Unit description and aim
At a time of rapid ongoing change as a result of globalisation, internationalisation and developing information communication technologies, the ability of educators and allied professionals to empower young people to develop substantive understanding of mathematics as a language to use in solving problems, making connections and communicating ideas in real life is of critical importance. In this unit, students will develop an understanding of the historical use of numbers and foundational mathematical discoveries and developments which paved the way for development of theories and solutions to perplexing and critical mathematical problems. Students will develop their knowledge and skills in current mathematical pedagogies such as inquiry-based learning, with a particular emphasis on problem posing. Approaches include the effective use of digital technologies and manipulatives. Forms of argumentation and proof are highlighted. Finally, students will consider mathematics curricula, ways of teaching number, students' construction of mathematical knowledge, and students' number difficulties and misconceptions. Therefore, the aim of this unit is equip students with advanced knowledge, integrated understanding and expert skills in mathematical content and pedagogical knowledge for the teaching of number in the middle years of schooling.
On successful completion of this unit, students should be able to:
LO1 - Examine the historical development of number, different number systems and structures in mathematics and their contribution to society (GA4, GA8; APST 2.4)
LO2 - Apply theories and research informing children’s mathematical learning and children’s development of mathematical concepts and processes in Number as required by Australian Curriculum: Mathematics (ACARA) and other relevant curriculum documents for the middle years (GA4, GA5, GA8, GA9, GA10; APST 1.2, 2.1, 2.2, 2.5)
LO3 - Explain number including natural numbers and their relationships, proportional reasoning and rate (GA5, GA9; APST 2.1)
LO4 - Locate and use technology and resources that facilitate understanding of number, number systems and elementary elements of number theory (GA8, GA10; APST 1.2, 2.1, 2.6)
LO5 - Synthesise the relevance of number development and application across all areas of the mathematics curriculum, including financial mathematics (GA5, GA8, GA9; APST 1.2H, 2.1, 2.2)
LO6 - Identify pedagogical issues related to the teaching and learning of number, numeracy in the middle school through inquiry-based learning including problem posing (GA4, GA5; APST 1.2, 2.1, 2.5, 3.1, 3.3)
LO7 - Analyse student difficulties and misconceptions and errors in learning number concepts in the middle years (GA4, GA5, GA8; APST 1.2, 5.1).
GA4 - think critically and reflectively
GA5 - demonstrate values, knowledge, skills and attitudes appropriate to the discipline and/or profession
GA8 - locate, organise, analyse, synthesise and evaluate information
GA9 - demonstrate effective communication in oral and written English language and visual media
GA10 - utilise information and communication and other relevant technologies effectively.
AUSTRALIAN PROFESSIONAL STANDARDS FOR TEACHERS
On successful completion of this unit, students should have gained evidence towards the following standards:
1.2 Understand how students learn (Highly Accomplished)
2.1 Content and teaching strategies of the teaching area (Highly Accomplished)
2.2 Content selection and organisation (Highly Accomplished)
2.4 Understand and respect Aboriginal and Torres Strait Islander people to promote reconciliation between Indigenous and non-Indigenous (Highly Accomplished)
2.5 Literacy and numeracy strategies (Highly Accomplished)
2.6 Information and communication technology (ICT) (Highly Accomplished)
3.1 Establish challenging learning goals (Highly Accomplished)
3.3 Use teaching strategies (Highly Accomplished)
5.1 Assess student learning (Highly Accomplished)
Topics covered will give consideration to mathematical content knowledge (MCK) and pedagogical content knowledge (PCK) and associated teaching methods, and include:
- Historical development of the nature of counting numbers, integers, rational numbers, real numbers, and imaginary numbers with particular reference to different number systems e.g., Egyptian, Roman, Babylonian, Chinese, and or Mayan and evolution of zero
- Theories and research informing children’s mathematical learning and children’s development of mathematical concepts and processes in Number as required by Australian Curriculum: Mathematics (ACARA) and other relevant curriculum documents for the middle years
- Factors and multiples, prime and composite numbers, divisibility relationships, integers, fractions (including decimal fractions), indices and index laws, and real numbers.
- properties of number i.e. commutative, associative and distributive properties of the number operations (addition, subtraction, multiplication and division)
- the mathematical calculations involved in financial decisions (e.g., simple interest)
- pedagogical aspects of inquiry-based learning, problem posing, manipulatives, and technology in the teaching and learning of number and numeracy
- diagnosing and remediating common student difficulties and misconceptions in number.
Learning and teaching strategy and rationale
This unit is offered in multi-mode Engagement for learning is the key driver in the delivery of this curriculum, therefore an active learning approach is utilised to support students in their exploration and demonstration of achievement of the unit’s identified learning outcomes. A range of strategies will be used to support active learning and may include: lectures, tutorials, workshops and seminars; synchronous and/or asynchronous digital engagement in reading/library tasks and presentations, learning activities, discussion forums and consultation as mediated through the LEO unit site. Other modes of delivery may include webinars and presentations.
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 across the semester. To achieve a passing standard in this unit, students will find it helpful to engage in the full range of learning activities and assessments utilised in this unit, as described in the learning and teaching strategy and the assessment strategy. The learning and teaching and assessment strategies include a range of approaches to support your learning such as reading, reflection, discussion, webinars, podcasts, video, workshops, and assignments etc.
Assessment strategy and rationale
In order to successfully complete this unit, postgraduate students need to complete and submit two graded assessment tasks. The assessment strategy used allows students to demonstrate their knowledge and skill related to number development in the middle years of schooling. The first is a literature review focused on number and the second task applies theory to a practical situation.
Overview of assessments
|Brief Description of Kind and Purpose of Assessment Tasks||Weighting||Learning Outcomes||Graduate Attributes|
Assessment Task 1
Students are required to write a critical review of the literature pertaining to the “big ideas” of number, where number understandings are linked to form a coherent whole including student difficulties, misconceptions, and errors.
Assessment Task 2
Extended writing task
Students select either A or B.
A. An assignment highlighting the historical and cultural development of number and focusing on problem posing and problem solution (e.g., students pose and solve two problems highlighting a cultural use of number and chose and solve two historical problems. One task should be an inquiry-based task.) Use the four tasks as a basis for a unit, to be shared with colleagues, highlighting the historical and cultural development of number using teaching strategies to develop and implement engaging learning.
B. Two small linked assignments where they (a) develop and solve an inquiry-based task with a substantive focus on number (including problem posing) and (b) a critical examination of their own implementation of the task with a class.
GA8, GA9, GA10
Representative texts and references
Clapham, C., & Nicholson, J. (2014). The concise Oxford dictionary of mathematics (5th ed.). Oxford, UK: Oxford University Press.
Singer, F., Ellerton, N., & Cai, J. (Eds.) (2013) Educational Studies in Education, 83, Special Issue on Problem Posing.
Stillman, G. (2013). Problem finding and problem posing for mathematical modeling. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modeling: From theory to practice. Series on mathematics education Vol. 8. Singapore: World Scientific.