Year
2023Credit points
10Campus offering
No unit offerings are currently available for this unitPrerequisites
EDMA163 Exploring Mathematics and Numeracy
Unit rationale, description and aim
This unit is designed to provide an introduction to early childhood (prior to school) and primary school mathematics education by investigating current directions in research and state and national documents. Emphasis will be placed on an approach to learning and teaching mathematics that is respectful of each child’s background and culture. The role of manipulatives, technology, language and mental processes in children’s developing concepts, understandings and skills will also be a focus, alongside the role of assessment interviews in identifying children’s current mathematical understanding. The use of this information to inform teaching, and develop positive attitudes to mathematics will be studied.
The unit aims to provide pre-service teachers with an understanding of theories of learning mathematics and effective teaching and learning in the contexts of Whole Number, Measurement and Geometry, specifically in early childhood (prior to school) and primary school mathematics education.
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 - explain why concerns for justice and for the dignity of all human beings are fundamental principles in mathematics education and the important role of self-esteem and positive attitudes to mathematics (GA1; APST 1.2, 4.1; ACECQA A6, C4, D4)
LO2 - demonstrate an ability to critically reflect on theories of and research informing children’s mathematical learning and children’s development of mathematical concepts and processes in Whole Number, Measurement and Geometry as addressed in state and national documents, from early childhood (prior to school) and through the primary school years (GA4, GA5; APST 1.2, 2.1, 2.3; ACECQA A1, A6, B1, B2, B3, E2)
LO3 - demonstrate an ability to critically reflect on the role of manipulatives and technology in children’s mathematical learning while investigating and developing teaching strategies that are relevant to various stages of learning, that are responsive to a range of abilities and that promote meaningful mathematical understanding as addressed in state and national documents from early childhood (prior to school) and the primary school years (GA4, GA5; APST 1.5, 2.3, 2.5, 2.6, 3.3, 3.4; ACECQA B1, B3, C1, C2, C3, C4)
LO4 - demonstrate an ability to critically reflect on the role of mathematics and numeracy education across the curriculum as addressed in state and national documents at all stages of learning for full participation in community life, work and further education (GA4, GA5; APST 2.1, 2.3; ACECQA B1, B2, B3).
Graduate attributes
GA1 - demonstrate respect for the dignity of each individual and for human diversity
GA4 - think critically and reflectively
GA5 - demonstrate values, knowledge, skills and attitudes appropriate to the discipline and/or profession
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. |
1.5 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. |
2.3 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. |
3.3 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. |
ACECQA CRITERIA
On successful completion of this unit, pre-service teachers should have developed the following specific knowledge:
A. Psychology and child development A1. Leaning, development and care A6. Diversity, difference and inclusivity |
B. Education and curriculum studies B1. Early Years Learning Framework B2. The Australian curriculum B3. Numeracy, science and technology |
C. Early childhood pedagogies C1. Alternative pedagogies and curriculum approaches C2. Play based pedagogies C3. Guiding behaviour / engaging young learners C4. Teaching methods and strategies |
D. Families and community partnerships D4. Socially inclusive practice |
E. History and philosophy of early childhood E2. Contemporary theories and practice |
Content
Topics will include:
- This unit’s mathematical content will focus on whole number including computational choice (mental, written, calculator, other) with appropriate links to measurement and geometry as detailed in state and national documents as well as the General Capability, Numeracy in the Australian Curriculum and relevant elements of Learning Outcomes in the Early Years Learning Framework.
- The role of the clinical interview is prioritised in this unit where students actively engage with approaches to learning and teaching mathematics that reflect a concern for justice and for the dignity of all human beings that promotes the importance of the affective domain in learning mathematics
- Theories of learning mathematics including relational and instrumental understanding will be linked to typical pathways/trajectories in young children’s mathematical learning, from early childhood (including prior to school) to the later primary years
- This unit will focus on the appropriate use of manipulatives (e.g., mathematical tools, games, materials and children’s literature) as well as the use of technology as a means to promote meaningful mathematical understanding
- Relevant national, state and territory curriculum documents and assessment.
Learning and teaching strategy and rationale
Pre-service teachers will be involved in a variety of teaching-learning strategies to progress and demonstrate their understandings in this unit. Participants will be involved in a variety of teaching-learning strategies to support learning, including: online engagement, lectures, tutorials, seminar presentations and group discussions, both online and face-to-face, self-directed study activities and assessment tasks. Some participation in appropriate educational settings maybe required.
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 in total with a normal expectation of 36 hours of directed study and the total contact hours should not exceed 36 hours. Directed study might include lectures, tutorials, webinars, podcasts etc. The balance of the hours then become private study.
Assessment strategy and rationale
The assessment tasks and their weightings are designed to allow pre-service teachers to progressively demonstrate achievement against the unit learning outcomes and demonstrate attainment of professional standards.
To enable assessment to best meet the needs of learners, three assessment possibilities are outlined below.
Minimum Achievement Standards
The assessment tasks for this unit are designed to demonstrate achievement of each learning outcome.
The total assessment tasks will amount to the equivalent of 4,000 words. Two major items or two minor and one major item must be selected from the following.
Overview of assessments
| Brief Description of Kind and Purpose of Assessment Tasks | Weighting | Learning Outcomes | Graduate Attributes |
|---|---|---|---|
Assessment Task 1 A case study of a child’s mathematical knowledge based on the use of a one-to-one interview. Judgments about the child’s mathematical development must be linked to a theoretical framework. The framework must also be used to inform the design of a follow-up activity and teaching strategies which targets students’ further conceptual development in the areas of Whole Number, Measurement and Geometry as addressed in state and/or national curriculum documents relevant to this unit. | 50% | LO1, LO2, LO3, LO4 | GA1 |
Assessment Task 2A Individually write a literature review exploring themes, ideas and issues related to the learning and teaching of mathematics in the primary classroom or early learning context pertaining to a particular mathematics topic relevant to this unit and addressing relevant Learning Outcomes OR | 50% | LO2, LO3 | GA4, GA5 |
Assessment Task 2B A weekly reflective journal that draws together understandings from the weekly lecture, tutorial activities and prescribed readings and observations from PCE experiences. These reflections must address each of the learning outcomes. | 50% | LO1, LO2, LO3, LO4 | GA1, GA4, GA5 |
Representative texts and references
Anghileri, J. (2006). Teaching number sense (2nd ed.). London: Continuum
Beckley, P., Compton, A., Johnston, J., & Marland, H. (2010). Problem solving, reasoning and numeracy: Supporting development in the early years foundation stage. London: Continuum
Bobis, J., Mulligan, J., & Lowrie, T. (2013). Mathematics for children: Challenging children to think mathematically (4th ed.). Frenchs Forest, NSW: Pearson Australia.
Copley, J. (2010). The young child and mathematics (2nd ed.). Reston, VA: National Council of Teachers of Mathematics
Reys, R. E., Lindquist, M. M., Lambdin, D. V., Smith, N. L., Rogers, A., Falle, J., & Frid, S. (2013). Helping children learn mathematics (1st Australian ed.). Milton, Qld: John Wiley & Sons.
Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2011). Teaching mathematics: Foundations to middle years. South Melbourne, Vic: Oxford University Press.
Sperry Smith, S. (2013). Early childhood mathematics (5th ed.). Upper Saddle River, NJ: Pearson.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Boston: Pearson.
Yelland, N., Butler, D., & Diezmann, C. (1999). Early mathematical explorations. Needham Heights, Ma: Pearson.
Jorgensen, R., & Dole, S. (2011). Teaching mathematics in primary schools (2nd ed.). Crows Nest, NSW: Allen & Unwin.