Professional Work
Profiling Teachers of Chance and Data
This project began as a response to the introduction of chance and data into the
mathematics curriculum in the early 1990s. There was concern about teacher
preparedness to teach the topics from early childhood to the senior secondary
level. Interviews were conducted with 72 teachers of grades K to 10 in the seven
Tasmanian government school districts. Analysis of the results of these
interviews provided valuable information on teachers beliefs, attitudes,
knowledge and methodology in teaching topics in the chance and data curriculum.
The possibility of conducting large scale professional development with teachers
motivated further work on the instrument used for the interviews in order to
produce a profile which could evaluate the results of professional development
programs. At the same time larger issues in the education community also were
motivating further interest in profiling teachers. These included national moves
to define and measure the competence of beginning and continuing teachers,
recognition that the accountability of systems is becoming tied to teacher
performance, and a general realisation of the need for teachers to reflect on
their teaching practice.
All of these factors led to the development of a profiling instrument, designed
to satisfy the criteria identified in the literature as necessary to measure
characteristics of good teaching of chance and data, while at the same time
staying within the practical constraints of an instrument which could be
administered economically. The final instrument was intended for use in a
face-to-face interview lasting up to 1.5 hours. The intention was for teachers
to have the choice of whether they answered the questions orally or in writing.
The sections of the profile represented the following factors associated with
the teaching of chance and data.
1. Teacher-initiated significant factors in the teaching of chance and data.
This section gave teachers the opportunity at the beginning of the interview to
reflect on their understanding of the task at hand.
2. Preparing to teach a unit in chance and data. Teachers were asked for a
planning outline for both a unit and an individual lesson; these provided
information on content knowledge, curriculum knowledge and pedagogical content
knowledge.
3. Teaching practices. This section presented self-report information in lieu of
classroom observation.
4. “Average” and “Sample” in chance and data. Two specific topics were selected
to explore content knowledge, pedagogical practice and appreciation of where
students have difficulties.
5. Confidence. Relative levels of confidence were self-reported for nine areas
of the chance and data curriculum.
6. Beliefs about statistics in everyday life. Ten items developed by other
researchers were used to gauge confidence in interpreting statistics met in
everyday life, belief in the social importance of statistics, and understanding
of the issue of sample size as used in social settings.
7. Student survey items. Teachers were asked to suggest both appropriate and
inappropriate student responses to six items which had previously been used in
student surveys. They were then asked about the potential use of the items in
teaching.
8. Teacher background. Questions focused on teacher training and years of
experience.
9. Professional development. These questions asked about current comfort in
relationship to resources for teaching chance and data, previous professional
development and perceived needs in the area.
The final profile was administered to 42 teachers at the end of 1996. Teachers
were primary (n = 15) or secondary including Years 11 and 12 (n = 27), from
state and private systems throughout Australia. Half of the 42 teachers were
interviewed over 1.5-hour periods, while the other half submitted the
questionnaire in writing (without face-to-face contact with the researchers).
All comments, written and oral, have been entered into files which can be
qualitatively or quantitatively analysed. Current focus is on quantitative
analysis of some items and qualitative analysis of teachers’ reflections on
given topics, practices, and appreciation of student understanding. “Sample” has
been the topic of one report, with “Average” to follow in the future. Topics
will be considered not only from a mathematical point of view but also from the
perspective of methodology, use of resources, and affective feelings about the
content. This research is ongoing, in particular with the opportunity to refine
the profile instrument after application in a consulting project involving
teachers in a Middle School Numeracy program.
References
1. Callingham, R.A., Watson, J.M., Collis, K.F., & Moritz, J.B. (1995). Teacher
attitudes towards chance and data. In B. Atweh & S. Flavel (Eds.), Proceedings
of the Eighteenth Annual Conference of the Mathematics Education Research Group
of Australasia (pp. 143-150). Darwin, NT: Mathematics Education Research Group
of Australasia.
2. Watson, J. M., & Moritz, J. B. (1997). Teachers' views of sampling. In N.
Scott & H. Hollingsworth (Eds.), Mathematics creating the future (pp. 345-353).
Adelaide: Australian Association of Mathematics Teachers, Inc.
3. Watson, J.M., & Moritz, J.B. (1997, December). Measuring teachers' reactions
to new areas of the curriculum: A case study from chance and data. A paper
presented at the Annual Conference of the Australian Association for Research in
Education, Brisbane, Queensland.
4. Watson, J.M. (1998). Professional development for teachers of probability and
statistics: Into an era of technology. International Statistical Review, 66,
271-298.
5. Watson, J.M. (2001). Profiling teachers’ competence and confidence to teach
particular mathematics topics: The case of chance and data. Journal of
Mathematics Teacher Education, 4, 305-337.
6. Watson, J., Beswick, K., Caney, A., & Skalicky, J. (in press). Profiling
teacher change resulting from a professional learning program. Mathematics
Teacher Education and Development.
7. Watson, J., Beswick, K., & Brown, N. (2006). Teachers’ knowledge of their
students as learners and how to intervene. In P. Grootenboer, R. Zevenbergen, &
M. Chinnappan (Eds.), Identities, cultures and learning spaces (Proceedings of
the 29 annual conference of the Mathematics Education Research Group of
Australasia, Canberra, pp. 551-558). Adelaide, SA: MERGA.
8. Beswick, K., Watson, J., & Brown, N. (2006). Teachers’ confidence and beliefs
and their students’ attitudes to mathematics. In P. Grootenboer, R. Zevenbergen,
& M. Chinnappan (Eds.), Identities, cultures and learning spaces (Proceedings of
the 29 annual conference of the Mathematics Education Research Group of
Australasia, Canberra, pp. 68-75). Adelaide, SA: MERGA.
9. Brown, N., Watson, J., Beswick, K., & Fitzallen, N. (2006). Numeracy in a
reform-based learning environment. Refereed paper to be presented at the annual
conference of the Australian Association for Research in Education, Adelaide,
December, 2006.
Contact me...
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