ABSTRACT
Calculus, the study of change in processes and systems, serves as the foundation for many STEM disciplines. Traditional, lecture-based calculus instruction may present a barrier for students seeking STEM degrees, limit their access to STEM professions, and block their potential to address society's challenges. A large-scale pragmatic trial with randomized student allocation was conducted to compare two calculus instruction styles: active student engagement (treatment condition) versus traditional, lecture-based instruction (control condition). A sample of 811 university students were studied across 32 sections taught by 19 instructors over three semesters at a large, US-based Hispanic-serving institution. Large effect sizes were consistently measured for student learning outcomes in the treatment condition, which demonstrates a new standard for calculus instruction and increased opportunities for completion of STEM degrees.
ABSTRACT
The Automatic Quasi-clique Merger algorithm is a new algorithm adapted from early work published under the name QCM (introduced by Ou and Zhang in 2007). The AQCM algorithm performs hierarchical clustering in any data set for which there is an associated similarity measure quantifying the similarity of any data i and data j. Importantly, the method exhibits two valuable performance properties: 1) the ability to automatically return either a larger or smaller number of clusters depending on the inherent properties of the data rather than on a parameter. 2) the ability to return a very large number of relatively small clusters automatically when such clusters are reasonably well defined in a data set. In this work we present the general idea of a quasi-clique agglomerative approach, provide the full details of the mathematical steps of the AQCM algorithm, and explain some of the motivation behind the new methodology. The main achievement of the new methodology is that the agglomerative process now unfolds adaptively according to the inherent structure unique to a given data set, and this happens without the time-costly parameter adjustment that drove the previous QCM algorithm. For this reason we call the new algorithm automatic. We provide a demonstration of the algorithm's performance at the task of community detection in a social media network of 22,900 nodes.
ABSTRACT
BACKGROUND: Substantial research has been conducted focusing on student outcomes in mathematics courses in order to better understand the ways in which these outcomes depend on the underlying instructional methodologies found in the courses. From 2009 to 2014, the Mathematical Association of America (MAA) studied Calculus I instruction in United States (US) colleges and universities in the Characteristics of Successful Programs of College Calculus (CSPCC). One aspect of this study attempted to understand the impact of these courses on student experience. RESULTS: In this paper, we describe results from an examination of the effect of course structure on students' attitudes and beliefs across different versions of Calculus I at a large research university in the USA. To do this, we implemented a follow-up study of the national MAA study of calculus programs in part to identify potential relationships between various course structures and changes in attitudes and beliefs during the course. We compare our results both internally across these course structures and to the national data set. CONCLUSIONS: We find that the statistically significant changes measured in confidence and enjoyment exhibit differences across the different calculus implementations and that these changes are statistically independent of the underlying student academic backgrounds as shown by standardized test scores and high school GPA. This suggests that these observed changes in attitudes and beliefs relate to the experience in our varied course structures and not to the academic characteristics of students as they enter the course. In addition to our findings, we show how this national study can be used locally to study effects of courses on student affective traits.
ABSTRACT
Sequence comparison is a primary technique for the analysis of DNA sequences. In order to make quantitative comparisons, one devises mathematical descriptors that capture the essence of the base composition and distribution of the sequence. Alignment methods and graphical techniques (where each sequence is represented by a curve in high-dimension Euclidean space) have been used popularly for a long time. In this contribution we will introduce a new nongraphical and nonalignment approach based on the frequencies of the dinucleotide XY in DNA sequences. The most important feature of this method is that it not only identifies adjacent XY pairs but also nonadjacent XY ones where X and Y are separated by some number of nucleotides. This methodology preserves information in DNA sequence that is ignored by other methods. We test our method on the coding regions of exon-1 of ß-globin for 11 species, and the utility of this new method is demonstrated.