This study investigates the effects of implementing a remediation program in a high school Advanced Placement Calculus AB course on student class grades and success in passing the AP Calculus AB exam. A voluntary remediation program was designed to help students understand the key concepts and big ideas in beginning Calculus. Over a period of eight years the program was put into practice and data on student participation and achievement was collected. Students who participated in this program were given individualized recitation activities targeting their specific misunderstandings, and then given an opportunity to retest on chapter exams that they had taken prior to remediation. Students were able to improve their scores on the original chapter exams and their grade in the class by demonstrating a greater understanding of the material after participating in the remediation sessions. This process was repeated for all chapter exams given during the academic year. In this study, a data analysis comparing the percent gain, after remediation, in each student’s overall class grade to their AP Calculus AB exam scores was conducted. Additionally, AP Calculus AB exam scores of students enrolled in these classes were compared to AP Calculus AB exam scores globally both pre and post implementation of the remediation program. The results of this study demonstrate that there is a substantial positive correlation between student participation in the remediation program and greater success on the AP Calculus AB exam. The average AP Calculus AB score for the students enrolled in AP Calculus AB during the eight-year period of implementing the remediation program increased by over 9%.

abstract: A sample of 127 high school Advanced Placement (AP) Calculus students from two schools was utilized to study the effects of an engineering design-based problem solving strategy on student performance with AP style Related Rate questions and changes in conceptions, beliefs, and influences. The research design followed a treatment-control multiple post-assessment model with three periods of data collection. Four high school calculus classes were selected for the study, with one class designated as the treatment and three as the controls. Measures for this study include a skills assessment, Related Rate word problem assessments, and a motivation problem solving survey. Data analysis utilized a mixed methods approach. Quantitative analysis consisted of descriptive and inferential methods utilizing nonparametric statistics for performance comparisons and structural equation modeling to determine the underlying structure of the problem solving motivation survey. Statistical results indicate that time on task was a major factor in enhanced performance between measurement time points 1 and 2. In the experimental classroom, the engineering design process as a problem solving strategy emerged as an important factor in demonstrating sustained achievement across the measurement time series when solving volumetric rates of change as compared to traditional problem solving strategies. In the control classrooms, where traditional problem solving strategies were emphasized, a greater percentage of students than in the experimental classroom demonstrated enhanced achievement from point 1 to 2, but showed decrease in achievement from point 2 to 3 in the measurement time series. Results from the problem solving motivation survey demonstrated that neither time on task nor instruction strategy produced any effect on student beliefs about and perceptions of problem solving. Qualitative error analysis showed that type of instruction had little effect on the type and number of errors committed, with the exception of procedural errors from performing a derivative and errors decoding the problem statement. Results demonstrated that students who engaged in the engineering design-based committed a larger number of decoding errors specific to Pythagorean type Related Rate problems; while students who engaged in routine problem solving did not sustain their ability to correctly differentiate a volume equation over time. As a whole, students committed a larger number of misused data errors than other types of errors. Where, misused data errors are the discrepancy between the data as given in a problem and how the student used the data in problem solving. / Dissertation/Thesis / Ph.D. Mathematics Education 2012