Professional Work
Concepts and Cognitive Conflict
The availability
of video clips of students expressing their opinions on chance and data concepts
and solutions to problems from earlier projects meant that new students could be
interviewed and provided with conflicting views to those they had expressed.
This was intended to some extent to mimic a classroom environment where students
express differing views. The chance to use particular students’ views
repeatedly provided a control not present in a classroom discussion. The ability
to argue back and forth was very limited, however, with the interviewer only able
to reiterate or perhaps clarify the opinion expressed on video. In this
project,20 students from each of Grades 3, 6, and 9 were interviewed with some
of the original protocols and during this time presented with alternative views
at a higher or lower level. These were contained on video clips with
typed transcripts, shown on a laptop computer. Of particular interest was the
power of higher level arguments to convince interviewees in a short period of
time. Also of concern was whether less viable responses at lower levels
would dissuade students from their original views. Students were chosen for
these interviews by their teachers as those who would express their views and
enjoy being challenged. Hence the students were likely to be of above average
ability in their grades.
Given the existence of data on longitudinal interviews after three or four years, and hence the documentation of improved levels of observed outcomes, it was possible to compare improvement in the two settings. Although this process was fraught with difficulties, particularly the retention and transfer of new levels of understanding obtained in a few minutes, it was still useful to make comparisons with a much longer period where specific intervention was not undertaken by the researchers. The Table contains some comparisons for different groups of students for several tasks.
Table. Percent of improved level of response after presentation of cognitive conflict and after a three- or four-year time span
|
Topic |
Cognitive Conflict |
3-4 Years |
|
Beginning inference - equal sized sets |
57% |
NA |
|
Representing in pictographs |
60% |
36% |
|
Proportional chance measurement |
33% |
33% (surveys) |
|
Beginning inference -unequal sized sets (proportional) |
30% |
31% |
|
Sampling |
22% |
78% |
|
Predicting from pictographs |
30% |
86% |
It is interesting to note that for what might be considered easier tasks –comparing sets of equal size and creating a pictograph – improvement levels with cognitive conflict are similar. For more difficult tasks involving proportional reasoning, understanding of sampling methodology, and the ability to predict from a graph (at grade 3), the improvement rates are also similar teach other but about half of that for the easier tasks. Comparisons with3-or-4-year improvement are not always as consistent. It is interesting to note however, that the two tasks relying on proportional reasoning for improvement were associated with outcomes that were similar for cognitive conflict interviews and longitudinal interviews. This is an area where further research could be very useful.
References
1. Watson, J.M., & Moritz, J.B. (2001). The role of cognitive conflict in developing students’ understanding of chance measurement. In J. Bobis, B. Perry, &M. Mitchelmore (Eds.) Numeracy and beyond (Proceedings of the 24th Annual Conference of the Mathematics Education Research Group of Australasia, Vol. 2, pp. 523-530). Sydney, NSW: MERGA.
2. Watson, J.M. (2002). Creating cognitive conflict in a controlled research setting: Sampling. In B. Phillips (Ed.), Proceedings of the Sixth International Conference on Teaching Statistics: Developing a statistically literate society, Cape Town, South Africa. Voorburg, The Netherlands: International Statistical Institute.
3. Watson, J.M. (2002). Inferential reasoning and the influence of cognitive conflict. Educational Studies in Mathematics, 51, 225-256.
4. Watson, J.M., & Moritz, J.B. (2001). Development of reasoning associated with pictographs: representing, interpreting, and predicting. Educational Studies in Mathematics, 48, 47-81.
5. Watson, J.M., & Caney, A. (in press). Development of reasoning about random events.Focus on Learning Problems in Mathematics.
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