Preface
The Australian senior mathematics curriculum (Australian Curriculum Assessment and Reporting Authority, n.d.a) includes four mathematics subjects:
- Essential Mathematics (EM);
- General Mathematics (GM);
- Mathematical Methods (MM); and Specialist Mathematics (SM).
All four subjects include topics about statistics: three each in EM and GM; two each in MM and SM.
Introduction
Some statistical topics in curriculum may be unfamiliar to some teachers, and hence a potential source of concern.
This is not a reflection on the teaching or mathematical ability of teachers:
a strong background in mathematics does not necessarily translate to statistical thinking
(Hannigan, Gill & Leavy, 2018; p. 427 (emphasis added))
and
…one cannot teach what one does not know
(Fennema & Franke, 1992; p. 147).
Why this book?
Evidence around the world suggests that mathematics teachers sometimes struggle to teach statistics, and do not feel confident to teach statistics (Batanero, Burril & Reading, 2011). Reasons may include that:
- statistics is not mathematics; statistics requires statistical thinking which is distinct from mathematical thinking;
- most teachers do not have experience, or initial teacher education, with statistics, and so lack specific statistical knowledge (Hannigan, Gill & Levy, 2013; Marshman, Dunn, McDougall, & Wiegand, 2015); and
- the language of mathematics and statistics is different, and even contradictory. These differences even manifest in otherwise-good school mathematics textbooks, which have errors, ambiguities and incorrect explanations when discussing statistics (Dunn, Marshman, McDougall, & Wiegand, 2015).
Research (Batanero, Burrill, & Reading, 2011) has found that teachers’ knowledge of essential statistical concepts is lacking in many areas of statistics (graphs, averages, variation, distributions, sampling and inference, correlation and regression, investigation), despite teachers having confidence that they understand them (Marshman, Dunn, McDougall, & Wiegand, 2015). This book will discuss some statistical terms and concepts that appear in the new mathematics curricula. We will also point to resources and data sets that teachers may find useful, and give a bit more that just the bare curricula bones, since:
To teach a topic well, teachers must have an in-depth knowledge not only of the specific [statistics] they teach, but also of the [statistics] that their students are to learn in the future. (Fennema & Franke, 1992; p. 147; “mathematics” replaced with “statistics”)
To understand the challenges of teaching statistics, we first compare mathematics and statistics.