### Abstract:

The purpose of this study was to describe middle school students' mathematical
dispositions in a problem-based learning [PBL] classroom. Eight volunteer students
from one 6th grade mathematics classroom participated in this study. The curriculum
used was the Connected Mathematics Project [CMP]. The main sources for data
collection were classroom observations, the Attitudes and Beliefs questionnaire, teacher
interviews, and student interviews. The CMP class routine consisted of four phases:
Warm-up, Launch, Explore, and Summarize. The teacher in this study had her students
investigate mathematics problems within cooperative small groups and share their ideas
in large group discussions. The teacher acted as a facilitator and encouraged her
students to try new ideas without fear of making mistakes.
The findings revealed that almost all of the students in this study demonstrated
positive mathematical dispositions. They volunteered and shared their ideas, both in
small cooperative group investigations and in large group discussions. They believed
mathematics was about "learning new ideas" and mathematics was "life" because it was
everywhere in their lives. They also mentioned the usefulness of numbers,
measurement, and geometry in their daily lives. All eight participants liked hands-on
activities and working on a mathematics project. Most of them agreed that they liked
mathematics because it was fun and interactive. Most also saw themselves as good at
mathematics. All of them agreed that mathematics was useful, and that one's
mathematics ability could be increased by effort. They also believed that there were no
gender differences in mathematics, even though in their class, they realized that boys
outperformed girls. Most of the students agreed that they could solve time-consuming
mathematics problems and that it was important to understand mathematical concepts.
None of them had negative feelings about group work; they learned from each other.
Finally, an analysis of the participants' mathematical dispositions was discussed.
Based on the Taxonomy of Educational Objects: Affective Domains by Krathwohl,
Bloom, and Masia (1964), the participants were categorized into three disposition
levels: Level 1: "receiving;" Level 2: "responding;" and Level 3: "valuing." Half of the
participants demonstrated dispositions at the high level (Level 3: "valuing") because of
their willingness to pursue and/or seek to do mathematics outside the classroom. Three
of them were in mathematics disposition Level 2.3: "satisfaction in response" because
they usually participated in the class activities. They were satisfied and enjoyed doing
mathematics. One of them demonstrated mathematical disposition Level 1.2:
"willingness to receive" because she listened to the whole class and group discussions
without sharing any ideas or asking for help when she needed it.