A weighted interpretation for the super Catalan numbers

The super Catalan numbers $T(m,n)=(2m)!(2n)!/2m!n!(m+n)!$ are integers which generalize the Catalan numbers. With the exception of a few values of $m$, no combinatorial interpretation in known for $T(m,n)$. We give a weighted interpretation for $T(m,n)$ and develop a technique that converts this weighted interpretation into a conventional combinatorial interpretation in the case $m=2$.Comment: 8 pages, 5 figure

Exploring Expressive Writing to Reduce Test Anxiety on an Introductory Psychology Exam

Denman Undergraduate Research Forum - Second Place Award for Psychological SciencesPrevious research suggests that a brief expressive writing exercise prior to a math exam can help alleviate anxiety and improve test-taking performance. Our study examined the effects of a short seven-minute expressive writing intervention among college students taking a mock introductory psychology exam. A total of N=93 students enrolled at The Ohio State University at Lima participated. Students first completed the Cognitive Test Anxiety Scale and a modified version of the Abbreviated Mathematics Anxiety Rating Scale in order to establish how much anxiety they typically experienced during exams. We then randomly assigned participants to either write about their thoughts, feelings, and worries regarding an upcoming exam (experimental condition) or to write about factual content related to the course (e.g., names of theorists, how theories differed from one another, or facts learned in the course; control condition). Students then completed a 51-item mock exam covering content typical of an introductory psychology course. All students rated their anxiety level at multiple time points (i.e. pre and post-intervention, before, during, and after the exam). We found that students in the expressive writing condition had a larger reduction in perceived anxiety from pre to post-intervention compared to the control condition. As predicted, students who engaged in expressive writing scored higher on the exam, relative to controls. However, when we covaried out their pre-study average exam grade, the between group effect vanished. Expressive writing reduced self-reported anxiety before taking a social science exam; however, the effect didn’t extend to objective performance on the exam itself. Additional research is needed to better understand how expressive writing may reduce test anxiety and benefit students.No embargoAcademic Major: Psycholog

Assistive Technology for Students with Multiple Disabilities

This research looks into the effectiveness of assistive technology for students with multiple disabilities in a classroom setting. Assistive technology is any item, piece of equipment or product system—whether acquired commercially, modified, or customized—that is used to increase, maintain, or improve functional capabilities of individuals with disabilities. This research also looks into the many obstacles that educators, building support staff and families face when trying to obtain assistive technology devices for their students. This research uses a thirteen question survey, sent out to several educational staff. The results of this research may be used to improve the effectiveness of said devices as well as inform the reader on how assistive technology is properly utilized for students with multiple disabilities

Does Diversity Ideology Moderate Participants’ Perceptions of Therapists Who Do and Do Not Broach?

Introduction. The literature has grown considerably regarding the act of broaching racial, ethnic, and cultural factors in therapy. Many have highlighted its positive impact on the therapeutic alliance, but little empirical work explores how individual differences influence a client’s response to broaching. This study assessed the effects of participant diversity ideology and therapist broaching behavior on perceptions of a therapist’s effectiveness. I hypothesized that participants in the therapists broaching condition would perceive the therapist to be more effective than participants in the no broaching condition. I also hypothesized that participants’ colorblind diversity ideology and therapist broaching condition would interact, such that participants who were higher in colorblindness would perceive the therapist less favorably when the therapist displayed broaching behaviors than when the therapist generally avoided broaching the topics of race, ethnicity and culture; however, participants low in colorblindness would show the opposite pattern. Method. One hundred and twenty-three undergraduate students were recruited from the university’s psychology subject pool. Participants completed all study materials online. They were randomly assigned to watch a video of a mock therapy session between a White therapist and a Black client. Videos were manipulated such that the therapist either broached the topic of race or avoided any discussion of race in response to the client’s presenting concerns. Participants also completed the Colorblindness Racial Attitudes Scale (CoBRAS), Session Rating Scale (SRS), and Therapist Cultural Comfort Scale (TCCS) to measure diversity ideology and therapist effectiveness. Analytic Approach. Exploratory factor analyses were conducted to ensure that the measures utilized were appropriate for the study. The two dependent variables (SRS and TCCS) were regressed onto the independent variables (CoBRAS, vignette condition, and their interaction) to evaluate the study hypotheses. Results. Consistent with the first hypothesis, participants reported more favorable perceptions of the broaching therapist compared to the therapist who did not broach. The second hypothesis was only supported when examining perceptions of positive cultural comfort. Participants with high colorblindness reported lower positive cultural comfort scores when viewing the broaching condition. Contrary to the second hypothesis, there was no interaction between participant ideology and broaching condition on ratings of therapist effectiveness. Discussion. The data suggests that clinicians who broach race in session are seen as more culturally competent and as having higher effectiveness than those who avoid these topics, regardless of an individual’s colorblindness levels. Broaching appears to be a low-risk, high-reward therapeutic behavior. Keywords: broaching; diversity ideology; colorblindness; therapist effectivenes

Minimal Noise-Induced Stabilization of One-Dimensional Diffusions

The phenomenon of noise-induced stabilization occurs when an unstable deterministic system of ordinary differential equations is stabilized by the addition of randomness into the system. In this paper, we investigate under what conditions one-dimensional, autonomous stochastic differential equations are stable, where we take the notion of stability to be that of global stochastic boundedness. Specifically, we find the minimum amount of noise necessary for noise-induced stabilization to occur when the drift and noise coefficients are power, polynomial, exponential, or logarithmic functions

Environment Matters: Examining the Lived Experience of First-Generation College Students at Private, Four-Year Universities

The purpose of this qualitative phenomenological study was to explore the lived experience of first-generation college students at two small, private, liberal arts universities. Initially, the study focused on the identity development of first-generation students and how their familial relationships and culture influenced their development. However, as the study developed, the college environment emerged as another significant environmental factor influencing students’ experiences and development. For the majority of participants, family offered support and encouragement in their academic endeavors prior to and during college, which positively influenced their success and persistence in college. Additionally, many participants named professors as a significant source of support and mentioned feeling known and cared for by professors. Participants also found academic and emotional support through relationships with peers, which developed through classes, on-campus jobs, and extracurricular involvement. Overall, participants felt a sense of belonging at their institutions. The community created around shared values at small, private institutions of higher education provided an environment conducive to the success and persistence of participants in this study. However, the majority of participants identified as White and middle class and attended predominantly White institutions (PWIs). Further study from the perspective of students of color at small, private PWIs would add to lessons learned about the influence of environment on the experiences of first-generation college students

Picture this: the value of multiple visual representations for student learning of quantum concepts in general chemistry

Mental models for scientific learning are often defined as, "cognitive tools situated between experiments and theories" (Duschl & Grandy, 2012). In learning, these cognitive tools are used to not only take in new information, but to help problem solve in new contexts. Nancy Nersessian (2008) describes a mental model as being [loosely] characterized as a representation of a system with interactive parts with representations of those interactions. Models can be qualitative, quantitative, and/or simulative (mental, physical, computational)" (p. 63). If conceptual parts used by the students in science education are inaccurate, then the resulting model will not be useful. Students in college general chemistry courses are presented with multiple abstract topics and often struggle to fit these parts into complete models. This is especially true for topics that are founded on quantum concepts, such as atomic structure and molecular bonding taught in college general chemistry. The objectives of this study were focused on how students use visual tools introduced during instruction to reason with atomic and molecular structure, what misconceptions may be associated with these visual tools, and how visual modeling skills may be taught to support students' use of visual tools for reasoning. The research questions for this study follow from Gilbert's (2008) theory that experts use multiple representations when reasoning and modeling a system, and Kozma and Russell's (2005) theory of representational competence levels. This study finds that as students developed greater command of their understanding of abstract quantum concepts, they spontaneously provided additional representations to describe their more sophisticated models of atomic and molecular structure during interviews. This suggests that when visual modeling with multiple representations is taught, along with the limitations of the representations, it can assist students in the development of models for reasoning about abstract topics such as atomic and molecular structure. There is further gain if students’ difficulties with these representations are targeted through the use additional instruction such as a workbook that requires the students to exercise their visual modeling skills

Language Use in Totalistic Social Groups

A totalistic social group is defined as a collection of individuals who share similar values and goals and who live together within intensive boundaries enforced by the group’s leadership and/or members themselves (Lifton 1969). The focus of this project is to better understand the effect of language on (I) a totalistic group’s social structure and (II) the ideologies and actions of members. The limited linguistic research on totalistic groups claims that leaders and members use language in order to enforce rules and beliefs, encourage conformity, and maintain as well as increase membership. By examining language practices in the US military, this project fills the current gap of limited data in the linguistic literature on totalism. My research suggests that certain language practices are created and used within totalistic communities in order to support an in-group mentality between members, dedication to the group’s leaders and efforts, and a powerful social structure. This project analyzes data collected from an anonymous online survey regarding language within the US military. For instance, the results of this survey suggested that respondents regarded language as a powerful tool in reinforcing the military’s hierarchical structure. This research therefore suggests that language practices are taught to military members in order to encourage certain desired behavior. Ultimately, this research demonstrates how language practices in totalistic groups determine the maintenance of power and the fortification of membership. Therefore, by providing new data on language and totalism, this project is shedding much needed light on an under-researched area of sociolinguistics

Sit Tibi Terra Levis

I never really knew my father’s father. He left behind only old cassette tapes, stories, and glimpses of memory from before he got sick. He had a rare genetic disease that killed him slowly, piece by piece, neuron by neuron. I remember playing hide and seek with him behind the cascading fabric roses in our living room, and I remember him rocking in his armchair, gently humming a song I didn’t recognize. I remember the smell of the hospital room where he died. I was 12. He was 67. Did my father have the same disease? Would he die just like his father- would I die just like him? I can’t remember the color of his eyes or the way he hugged me, the sound of his voice or how he laughed. Slowly, piece by piece, neuron by neuron, he disappears from my mind. Would I die just like him? Whenever my sister and I drove past a graveyard, we held our breath. I don’t know who taught us this game, but we played every time we sat together watching the world through glass and parallax. Small churchyards and cemeteries required only a few seconds without breath, but sometimes the graves went on seemingly forever, covering the rolling hills with names remembered and forgotten. Sometimes we had to hold our breath for minutes that stretched on for eternities. I could feel my heart pushing against my skin, calling out for air. We sat in the backseat silence, breathless as the dead outside the window, with hearts pounding urgent. Sometimes I walk through the woods in Starlight. The telephone birds warble in the leaves overhead, rustling as the wind gently breathes through the branches. Cicada song drowns the train whistles that echo up through the valley. Sometimes I sit by a stump with miles of roots buried under the mushroom laced moss: once it stretched above the clouds, now it rests below the earth. Sometimes surrounding trees share their water with the stump, but not enough to help its branches grow back. Is it dead or alive? Is it alive or dead? There was a hole in the ceiling of my grandmother’s old house. We were not allowed to climb up: too dangerous, my grandmother would say. But once, we felt brave, and pulled the small white string that revealed the pathway up to the attic. We tiptoed across wooden beams that split seas of mothballs and dust; we hid in racks of old coats and evening gowns. Amid the stacks of cardboard, we found a small shoebox filled with ghosts. The people on the countless decaying pages stared at us as we admired them. They were alive then, staring at the camera, laughing, smiling, full of dreams, full of heartache. Like us. But now they are dead. They are empty and motionless somewhere below moonwort and forget-me-nots. Like we will be. But still they stare at us, immortal in paper and silver and gelatin. The photographic prints in this book were processed like our bodies are processed after death. I brushed some with oil just as the ancient Greeks would’ve anointed their dead. Some, echoing the traditions of ancient Babylonians, I soaked in honey. For others, I simulated modern American practice of chemical embalming by washing the prints with soap before processing them with different combinations of photographic chemistry. Some of these are incompletely fixed, meaning they will continue to decompose and degrade over time. Others were soaked in fixer for days, leaving stains on the print as if it had been aging slowly for years. Including inscriptions from ancient Roman tombstones