Unit Outline
EPR320
Pedagogical Content Knowledge for Teaching Mathematics
Semester 1, 2026
Carol Murphy
Faculty of Education
Arts and Society (Portfolio)
CRICOS Provider Code: 00586B
Unit Coordinator
Carol Murphy
Email: Carol.Murphy@utas.edu.au
 
What is the Unit About?
Unit Description
This unit builds on your knowledge of contemporary research and evidence-based pedagogical practices for teaching mathematics from EPR220. The unit further explores high quality mathematics instruction and develops your skills in preparing to teach effectively  and consolidating knowledge of relevant curricula (including the Australian Curriculum V.9.0, and/or the Early Years Learning Framework for Australia V.2.0). You are provided opportunities to critically evaluate teaching practices, task design and use of representations that will progress students’ knowledge and skills towards proficiency.  The unit  will provide you with opportunities to develop skills in planning across a unit of work, assess students' learning and to reflect on your developing pedagogical content knowledge.
 
 
Intended Learning Outcomes
As per the Assessment and Results Policy 1.3, your results will reflect your achievement against specified learning outcomes.
On completion of this unit, you will be able to:
1
apply conceptual understanding of mathematical knowledge to effective teaching in relation to pedagogical content knowledge.
2
identify and interpret students mathematical understanding and make informed decisions regarding how to promote further understanding and address misconceptions.
3
apply contemporary theoretical and practical knowledge of mathematics pedagogy to plan and design a coherent teaching sequence with potential to scaffold learning.
4
identify high quality teaching materials and representations, including digital tools, and evaluate effectiveness in modelling and scaffolding student learning.
5
Synthesise literature to justify teaching practices in a scholarly manner, with correct usage of English and mathematical conventions.
Requisites
REQUISITE TYPE
REQUISITES
Pre-requisite
ESH220 or ESH319 or EPR220
Alterations as a result of student feedback
 
 
 
Teaching arrangements
ATTENDANCE MODE
TEACHING TYPE
LEARNING ACTIVITY
CONTACT HOURS
FREQUENCY
Online
Lecture (Online)
Lecture, teaching notes and readings provided in MyLO
3
1 time per fortnight
Tutorial (Online)
Engage with tasks and discussion boards/synchronous tutorial
2
Weekly
Attendance / engagement expectations
If your unit is offered On campus, it is expected that you will attend all on-campus and onsite learning activities. This is to support your own learning and the development of a learning community within the unit. If you are unable to attend regularly, please discuss the situation with your course coordinator and/or our UConnect support team.

If your unit is offered Online or includes online activities, it is expected you will engage in all those activities as indicated in the Unit Outline or MyLO, including any self-directed learning.

If you miss a learning activity for a legitimate reason (e.g., illness, carer responsibilities) teaching staff will attempt to provide alternative activities (e.g., make up readings) where it is possible.
 
 
 
 
How will I be Assessed?
 
For more detailed assessment information please see MyLO.
Assessment schedule
ASSESSMENT TASK #
ASSESSMENT TASK NAME
DATE DUE
WEIGHT
LINKS TO INTENDED LEARNING OUTCOMES
Assessment Task 1:
Lesson Plan
Week 4
25 %
LO1, LO2, LO3, LO4, LO5
Assessment Task 2:
Unit Plan
Week 8
40 %
LO1, LO2, LO3, LO4, LO5
Assessment Task 3:
Reflection on your PCK
Week 13
35 %
LO1, LO2, LO3, LO4, LO5
 
Assessment details
Assessment Task 1: Lesson Plan
Task Description:
The purpose of Assessment Task 1 is to provide you with the experience of applying conceptual understanding of mathematical content in the Australian Curriculum and to demonstrate your potential to plan for effective instruction that attends to how students learn.

Part 1 Lesson Plan 700 words.
You are required to prepare a plan for a short lesson (20 to 30 minutes) based on a specified topic in relation to Australian Curriculum V9, or to the Early Years Learning Framework for Australia, V2.0 (43A and E5Y students), for a chosen year or age group.
You will be provided with a choice of outline unit plans showing the AC v9 Achievement Standard (AS) and related Content Description(s) (CD) or to the EYLF learning outcome(s). You may choose one of these according to your preferred age group.
Based on the AS and CDs you should prepare Intended Learning Outcome(s) (ILOs) (max two) and key teaching points (including worked examples with the explanations, questions and prompts that you will use; opportunities to challenge students' recall of existing knowledge and apply to the new learning; quality teaching materials (which may include digital tools, manipulatives and or visual representations)) that will scaffold students' learning towards the ILO(s).
You will be provided with a lesson plan template to guide you in preparing your plan.

APA style referencing is not required for Part 1 Unit Plan but you should provide a list of resources and relevant URL websites where appropriate. GenAI use is allowed but must be acknowledge - see requirements for the rationale.

Part 2 Rationale 300 words.
The rationale should justify the coherence of your intended teaching that will include your use of explanations, prompts and questions in relation to your choice of worked examples, materials and representations. Explain how your plan will challenge students to recall existing knowledge and facts and enable progressive removal of scaffolding and develop proficiency.
You will be provided with a template to guide you.
You should use the key texts as well as other relevant literature to support your justification.

You may use AI, as well as other online materials, to support your preparation for the plan, but these will need to be adjusted to meet the template and Assessment Task criteria. You must identify where you have used AI or other resourced activities in your unit plan and indicate the adjustments that you made to the AI output in your rationale.

APA style referencing is required for Part 2 Rationale.

Completion of this Assessment Task relates to Australian Professional Standards for Teachers (APST) 2.1, 2.2, 2.3, 3.2, 3.3, 3.4
Task Length:
Part 1 lesson pan 700 words (not including AC/EYLF wording and template headings) Part 2 Rationale 300 words (not including references) Total 1000 words
Due Date:
Week 4
Weight:
25 %
 
CRITERION #
CRITERION
MEASURES INTENDED
LEARNING OUTCOME(S)
1
Organises a coherent teaching sequence with a clear explanation for beginning instruction that aligns with appropriate learning for a chosen year group in relation to AC v.9 or EYLF v2.0 (25%).
LO1, LO3
2
Lesson plan indicates worked examples, quality teaching materials, questions and prompts that will effectively scaffold learning using manageable tasks and defined goals (25%).
LO2
3
Rationale uses key texts and relevant literature to justify how your modelling of new skills and content (including worked examples, questions prompts and manageable steps) relates to research into students' learning (25%).
LO4
4
Communicates in a scholarly manner with correct use of mathematical terminology and conventions (25%).
LO5
 
Assessment Task 2: Unit Plan
Task Description:
The purpose of Assessment Task 2 is to provide you with the experience of applying conceptual understanding of the Australian Curriculum content to planning a sequence of lessons that demonstrate scaffolded progression of a new area of learning from novice to mastery and proficiency in independent problem solving.
Assessment Task 2 has two parts: Unit Plan and Rationale
Part 1 Unit Plan 1000 words
You are required to prepare a unit plan for 5 lessons or learning experiences based on a specified topic in relation to Australian Curriculum V9, or to the Early Years Learning Framework for Australia, V2.0 (43A and E5Y students), for a chosen year or age group.
You should prepare key teaching points (not lesson plans) for 5 lessons, according to the AC v9 Achievement Standard (AS) and related Content Description(s) (CD) or to the EYLF learning outcome(s) for your chosen year group.
You will be provided with a unit plan template and example unit plan to guide you in preparing your plan.
You may use AI, as well as other online materials, to support your preparation for the plan, but these will need to be adjusted to meet the template and Assessment Task criteria. You must identify where you have used AI or other resourced activities in your unit plan and reflect on their use in your rationale.
APA style referencing is not required for Part 1 Unit Plan.
Part 2 Rationale 600 words
The rationale should justify the progression of learning in your unit plan in relation to the AC ASs and CDs or the EYLF outcomes, as well as your choice of examples, resources, questions and prompts and your assessment of student learning.

You will be provided with a template to guide you.
You should use the key texts as well as other relevant literature to support your justification.
Where you have used AI or other online support material you should indicate this in your justification.
APA style referencing is required for Part 2 Rationale.

Completion of this Assessment Task relates to Australian Professional Standards for Teachers (APST) 2.1, 2.2, 2.3, 3.2, 3.3, 3.4
Task Length:
Part 1 unit plan 1000 words (not including template headings and AC/EYLF wording) Part 2 Rationale 600 words (not including references) Total 1600 words
Due Date:
Week 8
Weight:
40 %
 
 
CRITERION #
CRITERION
MEASURES INTENDED
LEARNING OUTCOME(S)
1
Unit plan ILOs and mathematical content aligns with appropriate learning for a chosen year group in relation to AC v.9 or EYLF v2.0 and demonstrates your conceptual understanding of the mathematics (25%).
LO1, LO3
2
Unit plan indicates effective instruction in teaching new learning across the five lessons, commencing with clear explanations and worked examples and scaffolding learning to independent problem solving (25%).
LO2
3
Rationale uses key texts and relevant literature to justify how your teaching and teaching materials will introduce the new learning and challenge students to recall and practice this learning developing to proficiency (25%).
LO4
4
Communicates in a scholarly manner with correct use of mathematical terminology (25%).
LO5
 
Assessment Task 3: Reflection on your PCK
Task Description:
Assessment Task 3 draws on your participation in tutorials and/or contributions to the discussion boards to reflect on your developing Pedagogical Content Knowledge based on the components of the Knowledge Quartet.
To demonstrate you have met the Unit ILOs, you will have participated in a range of activities across the 5 fortnightly topics. For this assessment task, you are required to select 5 of these activities from the discussion boards or tutorials, one from each of the fortnightly topics, and reflect on how the activity has impacted on your knowledge for teaching mathematics based on the Knowledge Quartet.
You should note the availability dates (start and end dates) for each of the topics to ensure that you have had the opportunity to contribute to at least one activity in each topic.
You may refer to a mix of online discussion posts and tutorials. Any discussion post should be more than 100 words and indicate how you responded to at least one other student’s post. Reflections on activities in the tutorials should indicate your contribution and responses within the tutorial. If you are using an activity from the discussion board, you must include image of your post(s). If you are using an activity from a tutorial you must give the date for attendance (monitored by your tutor).
You will be given guidance on how to focus your reflections and should refer to key texts and readings to inform your reflections.
Note that you will be assessed on the quality of your reflections and not your discussion posts or contribution to activities in tutorials.
Task Length:
1400 words
Due Date:
Week 13
Weight:
35 %
 
CRITERION #
CRITERION
MEASURES INTENDED
LEARNING OUTCOME(S)
1
Reflections demonstrate foundation and transformation knowledge in reviewing a use of resources and representations and are that is informed by key texts and readings (25%)
LO4
2
Reflections critically explore connection and contingency knowledge related to your developing teaching practices that support students’ mathematical understanding and are informed by in relation to key texts and readings (25%)
LO2
3
Reflections are communicated in an appropriate manner with evidence of correct language used to explain mathematical ideas and show correct usage of mathematical conventions (25%)
LO5
4
Range of activities indicates an appropriate level of participation to evidence application of pedagogical knowledge for teaching mathematics (25%)
LO1, LO3
 
 
 
How your final result is determined
To pass this unit, you need to demonstrate your attainment of each of the Intended Learning Outcomes, achieve a final unit grade of 50% or greater, and pass any hurdle tasks.
Academic progress review
The results for this unit may be included in a review of your academic progress. For information about progress reviews and what they mean for all students, see Academic Progress Review in the Student Portal.
Submission of assignments
Where practicable, assignments should be submitted to an assignment submission folder in MYLO. You must submit assignments by the due date or receive a penalty (unless an extension of time has been approved by the Unit Coordinator). Students submitting any assignment in hard copy, or because of a practicum finalisation, must attach a student cover sheet and signed declaration for the submission to be accepted for marking.
Academic integrity
Academic integrity is about acting responsibly, honestly, ethically, and collegially when using, producing, and communicating information with other students and staff members.

In written work, you must correctly reference the work of others to maintain academic integrity. To find out the referencing style for this unit, see the assessment information in the MyLO site, or contact your teaching staff. For more detail about Academic Integrity, see
Important Guidelines & Support.
Requests for extensions
If you are unable to submit an assessment task by the due date, you should apply for an extension.
 
A request for an extension should first be discussed with your Unit Coordinator or teaching support team where possible. A request for an extension must be submitted by the assessment due date, except where you can provide evidence it was not possible to do so. Typically, an application for an extension will be supported by documentary evidence: however, where it is not possible for you to provide evidence please contact your Unit Coordinator.
 
The Unit Coordinator must notify you of the outcome of an extension request within 3 working days of receiving the request.
Late penalties
Assignments submitted after the deadline will receive a late penalty of 5% of the original available mark for each calendar day (or part day) that the assignment is late. Late submissions will not be accepted more than 10 calendar days after the due date, or after assignments have been returned to other students on a scheduled date, whichever occurs first. Further information on Late Penalties can be found on the Assessments and Results Procedure.
 
Review of results and appeals
You are entitled to ask for a review of the marking and grading of your assessment task if there is an irregularity in the marking standards or an error in the process for determining the outcome of an assessment. Details on how to request a review of a mark for an assignment are outlined in the Review and Appeal of Academic Decisions Procedure.
 
 
 
Required Resources
Required reading materials
You will need access to the following text:
Van de Walle, J., et al. (2024. Primary and middle school mathematics: Teaching developmentally. Pearson Australia Second Edition (ebook available from library).
The Australian Curriculum, version 9. https://v9.australiancurriculum.edu.au/
Reading Lists provide direct access to all material on unit reading lists in one place. This includes eReadings and items in Reserve. You can access the Reading List for this unit from the link in MyLO, or by going to the Reading Lists page on the University Library website.
 
Recommended reading materials
Recommended Readings
Rowland et al. (2003) The Knowledge Quartet. In J. Williams (Ed.) Proceedings of the British Society for Research into Learning Mathematics, 23(3), pp. 97-102. https://bsrlm.org.uk/wp-content/uploads/2016/02/BSRLM-IP-23-3-17.pdf
Rowland, T., Turner, F., Thwaites, A. & Huckstep, P. (2009). Developing Primary Mathematics Teaching. SAGE. Chapter 3, Transformation: Using and understanding representations in mathematical teaching.
Turner, F. (2012). Using the Knowledge Quartet to develop mathematics content knowledge: The role of reflection on professional development. Research in Mathematics Education, 14, 253-272.
Recommended Journals:
Australian Primary Mathematics Classroom
The Australian Mathematics Teacher
 
Other required resources