Exploring Some Inattended Affective Factors In Performing Nonroutine Mathematical Tasks
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The purpose of this study was to describe students' attempts to solve nonroutine math problems and to explore possible correlates of their performance. The focus of this study was on inattended (i.e., intentionally avoided) dimensions that have been underrepresented in the literature, including attitudes, interests, values, aesthetics, metacognition, and representation. Both objective and subjective data — drawn from 13 separate sources — using quantitative and qualitative procedures, were analyzed. Fine-grained rubrics were developed and used to score student work on six nonroutine math problems. These objective data were complemented with students' written “logs” of their work in real time, followed by semi-structured debriefing interviews after they had finished. Structured scales were used to document students' math-related attitudes, career interests, and work-values, along with essays describing their long-term experience with math, in and out of school. Data was gathered on students' math-aesthetics, including the features of “attractive” problems and their individual preferences for the different modes of instructional explanation. School records provided students' demographic data and their scores on generic measures of aptitude and achievement. Students' age, art discipline, attendance, sending school district, socioeconomic status (SES), and ethnicity were not found to be correlates for either students' aptitude/achievement/experience measures or problem-solving ability. Girls significantly outperformed boys on ability/achievement/experience measures, but not on problem-solving measures. Individualized Education Plan (IEP) status was found to be a strong correlate of both aptitude/achievement/experience and problemsolving measures, with students without IEPs consistently scoring higher on all significant measures than students with IEPs. Overall, most math-related attitude variables had little effect on both aptitude/achievement/experience and problemsolving measures. However, there was strong evidence of students' math-aesthetics in problem solving. Specifically, students appreciating more than one type of solution scored consistently higher in problem-solving measures and frequency of use of higher-order internal representations. A close relationship between metacognition, aesthetics, and representation was found, as well as a strong link between mathematics and language usage. The discovery of students' use of higher-order internal representation during post-task video-taped interviews, undetected by paper-andpencil assessments, supported a conclusion that studies of problem-solving ability cannot be purely quantitative in method but must contain a qualitative component.
Perceptions of Judges Toward Rigor of High School Senior Capstone Projects at a Northern RI Charter School
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With trends toward high stakes testing moving inexorably forward, project-based components of Rhode Island's Performance Based Graduation system have been largely overlooked. Existing studies focus primarily on implementation of senior projects (Davidson, 2009; Lorenz, 1999; Mayer, 1999; Nicolini, 1999; Shaunessy, 2004; Singer & Hubbard, 2002). Some studies have found that increasing graduation requirements does not necessarily translate into rigor (Dounay, 2006; Lundsgaard, 2004). Less research exists on the lasting influence of projects as preparation for postsecondary pursuits (Egelson, Harman, & Bond, 2002; Pennacchia, 2010). Research on academic rigor is largely focused upon increasing course requirements (ACT, 2005; Christie, 2000; Kirst & Venezia, 2006; Peter D. Hart Research Associates, 2005) and not on performance-based assessments such as senior projects.
This study addressed the following research questions: What are the perceptions of judges of the extent of rigor of senior projects with respect to the work required to complete the written and technical (filmmaking) components of the project, and a formal presentation of the project? Is there a relationship between arts major selected and academic achievement; arts major selected and achievement on senior projects; and academic achievement and achievement on senior projects? Finally, are there differences among judges regarding their perceptions of rigor based upon the nature of their professional positions?
The study utilized a sequential, mixed methods design including a survey of N=53 judges. Survey findings informed the focus groups, which included the following categories of judges: arts faculty employed by the school (n=4), school alumni (n=3), educators (n=3), and artistic professionals (n=4).
Judges perceived that there is rigor built into the project design. Educators found that student performance with the written components was not up to expected levels, while several judges across focus groups found that students were not always adequately prepared for the oral presentation component. Analysis of student performance data found that there was no connection between arts major and performance on the capstone project.
It is anticipated that results from this study may help to shape a project for one school and perhaps make it a model for replication across other schools within the state.