Year
2023Credit points
10Campus offering
No unit offerings are currently available for this unitPrerequisites
EDLL515 Primary Mathematics 1
Incompatible
EDMA685 Mathematics Education 2
Unit rationale, description and aim
Graduate teachers are required to support and empower all learners of mathematics through by providing stimulating learning experiences. This is undertaken to demonstrate the value of mathematics and build knowledge of mathematics and numeracy as a tool for logical and creative problem solving providing a foundation for lifelong learning (Education Goals for Young Australians, Alice Springs (Mparntwe) Education Declaration).
In this unit, pre-service teachers consider issues (e.g., student diversity, student disengagement with mathematics, declining mathematical performance of Australian students in international testing) and strategies in planning, implementing, and monitoring learning experiences in primary school mathematics, with a focus on further Number and Algebra and Probability and Statistics. This will be supported by drawing on contemporary research, national and state curriculum documents and initiatives. Pre-service teachers will further explore theories of learning mathematics and effective teaching and learning strategies that enhance students’ understandings of mathematical concepts and skills.
This unit will develop the pre-service teacher’s skills to analyse, consolidate, and synthesise a range of different teaching approaches and learning activities. A range of formal and informal assessment strategies will be further examined with an emphasis on using student data to inform and differentiate teaching and therefore impact on students learning. Reporting on student achievement to meet professional accountability requirements will also be explored. Continuing on from EDLL515, pre-service teachers will further research and apply theoretical frameworks of numeracy education and quality pedagogy for planning teaching and assessment in Mathematics and identify ways how numeracy across other learning areas can be used to further students’ learning.
The aim of this unit is to further develop theoretical and practical principles of mathematics and to further extend the application of contemporary pedagogy of primary mathematics (from Foundation to Year 6) in the content strands of Number and Algebra (specifically on rational number including fractions, decimal decimals, percentages, proportional reasoning, and algebraic thinking) and Statistics and Probability, and further explore how the proficiency strands relate to these content areas.
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.
On successful completion of this unit, students should be able to:
LO1 - Critically analyse and describe a range of issues (e.g., student diversity, student disengagement with mathematics, declining mathematical performance of Australian students in international testing) and pedagogies related to contemporary mathematics teaching and learning in the areas of rational number, algebraic thinking, statistics, and probability (GA4, GA5, GA8, GA9; APST 1.2, 1.3, 1.5, 2.1, 2.5)
LO2 - Apply knowledge of learning pathways and continuums to develop learning and teaching activities that address the needs of all learners by using a range of resources (including the ethical use of digital technologies) to develop their mathematical understanding, fluency, problem solving and reasoning and communication skills (GA4, GA5, GA7, GA8, GA9; APST 2.1, 2.2, 2.5, 2.6, 3.1, 3.2, 3.3, 3.4, 5.1, 5.2)
LO3 - Critically analyse student assessment data and moderate judgements to identify student learning needs to inform planning for mathematics teaching and learning (GA3, GA4, GA5, GA8; APST 1.2, 2.1, 5.1, 5.3, 5.4)
LO4 - Develop and implement lesson sequences and teaching strategies and evaluate student learning including the provision of constructive and timely feedback to learners (GA4, GA5, GA7, GA8, GA9, GA10; APST 2.1, 2.2, 2.3, 2.5, 3.3, 3.4, 3.6, 5.1, 5.2)
LO5 - Apply knowledge of professional practice to engage students and their parents/carers in the educational process including reporting practices for sharing student learning with students and stakeholders (GA3, GA4, GA5, GA9, GA10; APST 3.7, 5.5, 7.3)
Graduate attributes
GA3 - apply ethical perspectives in informed decision making
GA4 - think critically and reflectively
GA5 - demonstrate values, knowledge, skills and attitudes appropriate to the discipline and/or profession
GA7 - work both autonomously and collaboratively
GA8 - locate, organise, analyse, synthesise and evaluate information
GA9 - demonstrate effective communication in oral and written English language and visual media
GA10 - utilise information and communication and other relevant technologies effectively.
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. |
2.2 Organise content into an effective learning and teaching sequence. |
2.3 Use curriculum, assessment and reporting knowledge to design learning sequences and lesson plans. |
2.5 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. |
3.7 Describe a broad range of strategies for involving parents/carers in the educative process. |
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 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. |
7.3 Understand strategies for working effectively, sensitively and confidentially with parents/carers. |
Content
Rational number, algebraic thinking, and probability and statistics will form the mathematical content basis of this unit.
Topics will include:
- Current national, state, and territory initiatives in mathematics education
- Incorporating the mathematical content and proficiencies
- Integrating the mathematical content strands to facilitate connections across dimensions of mathematics
- 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.
- Big ideas in mathematics
- Learning pathways and continuums
- Powerful pedagogical actions in mathematics
- Scaffolding learning
- Targeted intervention strategies
- Literacy demands
- Approaches for different levels of planning
- Promoting productive discourse and collaborative argumentation
- Selecting tasks and models that promote deep learning
- 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 the teaching and learning 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
- Moderation of student learning outcomes
- Interpretation and analysis of student data including NAPLAN against class, state, and national norms
- Analysis of data and future planning
- Reporting of student learning outcomes to parents/carers and other stakeholders – types of reports
- Ways of engaging families/caregivers in mathematics
- Effective contexts for mathematics learning
- Identifying opportunities to use Numeracy across the curriculum (e.g., children’s literature, real life contexts, games, problem solving and investigations)
- Expanding the concept of integrating numeracy across teaching areas (from the prior unit) to additional contexts in light of critical reflection on increased professional experience.
Learning and teaching strategy and rationale
The learning and teaching approach for this unit has been developed in reflection of the unique context for learning within the Teach For Australia program, which is employment-based, situated in both national and regionalised teaching and learning contexts, as well as in reference to EDLL515. The learning opportunities in the unit enable students to access and build upon knowledge and skills developed within the first primary mathematics units. A range of teaching and learning strategies are employed to reflect contemporary mathematics and numeracy learning pedagogies as can be applied in primary contexts particularly with regards to foci emphasised within this unit which are situated within the professional experience of the participants. It include interactive learning experiences; student-led discussions and group work; directed hands-on learning activities; real-world problem-solving; and the integration of ICT 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 LEO (Learning Environment Online) unit site.
Assessment strategy and rationale
The assessment tasks and their weightings are designed so that the pre-service teachers can progressively achieve the Course Learning Outcomes and the Professional Standards and is consistent with University assessment requirements (https://policies.acu.edu.au/student_policies/assessment_policy_and_assessment_procedures).
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 EDLL616, the assessment focusses 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 using and developing of resources for learning (Task 1), planning for teaching, learning and assessment (Task 2), and demonstrating broad content and pedagogical content knowledge (Task 3).
Overview of assessments
| Brief Description of Kind and Purpose of Assessment Tasks | Weighting | Learning Outcomes | Graduate Attributes |
|---|---|---|---|
Assessment Task 1: High Impact Pedagogical Approaches (CTITE 5) Identify and critically analyse two pedagogical approaches that are aligned with research and best practice connecting to how students learn in a mathematics content area of rational number (fractions, decimal fractions, percentages). These approaches should develop students’ mathematical knowledge and understanding, mathematical language and communication, and thinking processes in your chosen rational number area. At least one pedagogical approach should support the delivery of an integrated primary curriculum or topic. Include a professional plan for implementation of these approaches in the classroom. | 30% | LO1 | GA4, GA5, GA8, GA9 |
Assessment Task 2: Implementation Revise as needed the pedagogical approaches and implementation plan from Task 1. Using research on learning pathways/continuums, develop three sequential activities using a range of resources for each pedagogical approach which also caters for learners with diverse learning needs. Discuss your approach with a colleague to gain feedback on how you might differentiate teaching to meet the diverse learning needs of students, and how you might generate assessment data on student learning. Implement the three sequential activities with a group of students, ensuring that digital technologies are used to support teaching and learning. Either video yourself or ask a colleague to observe the implementation. Critically reflection on the approach, activities, impact on student learning, provision of feedback to students and implications for future teaching and personal development. | 30% | LO1, LO2, LO3, LO4 | GA3, GA4, GA5, GA7, GA8, GA9, GA10 |
Task 3: Analysis of classroom numeracy needs Collect and analyse assessment data for a whole class. Recommend differentiation plans for learners across the full range of backgrounds and needs for a unit of work. Implement plans for two learners with one demonstrating characteristics that are significantly above the average for their year level. Incorporate samples of student work, reflecting the diversity of learners and the types of feedback provided to the students. Using insights from the student assessment data, evaluate the impact of your teaching. Include ideas for engaging parents/carers in the learning process. | 40% | LO2, LO3, LO4, LO5 | GA3, GA4, GA5, GA7, GA8, GA9, GA10 |
Representative texts and references
Required text(s)
Australian Curriculum Mathematics. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/
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.). Melbourne, Vic: Pearson.
Recommended references
Calder, N., Larkin, K., & Sinclair, N. (2018). Using mobile technologies in the teaching and learning of mathematics. Singapore: Springer.
Lamon, S. J. (2020). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers (4th ed.). New York, NY: 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.
Reys, R. E., Rogers, A., Bennett, S., Cooke, A., Robson, K., Ewing B., & West, J. (2020). Helping children learn mathematics (3rd Australian ed.). Milton, Qld: John Wiley & Sons Australia.
Serow, P., Callingham, R. A., Muir, T., & Muir, T. (2016). Primary mathematics: Capitalising on ICT for today & tomorrow (2nd ed.). Port Melbourne, Vic: Cambridge University Press.
Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2015). Teaching mathematics: Foundations to middle years (2nd ed.). South Melbourne, Vic: Oxford University Press.
Siegler, R. S., & Lortie-Forgues, H. (2017). Hard lessons: Why rational number arithmetic Is so difficult for so many people. Current Directions in Psychological Science, 26(4), 346–351. https://doi.org/10.1177/0963721417700129
Van Hoof, J., Verschaffel, L., Ghesquière, P., & Van Dooren, W. (2017). The natural number bias and its role in rational number understanding in children with dyscalculia. Delay or deficit? Research in Developmental Disabilities, 71, 181–190. https://doi.org/10.1016/j.ridd.2017.10.006
Way, J., Attard, C., Anderson, J., Bobis, J., McMaster, H., & Cartwright, K. (2020). Research in mathematics education in Australasia 2016-2019. Singapore: Springer.