Unit rationale, description and aim
This unit functions as a preparatory pathway for students seeking admission to Initial Teacher Education, where well‑developed numeracy capability underpins curriculum engagement, assessment literacy, professional decision‑making, and successful completion of mandated literacy and numeracy requirements. Students will develop mathematical knowledge, confidence and habits of reasoning. The unit supports equity of access to teacher education by providing structured opportunities to consolidate and extend foundational mathematical understanding in ways appropriate to tertiary study.
In this unit, students develop conceptual understanding, procedural fluency and mathematical reasoning across number, proportional reasoning, algebraic thinking, measurement, statistics and probability. Learning experiences emphasise structured and explicit engagement in inquiry, problem solving and mathematical modelling in real‑world contexts, with a strong focus on representing, explaining and justifying mathematical ideas using graphical, numerical and algebraic forms. Digital technologies are used to support exploration, representation and communication of mathematical relationships. Throughout the unit, students are supported to develop confidence in mathematical language and reasoning aligned to university expectations.
The aim of this unit is to prepare students for successful progression into mathematics and curriculum units within initial teacher education programs by developing the mathematical understanding, reasoning and communication skills required for tertiary‑level study.
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.
Apply core mathematical concepts across number, al...
Learning Outcome 01
Analyse relationships between variables using prop...
Learning Outcome 02
Communicate mathematical reasoning using accurate ...
Learning Outcome 03
Solve mathematical problems using modelling, estim...
Learning Outcome 04
Content
Topics will include:
- Number concepts including counting, place value, natural numbers, integers, factors and prime numbers
- Rational numbers and their representations as fractions, decimals and percentages, including equivalence and operations
- Additive and multiplicative thinking, including rates, ratios and proportional reasoning
- Computational strategies including mental computation, estimation, calculator use and checking for reasonableness
- Algebraic thinking, including the use of symbols, expressions and equations to represent relationships between variables
- Linear relationships and simple non‑linear relationships, including quadratic and introductory exponential models, represented graphically, numerically and algebraically
- Solving problems using algebraic, numerical and graphical techniques, including changing the subject, factorisation, simultaneous equations and interpretation of graphs
- Measurement concepts including length, area, volume, capacity, mass, time, temperature and derived measures such as speed and density
- Use of standard units and conversion between metric and commonly used measurement systems, including estimation and precision
- Data collection and investigation, including populations and samples, categorical, numerical and time‑series data
- Representation and interpretation of data using appropriate tables, graphs and summary measures
- Introductory probability concepts, including experimental and theoretical probability, randomness, long‑run frequency and simple probability models
- Mathematical modelling and problem solving in real‑world contexts, with reflection on assumptions, uncertainty and limitations
Assessment strategy and rationale
Assessment tasks are designed to progressively develop and evaluate mathematical understanding, reasoning and communication consistent with expectations of readiness for initial teacher education. The assessment sequence emphasises scaffolding, feedback and increasing independence, providing multiple opportunities for students to consolidate learning before high‑stakes, secure assessment.
Early assessment focuses on guided and collaborative application of mathematical concepts, supported by structured prompts, exemplars and formative feedback. Students will be supported to use generative AI appropriately to develop their knowledge and skills. Subsequent assessment requires increasingly independent selection and application of mathematical methods, representations and explanations in real-world contexts. Feedback from earlier tasks supports refinement of reasoning and communication.
The final examination provides assurance that students can independently apply mathematical knowledge and reasoning across a broad range of topics under controlled conditions. Collectively, the assessment tasks provide valid and reliable evidence of achievement of the unit learning outcomes and readiness for progression into AQF Level 6 and 7 mathematics and curriculum units.
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
Assessment Task 1: Mathematical investi...
Assessment Task 1: Mathematical investigation presentation
Conduct and present a guided mathematical investigation based on a real‑world context. Apply linear, quadratic or simple exponential relationships to model a problem using appropriate numerical, algebraic and graphical representations. Explain mathematical reasoning, justify methods used and interpret results using accurate mathematical language and visual representations.
20%
Assessment Task 2: Real-world problem-s...
Assessment Task 2: Real-world problem-solving logbook
Complete an individual logbook that documents the solution of mathematical problems drawn from real‑world contexts. Apply mathematical modelling, proportional reasoning, algebraic thinking, measurement and data interpretation using numeric, graphical and digital representations. Explain reasoning and reflect briefly on the effectiveness of methods used.
30%
Assessment Task 3: Examination &nb...
Assessment Task 3: Examination
Demonstrate independent application of mathematical knowledge and reasoning in a written examination. Solve problems across number, algebra, proportional reasoning, measurement, statistics and probability, including unfamiliar contexts, using appropriate methods and representations.
50%
Learning and teaching strategy and rationale
Students will be supported to develop mathematical understanding, confidence and reasoning through explicit, scaffolded instruction aligned with the expectations of tertiary study and initial teacher education programs. Teaching approaches prioritise clear explanation of mathematical concepts through worked examples, guided practice and gradual release of responsibility. Core ideas are introduced through lecturer modelling, with explicit attention to mathematical language, representations and reasoning processes.
Learning activities are sequenced to move from structured tasks to more open-ended problem solving and modelling, enabling students to consolidate foundational skills before applying them in unfamiliar contexts. Tutorials and workshops provide opportunities for guided practice, peer discussion and rehearsal of mathematical explanations, supporting students to articulate reasoning and respond to feedback. Digital technologies, including generative AI, support visualisation, representation and exploration of mathematical relationships.
Formative feedback is embedded throughout the unit to support diverse students through low stakes tasks, worked solution discussions and tutor feedback, enabling students to identify misconceptions, reflect on learning and take increasing responsibility for improvement. This approach inducts students into the reasoning, independence
Representative texts and references
Representative texts and references
Recommended references
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Booker, G. (2021). Building numeracy: From assessment to conceptual understanding and fluency. Oxford University Press.
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Lamon, S. J. (2020). Teaching fractions and ratios for understanding: essential content knowledge and instructional strategies for teachers (4th ed.). Taylor and Francis.
Matthews, C. (2019). Maths as storytelling: Maths is beautiful (chapter 7). In K. Price & J. Rogers (Eds.), Aboriginal and Torres Strait Islander education: An introduction for the teaching profession (pp. 138–160). Cambridge University Press.
Smalley, R. T. (2011). Adults returning to study VCE Mathematics: lifelong learning, transition and engagement, and the adult learner (Doctoral dissertation, Monash University).
Svensson, C. K., & Ghosh, T. K. (2021). Introduction: Methods of Data Representation, Interpretation, and Analysis. In Theory and Practice of Contemporary Pharmaceutics (pp. 3-30). CRC Press.
Siklos, S. (2019). Advanced problems in mathematics: preparing for university (New revised edition.). Open Book Publishers.
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Tynan, D., Caruso, N., Dowsey, J., Flynn, P., Lamson, D., & Swedosh, P. (2015). Cambridge Checkpoints VCE Specialist Maths Units 1 and 2. Cambridge University Press.
Van d Walle, J., Bay-Williams, J. M., & John Van de/Karp Walle (Karen S.). (2023). Elementary and Middle School Mathematics: Teaching Developmentally, Global Edition.