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 understanding mathematics as a language to solve problems, make connections and communicate ideas in real life is of critical importance. In this unit students will develop content and pedagogical knowledge for teaching algebra and functions in the middle years. Students will develop knowledge of the historical development and social aspects of algebra and functions before focusing on current mathematical pedagogies, such as inquiry-based learning, with a particular emphasis on problem solving. The unit emphasises forms of argumentation in relation to algebraic thinking, particularly as related to generalisation. Students will develop an understanding of student knowledge related to algebra, algebraic and functional thinking as well as potential difficulties and misconceptions. Approaches include the effective use of digital technologies and manipulatives. 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 algebra and functions in the middle years of schooling.
On successful completion of this unit, students should be able to:
LO1 - Examine the historical and cultural development of algebra and functions 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 Algebra and Functions 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 - Articulate understandings of multiple representation in the teaching and learning of algebraic thinking (i.e., numerical, symbolic, visual (concrete and diagrammatic), and in functional thinking (i.e., graphical, numerical, symbolic, visual (concrete and diagrammatic) and apply this knowledge (GA5, APST 2.1)
LO4 - Use technologies and resources including graphing calculators and applets that will enhance understanding of algebra and functions (GA8, GA10; APST 2.1, 2.6, 3.1)
LO5 - Evaluate the relationship between algebra, functions and other areas of the mathematics curriculum, in particular number (GA4, GA5, GA8, GA9, GA10; APST 1.2, 2.1, 2.2, 2.5)
LO6 - Analyse student difficulties and misconceptions in learning algebra and functions 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 Australians (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)
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 algebra
- Graphical representation of functions to include polynomials, exponentials, logarithms, power functions, reciprocal functions, trigonometric functions
- Solving equations to include linear and quadratic trigonometric logarithmic equations
- Use of graphing calculators and other appropriate technologies appropriate software for teaching and learning of algebra and functions in the middle school
- pedagogical aspects of teaching and learning algebra and functions through inquiry-based learning including problem finding, problem posing, investigative approaches, mathematical modelling and technology
- common student difficulties, misconceptions and errors in algebraic and functional thinking and reasoning underpinning the development of algebra and functions in the middle years.
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 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 related algebra and functions in the middle years of schooling a creative and practical manner. The first task focuses on problem solving; the second task focuses on teaching and learning of algebra and functions.
Overview of assessments
|Brief Description of Kind and Purpose of Assessment Tasks||Weighting||Learning Outcomes||Graduate Attributes|
Assessment Task 1
Develop and solve a set of problem solving tasks involving the use of algebraic and functional thinking aimed at addressing student common difficulties, misconceptions and errors, incorporating the use of technology and multiple representations. At least one problem solving task must have a focus related to the historical development of algebra or use of algebra within society.
Assessment Task 2
Extended Writing Task
An assignment focusing on literature related to the teaching and learning of algebraic and functional thinking in the middle years through inquiry-based learning including problem solving
LO2, LO4, LO5, LO6
Representative texts and references
Kamol, N., & Yeap, B. H. (2010). Upper primary school students' algebraic thinking. In L. Sparrow, B. Kissane & C. Hurst (Eds.). Shaping the Future of Mathematics Education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia, Freemantle, Vol. 1, pp. 289-296. Adelaide: MERGA
van den Kieboom, L. A., & Magiera, M. T. (2012). Cultivating algebraic representations. Mathematics Teaching in the Middle School, 17(6), 353-357.
Windsor, W. (2010). Algebraic thinking: A problem solving approach. In L. Sparrow, B. Kissane & C. Hurst (Eds.), Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia, Freemantle, Vol. 2, pp. 665-672. Adelaide: MERGA.
Zawojewski, J. S., & Magiera, M. T., & Lesh, R. (2013). A proposal for a problem-driven mathematics curriculum framework. Mathematics Enthusiast, 10(1&2), 469-506.