Daniel J. Brahier
Department of Educational Curriculum & Instruction
Bowling Green State University
Bowling Green, OH 43403

JANUARY 1996

MORE MUSINGS ON DISPOSITION

During "finals week" one of Dan Brahier's Elementary Mathematics Methods students came to see him to discuss her performance in the six-week field component. She explained that her mathematics teaching was not as smooth as she would have liked it and felt that her fear of math was at the root of the problem. She said that she had done well in math all the way through Geometry in her sophomore year of high school. "From there," she explained, "everything else has been a blur!" Finally, she expressed the lack of confidence that she felt when confronted with a teaching methods course in mathematics.

T he conversation took Dan by surprise because "Amy" had been a fairly strong student in the university classroom. Academically, she was near the top of her class, and although somewhat quiet and shy at times, she could be an effective contributor to classroom discussions. He wondered why it had never occurred to him that her shy classroom behavior was a result of her lack of confidence and her fear of mathematics and "mused" on the question, "What if I had known that on the first day? What might I have done to help her overcome her anxieties?" But it was too late--methods was over. "Amy" left the class with a satisfactory, but less than stellar grade and continued frustrations with math.

In the last issue of the RCDPM Newsletter, we identified the major components of mathematical disposition-confidence, flexibility, willingness to attempt a variety of problem solving strategies, perseverance, interest, curiosity, and valuing the applications of mathematics in our culture and our world. We also raised questions such as: Do you gather attitudinal data at the beginning of a school year or semester? Does it seem that emphasis has been placed on diagnosing mathematical skills with relatively little attention to affective concerns known to be critical to student performance? Why? How might the teacher effectively use information regarding dispositions such as confidence and persistence, if it were measurable and the data were available early in a course? We thank the RCDPM members who took the time to write us with their reflections on the importance of measuring mathematical disposition and making use of the data in the classroom.

Jim Heddens raised the point that the issue of mathematical disposition and its implications is relatively "new" to many mathematics educators and that we may need an awareness period during which mathematics educators can gather information about what defines disposition.

Carole Bauer of Triton College in Illinois, wrote, "At the beginning of the semester I have students fill out a questionnaire. I ask them to list any items that might prevent their completion of the course--for example Math Anxiety. I try to follow up to some degree and assist students in recognizing their problems and how to possibly analyze the basis of the problem." She added that, "all of this is rather informal."

George Bright responded to our musing with several thoughts and further questions to consider. He wrote, "Increasingly I have become acutely aware of the importance of the 'teacher' in creating an atmosphere in which students are willing to share. This raises the question of how assessment of disposition of students is filtered by the assessor's own disposition.

Specifically the evaluations of workshops that I conduct with inservice teachers provide evidence that the way I ask questions and probe teachers' thinking is positively received by them and is helpful to them in understanding their own thinking. They believe that similar techniques will help them understand their own students' thinking. However, when I use what I think are the same questioning techniques with preservice teachers, they react much differently. They see the questions as putting them on the spot, and they often become defensive about interacting with me.

Are the differences in reactions indicative of differences in disposition? Indicative of differences in views about the nature of mathematics? Indicative of differences in views about what a mathematics teacher should do in class? Or improving the disposition of inservice teachers and interfering with the development of appropriate dispositions of preservice teachers? I'm not sure, but I am becoming more convinced that there may never be any clear way to measure disposition. Is it even a useful concept to think about?"

Have you met an "Amy" in your classes? If so, how have you intervened? At what point is disposition considered in planning, implementing, and evaluating lessons in mathematics? What are your reflections on George's questions--specifically, is disposition a worthy issue with which to concern ourselves? If so, why? If not, why not?