptions and issues that impact on children’s learning i.e., what makes learning this topic easy or hard for students. Discuss recommendations for effective pedagogical approaches to develop the chosen concept, including reference to appropriate curriculum documentation (e.g., ACARA or equivalent, Early Years Learning Framework) in view of the ideas presented in the literature review.

Choose a school year level (Years 3 - 6) and develop an overview for 5 effective sequential learning lessons that form a unit of work for the chosen concept, as well as appropriate assessment strategies for the unit. The overview should reflect the recommendations made in your discussion above.

Drawing on content of the literature review, designing a sequence of learning that demonstrates enactment of your specialize mathematical knowledge for teaching. Your unit plan should be a synthesis of ideas within the literature review and it needs to attend to the following key elements:

  • A rationale to justify the approach to teaching and learning used
  • Specific learning objectives and success criteria for learners
  • Curriculum links (content and proficiency strands)
  • A description of the way in which cross-curriculum priorities and general capabilities are included.
  • Explicit teaching and learning experiences (based on socio-constructivist learning approaches)
  • High impact teaching strategies including an appropriate range of teaching strategies incorporating ICT, meeting learning intentions and learning goals for students of varying abilities and from diverse backgrounds, including students with disability and students from Aboriginal and Torres Strait Islander backgrounds
  • Tasks which elicit higher order thinking including investigations, open-ended tasks, modelling
  • Effective resources to support learning including manipulatives, games and visual representations
  • Appropriate and ethical use of digital technologies
  • Purposeful ways to cater for diversity
  • Teacher questioning
  • Assessment strategies and ways of providing timely and appropriate feedback to students to improve learning.
  • <

40%

LO1, LO2, LO3, LO4

Assessment Task 3

Examination

Extended response and short answer questions demonstrating understandings of issues related to contemporary mathematics teaching, pedagogies, theories, issues, and the mathematical knowledge for teaching (specialised subject-matter knowledge and pedagogical content knowledge) required for teaching early childhood and primary school mathematics. 

30%

LO1, LO3, LO4

Representative texts and references

Required text(s)

Australian Curriculum: Mathematics https://www.australiancurriculum.edu.au/senior-secondary-curriculum/mathematics/

Australian Children’s Education and Care Quality Authority. Early Years Learning Framework https://www.acecqa.gov.au/acecqa-approved-learning-frameworks-version-2.0-communications-toolkit

Relevant state and territory Mathematics curriculum documents

Van de Walle, J., Karp. K. S., Bay-Williams, J. M., & Brass, A. (2019). Elementary and middle school mathematics: Teaching developmentally (1st Australian ed.). Pearson.

Recommended references

Booker, G., Bond, D., Sparrow, L., & Swan, P. (2020). Teaching primary mathematics (6th ed.).Pearson Australia.

Calder, N., Larkin, K., & Sinclair, N. (2018). Using mobile technologies in the teaching and learning of mathematics. Springer.

Lamon, S. J. (2020). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers (4th ed.). Routledge.

Leavy, A., Meletiou-Mavrotheris, M., & Paparistodemou, E. (Eds.). (2018). Statistics in early childhood and primary education: Supporting early statistical and probilistic thinking. Singapore: Springer.

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

Masalski, W., & Elliot, P. (2005). Technology-supported mathematics learning environments. (2005 Yearbook). Reston, VA: National Council of Teachers of Mathematics.

Reys, R. E., Rogers, A., Bennett, S., Cooke, A., Robson, K., Ewing B., & West, J. (2020). Helping children learn mathematics (3rd Australian ed.). John Wiley & Sons Australia.

Siemon, D., (2021). Teaching mathematics: Foundations to middle years (3rd ed.). Oxford University Press.

Way, J., Attard, C., Anderson, J., Bobis, J., McMaster, H., & Cartwright, K. (2020). Research in mathematics education in Australasia 2016-2019. Springer.

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