The Relationship between the Advanced Placement Calculus AB Exam and Student Achievement in College Level Math 1710-Calculus I

The purpose of this dissertation was to investigate the relationship between the Advanced Placement Calculus AB exam and student achievement in college level Math 1710-Calculus I. The review of literature shows that this possible relationship is based on Alexander Astin's longitudinal input-environment-outcome (I-E-O) model. The I-E-O model was used to analyze the relationship between the input and outcome of the two variables. In addition, this quantitative study determined the relationship between a score of 3 or lower on the Advanced Placement Calculus AB exam and student achievement in college level Math 1710-Calculus I. The sample population of this study contained 91 students from various high schools in Texas. Spearman's rank correlation revealed there was a statistically significant relationship between Advanced Placement Calculus AB exam scores and final grades in Math 1710-Calculus I

From Legos and Logos to Lambda: A Hypothetical Learning Trajectory for Computational Thinking

This thesis utilizes design-based research to examine the integration of computational thinking and computer science into the Finnish elementary mathematics syllabus. Although its focus is on elementary mathematics, its scope includes the perspectives of students, teachers and curriculum planners at all levels of the Finnish school curriculum. The studied artifacts are the 2014 Finnish National Curriculum and respective learning solutions for computer science education. The design-based research (DBR) mandates educators, developers and researchers to be involved in the cyclic development of these learning solutions. Much of the work is based on an in-service training MOOC for Finnish mathematics teachers, which was developed in close operation with the instructors and researchers. During the study period, the MOOC has been through several iterative design cycles, while the enactment and analysis stages of the 2014 Finnish National Curriculum are still proceeding.The original contributions of this thesis lie in the proposed model for teaching computational thinking (CT), and the clarification of the most crucial concepts in computer science (CS) and their integration into a school mathematics syllabus. The CT model comprises the successive phases of abstraction, automation and analysis interleaved with the threads of algorithmic and logical thinking as well as creativity. Abstraction implies modeling and dividing the problem into smaller sub-problems, and automation making the actual implementation. Preferably, the process iterates in cycles, i.e., the analysis feeds back such data that assists in optimizing and evaluating the efficiency and elegance of the solution. Thus, the process largely resembles the DBR design cycles. Test-driven development is also recommended in order to instill good coding practices.The CS fundamentals are function, variable, and type. In addition, the control flow of execution necessitates control structures, such as selection and iteration. These structures are positioned in the learning trajectories of the corresponding mathematics syllabus areas of algebra, arithmetic, or geometry. During the transition phase to the new syllabus, in-service mathematics teachers can utilize their prior mathematical knowledge to reap the benefits of ‘near transfer’. Successful transfer requires close conceptual analogies, such as those that exist between algebra and the functional programming paradigm.However, the integration with mathematics and the utilization of the functional paradigm are far from being the only approaches to teaching computing, and it might turn out that they are perhaps too exclusive. Instead of the grounded mathematics metaphor, computing may be perceived as basic literacy for the 21st century, and as such it could be taught as a separate subject in its own right