Outline

Overview

In this second unit of study in Mathematics pedagogy and curriculum, students will explore children's development of number sense and understandings of number operations (up to the end of Stage 2 of the curriculum). In practical workshops, students will gain experience in the use of a variety of representations of number and of age-appropriate and inclusive pedagogies for young children. Students will learn the technique of diagnostic interview and develop assessment-based teaching plans. The mathematics content focus is numeration, operations and algebraic thinking.

Unit details and rules

Academic unit	Education
Credit points	6
Prerequisites ?	36cp of 1000-level EDUP units
Corequisites ?	None
Prohibitions ?	None
Assumed knowledge ?	None
Available to study abroad and exchange students	No

Teaching staff

Coordinator	Jennifer Way, jennifer.way@sydney.edu.au
Lecturer(s)	Jennifer Way, jennifer.way@sydney.edu.au
Tutor(s)	Katherin Cartwright, katherin.cartwright@sydney.edu.au

Type	Description	Weight	Due	Length
Assignment	Critical Reflection: Early number learning Online discussion with a group of peers across weeks 3, 6 & 12.	40%	Multiple weeks	1750
Outcomes assessed:
Assignment	Planning from diagnostic assessment Conduct an interview, analyse and plan teaching. Small group.	60%	Please select a valid week from the list below	2750
Outcomes assessed:
Small test	Number knowledge Online quiz on numeration & number properties	0%	Week 11	30 minutes
Outcomes assessed:
= hurdle task ? = group assignment ?

Assessment summary

Critical reflection - Contribute well-reasoned arguments, evidence-based opinions and well-considered questions to a professional discussion with peers. Complete a self-assessment of levels of critical reflection using a rubric.
Planning from diagnostic assessment - working with a partner, conduct a diagnostic interview with a 4-6 year old child, analyse the data and design appropriate learning experiences for the child, using the proformas provided.
Number Knowledge - complete an online quiz to test your knowledge of numeration and number properties and consider the feedback. Retake the test to improve your score.

Detailed information for each assessment can be found on Canvas

Assessment criteria

Result	Mark Range	Description
HD	85-100	Awarded when you demonstrate the learning outcomes for the unit at an exceptional standard
DI	75-84	Awarded when you demonstrate the learning outcomes for the unit at a very high standard
CR	65-74	Awarded when you demonstrate the learning outcomes for the unit at a good standard
PA	50-64	Awarded when you demonstrate the learning outcomes for the unit at an acceptable standard
FA	0-49	When you don’t meet the learning outcomes of the unit to a satisfactory standard

For more information see guide to grades.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

Deduction of 5% of the maximum mark for each calendar day after the due date.
After ten calendar days late, a mark of zero will be awarded.

Academic integrity

The Current Student website provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

Use of generative artificial intelligence (AI) and automated writing tools

You may only use generative AI and automated writing tools in assessment tasks if you are permitted to by your unit coordinator. If you do use these tools, you must acknowledge this in your work, either in a footnote or an acknowledgement section. The assessment instructions or unit outline will give guidance of the types of tools that are permitted and how the tools should be used.

Your final submitted work must be your own, original work. You must acknowledge any use of generative AI tools that have been used in the assessment, and any material that forms part of your submission must be appropriately referenced. For guidance on how to acknowledge the use of AI, please refer to the AI in Education Canvas site.

The unapproved use of these tools or unacknowledged use will be considered a breach of the Academic Integrity Policy and penalties may apply.

Studiosity is permitted unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission as detailed on the Learning Hub’s Canvas page.

Outside assessment tasks, generative AI tools may be used to support your learning. The AI in Education Canvas site contains a number of productive ways that students are using AI to improve their learning.

Learning support

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Weekly schedule

WK	Topic	Learning activity
Week -02	Concept development and mathematical representations Early number sense	Lecture (1 hr)
Week -02	Early number sense, subitizing, counting with understanding, cardinal and ordinal number. Selecting and adapting resources – digital, concrete, books and rhymes. Connecting with Numeracy learning outside the school.	Tutorial (2 hr)
Week -03	Developing early arithmetic strategies based on counting	Lecture (1 hr)
Week -03	Early arithmetic strategies based on counting Games as learning activities and inclusive practices for diverse student needs Structure of a number skills lesson	Tutorial (2 hr)
Week -04	Developing addition & subtraction – non-counting strategies (Facile/flexible) Promoting fluency with number facts	Lecture (1 hr)
Week -04	Promoting fluency with number facts, vocabulary development and verbal explanations of mental strategies. Problem solving and recording – working mathematically processes. The role of drawing and interpreting children’s work samples, catering for variation in student characteristics.	Tutorial (2 hr)
Week -05	Assessing number strategies through diagnostic interview Tracking student progression and principles of assessment-based planning	Lecture (1 hr)
Week -05	Assessing number strategies through diagnostic interview Tracking student progression and principles of assessment-based planning	Tutorial (2 hr)
Week 01	The role of motivation & engagement in mathematics learning and teaching. (Assessment 1 briefing) Number in the syllabus (Stages ES1-S2), Numeracy Learning Progression	Lecture (1 hr)
Week 01	Number in the syllabus (Stages ES1-S2) Inclusive practices for diverse student needs - approaching number sequencing and numeral recognition in different ways	Tutorial (2 hr)
Week 06	Numeration systems – understanding place value	Lecture (1 hr)
Week 06	Exploring bases and alternative algorithms Number properties and their applications	Tutorial (2 hr)
Week 07	Applying place value thinking for addition and subtraction. Structured and open number lines	Lecture (1 hr)
Week 07	Using ‘Number Talks’ (&Talk Moves) to develop and assess mental calculation and representational strategies. Moving towards written algorithms through modelling and verbalization, including digital enablers. (Decomposition and Equal addends methods)	Tutorial (2 hr)
Week 08	Development of early multiplication and division	Lecture (1 hr)
Week 08	Inclusive pedagogy for equal groups and skip-counting and Sharing and Grouping division problems – with emphasis on minimizing language barriers. Exploring factors and multiples with arrays	Tutorial (2 hr)
Week 09	Extending multiplication & division strategies - moving from additive to multiplicative thinking – Numeracy Learning Progression	Lecture (1 hr)
Week 09	Exploring informal recording of multiplication and division strategies. Lesson structures for promoting conceptual reasoning (revisit L-E-S lessons)	Tutorial (2 hr)
Week 10	Pattern, spatial structure and mathematical thinking	Lecture (1 hr)
Week 10	Patterning workshop – diverse representations, digital resources, the emergence of generalisation. Strategies for finding number patterns and building the language of pattern	Tutorial (2 hr)
Week 11	Number relations and algebraic thinking Inductive and deductive reasoning	Lecture (1 hr)
Week 11	Exploring odd and even numbers and other number properties. Scaffolding number investigations to cater for a range of student needs Calculators and apps as investigation tools	Tutorial (2 hr)
Week 12	Early fraction concepts, representation and language. Anticipating student difficulties and avoiding misconceptions	Lecture (1 hr)
Week 12	Anticipating student difficulties and avoiding misconceptions. Introducing odd denominators. Pedagogy for exploring the relationships between halves, quarters and eighths.	Tutorial (2 hr)

Attendance and class requirements

Attendance at both lectures and tutorials are needed to meet the 90% attendance requirements.

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Required readings

NSW Mathematics K-6 Syllabus 2023

See Library links in Canvas

Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

LO1. Demonstrate familiarity with current educational theory and research (including the role of motivation and engagement in learning) as they relate to the teaching and learning of mathematics.
LO2. Explore a child’s understanding of early number through informal assessment, and specifically by undertaking a diagnostic interview and analysing the results using a developmental learning framework.
LO3. Design learning experiences based on the results of an assessment of a child and using knowledge of the NSW syllabus and support documents.
LO4. Discuss research-based knowledge of inclusive pedagogies associated with the teaching of mathematics, including strategies to address the learning needs of students from Aboriginal and Torres Strait Islander backgrounds, cultural and linguistic diversity of students, and students with disability.
LO5. Critically reflect on emerging beliefs about how to teach mathematics, particularly regarding interpretations of student ‘abilities’.
LO6. Reflect on the appropriate use of digital technologies to enhance a child's mathematical thinking.
LO7. Demonstrate increased content knowledge of mathematics, pertaining to number properties, numeration systems and algebraic thinking, and pedagogical content knowledge for early number concepts.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1	Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
GQ2	Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
GQ3	Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
GQ4	Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
GQ5	Inventiveness Generating novel ideas and solutions.
GQ6	Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.
GQ7	Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
GQ8	Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.
GQ9	Influence Engaging others in a process, idea or vision.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Alignment with Competency standards

Outcomes	Competency standards
	Australian Professional Standards for Teachers (Graduate Level – UG and MTeach) - 1.2.1. (Graduate) Demonstrate knowledge and understanding of research into how students learn and the implications for teaching. 1.5.1. (Graduate) Demonstrate knowledge and understanding of strategies for differentiating teaching to meet the specific learning needs of students across the full range of abilities. 2.1.1. (Graduate) Demonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area. 6.2.1. (Graduate) Understand the relevant and appropriate sources of professional learning for teachers.
	Australian Professional Standards for Teachers (Graduate Level – UG and MTeach) - 1.2.1. (Graduate) Demonstrate knowledge and understanding of research into how students learn and the implications for teaching. 2.1.1. (Graduate) Demonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area. 2.3.1. (Graduate) Use curriculum, assessment and reporting knowledge to design learning sequences and lesson plans. 5.1.1. (Graduate) Demonstrate understanding of assessment strategies, including informal and formal, diagnostic, formative and summative approaches to assess student learning.
	Australian Professional Standards for Teachers (Graduate Level – UG and MTeach) - 3.2.1. (Graduate) Plan lesson sequences using knowledge of student learning, content and effective teaching strategies. 3.3.1. (Graduate) Include a range of teaching strategies.
	Australian Professional Standards for Teachers (Graduate Level – UG and MTeach) - 1.3.1. (Graduate) Demonstrate knowledge of teaching strategies that are responsive to the learning strengths and needs of students from diverse linguistic, cultural, religious and socio-economic backgrounds. 1.4.1. (Graduate) Demonstrate broad knowledge and understanding of the impact of culture, cultural identity and linguistic background on the education of students from Aboriginal and Torres Strait Islander backgrounds. 1.6.1. (Graduate) Demonstrate broad knowledge and understanding of legislative requirements and teaching strategies that support participation and learning of students with disability. 2.1.1. (Graduate) Demonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area. 2.3.1. (Graduate) Use curriculum, assessment and reporting knowledge to design learning sequences and lesson plans.
	Australian Professional Standards for Teachers (Graduate Level – UG and MTeach) - 1.1.1. (Graduate) Demonstrate knowledge and understanding of physical, social and intellectual development and characteristics of students and how these may affect learning. 1.3.1. (Graduate) Demonstrate knowledge of teaching strategies that are responsive to the learning strengths and needs of students from diverse linguistic, cultural, religious and socio-economic backgrounds. 6.4.1. (Graduate) Demonstrate an understanding of the rationale for continued professional learning and the implications for improved student learning.
	Australian Professional Standards for Teachers (Graduate Level – UG and MTeach) - 2.6.1. (Graduate) Implement teaching strategies for using ICT to expand curriculum learning opportunities for students. 3.4.1. (Graduate) Demonstrate knowledge of a range of resources, including ICT, that engage students in their learning.
	Australian Professional Standards for Teachers (Graduate Level – UG and MTeach) - 2.1.1. (Graduate) Demonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area.

Australian Professional Standards for Teachers (Graduate Level – UG and MTeach) -

Competency code	Taught, Practiced or Assessed	Competency standard
1.1.1		(Graduate) Demonstrate knowledge and understanding of physical, social and intellectual development and characteristics of students and how these may affect learning.
1.2.1		(Graduate) Demonstrate knowledge and understanding of research into how students learn and the implications for teaching.
1.3.1		(Graduate) Demonstrate knowledge of teaching strategies that are responsive to the learning strengths and needs of students from diverse linguistic, cultural, religious and socio-economic backgrounds.
1.4.1		(Graduate) Demonstrate broad knowledge and understanding of the impact of culture, cultural identity and linguistic background on the education of students from Aboriginal and Torres Strait Islander backgrounds.
1.5.1		(Graduate) Demonstrate knowledge and understanding of strategies for differentiating teaching to meet the specific learning needs of students across the full range of abilities.
1.6.1		(Graduate) Demonstrate broad knowledge and understanding of legislative requirements and teaching strategies that support participation and learning of students with disability.
2.1		Content and teaching strategies of the teaching area
2.1.1		(Graduate) Demonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area.
2.2.1		(Graduate) Organise content into an effective learning and teaching sequence.
2.3.1		(Graduate) Use curriculum, assessment and reporting knowledge to design learning sequences and lesson plans.
2.4.1		(Graduate) Demonstrate broad knowledge of, understanding of and respect for Aboriginal and Torres Strait Islander histories, cultures and languages.
2.6.1		(Graduate) Implement teaching strategies for using ICT to expand curriculum learning opportunities for students.
3.2.1		(Graduate) Plan lesson sequences using knowledge of student learning, content and effective teaching strategies.
3.3.1		(Graduate) Include a range of teaching strategies.
3.4.1		(Graduate) Demonstrate knowledge of a range of resources, including ICT, that engage students in their learning.
5.1.1		(Graduate) Demonstrate understanding of assessment strategies, including informal and formal, diagnostic, formative and summative approaches to assess student learning.
6.2.1		(Graduate) Understand the relevant and appropriate sources of professional learning for teachers.
6.4.1		(Graduate) Demonstrate an understanding of the rationale for continued professional learning and the implications for improved student learning.

Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

This is new unit. Student feedback will be used to refine the unit.

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Alignment with Competency standards

Responding to student feedback

Responding to student feedback

Disclaimer

On this page

Useful links

EDUP2035: Teaching Primary Mathematics 2

Semester 2, 2023 [Normal day] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Attendance and class requirements

Study commitment

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Alignment with Competency standards

Responding to student feedback

Responding to student feedback

Disclaimer

On this page

Useful links