Year
2022Credit points
10Campus offering
No unit offerings are currently available for this unitPrerequisites
Nil
Incompatible
EDMA504 Mathematics Education 1
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 will be introduced to theories of learning mathematics and effective teaching and learning strategies that enhance students’ understandings of mathematical concepts and skills with a particular emphasis on Number and Algebra, Measurement and Geometry. Using the Australian Curriculum: Mathematics, pre-service teachers will become proficient in planning, teaching and assessing primary school mathematics. Ways to foster and embed creativity, confidence and positive attitudes in mathematics, and cater for a range of learners and their needs, will also be investigated. Regular opportunities to advance mathematical understanding, problem solving, reasoning, and fluency will permeate the unit. Embedded within the unit is the development of the pre-service teacher’s own content knowledge.
The aim of this unit is to introduce pre-service teachers to primary school mathematics education by discussing and investigating current directions in mathematics education, including social justice issues; and drawing on contemporary research, national and state curriculum documents and initiatives with a focus on the content strands of Number and Algebra (whole number & place value, money & financial mathematics, patterns and Measurement and Geometry for the primary school years.
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 - Investigate and synthesise effective theories and approaches to teaching mathematics that engage and promote positive dispositions for diverse students across the full range of abilities (GA1, GA4, GA8; APST 1.1, 1.2, 1.3, 1.5, 2.1, 3.3)
LO2 - Implement formative and diagnostic assessments, interpret assessment data to inform planning of learning experiences, and apply feedback practices that support students’ diverse learning needs (GA3, GA4, GA5, GA8; APST 1.2, 1.5, 2.1, 2.3, 5.1, 5.2, 5.4)
LO3 - Apply theories and research about primary school students’ development of mathematical concepts and proficiencies to create effective learning experiences for learners using a range of resources (e.g., digital technologies, concrete materials/manipulatives) and real-life contexts (GA4, GA5, GA8; APST 1.2, 2.1, 2.2, 2.3, 2.6, 3.1, 3.2, 3.3, 3.4, 4.1)
LO4 - Design learning sequences and organise lesson activities to support students’ mathematical learning of Whole Number, Measurement and Geometry incorporating appropriate use of digital technologies and including ways of influencing students’ dispositions towards mathematics (GA4, GA5, GA8, GA9; APST 1.2, 2.1, 2.2, 2.6, 3.1, 3.2, 3.3, 3.4)
Graduate attributes
GA1 - demonstrate respect for the dignity of each individual and for human diversity
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
GA8 - locate, organise, analyse, synthesise and evaluate information
GA9 - demonstrate effective communication in oral and written English language and visual media
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. |
1.3 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. |
2.6 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. |
4.1 Identify strategies to support inclusive student participation and engagement in classroom activities. |
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. |
5.4 Demonstrate the capacity to interpret student assessment data to evaluate student learning and modify teaching practice. |
Content
The teaching and learning of the Mathematical content strands of Number (with a focus on number and place value, and money and financial mathematics) and Algebra, and Measurement and Geometry is the focus of this unit and embedded within all topics.
Topics will include:
- Theoretical and philosophical underpinnings of the role and function of Mathematics and numeracy in the 21st century
- Contexts of curriculum
- state and national curriculum documents, social and cultural perspectives in mathematics
- the proficiency strands of the Australian Curriculum: Mathematics; understanding, fluency, problem-solving, and reasoning
- Students and mathematical understanding
- theories of students’ mathematical learning; and how they develop mathematical understanding, fluency, problem solving and reasoning skills.
- student misconceptions
- Mathematical pedagogy
- strategies to enhance all students’ learning through the use of manipulatives (concrete materials/manipulatives), visual, symbol, and language in representing mathematical ideas
- application of digital technologies to teaching and learning in Mathematics and numeracy
- strategies for extending student learning through authentic experiences across the proficiency strands
- designing lesson sequences and mathematical learning activities for diverse students across all abilities
- management and organisation of mathematical learning activities during mathematics lessons
- Developing a mathematical mindset or relevant mathematic dispositions
- strategies to promote self-esteem and positive attitudes to mathematics
- the role of errors in mathematics learning
- need for productive struggle
- Purposes and approaches to formative and summative assessment in mathematics
- Identifying opportunities to use Numeracy across the curriculum
Learning and teaching strategy and rationale
Engagement for learning is the key driver in the delivery of this unit, which is designed to support 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, and includes opportunities to learn face-to-face as well as online and independently. Thus, a range of teaching and learning strategies are employed to reflect contemporary mathematics and numeracy learning pedagogies as can be applied in primary contexts and applied in real-time to the continuous professional experience of pre-service teachers of the course. These 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 this unit, the assessment focusses on pedagogies for developing mathematics and numeracy in Number and Algebra, and Measurement and Geometry. The three tasks are sequenced to allow feedback and progressive understanding, development and understanding of how students learn mathematics and the development and implementation of high impact implementation pedagogies for Mathematics guided by assessment data. A pass is required in all assessment tasks to demonstrate meeting all learning outcomes.
Overview of assessments
| Brief Description of Kind and Purpose of Assessment Tasks | Weighting | Learning Outcomes | Graduate Attributes |
|---|---|---|---|
Assessment Task 1: Learning Mathematics Report Research how children learn mathematics, drawing on relevant learning theories, and identify implications for contemporary teaching, learning, and assessment in primary mathematics classrooms. Choose a group of learners (e.g., students with diverse linguistic, cultural or socio-economic backgrounds) and identify teaching strategies for differentiating teaching and engaging learners using insights from appropriate mathematics education literature (with some support from mathematics teacher professional journals). Include strategies that teachers use to influence students’ positive dispositions towards mathematics. | 30% | LO1 | GA1, GA4, GA8 |
Assessment Task 2: Assessment of Learners and Responsive Lessons Develop or modify an assessment to assess and report on two students’ mathematics learning, including feedback for the both of the students. Based on the analysis of data, develop two differentiated lessons to address any misconceptions and further the mathematical understanding of the students. Include in the lessons, ways of incorporating appropriate use of digital technologies and ways that teachers can support the development of positive affect for and towards mathematics. | 40% | LO2, LO3 | GA3, GA4, GA5, GA8 |
Assessment Task 3: Unit Plan Critically review the literature related to the learning of multiplicative thinking, including key skills and strategies, possible student misconceptions and issues that impact on children’s learning, i.e., what aspects of multiplicative thinking are easier to learn, and which aspects prove challenging for primary school learners. Discuss recommendations for effective pedagogical approaches to develop multiplicative thinking, including reference to appropriate mathematics education literature (research and professional texts), curriculum documentation (e.g., ACARA). Develop an overview for three (3) sequential learning activities/lessons that form a unit of work for multiplicative thinking, as well as appropriate questioning techniques and use of digital technologies, informal assessment strategies, and ways to influencing student dispositions for the unit of work. | 30% | LO1 LO3, LO4 | GA1, GA4, GA5, GA8, GA9 |
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, Australia: Pearson.
Recommended references
Askew, M. (2016). A practical guide to transforming primary mathematics: Activities and tasks that really work. New York: Routledge.
Ball, D. B., & Ruhama, E. (Eds.). (2009). The professional education and development of teachers of mathematics: The 15th ICMI study. New York, NY: Springer.
Diezmann, C., Yelland, N., & Butler, D. (2014). Early mathematical explorations. London, England: Cambridge University Press.
Goos, M., Geiger, V., Dole, S., Forgasz, H., & Bennison, A. (2019). Numeracy across the curriculum : research-based strategies for enhancing teaching and learning. Allen & Unwin.
Reys, R. E., Rogers, A., Bennett, S., Cooke, A., Robson, K., Ewing B., & West, J. (2019). Helping children learn mathematics (3rd Australian ed.). Milton, Australia: John Wiley & Sons Australia.
Serow, P., Callingham, R. A., & Muir, T. (2016). Primary mathematics : Capitalising on ICT for today & tomorrow (2nd ed.). Melbourne, Australia: Cambridge University Press.
Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2015). Teaching mathematics: Foundations to middle years (2nd ed.). Melbourne, Vic: Oxford University Press.
Way, J., Attard, C., Anderson, J., Bobis, J., McMaster H., & Cartwright, K. (2020). Research in mathematics education in Australasia 2016-2019. Singapore: Springer Publishers.