Naneh Apkarian

Naneh Apkarian
Arizona State University | ASU · School of Mathematical and Statistical Sciences

Doctor of Philosophy

About

38
Publications
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290
Citations

Publications

Publications (38)
Article
Full-text available
Inquiry-Based learning (IBL) is a fairly well-known term in the United States (US) describing a range of student-centered or active pedagogical approaches in mathematics. However, the ‘big tent’ definitions of IBL mean that there is much variation in IBL users’ instructional practices, variation which we set out to codify. Cluster analysis of self-...
Article
Full-text available
Background Implementing research-based teaching practices has been repeatedly cited as an important factor for student success in university mathematics courses. Many research-based practices increase the amount of student–student and/or student–instructor interaction. However, some instructors are hesitant to implement such practices because they...
Article
Full-text available
Mounting evidence of the effectiveness of active learning strategies has prompted many mathematics departments to start engaging in transformational change efforts. Change, however, especially change in instructional practice, is a challenging endeavor. Some departments are using coordination of multi-section courses as a vehicle to enact changes a...
Article
Active Learning is becoming a standard method of delivering instruction in mathematics courses across the country. Researchers, administrators, policy makers, and instructors all need access to valid means of measuring practices used in the classroom. Drawing on the Postsecondary Instructional Practices Survey, the Student Postsecondary Instruction...
Article
Full-text available
Background Active learning used in science, technology, engineering, and mathematics (STEM) courses has been shown to improve student outcomes. Nevertheless, traditional lecture-orientated approaches endure in these courses. The implementation of teaching practices is a result of many interrelated factors including disciplinary norms, classroom con...
Preprint
Full-text available
A compilation of descriptive statistics of responses to the X-PIPS-M suite of surveys for students, student instructors, and faculty instructors of introductory mathematics courses. Data were obtained from Precalculus, Calculus 1, and Calculus 2 courses at 12 universities during the 2017-18 and 2018-19 academic years, as part of the Progress throug...
Conference Paper
Full-text available
Contributing to the effort to diversify the demographics in STEM disciplines, we examined the effect of role models in students’ perceptions of precalculus and calculus courses. Drawing from Dasgupta’s stereotype inoculation model (2011a) in which ingroup experts can serve as “social vaccines” to protect against negatively stereotyped groups, we te...
Article
Full-text available
This paper reports a study of university students’ experiences of learning mathematics in an introductory differential equations course that takes an inquiry approach to learning and teaching. The students are on a trajectory leading toward a bachelor’s degree in mathematics to be followed by a year-long teacher education credential program. The an...
Article
Full-text available
In this paper, we investigate leadership related to the instruction of lower division undergraduate courses at five university mathematics departments with strong calculus programs. We use social network analysis to identify patterns of influence on instruction, using the relations: advice seeking, instructional material sharing, discussion of inst...
Article
Full-text available
Six common beliefs about the usage of active learning in introductory STEM courses are investigated using survey data from 3769 instructors. Three beliefs focus on contextual factors: class size, classroom setup, and teaching evaluations; three focus on individual factors: security of employment, research activity, and prior exposure. The analysis...
Article
San Diego State University recently embarked on a major initiative to revitalize the Precalculus, Calculus 1, Calculus 2 sequence. In addition to program features such as course coordination, a new active learning component led by graduate teaching assistants (GTAs) was added to each of the Precalculus, Calculus 1, and Calculus 2 courses, and a pro...
Article
Precalculus and single-variable calculus courses are a critical early juncture for the success of science, technology, engineering, and mathematics (STEM) students in the United States (US). The default course structure is often a required three-term sequence of precalculus, differential calculus, and integral calculus. In this paper we analyse var...
Article
Classrooms which involve students in mathematical discourse are becoming ever more prominent for the simple reason that they have been shown to support student learning and affinity for content. While support for outcomes has been shown, less is known about how or why such strategies benefit students. In this paper, we report on one such finding: n...
Conference Paper
Full-text available
This paper presents narratives of change at three university mathematics departments in response to administrative insistence on improvements in the face of pressure from engineering colleges. Specifically, these three departments were faced with the prospect of losing calculus teaching to another unit on campus and reacted to prevent that outcome....
Article
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The networking of theories is an increasingly common and powerful approach to analyzing complex phenomena such as learning processes in classrooms. In this paper, we aim to advance the theoretical coordination of two approaches that we have previously combined to analyze individual, small group, and whole class mathematical progress. The theoretica...
Article
Research suggests that science, technology, engineering, and mathematics (STEM) departments are a productive unit of focus for systemic change efforts. In particular, they are relatively coherent units of culture, and cultural changes are critical to creating sustainable improvements. However, the STEM disciplines are often treated as a monolith in...
Article
The Mathematical Association of America’s Precalculus to Calculus: Insights and Innovations conference brought together representatives of mathematics departments from across the country with members of two national research projects to share and discuss both research findings and on-the-ground concerns of faculty. In this article, we report on maj...
Article
Full-text available
This study furthers the theory of conceptual blending as a useful tool for revealing the structure and process of student reasoning in relation to the Sierpinski triangle (ST). We use conceptual blending to investigate students’ reasoning, revealing how students engage with the ST and coordinate their understandings of its area and perimeter. Our a...
Article
Full-text available
This paper describes a method for using instructional analytics to support changes in teaching practice. The study took place in a discourse-focused undergraduate mathematics classroom taught by an experienced instructor. Using the classroom observation tool EQUIP and social network surveys, we generated quantitative data on patterns of student par...
Conference Paper
Full-text available
In this report we present findings from a preliminary investigation aimed at describing models of course coordination systems currently in place within university precalculus and single variable calculus courses. Hierarchical cluster analysis was used on national survey data to identify homogeneous clusters of courses based on the intended use of u...
Article
We present findings from a recently completed census survey of all mathematics departments in the United States that offer a graduate degree in mathematics. The census survey is part of a larger project investigating institutional features that influence student success in the introductory mathematics courses that are required of most STEM majors i...
Technical Report
Full-text available
This guide proposes an inclusive approach to the organization or categorization of existing theories and knowledge, as well as the development of new knowledge and theory. This guide is intended to help researchers and scholars maintain awareness of their decisions to include and/or exclude certain scholarship, and to report and reduce the limitati...
Article
Full-text available
Background This paper adapts the four-frame model of organizational change to the context of higher education. We offer the model as a tool for researchers and change agents who wish to study and enact systemic change within STEM departments. We provide the four frames in contrast to overly simplistic models of change that have been shown to be unl...
Conference Paper
Full-text available
In this report, we present an analysis of 10 individual interviews with graduate mathematics education students about the area and perimeter of the Sierpinski triangle (ST). We use conceptual blending as a theoretical and methodological tool for analyzing students' reasoning to investigate how students encounter and cope with the ST having zero are...
Article
This article presents a case study that details the successes and lessons learned by faculty and administrators at San Diego State University (SDSU) who are in the process of implementing a substantial improvement to the Precalculus to Calculus 2 sequence. Improvement efforts have been informed by national studies of successful programs and center...
Poster
Full-text available
The National Science Foundation has supported two large scale projects to examine the programs and structures related to Precalculus through Calculus 2 courses (P2C2) that promote student success in undergraduate mathematics. The two projects, Progress through Calculus (PtC) and Student Engagement in Mathematics through an Institutional Network for...
Conference Paper
Full-text available
Many universities have begun to coordinate their introductory mathematics courses to handle multiple sections of the same course, a situation necessitated by the large numbers of students taking precalculus and calculus. Robust coordination systems consist of two major elements: uniform course elements (e.g., common text; exams) and regular instruc...
Conference Paper
Improvement of mathematics courses in the first two years of college has recently become a priority in the United States. This is evidenced by multiple calls to enhance undergraduate education in the mathematical sciences and by funding allocated to related research and instructional improvement projects. As stakeholders make decisions to invest in...
Article
In this MAA FOCUS article we highlight cross-cutting themes that emerged from discussion groups of conference participants at an MAA-sponsored and NSF-funded conference, Precalculus to Calculus: Insights and Innovations.
Conference Paper
Full-text available
In this paper we analyze variations in the structure of courses designed for the Precalculus through Calculus 2 (P2C2) sequence. We examine the nature of such variations, frequency nationally, and how DFW rates and instructional approach compare to the standard courses. While most identified variations in course structures have on average lower DFW...
Poster
The study presented here examines the active learning strategies currently in place in the Precalculus through single variable calculus sequence. While many lament the lack of active learning in undergraduate mathematics, our work reveals the reality behind that feeling. Results from a national survey of mathematics departments allow us to report t...
Conference Paper
Full-text available
Typical goals for inquiry-oriented mathematics classrooms are for students to explain their reasoning and to make sense of others’ reasoning. In this paper we offer a framework for interpreting ways in which engaging in the reasoning of someone else is productive for the person who is listening. The framework, which captures the relationship betwee...
Conference Paper
Full-text available
Calculus is typically the first undergraduate mathematics course for science, technology, engineering, and mathematics (STEM) majors in the United States. Internationally as well as domestically, first year mathematics courses are credited with preventing students from continuing along STEM paths. A recent study of the features that characterize ex...
Article
Full-text available
Metagenomics is a primary tool for the description of microbial and viral communities. The sheer magnitude of the data generated in each metagenome makes identifying key differences in the function and taxonomy between communities difficult to elucidate. Here we discuss the application of seven different data mining and statistical analyses by comp...

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