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NMBR140 Introduction to Mathematical Thinking

Unit rationale, description and aim

This unit is designed to provide an introduction to primary school mathematics education by investigating current directions in research, the Australian Curriculum: Mathematics and other relevant curriculum documents. The unit will introduce theories of knowledge needed for teaching mathematics, learning mathematics and effective teaching and learning through the content strands of Number (restricted to Whole Number), Measurement and Geometry. Emphasis will be placed on pre-service teachers’ further personal development of the concepts, substance, and structure of the mathematical content as well as strategies for teaching mathematics. Approaches to learning and teaching mathematics that are effective and respectful of each student’s background and culture will be a focus. A range of resources to engage students in the learning of mathematics will also be used, including digital technologies, with a view to developing students’ self-esteem and a positive disposition toward mathematics. Methods of assessment will be considered to identify students’ current mathematical understanding and to inform teaching.

The aim of this unit is to provide pre-service teachers with an introduction to primary school mathematics education by investigating diverse theories of knowledge needed for teaching mathematics, learning mathematics and effective teaching and learning through the content strands of Number (restricted to Whole Number), Measurement and Geometry.

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, high expectations, and positive attitudes to mathematics (GA1; APST 1.2, 1.3, 4.1)

LO2 - demonstrate an ability to critically reflect on and enhance their own personal mathematical knowledge needed for teaching, and demonstrate an understanding of the historical and cultural development of mathematical idea (GA4, GA5; APST 2.1)

LO3 - apply theories and research about primary aged student’s development of mathematical concepts and proficiencies to create powerful learning experiences for students in Whole Number, Measurement and Geometry as required by Australian Curriculum: Mathematics and other relevant curriculum documents (GA4, GA5; APST 1.2, 1.5, 2.3, 3.3)

LO4 - demonstrate an ability to critically reflect on the Australian Curriculum: Mathematics and the effectiveness of different approaches to teaching mathematics that cater for students across a full range of abilities, particularly the formative, summative and diagnostic uses of assessment data, and apply these approaches to support students’ diverse learning needs (GA4, GA5; APST 1.2, 1.3, 1.5, 2.3, 2.5, 3.3, 5.1, 5.4)

LO5 - use language, symbols, resources including ICT as tools to design learning sequences and lesson activities to support student’s mathematical learning of Whole Number, Measurement and Geometry, as outlined in relevant documents (GA4, GA5; APST 2.1, 2.3, 2.5, 2.6, 3.3, 3.4)

LO6 - critically reflect on the role of mathematics and numeracy education across the curriculum for full participation in community life, work and further education, including how mathematics is a powerful tool in making sense of the world (GA1, GA4, GA5; APST 2.1, 2.3, 2.5).

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 


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.

1.3 Demonstrate knowledge of teaching strategies that are responsive to the learning strengths and needs of students from diverse linguistic, cultural, religious and socioeconomic backgrounds.

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.

5.1 Demonstrate understanding of assessment strategies, including informal and formal, diagnostic, formative and summative approaches to assess student learning.

5.4 Demonstrate the capacity to interpret student assessment data to evaluate student learning and modify teaching practice.


Topics will include:

  • Models of the mathematical knowledge needed for teaching
  • A focus on relevant content and proficiencies as detailed in the Australian Curriculum: Mathematics and other state and national documents
  • Interviews and open-ended diagnostic tasks are prioritised approaches to assessment that inform the learning and teaching of mathematics and reflect the significant connections between validity, fairness, a concern for justice and for the dignity of all human beings
  • Implications of various relevant theories of learning for the teaching of mathematics are explored, with emphasis on those that support conceptual understanding and the critical influence of the teacher on student learning
  • Typical pathways/trajectories in young children’s mathematical learning, from pre-school to later primary years are investigated and applied to the design of learning experiences that are appropriate to student needs
  • Informed, critical uses of manipulatives, words and symbols, students’ interests in creating contexts, and digital technology are expected in the design of learning experiences for students
  • How to set up and manage mathematical learning experiences for individual, group and whole class teaching and learning.

Mathematics content basis for the teaching in this Unit will be Number (restricted to Whole Number), Measurement and Geometry as required in Primary School. This will include pre-service teacher reflection on and enhancement of their personal knowledge.

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. Pre-service teachers 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 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 becomes 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. In order to pass this unit, participants are required to submit and engage in all assessment tasks.

The total assessment tasks will amount to the equivalent of 4,000 words.

Overview of assessments

Brief Description of Kind and Purpose of Assessment TasksWeightingLearning OutcomesGraduate Attributes

Assessment Task 1

Assess student learning, interpret and report on student data and subsequently plan specifically targeted teaching.

(Equivalent to 2,000 words)

Interview two students at different years of primary school, recording the responses of each student accurately in respect of the interview protocols. Interpret the data about each student to form judgments about their mathematical development with reference to a theoretical framework or trajectory. Summarise the data about each student in a summary report suitable for reading by another teacher, using professional language and presentation. Design a follow-up lesson for each student that targets a need that was identified in the interview. Link the lesson outcomes to the Australian Curriculum: Mathematics and other state and/or national curriculum documents and explicitly use materials, symbols and language to support the learning of each student.


LO1, LO2, LO3, LO4, LO5, LO6

GA1, GA4, GA5

Assessment Task 2a – CHOICE- For the purposes of national moderation all campuses must select the same task

(Equivalent to 2,000 words)

Individually, write a literature review exploring themes, ideas and issues related to the learning, teaching and assessment of Whole Number (including calculation), Geometry or Measurement. Synthesise and critique ideas from a range of scholarly sources that reflect a balance of teacher and pure research publications. Present a coherent discussion and cite/reference appropriately to the discipline.

OR Assessment Task 2b

(Equivalent to 2,000 words)

A weekly reflective journal that draws together understandings from the weekly lecture, tutorial/workshop activities and prescribed readings and observations from professional experiences. The journal entries demonstrate critical reflection and growing understanding of (a) their own developing content knowledge for teaching, (b) application of theory and research to understanding how students learn, (c) teaching strategies to best support the learning of all students, (d) the varied use of assessment to use the data collected to focus future teaching, and (e) the application of pedagogical content knowledge though making connections between these.

NOTE: This task assumes participants have a one day a week placement or similar during the semester.


LO2, LO3, LO4

GA1, GA4, GA5

Representative texts and references

Anghileri, J. (2006). Scaffolding practices that enhance mathematics learning. Journal of Mathematics Teacher Education, 9(1), 33–52.

Booker, G., Bond, D., Sparrow, L., & Swan, P. (2014). Teaching primary mathematics (5th ed.). Frenchs Forest, NSW: Pearson Australia.

Copley, J. (2010). The young child and mathematics (2nd ed.). Reston, VA: National Council of Teachers of Mathematics.

Forgasz, H., & Rivera, F. (2012). Towards equity in mathematics education: Gender, culture, and diversity. Heidelberg, Germany: Springer.

Masalski, W. & Elliot, P. (2005). Technology-supported mathematics learning environments. (2005 Yearbook). Reston, VA: National Council of Teachers of Mathematics.

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.

Van de Walle, J., Karp, K., & Bay-Williams, J. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Boston: Pearson.

Wyatt-Smith, C., Elkins, J., & Gunn, S. (Eds.). (2011). Multiple perspectives on difficulties in learning literacy and numeracy (pp. 275-293). Dordrecht, The Netherlands: Springer.

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