Unit rationale, description and aim
The foundations of Mathematics education draw on the analysis of mathematical task structures, cognitive and psychological processes involved in teaching and learning, and the influence of social and cultural contexts on learners. Research into effective mathematics teaching highlights the importance of general pedagogical knowledge, mathematics-specific pedagogical content knowledge, and subject matter knowledge. This unit integrates all three areas to support pre-service teachers in developing the knowledge and skills needed for effective mathematics teaching.
Pre-service teachers will explore the importance of mathematical knowledge for teaching and how to align their practice with curricula, while also addressing diverse learner needs. Emphasis is placed on respectful and inclusive approaches to teaching that value students’ academic needs, backgrounds, experiences and cultural identities. The unit examines a range of teaching strategies, including digital and physical manipulatives, and cognitive processes that support the development of mathematical understanding. Assessment practices are explored, focusing on identifying students’ mathematical thinking and using data to guide planning and instruction.
The unit aims to consolidate mathematics education for primary contexts. It focuses on planning, teaching, and assessing the strands Number, Algebra, Measurement, and Space (Geometry). Current learning theories and subject matter knowledge will support effective and responsive mathematics teaching.
Campus offering
No unit offerings are currently available for this unit.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 student learning needs based on analysis ...
Learning Outcome 01
Design effective teaching and assessment of Mathem...
Learning Outcome 02
Apply evidence-based mathematics pedagogy and lear...
Learning Outcome 03
Use a range of teaching, learning and assessment r...
Learning Outcome 04
Justify the selection and use of teaching, learnin...
Learning Outcome 05
Content
Topics will include:
· Developing fraction concepts using models and representations
· Developing decimal thinking in the primary years
· Teaching proportional reasoning in the primary years
· Planning units of work in primary mathematics
· Catering for diversity in primary mathematics
· Applying assessment in primary mathematics
· Teaching and learning numeracy across the curriculum
· Understanding and teaching algebraic thinking
· Understanding and teaching probability and statistics
· Understanding and teaching geometry and measurement
· Using technology to teach concepts in primary mathematics
· Understanding and teaching numeracy across the curriculum
· Effective home-school connections, involving parents and families in student learning in primary mathematics
Assessment strategy and rationale
The assessments are designed to support diverse learning needs and professional growth, with tasks focused on designing and evaluating mathematics assessment strategies, critiquing research literature, and developing a learning sequence.
The two assessment tasks reflect real-world teaching responsibilities and support the development of professional knowledge, practice, and engagement, providing pre-service teachers with the opportunity to demonstrate academic and professional capabilities. Task 1 focuses on using diagnostic formative assessment interviews to analyse student understanding. Task 2 requires the critical evaluation of research literature and curriculum documents to design a research-informed sequence of mathematics learning that enhances student understanding and mathematical proficiency. Pre-service teachers will be carefully scaffolded to access and use a range of resources, including ICTS and generative AI, to support the completion of the assessment.
To pass this unit, students are required to submit all assessments and achieve an overall passing grade of 50% across the two tasks.
Overview of assessments
Assessment Task 1: Case Study in Mathematics Lear...
Assessment Task 1: Case Study in Mathematics Learning Progression
Conduct a case study project with one student in Years 3-4 to analyse their understanding, progression and next-steps in learning rational number concepts. Collect, appraise and moderate data, including a diagnostic interview and other evidence of student learning, to identify the selected student’s current understandings and next-steps learning with reference to curricula and developmental progressions. Then, use your data analysis to develop a next-steps teaching plan using AI prompts and tools. Critically evaluate the AI plan with reference to literature, adjusting as necessary, and reflect on your professional learning throughout the project.
50%
Assessment Task 2: Learning Sequence with Rationa...
Assessment Task 2: Learning Sequence with Rationale
Develop a learning sequence for Years 5-6 comprising five lessons focused on a selected mathematics area from number, patterns and algebra, or chance and data. The learning sequence should incorporate: (1) a range of teaching strategies, including the use of open-ended tasks and investigations, (2) differentiation for supporting diverse learners, (3) the appropriate and ethical use of ICT learning tools, and (4) formative and summative assessment plans for monitoring and responding to students’ learning. Use appropriate state and territory curricula to construct a rubric for assessing student progress and achievement. Then, develop a rationale that outlines your pedagogical decision-making in relation to selected teaching, learning and assessment strategies and with reference to literature.
50%
Learning and teaching strategy and rationale
This unit adopts a social constructivist approach to develop pre-service teachers’ knowledge and skills in planning, assessment, and effective pedagogy. Through active engagement and collaborative learning, pre-service teachers will deepen their understanding of teaching strategies by engaging in critical reading, discussion, and practice. Key teaching skills—including planning, assessing, and synthesising information—will be developed throughout the unit.
This unit equips pre-service teachers with the knowledge, skills, and understanding required to teach Mathematics in primary school settings, with reference to national and relevant state curricula. Pre-service teachers will engage with a combination of theoretical and practical learning experiences, with a focus on core numeracy skills developed throughout the primary years. Consideration is given to the ways that diverse learners can be provided with access to and opportunities for success in Mathematics.
Learning experiences include video lectures, group discussions, self-directed tasks, and assessment activities. A variety of strategies will be used to support learning, including reading, reflection, webinars, podcasts, and videos. The teaching team will model online platforms and technologies to reflect authentic use in contemporary classrooms. The unit is designed to connect theory with practice, and to promote inclusive, responsive teaching in diverse educational settings.
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:
Relating toDemonstrate knowledge and understanding of research into how students learn and the implications for teaching.
Relevant Learning OutcomeLO2, LO3
Relating toDemonstrate knowledge of teaching strategies that are responsive to the learning strengths and needs of students from diverse linguistic, cultural, religious and socioeconomic backgrounds
Relevant Learning OutcomeLO1, LO4, LO5
Relating toDemonstrate knowledge and understanding of strategies for differentiating teaching to meet the specific learning needs of students across the full range of abilities.
Relevant Learning OutcomeLO4
Relating toDemonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area.
Relevant Learning OutcomeLO1, LO5
Relating toUse curriculum, assessment and reporting knowledge to design learning sequences and lesson plans.
Relevant Learning OutcomeLO1, LO2, LO3
Relating toKnow and understand literacy and numeracy teaching strategies and their application in teaching areas.
Relevant Learning OutcomeLO1
Relating toImplement teaching strategies for using ICT to expand curriculum learning opportunities for students.
Relevant Learning OutcomeLO4
Relating toPlan lesson sequences using knowledge of student learning, content and effective teaching strategies.
Relevant Learning OutcomeLO1, LO2, LO5
Relating toInclude a range of teaching strategies.
Relevant Learning OutcomeLO5
Relating toDemonstrate knowledge of a range of resources, including ICT, that engage students in their learning.
Relevant Learning OutcomeLO4
Relating toIdentify strategies to support inclusive student participation and engagement in classroom activities.
Relevant Learning OutcomeLO4
Relating toDemonstrate understanding of assessment strategies, including informal and formal, diagnostic, formative and summative approaches to assess student learning.
Relevant Learning OutcomeLO1, LO2
Relating toDemonstrate the capacity to interpret student assessment data to evaluate student learning and modify teaching practice.
Relevant Learning OutcomeLO5
Australian Institute for Teaching and School Leadership (AITSL) Core Content
On successful completion of this unit, pre-service teachers should have developed the following industry specific knowledge based on the AITSL Core Content:
Relating toHow to use formative assessment practices to gather and interpret information about student learning as learning is taking place – for example, use of simple, low-key assessments such as exit slips, quick quizzes or targeted oral questioning to prompt students to articulate their reasoning and identify common student misconceptions.
Relevant learningLO2
Relating toHow to design summative assessment to assess students against a standard or benchmark to gain an understanding of the level of mastery attained.
Relevant learningLO2, LO3
Relating toHow to produce and use developmental rubrics with criteria tailored to the specific task and/or work samples so that students understand what is expected.
Relevant learningLO2
Relating toA conceptual understanding of the six strands of mathematics: number, algebra, geometry, measurement, statistics and probability; and the four proficiencies: understanding, fluency, problem solving and reasoning.
Relevant learningLO1
Relating toThe research that shows numeracy is a fundamental component of learning, discourse, and critique across all areas of the curriculum and improves students’ understanding of and engagement with material within and beyond the mathematics curriculum.
Relevant learningLO2, LO3
Relating toHow to deliver explicit numeracy instruction followed by a progressive removal of scaffolding as students become more proficient through a combination of underpinning mathematical concepts and skills (numerical, spatial, graphical, statistical, and algebraic); mathematical thinking and strategies; and general thinking skills as appropriate to discipline and discipline-specific curriculum and pedagogical studies as outlined in standard 4.2.
Relevant learningLO2, LO3
Relating toThe importance of independent problem-solving once a student approaches proficiency in underpinning mathematical concepts.
Relevant learningLO5
Representative texts and references
Representative Texts and References
Australian Curriculum Mathematics. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/.
Relevant state and territory Mathematics curriculum documents.
Baker, P., Callingham, R., & Muir, T. (2023). Primary mathematics: Integrating theory with practice (4th ed.). Cambridge.
Van de Walle, J., Karp, K., Bay-Williams, J., & Brass, A. (2019). Primary and middle years mathematics: Teaching developmentally (1st Australian ed). Pearson Australia.
Recommended References
Booker, G., Bond, D., & Seah, R. (2020). Teaching primary mathematics (6th ed.). Pearson Australia.
Ball, D. B., & Ruhama, E. (Eds.). (2009). The professional education and development of teachers of mathematics: The 15th ICMI study. Springer.
Bishop, A., Tan, H., & Barkatsas, T. N. Eds.). (2015). Diversity in mathematics education: Towards inclusive practices. Springer.
Clements, D.H., & Sarama, J. (2021). Learning and teaching early math: The learning trajectories approach. Routledge.
Liljedahl, P. (2020). Building thinking classrooms in mathematics, grades K-12. Corwin.
Goos, M., Geiger, V., Dole, S., Forgasz, H., & Bennison, A. (2019). Numeracy across the curriculum. Allen & Unwin
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.
Roos, H. Students’ voices of inclusion in mathematics education. Educ Stud Math 113, 229–249 (2023). https://doi.org/10.1007/s10649-023-10213-4
Siemon, D. (2021). Teaching mathematics: Foundations to middle years (2nd ed.). Oxford University Press.
Smith, M.S., & Stein, M.K. (2018). Five practices for orchestrating productive mathematical discussion (2nd ed.). National Council of Teachers of Mathematics (NTCM).