Expository Writing
Watson, J., Fitzallen, N., Wilson, K., & Creed, J. (in press). The
representational value of hats. Mathematics Teaching in the Middle School.
This article demonstrates the value of a recent graphing innovation, the hat
plot, in representing and interpreting data sets.
Watson, J.M. (2007). The foundations of chance and data. Australian Primary
Mathematics Classroom, 12(1), 4-7.
The fortunes of chance and data have fluctuated in the mathematics curriculum in
Australia since their emergence in the National Statement (Australian Education
Council [AEC], 1991) in the early 1990s. Their appearance in Australia followed
closely on similar moves in the United States (National Council of Teachers of
Mathematics [NCTM], 1989). In both countries the topics, taken together, were
given a section status equal to other areas of the mathematics curriculum, such
as space or algebra. In Australia this was reflected in the state curricula of
many states (e.g., Department of Education and the Arts [DEA], 1993; Curriculum
Council, 1998) but not all (e.g., Board of Studies NSW, 1989). In recent years
chance and data have held their place in the United States (NCTM, 2000) but in
some places in Australia have been diluted by being merged with other parts of
the curriculum, for example both chance and data with measurement (e.g.,
Victoria Curriculum and Assessment Authority, 2005) or chance with number (Board
of Studies NSW, 2002). As discussions proceed on national consistency across the
state mathematics curricula in Australia, the place of chance and data appears
to be in further jeopardy. Whether this is due perhaps to a lack of appreciation
of the need for statistical literacy skills in all students who leave school
(see e.g., Rubin, 2005) or perhaps to a traditional concern to cater for the
elite mathematics talent who will study mathematics at university, is beyond the
scope of this article to consider.
Watson, J.M., & Shaughnessy, J.M. (2004). Proportional reasoning: Lessons
from research in data and chance. Mathematics Teaching in the Middle School, 10,
104-109.
Fenton, P., & Watson, J. (2001). Triangular numbers: Fact or fiction? Australian
Primary Mathematics Classroom, 6(1), 10-14.
Watson, J.M. (2002). When 2 + 2 ≠ 4 and 6 + 6 ≠ 12 in data and chance. New
England Mathematics Journal, 34(2), 56-68.
This article contains two cautionary tales based on my experience working with
students, adults, and teachers on research and professional development projects
involving data and chance. The first arose from observing two grade 9 boys who
ignored instructions and then tried to supplement samples of size two with other
samples of size two in order to make samples of size four. The second was
related to several observations of students and adults expressing beliefs about
dice-tossing that were contrary to my expectations: either expecting peaks in
distributions that should be uniform or expecting uniformity in distributions
that should be peaked. The solution to the dilemmas presented in these two tales
would appear to be the creation of cognitive conflict to illustrate forcefully
the importance of sample size and the difference between equally likely and
non-equally likely outcomes. To handle the situations however, teachers need to
be aware that these beliefs may be abroad, to experience the activities that can
lead to conflict resolution, and then to plan their own strategies.
Watson, J.M. (2004). Quantitative literacy in the media: An arena for problem
solving. Australian Mathematics Teacher, 60(1), 34-40.
Watson, J.M., & Shaughnessy, J.M. (2004). Proportional reasoning: Lessons from
research in data and chance. Mathematics Teaching in the Middle School, 10,
104-109.
Watson, J.M. (2002). Lessons from variation research II: For the classroom. In
M. Goos & T. Spencer (Eds.), Mathematics – making waves. (Proceedings of the
Nineteenth Biennial Conference of the Australian Association of Mathematics
Teachers Inc., Brisbane, pp. 424-432). Adelaide, SA: AAMT, Inc.
This workshop will feature various activities devised as part of a research
project studying students’ understanding of variation and their improved
outcomes following a chance and data unit emphasising variation. The activities
arose from interview protocols and survey items used with students, from lessons
taught by project teachers, or from professional development sessions led by the
author with teachers. Each will be presented with a curriculum mapping
associated with the topics in the chance and data curriculum. The stacked dot
plot (or line plot) will be introduced as a straightforward means of
representing data and displaying variation.
Other work: The Chance and Data Professional Development CD
Produced: September 1996
Development, production, delivery and evaluation of a Professional Development
(PD) package for teachers of Chance & Data. The PD integrated package of
materials includes a multimedia CD-ROM. The CD-ROM includes curriculum
documents, classroom activities, as well as many examples of student responses
to a variety of questions from research surveys and video-taped interviews.
Teachers will undertake PD using the PD package, with support offered for
content and technical aspects. Evaluation of the PD package and its
effectiveness for PD of teachers was based on responses from teachers.
Faculty of Education
University of Tasmania
Private Bag 66 Hobart Tasmania Australia 7001
Phone: 61-3-6226-2570; Fax: 61-3-6226-2569
Jane.Watson@utas.edu.au