Year
2023Credit points
10Campus offering
No unit offerings are currently available for this unitPrerequisites
NilUnit rationale, description and aim
This unit focuses on the teaching and learning of algebra and function in the middle years of schooling. This unit reflects current mathematical pedagogies, such as inquiry-based learning, with a particular emphasis on problem solving. Approaches include the effective use of digital technologies and manipulatives. Forms of argumentation in relation to algebraic thinking at the middle school level, particularly as related to generalisation are highlighted. This unit provides the learner with knowledge of the historical development and social aspects of algebra and functions.
The aim of this unit is to allow pre-service teachers to incorporate understanding of student knowledge related to algebra, potential difficulties and misconceptions and enhance teacher pedagogy in the classroom.
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 - critically examine the historical and cultural development of algebra and functions and their contribution to society (GA4, GA8; APST 2.1)
LO2 - demonstrate a knowledge and understanding 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) as identified in the Australian Curriculum: Mathematics, and apply this knowledge to problems in both familiar and unfamiliar settings including a range of function types (GA5; APST 2.1)
LO3 - use and critique appropriate generic software such as spreadsheets as well as technologies developed specifically for the teaching of algebra and functions such as graphing calculators and applets in exploratory investigations to develop understandings of equality, variables, generality and functional thinking (GA8, GA10; APST 2.1, 2.6, 3.1)
LO4 - demonstrate an understanding of pedagogical aspects of the teaching and learning of algebra and functions in the middle years through inquiry-based learning including problem solving (GA4, GA5; APST 1.2, 2.1, 2.5, 3.1, 3.3)
LO5 - identify and analyse student difficulties and misconceptions and common errors in learning algebra and functions (GA4, GA5, GA8; APST 1.2, 5.1).
Graduate attributes
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
GA10 - utilise information and communication and other relevant technologies effectively.
AUSTRALIAN PROFESSIONAL STANDARDS FOR TEACHERS - GRADUATE LEVEL
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. |
2.1 Demonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area. |
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. |
3.1 Set learning goals that provide achievable challenges for students of varying abilities and characteristics. |
3.3 Include a range of teaching strategies. |
4.5 Demonstrate an understanding of the relevant issues and the strategies available to support the safe, responsible and ethical use of ICT in learning and teaching. |
5.1 Demonstrate understanding of assessment strategies, including informal and formal, diagnostic, formative and summative approaches to assess student learning. |
Content
Topics covered will give consideration to Australian Curriculum: Mathematics content knowledge (MCK) and pedagogical content knowledge (PCK) and associated teaching methods will include:
- Historical and cultural 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.
- Pedagogical aspects of teaching and learning algebra and functions through inquiry-based learning including problem finding, problem posing, investigative approaches, mathematical modelling and technology.
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.Teaching and learning organisation can take several forms. This could include intensive weekend classes, intensive one week winter or summer schools or weekly face-to-face classes during semester, all supported and enhanced by web-based tools. Attendance at, and full participation in, face to face classes is critical to enable learning of the required content
Pre-service teachers will be expected to participate in online discussion and sharing via eLearning to augment the face-to-face learning and support reflective practice. Class resources will be available via eLearning as will access to relevant web links.
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 then become 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, pre-service teachers are required to submit or participate in all assessment tasks, meet specified attendance requirements.
The total assessment tasks will amount to the equivalent of 4,000 words.
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 common difficulties, misconceptions and errors, incorporating the use of technology and multiple representations. At least on problem solving task must have a focus related to the historical development of algebra or use of algebra within society. | 50% | LO1, LO2, LO3 | GA4, GA5, GA8, GA10 |
Assessment task 2: An assignment focussing on literature related to the teaching and learning of algebraic and functional thinking in the middle years through inquiry-based learning including problem solving (e. g., online discussion of pertinent literature followed by essay focussing on one key area such as understanding of generality). This essay should be able to be shared with colleagues to use in developing and implementing engaging learning. | 50% | LO2, LO4, LO5 | GA4, GA5, GA8 |
Representative texts and references
Banerjee, R., & Subramaniam, K. (2011). Evolution of a teaching approach for beginning algebra. Educational Studies in Mathematics, 80(3), 351-367.
Charles, R. (2005). Big ideas and understandings as the foundation for elementary and middle school mathematics. Journal of Mathematics Education Leadership, 7(3), 9-24. Available: http://www.authenticeducation.org/bigideas/sample_units /math_samples/BigIdeas_NCSM_Spr05v7.pdf
Graham, K., Cuoco, A., & Zimmerman, G. (2009). Focus in high school mathematics: reasoning and sense making in algebra. Reston, VA: NCTM.
Joseph, G. G. (2011). The crest of the peacock: Non-European roots of mathematics (3rd ed.). Princeton, NJ: Princeton University Press.
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, SA: MERGA
van den Kieboom, L. A., & Magiera, M. T. (2012). Cultivating algebraic representations. Mathematics Teaching in the Middle School, 17(6), 353-357.
van den Kieboom, L. A., Magiera, M. T., & Moyer, J. (2010). Pre-service teachers’ knowledge of algebraic thinking and the characteristics of the questions posed for students. Paper presented at the 2010 annual meeting of the American Educational Research Association. Retrieved from the AERA Online Paper Repository http://www.aera.net/repository
White, A. (2008). Learning mathematics in the middle years. In H. Forgasz, et al (Eds.), Research in mathematics education in Australasia, 2004-2007 (pp. 41-72). Adelaide, SA: Rotterdam, The Netherlands: Sense.
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, SA: 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.