Year
2021Credit points
10Campus offering
No unit offerings are currently available for this unit.Prerequisites
EDMA241 Mathematics Education 1: Curriculum, Pedagogy and Assessment
Unit rationale, description and aim
This unit is designed to provide pre-service teachers with in-depth understanding of the underlying principles and concepts that enable teachers to critically evaluate strategies in planning, implementing, monitoring and assessing learning experiences for the Australian Curriculum: Mathematics primary. Pre-service teachers will develop and implement a culturally aware and responsive curriculum and pedagogy that demonstrates concern for justice and the dignity of all. Promoting critical thinking and judgement, this unit will explore theories of mathematical learning and research into mathematics education issues and their implications for learning and teaching. The structure and content of relevant primary education mathematics curriculum will be critically reviewed, with particular emphasis on rational number, algebraic thinking, and statistics and probability. 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 concepts that enable teachers to critically analyse, consolidate and synthesise a range of different learning activities, teaching approaches and informal and formal assessment strategies.
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 - evaluate teaching programs through analysis of the effectiveness of a range of different types of mathematics learning experiences that contribute to an inclusive mathematics pedagogy, including open-ended tasks, teacher questioning and learning experiences to enhance student learning outcomes (GA4, GA5, GA6, GA8; APST 2.5, 3.3, 3.6)
LO2 - implement strategies, including the ethical use of ICT, that cater for the diverse needs of learners, with appropriate assessment and moderation, constructive and timely feedback and reporting practices for shared understandings of progress with students and stakeholders (GA1, GA4, GA5, GA8; APST 1.5, 2.5, 2.6, 3.3, 5.1, 5.2, 5.3, 5.4. 5.5)
LO3 - use initiative and creativity to reflect upon and make informed judgements about the appropriateness of generally agreed principles of learning and teaching mathematics (GA4, GA5, GA8; APST 1.2)
LO4 - present a clear and coherent knowledge of research about pedagogical approaches, student understandings and dispositions in relation to rational number, algebraic thinking, and statistics and probability (GA4, GA5, GA8; APST 1.2, 2.1, 2.5)
LO5 - evaluate student learning needs, based on interpretation of student assessment data for analysis, 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 (GA1, GA4, GA6, GA8; APST 2.2, 2.3, 3.2, 5.3, 5.4)
LO6 - demonstrate personal competence and confidence in mathematical knowledge to a level appropriate for a graduate teacher, concepts and processes related to rational number, algebraic thinking, and statistics and probability (GA5; APST: 2.1).
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
GA6 - Solve problems in a variety of settings taking local and international perspectives into account
GA8 - locate, organise, analyse, synthesise and evaluate information
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. |
2.2 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. |
3.6 Demonstrate broad knowledge of strategies that can be used to evaluate teaching programs to improve student learning. |
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 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 learning teaching of mathematics: (e.g., informal and formal, including diagnostics approaches to formative and summative assessment of cognitive and affective learning)
- Strategies to provide accurate written and oral feedback for students in relationship to their numeracy development with exploration of any ethical issues regarding feedback and responses
- Assessment-related issues and the purposes, characteristics, and limitations of various types of assessments
- Interpreting assessment data and its links to planning and school based policies
- Reviewing national testing requirements and its impact on teaching and learning eg NAPLAN
- Moderation practices for comparing individual and group differences within classrooms, state and national levels
- Diagnosing and planning for support of learners to who are working beyond or below stage outcomes
- Approaches for different levels planning for mathematics teaching as identified in the Australian Curriculum: Mathematics
- Incorporating the mathematical content and proficiencies
- Integrating the mathematical content strands to facilitate connections across dimensions of mathematics
- Effective contexts for mathematics learning (e.g. children’s literature, real life contexts, games, problem solving and investigations)
- Identifying opportunities to use Numeracy across the curriculum
- Powerful pedagogical actions in mathematics (e.g. creating powerful learning environments, grouping practices, scaffolding learning, attending to literacy demands, promoting productive discourse and collaborative argumentation, questioning and prompting), selecting tasks and models that promote deep learning and knowing and using pedagogical knowledge
- Current national, state, and territory initiatives in mathematics education
The teaching of rational number, algebraic thinking, and probability and statistics as found within the Australian Curriculum: Mathematics will form the content basis of this unit.
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 should expect to participate in a range of the following: 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 may be required, in particular tasks expected on classroom placement.
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 approximatelyDuration: 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.
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. In order to pass this unit, students are required to submit or participate in all assessment tasks.
Overview of assessments
| Brief Description of Kind and Purpose of Assessment Tasks | Weighting | Learning Outcomes | Graduate Attributes |
|---|---|---|---|
Assessment Task 1 Evaluating assessment strategies for subsequent informed planning and use of teaching strategies (Equivalent to 2000 words) Evaluate the effectiveness of the following two assessment strategies: a. Rational Number Interview b. Using assessment rubrics for open-tasks a) Rational Number Interview: Assess a student using the Rational Number Interview and complete the record sheet (attach the record sheet as an appendix to your assignment) (equivalent to 160 words). Describe your insights about the student’s mathematical knowledge and any misconceptions (320 words). Critically evaluate the usefulness of this assessment strategy for gaining knowledge about student’s current mathematical knowledge with the purpose of providing feedback to students that can also be moderated for consistency of judgements and used to plan future learning opportunities (that may include the use of digital technologies and cater for the diverse needs of learners and contribute to an inclusive pedagogy). Alignment to the Australian Curriculum: Mathematics must be made (320 words). b) Using assessment rubrics for open-tasks: Design a one A4 page assessment rubric for the assigned open task. Produce a work sample that shows full understanding of the mathematics (equivalent to 480 words). Critically evaluate the usefulness of this assessment strategy for gaining knowledge about student’s current mathematical knowledge that can be used to provide feedback to students about their learning and to plan future learning opportunities (that include the use of digital technologies and cater for the diverse needs of learners and contribute to an inclusive pedagogy (320 words). | 50% | LO1, LO5, LO6 | GA1, GA4, GA5, GA6, GA8 |
Assessment Task 2 CHOICE - For the purposes of national moderation all campuses must select the same task a) Developing research-informed learning pathways (Equivalent to 2000 words) Choose one area of mathematical focus – Rational number (beyond fractions and decimal fractions i.e., proportion reasoning, ratio), probability, statistics or algebraic thinking. Review the literature to identify current research related to the children’s learning of the chosen mathematical focus throughout primary school. Reflect on and discuss the latest academic thinking and research about student’s learning of the concepts within your chosen focus. Your literature review needs to include the following: 1. Insights about the key understandings students need to construct and possible learning trajectories 2. Insights about how students best learn these concepts. 3. Misconceptions, partial conceptions, and difficulties students may encounter that we as teachers need to be aware of in order to avoid these misconceptions developing and/or address them if we notice them. Based on the findings from the literature review: 1. Discuss the appropriateness of the Australian Curriculum and other curriculum resources. 2. Discuss the implications for:
Create a series of 3 tasks (related to your mathematical focus area) that reflect your findings. OR Assessment Task 2b b) Designing a research-informed Unit of Work (Equivalent to 2000 words) Write a critical review of literature relating to a particular content area (rational number (beyond fractions and decimal fractions i.e., proportion reasoning, ratio), statistics and probability, algebraic thinking). Discuss critically the relevant curriculum documents in light of insights gleaned from the literature; and, plan a unit of work for the content area, for a particular year level. The unit of work must include relevant assessment strategies, a range of teaching strategies and ways to differentiate learning with alignment to the Australian Curriculum: Mathematics. OR Assessment Task 2c c) A choice from 2 items for Part I (Planning inclusive tasks) and Part II (Designing a research-informed Family Information Session and pamphlet Part I (a) Mathematics Video Stimulus Lesson(s) 25% (Equivalent to 1000 words) Create a 3 minute video clip, focusing on rational number, algebraic thinking or statistics and probability, that highlights the mathematical language required for a particular age group, for use as a stimulus to introduce the learning in a lesson. Provide a description of the way in which this video will be implemented into lessons, including prompts or questions that lead to mathematical investigations. OR Part I (b) Photograph/Video Prompted Investigation 25% (Equivalent to 1000 words) Take a series of 3 photographs or create a short video from the local area that enables children to explore the mathematics under focus (rational number, algebraic thinking or statistics and probability) and some prompts and questions that lead to mathematical investigation based on the photo AND PART II Designing a research-informed Family Information Session and Pamphlet 25% (Equivalent to 1000 words) Working in groups of 3, plan a mathematics information session for families, focusing on rational number, algebra or statistics and probability, including some at- home tasks for families to do as possible homework activities. Create an information pamphlet to support your information session. The information session and pamphlet must show evidence of being informed by the literature. | 50% | LO1, LO2, LO3, LO4, LO5 | GA4, GA5, GA8 |
Representative texts and references
Anthony, G., & Walshaw, M. (2009). Characteristics of effective teachers of mathematics: A view from the west. Journal of Mathematics Education, 2(2), 147-164.
Ball, D. B., & Ruhama, E. (Eds.). (2009). The professional education and development of teachers of mathematics: The 15th ICMI study. New York, NY: Springer.
Borko, H., Roberts, S., & Shavelson, R. (2008). Teacher decision-making: From Alan Bishop till today. In P. C. Clarkson & N. Presmeg (Eds.), Critical issues in mathematics education (pp. 37-67). New York, NY: Springer.
Forgasz, H., Barkatsas, A, Bishop, A., Clarke, B, Keast, S., Seah, W. T., & Sullivan, P. (2008). Research in mathematics education in Australasia 2004-2007. Rotterdam, The Netherlands: Sense.
Lee, S. -J., Brown, R. E., & Orrill, C. H. (2011). Mathematics teachers' reasoning about fractions and decimals using drawn representations. Mathematical Thinking and Learning, 13(3), 198-220.
Perry, B., Lowrie, T., Logan, T., MacDonald, A., & Greenlees, J. (2012). Research in mathematics education in Australasia 2008-2011. Rotterdam, The Netherlands: Sense.
Smith, M.S., & Stein, M.K. (in press). Orchestrating productive mathematics discussions: What can novice teachers learn? In. L. Resnick, C. Asterhan, & S. Clarke (Eds.), Socializing intelligence through academic talk and dialogue. Washington, DC: American Educational Research Association.
Smith, M. S., Engle, R., Smith, M., & Hughes, E. (2008). Orchestrating productive mathematics discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313-340.