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Unit of study_

EDUP2005: Mathematics Education 1: Early Number

Semester 2, 2022 [Normal day] - Camperdown/Darlington, Sydney

This is the first unit of study in Mathematics Education. Students will be introduced to key issues associated with how children acquire early mathematical concepts, processes and knowledge. The development of number sense and early mental arithmetic strategies will be a major focus of content for this unit of study. As part of this unit of study students will be required to assess a child from the K-2 grades using an interview schedule and to use the results to plan activities that demonstrate knowledge of worthwhile mathematical tasks.

Unit details and rules

Unit code EDUP2005
Academic unit Education
Credit points 4
Prohibitions
? 
None
Prerequisites
? 
66 credit points including EDUP2002 and EDUP2004 and EDUP2006 and EDUP2007
Corequisites
? 
None
Assumed knowledge
? 

None

Available to study abroad and exchange students

Yes

Teaching staff

Coordinator Jennifer Way, jennifer.way@sydney.edu.au
Tutor(s) Katherin Cartwright, katherin.cartwright@sydney.edu.au
Type Description Weight Due Length
Assignment Reflection on readings and resources
Online discussion in small groups
40% Multiple weeks 1000 words
Outcomes assessed: LO1 LO4 LO5 LO6 LO7 LO8
Assignment hurdle task group assignment Assessing and analysing early number strategies
Written assessment report and lesson ideas
60% Week 08 2000 words
Outcomes assessed: LO2 LO3 LO4 LO7
hurdle task = hurdle task ?
group assignment = group assignment ?

Assessment summary

  • Reflection on readings and resources: The overall purpose of this assignment is for you demonstrate the ability to learn from your reflections on the readings, and to participte in productive professional dialogue that supports the learning of your peers. This assignment involves individual work but also relies on group discussion.
  • Assessing and analysing early number strategies: The overall purpose of this assignment is for to demonstrate the ability to conduct an assessment interview, interpret the child's responses in relation to a learning framework, and to plan for further learning, being mindful of syllabus requirements. This assignment is completed in pairs. 

Detailed information for each assessment can be found on Canvas.

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a High distinction indicates work of an exceptional standard, a Distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name

Mark range

Description

High distinction

85 - 100

work of an exceptional standard

Distinction

75 - 84

work of a very high standard

Credit

65 - 74

work of good standard

Pass

50 - 64

work of an acceptable standard

Fail

0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

For more information see sydney.edu.au/students/guide-to-grades

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.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

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.

WK Topic Learning activity Learning outcomes
Week 01 Introduction to mathematics education. Early years developmental consideration (embodiment, language, emerging drawing). Intro to Assignment 1 Lecture (1 hr) LO1
Intro to NSW K-2 syllabus Sorting & classifying – concept of ‘group’ – compose basic lesson plan. Tutorial (1 hr) LO1
Week 02 Early number sense Rational counting Finger counting Intro to Developmental frameworks & Numeracy Progression Lecture (1 hr) LO1 LO4
Rhymes, songs, books & numerals as resources Cardinal and ordinal number Using digital images and learning objects (Number Trains) Tutorial (1 hr) LO1 LO4 LO7
Week 03 Counting as an early arithmetic strategy. Intro to Assignment 2. Lecture (1 hr) LO1 LO2 LO4 LO6
Walking the number track – number before & after. Activities and resources to develop counting strategies for addition and subtraction. Tutorial (1 hr) LO1 LO2 LO4 LO6
Week 04 Developing addition & subtraction – non-counting mental strategies with 1 & 2 digit numbers (Facile/flexible) The working mathematically processes. Lecture (1 hr) LO1 LO2 LO4 LO5
Games as learning activities Building confidence and fluency and developing representation of thinking Tutorial (1 hr) LO1 LO4 LO5
Week 05 Developing understanding of the number line. Teaching strategies for developing mathematical reasoning. Intro to Number Talks Lecture (1 hr) LO1 LO4 LO6 LO8
Experiential approach to understanding the structure of the number line Empty number lines to show mental strategies Tutorial (1 hr) LO1 LO4 LO8
a) Pre-recorded additional lecture: Development of children’s mathematical drawing - Week 4; b) Knowledge quiz (online) - Weeks 5/6; c) Draft lesson plan - Week 10 Independent study (2 hr) LO1 LO5 LO8
Week 06 Flexible understanding of Place Value. Modelling of place value Lecture (1 hr) LO1 LO4
Counting by 10 and 100 Base 10 blocks (MAB) workshop (Digital game: Wishball) Tutorial (1 hr) LO1 LO2 LO4 LO7
Week 07 Early multiplication & division concepts and processes Lecture (1 hr) LO1 LO4 LO6 LO8
Working with equal groups – Skip counting. Introducing the array structure Tutorial (1 hr) LO1 LO2 LO4
Week 08 Early fraction sense Lecture (1 hr) LO1 LO4 LO5 LO8
Partitioning and division Representation of fractions Tutorial (1 hr) LO1 LO4 LO8
Week 09 Pattern, structure, number relations and algebraic thinking Lecture (1 hr) LO1 LO4 LO6 LO8
Patterning – generalising – working mathematically Number relations – odd/even. Using calculators as investigation tools. Commutative property Tutorial (1 hr) LO1 LO4 LO7
Week 10 Problem solving, investigating and challenging tasks. Lecture (1 hr) LO1 LO4 LO5 LO6
Number problems and open-ended-tasks. Scaffolding and questioning Tutorial (1 hr) LO1 LO4 LO6
Week 11 Teaching for conceptual understanding Catering for diverse student needs Lecture (1 hr) LO1 LO4 LO5 LO6
Lesson planning/refining workshop Tutorial (1 hr) LO1 LO4 LO5 LO8

Attendance and class requirements

Attendance: The Sydney School of Education and Social Work requires attendance of at least 90 percent of all seminars, workshops or lectures. Where a student is unable to attend at the required rate evidence of illness or misadventure may be required and the student may be required to undertake extra work. Students should discuss the circumstances of their absence(s) with the co-ordinator of the unit of study. Further details are provided in the School canvas site: https://canvas.sydney.edu.au/courses/13426

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 4 credit point unit, this equates to roughly 80-100 hours of student effort in total.

Required readings

All readings for this unit can be accessed on the Library Readings link available on Canvas.

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, research and curriculum documents as they relate to the teaching and learning of mathematics
  • LO2. explore a child’s understanding of early number by undertaking a diagnostic interview and analysing the results using a developmentally-based learning framework
  • LO3. design a sequence of lesson ideas 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 quality pedagogies associated with the teaching of mathematics
  • LO5. reflect critically upon personal beliefs, experiences, attitudes and learning style toward mathematics and consider how this may impact on an individual's teaching of mathematics
  • LO6. explain the role mathematics plays in developing numeracy
  • LO7. reflect on the appropriate use of digital technologies to enhance a child's mathematical thinking
  • LO8. demonstrate increased content knowledge of mathematics.

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
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9
Australian Professional Standards for Teachers (Graduate Level – UG and MTeach) -
Competency code Taught, Practiced or Assessed Competency standard
1.1.1 P A (Graduate) Demonstrate knowledge and understanding of physical, social and intellectual development and characteristics of students and how these may affect learning.
1.2.1 P A (Graduate) Demonstrate knowledge and understanding of research into how students learn and the implications for teaching.
1.5.1 P A (Graduate) Demonstrate knowledge and understanding of strategies for differentiating teaching to meet the specific learning needs of students across the full range of abilities.
2.3.1 P A (Graduate) Use curriculum, assessment and reporting knowledge to design learning sequences and lesson plans.
3.3.1 P A (Graduate) Include a range of teaching strategies.
4.1.1 P A (Graduate) Identify strategies to support inclusive student participation and engagement in classroom activities.
5.1.1 P A (Graduate) Demonstrate understanding of assessment strategies, including informal and formal, diagnostic, formative and summative approaches to assess student learning.
5.4.1 P A (Graduate) Demonstrate the capacity to interpret student assessment data to evaluate student learning and modify teaching practice.

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

Some modifications to the assignment tasks have been made in response to feedback from students.

Site visit guidelines

If you are undertaking professional experience/field education placement as part of your enrolment in this unit of study, please assess your specific needs and requirements for the safe and successful completion of an external placement within a host organisation. You will be given the opportunity to disclose any health issues that have a work health and safety significance before arranging a placement so that your safety, and the safety of others, can be properly assessed. The Professional Experience Coordinator/Field Education Manager will work to ensure that the workplace assignment to you is appropriate for your needs and requirements. If you are experiencing disability, and require reasonable adjustments to be arranged, please contact Disability Services as early as possible prior to commencing the internship. Please note, in all cases, and for the purpose of organising reasonable adjustments, only the impact and not the nature, of your disability will be disclosed to the host organisation.

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.