Year
2024Credit points
10Campus offering
Prerequisites
EDMA290 Mathematics Curriculum, Pedagogy and Assessment 1 (B-12)
Incompatible
EDMA342 Mathematics Education 2: Curriculum, Pedagogy and Assessment , EDMA360 Mathematics: Learning and Teaching 2
Unit rationale, description and aim
The Australian Curriculum: Mathematics aims to ensure that students:
- become confident, proficient and effective users and communicators of mathematics, who can investigate, represent and interpret situations in their personal and work lives, think critically, and make choices as active, engaged, numerate citizens
- develop proficiency with mathematical concepts, skills, procedures and processes, and use them to demonstrate mastery in mathematics as they pose and solve problems, and reason with number, algebra, measurement, space, statistics and probability
- make connections between areas of mathematics and apply mathematics to model situations in various fields and disciplines
- foster a positive disposition towards mathematics, recognising it as an accessible and useful discipline to study
- acquire specialist mathematical knowledge and skills that underpin numeracy development and lead to further study in mathematics and other disciplines
Pre–service teachers must develop effective instructional and assessment strategies in mathematics to facilitate these curriculum aims for learners.
In this unit, pre–service teachers should develop and implement a responsive curriculum and pedagogy that demonstrates concern for justice and the dignity and diversity of all learners. Promoting critical thinking and judgement, this unit will explore theories of mathematical learning, mathematics education research issues, and the implications specifically related to learning, teaching and assessment of the Number (rational numbers), Algebra, Statistics, and Probability curriculum strands. This unit will promote cognitive skills to analyse, consolidate and synthesise a range of different learning activities 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 learning and teaching, report on student achievement and meet professional accountability requirements.
This unit aims to provide pre–service teachers with in–depth understanding of the underlying principles and pedagogies that enable teachers to critically evaluate planning, teaching, and assessment strategies for V.9 of Australian Curriculum: Mathematics F–6.
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 Number | Learning Outcome Description | Relevant Graduate Capabilities |
|---|---|---|
| LO1 | Evaluate student learning needs, based on analysis of student assessment data, moderation and consistent and comparable judgement to inform planning for mathematics teaching with reference to the Australian Curriculum: Mathematics and other relevant mathematics curriculum documents (APST 1.2, 2.1, 5.1, 5.3, 5.4) | GC1, GC2, GC4, GC7, GC8, GC9, GC11, GC12 |
| LO2 | Research, design and evaluate assessment tasks and rubrics to measure and report student mathematical content knowledge (APST 1.2, 2.3, 5.1, 5.2, 5.3, 5.4, 5.5) | GC1, GC2, GC7, GC9, GC10, GC11 |
| LO3 | Research, evaluate and develop a range of different types of mathematics learning experiences that contribute to an inclusive mathematics pedagogy including open-ended tasks, investigations, teacher questioning and learning contexts that enhance student learning outcomes (APST 1.2, 2.1, 2.2, 2.3, 2.5, 3.3, 3.4, 3.6) | GC1, GC7, GC9, GC11 |
| LO4 | Describe and apply strategies, including the ethical use of ICT, that cater for students with diverse backgrounds, including languages, cultures, abilities and talents (APST 1.2, 1.5, 2.1, 2.5, 2.6, 3.3, 3.4, 4.1, 4.5) | GC1, GC2, GC6, GC7, GC9, GC10, GC11 |
| LO5 | Apply pedagogical approaches, student understandings and dispositions in relation to Number (focusing on rational numbers), Algebra (patterns and algebra), Statistics, and Probability (chance and data representation and interpretation) to develop a sequence of learning (APST 1.1, 1.2, 2.1, 2.2, 2.5, 2.6, 3.2, 3.3, 3.4, 5.1) | GC2, GC9, GC11 |
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. |
1.5 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. |
3.2 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. |
4.1 Identify strategies to support inclusive student participation and engagement in classroom activities. |
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 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. |
Content
Topics will include:
- 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, inquiry based learning 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)
- Diagnosing and planning for support of learners who are working beyond or below expected outcomes,
- Assessment practices to guide learning and teaching of mathematics (e.g., informal and formal, including diagnostic, formative and summative assessment of cognitive and affective learning),
- Assessment-related issues and the purposes, characteristics, and limitations of various types of assessments,
- Interpreting assessment data and its links to planning and teaching,
- Reviewing national testing requirements and its impact on teaching and learning (e.g., NAPLAN, TIMSS and PISA),
- Strategies to provide accurate written and oral feedback for students about their numeracy development, with exploration of any ethical issues regarding feedback,
- Moderation practices for comparing individual and group differences within classrooms, state and national levels,
- Approaches to planning for mathematics teaching and learning as identified in the Australian Curriculum: Mathematics that
- incorporate both mathematical content and proficiencies and address the general capabilities and cross curriculum priorities as appropriate
- Articulates effective contexts for mathematics teaching and learning (e.g. children’s literature, real life contexts, games, problem solving and investigations)
- Identifies opportunities to use mathematics and numeracy across the curriculum
The teaching of rational number, algebraic thinking, and probability and statistics as described by the Australian Curriculum: Mathematics will form the content basis of this unit.
Learning and teaching strategy and rationale
This unit applies a social constructivist approach to develop understanding of planning and assessment, and skills in applying effective pedagogies through active engagement and collaborative learning. Pre-service teachers will build on their understanding of teaching strategies through critical reading, , discussion and practice. Teaching skills of planning and assessing, and locating, critiquing and synthesising information will be developed.
Pre-service teachers should expect to participate in a range of the following: video lecture presentations, group discussions, self-directed study activities, and assessment tasks.
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. The learning and teaching and assessment strategies include a range of approaches to support learning such as reading, reflection, discussion, webinars, podcasts, video etc.
The unit is hosted on a Learning Management System (LMS) site with resources and online links, announcements, and a discussion board to post questions and reflections that promote connection between content and educational experiences. Technology used will be modelled by the teaching team to reflect the nature of technology in 21st century classrooms. Pre-service teacher online platforms will include the LMS. Online materials will be available in advance and as post-learning material. The announcements platform will serve as the main communication platform for all pre-service teachers. The use of forums will be made available to exchange ideas and reflect on learning.
Mode of delivery: This unit may be offered in different modes to cater to the learning needs and preferences of a range of participants.
On Campus
Most learning activities or classes are delivered at a scheduled time, on campus, to enable in-person interactions. Activities will appear in a student’s timetable.
Multi-mode
Learning activities are delivered through a planned mix of online and in-person classes, which may include full-day sessions and/or placements, to enable interaction. Activities that require attendance will appear in a student’s timetable.
Online unscheduled
Learning activities are accessible anytime, anywhere. These units are normally delivered fully online and will not appear in a student’s timetable.
Online scheduled
All learning activities are held online, at scheduled times, and will require some attendance to enable online interaction. Activities will appear in a student’s timetable.
ACU Online
In ACU Online mode, this unit is delivered asynchronously, fully online using an active, guided learning approach. Pre-service teachers are encouraged to contribute to asynchronous weekly discussions and receive regular and timely feedback on their learning.
Assessment strategy and rationale
A range of assessment procedures are used to meet the unit learning outcomes and develop graduate attributes and professional standards and criteria consistent with University assessment requirements. The assessment options cater for differing learning needs including: designing and evaluating assessment strategies for mathematics; critiquing research literature to inform teaching; and developing a sequence of lessons.
The three assessment tasks and their weightings are designed to allow pre-service teachers to progressively demonstrate achievement against the course learning outcomes by demonstrating academic and professional standards. Pre-service teachers will focus on developing understanding of, and skills across the professional knowledge, practice and engagement needed to meet expectations of the Graduate Attributes and the Australian Professional Standards for Teachers: Graduate level.
Through completing Task 1 pre-service teachers will have the opportunity to demonstrate their ability to use and their understanding of the efficacy of diagnostic formative assessment interviews. Through completing Task 2 the pre-service teacher will deepen their understanding of assessment rubrics and their use to assess student solutions to open-ended mathematics tasks or investigations, as well as the affordances and limitations of both 1-1 interviews and assessment rubrics in mathematics. In Task 3 pre-service teachers will demonstrate their ability to critically review research literature and curriculum documents and a learning sequence that enhances student understanding and proficiencies in mathematics. These assessment tasks model the ‘real world’ of classrooms and teaching responsibilities.
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 EDMA291 includes a Critical Task: Assessment Task 3 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 3 in order to pass this unit.
Overview of assessments
| Brief Description of Kind and Purpose of Assessment Tasks | Weighting | Learning Outcomes |
|---|---|---|
Assessment Task 1 Case Study Analysis Pre-service teachers will be assigned a case study (note: other pre-service teachers from the 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 data. Individually, review and analyse the assessment data. Identify:
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 recent learning experiences, propose recommendations for future teaching and learning. 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 | 20% | LO1, LO2, LO3 |
Assessment Task 2 Using assessment rubrics for open-ended tasks or investigations Produce at least 2 worked solutions to one open-ended task that show different approaches to solving the task and which clearly demonstrate MCK. Design an A4 page assessment rubric to assess any possible response for the open-ended task. Compare and contrast the usefulness of the two assessment strategies investigated in Assessment 1 and 2 (1-1 diagnostic interviews and rubrics for open-ended tasks) for gaining knowledge about students’ mathematical knowledge and proficiencies that can be used to provide feedback to students about their learning and to plan future learning opportunities which cater for the diverse needs of learners and contribute to an inclusive pedagogy. | 30% | LO1, LO2, LO3, LO4 |
Assessment Task 3 Designing a research-informed Sequence of Learning Critical Task Critically review the literature related to the learning pathway (from F-6) 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. Develop an overview for 5 effective sequential learning activities/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. Your unit plan should attend to the following key elements:
| 50% | LO2, LO3, LO4, LO5 |
Representative texts and references
Required text(s)
Australian Curriculum Mathematics. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/.
Baker, P., Callingham, R., & Muir, T. (2023). Primary mathematics: Integrating theory with practice (4th ed.). Cambridge.
Relevant state and territory Mathematics curriculum documents.
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.
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).