Professional Work
Collaborative Problem Solving in Chance and Data
This project was related to other research associated with the Chance and
Data part of the mathematics curriculum. The main objective was to explore the
outcomes of problem solving involving higher order thinking related to chance
and data, in collaborative learning situations. The major conjecture of the
study grew out of observations in a previous project. It was observed that
students from grade 6 working in groups produced higher level cognitive outcomes
on an activity involving association of variables in a set of data, than did
students from grade 9 working individually. This outcome suggested the need for
comparison of students working individually and in groups on higher order tasks
from the chance and data curriculum.
Videotapes were made of students working collaboratively in groups of three on
one task and then of some or all of these students working individually on
another task. Transcripts were then made for the analysis of two types of
behaviour and the interaction of these: (1) the developmental level of cognitive
functioning taking place with respect to the mathematics in the task, and (2)
the degree of collaboration taking place for those working in groups. Several
questions are being addressed from the data collected, including the difference
in cognitive performance for individual students when they work alone or
collaboratively, the effect of collaboration on the level of mathematical
outcome for groups, and differences in cognitive outcomes for different students
working collaboratively. The last question is being explored for some students
who were interviewed individually on the same task following working in groups.
Four higher level tasks have been employed in various settings during the
project. Task 1 is based on 16 data cards containing information on school
students, including eye colour, age, weight, favourite activity and number of
fast food meals eaten per week. Students are asked to find and justify
associations in the data set. Task 2 is based on an idea of Pereira-Mendoza and
involves students working with two dice, one fair and one loaded. Students are
asked to decide and justify which is unfair and then to comment on other dice
configurations created by a software package. Task 3 uses questions from other
researchers on sampling and randomisation and gives students the opportunity to
simulate outcomes on a computer with a probability simulator. Task 4 explores
students' understanding of the concept of average and weighted averages, and
allows for the construction of data sets to meet specific criteria.
The most recent work in this project involved an entire classroom (27 students)
working in groups of three to create posters associated with Task 1. Up to five
video cameras were used as half of the class at a time worked in its usual
fashion in the classroom. At the end, class presentations were made and the
students interviewed individually. This type of research is breaking down the
barriers between researchers and schools; in this case the school was pleased
that the researchers brought a challenging task to the school, the students
enjoyed taking part, and the researchers hoped to gain insights from observing
cognition and collaboration in the most natural context possible. The analyses
of these data have focussed on whether asking for help is helpful, on students’
recall of the events taking place during collaboration, or the association of
representation and hypothesizing, and on the effect of collaboration on
outcomes.
References
1. Watson, J.M., Collis, K.F., Callingham, R.A., & Moritz, J.B. (1995). A model
for assessing higher order thinking in statistics. Educational Research and
Evaluation, 1, 247-275.
2. Lidster, S.T., Watson, J.M., Collis, K.F., & Pereira-Mendoza, L. (1996). The
relationship of the concept of fair to the construction of probabilistic
understanding. In P. C. Clarkson (Ed.), Technology in mathematics education (pp.
352-359). Melbourne: Mathematics Education Research Group of Australasia.
3. Moritz, J. B. (1996). Interrogating Collaborators: Techniques for Mathematics
Education Research. Paper prepared for presentation at the symposium
Contemporary Approaches to Research in Mathematics, Science, Health and
Environmental Education, Melbourne, 3 December 1996.
4. Watson, J.M., & Callingham, R.A. (1997). Data cards: An introduction to
higher order processes in data handling. Teaching Statistics, 19, 12-16.
5. Lidster, S.T., Chick, H.L., & Watson, J.M. (1997). Developing cognition in
interpreting data. In N. Scott & H. Hollingsworth (Eds.), Mathematics creating
the future (pp. 202-209). Adelaide: Australian Association of Mathematics
Teachers, Inc.
6. Watson, J.M., & Chick, H.L. (1997, December). Collaboration in mathematical
problem solving. A paper presented at the Annual Conference of the Australian
Association for Research in Education, Brisbane, Queensland.
7. Chick, H.L., & Watson, J.M. (1998). Showing and telling: Primary students’
outcomes in data representation and interpretation. In C. Kanes, M. Goos, & E.
Warren (Eds.), Teaching mathematics in new times. Volume 1 (pp. 153-160).
Brisbane: Mathematics Education Research Group of Australasia.
8. Watson, J.M., & Chick, H.L. (2001). Does help help?: Collaboration during
mathematical problem solving. Hiroshima Journal of Mathematics Education, 9,
33-73.
9. Watson, J.M., & Chick, H.L. (2001). Factors influencing the outcomes of
collaborative mathematics problem solving—An introduction. Mathematical Thinking
and Learning, 3(2&3), 125-173.
10. Chick, H.L., & Watson, J.M. (2001). Data representation and interpretation
by primary school students working in groups. Mathematics Education Research
Journal, 13, 91-111.
11. Chick, H.L., & Watson, J.M. (2002). Collaborative influences on emergent
statistical thinking—A case study. Journal of Mathematical Behavior, 21,
371-400.
12. Watson, J.M., & Chick, H.L. (2001). A matter of perspective: Views of
collaborative work in data handling. In M. van den Heuvel-Panhuizen (Ed.),
Proceedings of the 25th conference of the International Group for the Psychology
of Mathematics Education (Vol. 4, pp. 407-414). Utrecht: Freudenthal Institute.
13. Watson, J.M., & Chick, H.L. (2005). Collaborative statistical investigations
in diverse settings. International Journal of Mathematical Education in Science
and Technology, 36, 573-600.
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