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 understand 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 mathematical content and pedagogical knowledge for teaching statistics and probability in the middle years (Years 5-9). The unit provides students with knowledge of the historical development and social aspects of statistics and probability before focusing on current mathematical pedagogies, such as inquiry-based learning, with a particular emphasis on mathematical modeling and forms of argumentation in relation to statistical thinking. The unit also focuses on developing students' understanding of student statistical and probabilistic knowledge as well as potential difficulties and misconceptions. Approaches include the effective use of digital technologies and manipulatives. 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 statistics and probability in the middle years of schooling.
On successful completion of this unit, students should be able to:
LO1 - Examine the historical and social aspects of statistics and probability (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 Statistics and Probability 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 various ways of representing and interpreting data and apply this knowledge to problems in both familiar and unfamiliar settings (GA5; APST 2.1)
LO4 - Use technologies and resources such as TinkerPlots and Fathom that will enhance understanding of statistics and probability (GA8, GA10; APST 2.1, 2.6, 3.1)
LO5 - Evaluate the relationship between statistics, probability and other areas of mathematics curriculum and their relevance to numeracy (GA4, GA5; APST 2.5)
LO6 - Apply pedagogical aspects of the teaching and learning of statistics and probability in the middle years through inquiry-based learning including the uses and misuses of statistics and probability in society (GA4, GA5, GA8; APST 1.2, 3.3, 5.1)
LO7 - Analyse student difficulties and misconceptions and errors in learning statistics and probability 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)
2.4 Demonstrate broad knowledge of, understanding of and respect for Aboriginal and Torres Strait Islander histories, cultures and languages (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:
- empirical and theoretical probability frequentist and equally likely outcome approaches to probability.
- Simulation methods (e.g., Monte Carlo methods using Buffon’s needle).
- Displays and measures of characteristics of distribution including central location and spread of data (e.g., dot plots, box plots, stem and leaf plots, mean, median, mode, interquartile range, SAD, and MAD).
- uses and misuses of statistics in society.
- appropriate software in for teaching and learning of statistics and probability in the middle school.
- pedagogical aspects of teaching and learning statistics and probability through inquiry-based learning including problem finding, problem posing, investigative approaches, mathematical modelling and technology
- common student difficulties, misconceptions and errors in statistical and probabilistic reasoning underpinning the development of statistical thinking and numeracy in the real world.
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 statistics and probability in the middle years of schooling in a creative and practical manner. There are two tasks; the first draws on theoretical information and presents in an accessible manner for teachers; the second task applies knowledge in a teaching and learning situation in the middle years of schooling.
The total assessment tasks will be equivalent to 5,500 words.
Overview of assessments
|Brief Description of Kind and Purpose of Assessment Tasks||Weighting||Learning Outcomes||Graduate Attributes|
Assessment Task 1
Extended written task
Research a statistician or mathematician who made a substantial contribution to the historical development of the statistical and/ or probabilistic ideas taught in the middle school (e.g., Nightingale, Playfair). Use this research as the basis of a teacher professional reading highlighting and exemplifying the mathematical, probabilistic or statistical ideas at the middle years level and historical and societal context in which the particular statistical or probabilistic ideas arose. This article should be able to be shared with colleagues to use in developing and implementing engaging learning.
GA4, GA5, GA8
Assessment Task 2
Extended writing task
Students will be required to develop a response to one of the following options:
1.An assignment focusing on the development of at least 2 big ideas in statistical thinking in the middle years with a modeling emphasis (e.g., students pose and solve a series of small application and modeling tasks, or two small modeling tasks and one extended modeling task. At least one task should use technology as a critical component in data analysis or data generation.) Use the tasks as a basis for a unit with an interdisciplinary focus, to be shared with colleagues, highlighting the development of the focus ideas using inquiry-based teaching strategies to develop and implement engaging learning
2.Two small assignments where they (a) develop and solve an interdisciplinary inquiry-based task with a substantive focus on statistics and probability for middle school students (including mathematical modeling and use of digital technology) and (b) a critical examination of their own implementation of the task with a class.
Representative texts and references
Ben-Zvi, D., Aridor, K., Makar, K., & Bakker, A. (2012). Students’ emergent articulations of uncertainty while making informal statistical inferences. ZDM—The International Journal on Mathematics Education, 44(7), 913-925.
Brown, J. P. (2013). Inducting year 6 students into a culture of mathematising as a practice. In G. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 295-305). Dordrecht, The Netherlands: Springer.
Callingham, R., Watson, J., & Burgess, T. (2012). Uncertainty in mathematics education: what to do with statistics. In B. Perry, T. Lowrie, T. Logan, A. MacDonald, & J. Greenlees (Eds.), Research in mathematics education in Australasia, 2008-20011 (pp. 267-287). Rotterdam, The Netherlands: Sense.
Lamb, J., & Visnova, J. (2013). On comparing mathematical models and pedagogical learning. In G. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 457-466). Dordrecht, The Netherlands: Springer.
Stillman, G. (2013). Problem finding and problem posing for mathematical modelling. In N. H. Lee & K. E. D. Ng (Eds.), Mathematical modelling: From theory to practice. Series on mathematics education Vol. 8. Singapore: World Scientific.