Year
2024Credit points
10Campus offering
No unit offerings are currently available for this unit.Prerequisites
NilUnit rationale, description and aim
This unit focuses on the teaching and learning of statistics and probability in the middle years of schooling. This unit reflects current mathematical pedagogies, such as inquiry-based learning, with a particular emphasis on mathematical modelling. Approaches include the effective use of digital technologies and manipulatives. Forms of argumentation in relation to statistical thinking at the middle school level are highlighted. This unit provides the learner with knowledge of the historical development and social aspects of statistics and probability.
This unit aims to assist pre-service teachers in developing their understanding of student statistical and probabilistic knowledge, 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.
| Learning Outcome Number | Learning Outcome Description | Relevant Graduate Capabilities |
|---|---|---|
| LO1 | Demonstrate an understanding of the historical and social aspects of statistics and probability (APST 2.1) | GC1, GC5, GC6 |
| LO2 | Critique the Australian Curriculum: Mathematics to demonstrate a knowledge of representing and interpreting data in order to apply this knowledge to problems in both familiar and unfamiliar settings (APST 2.1, 2.5, 2.6) | GC2, GC7, GC11 |
| LO3 | Use and critique appropriate generic software such as spreadsheets as well as technologies developed specifically for the teaching of statistics and probability such as TinkerPlots and Fathom in exploratory investigations to present data in a variety of ways by designing, implementing and analysing simulations of real situations (APST 2.1, 2.6, 3.1) | GC1, GC9, GC10 |
| LO4 | Demonstrate an understanding of the relationship between statistics, probability and other areas of mathematics and their relevance to numeracy and literacy in mathematical learning (APST 2.5) | GC2, GC7, GC11 |
| LO5 | Demonstrate an understanding of pedagogical aspects of the teaching and learning of statistics and probability in the middle years including the uses and misuses of statistics and probability in society and student difficulties and misconceptions and common errors (APST 1.2, 3.3). | GC1, GC8, GC9 |
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. |
Content
Topics covered will give consideration to the Australian Curriculum: Mathematics content knowledge (MCK) and pedagogical content knowledge (PCK) and associated teaching methods will include:
- Historical and cultural development of statistics and probability
- 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
Pre-service teachers will be involved in a variety of teaching-learning strategies to progress and demonstrate their understandings in this unit. 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
Students 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, students 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 |
|---|---|---|
Assessment Task 1: 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 journal article 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. (1600 words) | 40% | LO1, LO2 |
Assessment Task 2: CHOICE An assignment focussing on the development of at least 2 big ideas in statistical thinking in the middle years with a modelling emphasis (e.g., pre-service teachers pose and solve a series of small application and modelling tasks, or two small modelling tasks and one extended modelling 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. OR Two small assignments where pre-service teachers (a) develop and solve an interdisciplinary inquiry-based task with a substantive focus on statistics and probability for middle school students (including mathematical modelling and use of digital technology) and (b) an examination of their own intended implementation of the task with a class. (equiv 2400 words) | 60% | LO2, LO3, LO4, LO5 |
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.
Joseph, G. G. (2011). The crest of the peacock: Non-European roots of mathematics (3rd ed.). Princeton, NJ: Princeton University Press.
Kader, G., & Mamer, J. (2008). Statistics in the middle grades: Understanding center and spread. Mathematics Teaching in the Middle School, 14(1), 38-43.
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.
Nelson, R. D. (Ed.). (2008). The Penguin Dictionary of Mathematics. London, England: Penguin UK.
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.
Robson, E., & Stedall, J. (Eds.), (2009). The Oxford handbook of the history of mathematics. Oxford: Oxford University Press.
Shaughnessy, M., Chance, B., & Kranendonk, H. (2009). Focus in high school mathematics: reasoning and sense making in statistics and probability. Reston, VA: NCTM