Unit rationale, description and aim
Preservice teachers will develop a deep understanding of numeracy differentiation as a responsive, evidence‑informed approach to supporting and extending student learning across a continuum of need. This unit builds upon preservice teachers’ knowledge through previous mathematics curriculum, pedagogy and assessment units. Numeracy is fundamental to students’ engagement with curriculum knowledge, problem solving and reasoning across primary and secondary learning areas. Effective numeracy differentiation requires teachers to identify students’ current understandings, misconceptions and partial knowledge, and to respond through targeted, data‑informed teaching practices.
This unit focuses on assessment‑informed numeracy intervention with a mathematical emphasis on Number and Algebra. Preservice teachers learn to interpret evidence from assessment tasks, situate learners within numeracy learning trajectories, and design targeted instructional responses that address identified needs while promoting interconnected conceptual understanding, fluency and multi-representational reasoning. The unit addresses whole‑class, small‑group and individual differentiation within a multi‑tiered system of support and includes strategies for monitoring progress and communicating effectively with families.
The aim of this unit is to equip preservice teachers with the knowledge, skills and professional judgement required to design, implement and evaluate numeracy differentiation strategies that improve learning outcomes for diverse learners, including those requiring additional support and those demonstrating high levels of mathematical capability.
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.
Analyse numeracy assessment data to identify stude...
Learning Outcome 01
Interpret numeracy learning trajectories and progr...
Learning Outcome 02
Design evidence informed numeracy assessment tasks...
Learning Outcome 03
Develop justified and targeted numeracy differenti...
Learning Outcome 04
Communicate numeracy learning needs, progress and ...
Learning Outcome 05
Content
Topics will include:
- What is numeracy differentiation and who needs it? Exploring three tiers of intervention
- Interpreting assessment data for differentiation, intervention and for monitoring progress in the domain of number and algebra
- Whole class/small group targeted numeracy differentiation, including adaptation for vulnerable students and extension for highly capable students (Tiers 1 and 2)
- Dyscalculia – at risk vs specific learning disability; individual intervention (Tier 3)
- Designing mathematics differentiation to support understanding: Balancing cognitive demand, conceptual development, and learner needs
- Pedagogical strategies for inclusive mathematics learning
- Problem-solving approaches with differentiation
- Explicit numeracy instruction in number and algebra
- Culturally responsive teaching
Assessment strategy and rationale
Assessment in this unit is designed to progressively develop and demonstrate preservice teachers’ capacity to assess, analyse and respond to numeracy learning needs through targeted differentiation and intervention. The assessment strategy reflects authentic professional practice by requiring engagement with assessment evidence, interpretation of numeracy learning progressions, design of instructional responses, and professional communication with families. Together, the assessment tasks provide opportunities for feedback and reflection.
Task 1 focuses on analysing student responses to identify misconceptions and partial understandings and on designing a numeracy support script that demonstrates explicit instruction, responsive questioning and reflective practice. Task 2 builds on this analysis by requiring the design and justification of targeted intervention plans and the composition of professional communication for parents or carers, demonstrating integration of assessment, teaching and reporting practices. Generative artificial intelligence tools may be used ethically to support planning and drafting, with appropriate acknowledgment in accordance with university policy.
To pass this unit, students are required to submit all assessment tasks and achieve a combined mark of at least 50%.
Overview of assessments
Assessment Task 1: Numeracy support script ...
Assessment Task 1: Numeracy support script
Analyse a set of supplied student responses to numeracy learning tasks to identify misconceptions, partial understandings and potential barriers to learning. Develop a numeracy support script that demonstrates selected teaching strategies, including appropriate use of explicit teaching, questioning and representations or resources to support and/or extend learners’ mathematical understanding. Explain the mathematical thinking evident in the student responses with reference to relevant scholarly literature and reflect on the professional knowledge, skills and beliefs required to support students’ numeracy progression.
50%
Assessment Task 2: Differentiation plan ...
Assessment Task 2: Differentiation plan
Design two targeted small‑group numeracy intervention plans based on assessment data: one to address identified gaps in learning and one to extend learning. Develop a sequence of numeracy tasks aligned with research‑based learning trajectories or curriculum expectations and outline teaching strategies and assessment practices for effective implementation and progress monitoring. Compose a professional communication for parents or carers that explains students’ strengths, learning needs and planned interventions. Justify all pedagogical and assessment decisions with reference to relevant research and curriculum documents.
50%
Learning and teaching strategy and rationale
Preservice teachers engage in interactive, practice‑oriented learning experiences designed to develop their capacity to analyse assessment data, interpret numeracy progressions, and design targeted differentiation and intervention. Teaching strategies emphasise active participation through workshops, guided analysis of student work samples, collaborative problem solving, and structured reflection on teaching practice. These approaches support preservice teachers with diverse learning needs to connect theory with practice and develop professional judgement in responding to diverse numeracy learning needs.
Learning activities model evidence‑informed numeracy pedagogy, including explicit teaching, the use of representations and manipulatives, scaffolded questioning, and strategies for cognitive overload. Classroom scenarios are used to support analysis of misconceptions and to design instructional responses aligned with multi‑tiered systems of support. Opportunities for peer discussion and feedback promote critical reflection and shared professional learning. Inclusive teaching and learning practices promote equitable access and draw on a diverse range of resources, equipping preservice teachers with the knowledge and skills required for their future professional practice.
Technology‑enhanced learning supports flexible access to resources, collaborative planning, and analysis of assessment evidence. This progressively builds preservice teachers’ confidence and competence in implementing numeracy intervention practices that support, accelerate and extend student learning in alignment with curriculum, assessment and reporting requirements.
Representative texts and references
Recommended texts and documents
Australian Curriculum https://www.australiancurriculum.edu.au/
Australian Curriculum, Assessment and Reporting Authority (ACARA) www.acara.edu.au
Australian Curriculum National Literacy and Numeracy Learning Progressions https://www.australiancurriculum.edu.au/resources/national-literacy-and-numeracy-learning-progressions/
Relevant state and territory Mathematics curriculum documents
Recommended references
Baker, P., Callingham, R., & Muir, T. (2023). Primary mathematics: Integrating theory with practice (4th ed.). (Chapter 12: Diversity in the primary mathematics classroom). Cambridge.
Boaler, J. (2016). Mathematical mindsets. San Francisco, CA: Jossey-Bass.
Bragg, L. A., Herbert, S., & Brown, J. P. (2020). Engaging Families in Mathematics Education. MTT_Engaging_Families_in_Mathematics_Education.pdf
Butterworth, B. & Laurillard, D. (2010). Low numeracy and dyscalculia: Identification and intervention. ZDM Mathematics Education 42, 527–539. https://doi.org/10.1007/s11858-010-0267-4Links to an external site.
Douglas H. Clements, & Julie Sarama (2014). Learning and teaching early math: The learning trajectories approach (2nd ed.). Routledge.
Forbringer, L., & Fuchs, W. (2014). Rti in math : Evidence-based interventions for struggling students. New York, NY: Routledge, Taylor & Francis Group.
Hunter, J., & Miller, J. (2020). Using a culturally responsive approach to develop early algebraic reasoning with young diverse learners. International Journal of Science and Mathematics Education [online] https://doi.org/10.1007/s10763-020-10135-0
Jacobs, V. R., Empson, S. B., Jessup, N. A., Dunning, A., Pynes, D., Krause, G., & Franke, T. M. (2022). Profiles of teachers’ expertise in professional noticing of children’s mathematical thinking. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-022-09558-zLinks to an external site.
Lambert, R. (2024). Rethinking disability and mathematics: A UDL math classroom guide for grades K–8. Corwin
Paul A. Kirschner, Carl Hendrick, & Jim Heal (2022). How Learning Happens: Seminal Works in Educational Psychology and What They Mean in Practice.
Ng, A., & Goff, W. (2024). Teaching mathematics equitably to all students. In J. Van de Walle, K. Karp, J. Bay-Williams, A. Brass, & S. Livy (Eds.). Primary and middle years mathematics: Teaching developmentally. Pearson.
Suurtamm, C., Thompson, D., Kim, R., Moreno, L., Sayac, N., Schukajlow, S., Silver E., Ufer, S., & Vos, P. (2016). Assessment in mathematics education: Large-scale assessment and classroom assessment. ICME-13 Topical Surveys 2366-5947). Cham: Springer International Publishing.
Taylor-Cox, J. (2013). Math intervention: Building number power with formative assessments, differentiation, and games, grades PreK-2. New York, NY: Routledge.
Wright, R., Ellemor-Collins, D., & Tabor, P. (2012). Developing number knowledge: Assessment, teaching & intervention with 7–11-year-olds. London: SAGE Publications.