Teaching Mathematics: The Stories of Six Teachers

Mathematics is recognized as an area in which we see significant teacher shortages at both the middle and secondary school level. The purpose of this qualitative study was to identify personality characteristics of six mathematics teachers by interviewing those teachers and having them relate traits they perceived in themselves that helped them teach effectively. The study’s participants were in-service teachers currently practicing in public school settings in North Dakota. Two teachers from the pool of potential participants were chosen for their certification at each of the following grade levels: elementary, secondary, and dual certification in elementary and secondary education. Both of the dually certified teachers were teaching at the secondary level. The following three themes were developed from analysis of the interviews of six mathematics teachers. Theme one: certain personality characteristics contribute to positive learning environments for students. Theme two: certain teaching methods encourage students to take responsibility for their learning. Theme three: role models, favorite teachers, family, and/or coaches influenced the teachers\u27 decision to make mathematics teaching their career choice. Recruiting efforts to find more mathematics teachers to address shortages would be greatly enhanced by identifying students with an aptitude in mathematics and comparing their personal characteristics with those self-identified by selected mathematics teachers

Data-driven discovery of coordinates and governing equations

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam's razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom autoencoder to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional dynamical systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. It is the first method of its kind to place the discovery of coordinates and models on an equal footing.Comment: 25 pages, 6 figures; added acknowledgment

Fear of Breast Cancer Recurrence in African-American and Caucasian Breast Cancer Survivors

poster abstractProblem. Fear of breast cancer recurrence is a concern for 55-90% of long-term breast cancer survivors. Background. Fear of recurrence is recognized as a prevalent and long-term psychosocial consequence of surviving cancer. Breast cancer survivors often identify more than one worry about what a recurrence might threaten in their health, work, and family function (Vickberg, 2001, 2003; Ziner, 2008). Although more research has been conducted with Caucasian breast cancer survivors, less is known about the nature of fear of recurrence worries in African American breast cancer survivors. Purpose. The purpose of this study was to compare fear of recurrence and worries related to thoughts of recurrence between African-American (AA-BCS) and Caucasian breast cancer survivors ( C-BCS). Theory. Emotion theorist, such as Lazarus (1991) suggest that fear is an emotional response to an identifiable object, thought or event that is perceived as harmful. Methods. This is a secondary analysis of a larger study comparing quality of life of AA-BCS and C-BCS using a cross-section survey design. Sample. Female breast cancer survivors ( AA-BCS N = 62, C-BCS N = 72) who were 2-10 years post treatment. Measures. Concerns about Recurrence Sale (CARS) Vickberg (2003) is a scale with 30 Likerttype items and 5 sub-scales: Fear of recurrence Index (overall fear frequency, intensity and consistency). Four (4) subscales of what BCS worry about: Health worries, Role worries, Womanhood worries, and Death worries. Validity. Content analysis of focus group data (N=21) AA-BCS showed that no changes were recommended in the CARS. (Russell, Personal communication) Reliability. The CARS and subscales were found to have Good to adequate Cronbach’s alpha’ for AA-BCS and C-BCS. Specifically, FRI = .92 AA-BCS, .90 C-BCS, Health worries = .93 AA-BCS, .92 C-BCS, Role worries = .75 AA-BCS, .87 C-BCS, Womanhood worries .89, AABCS, .90, C-BCS, Death worries .81 AA-BCS, .92 C-BCS. Analysis. ANCOVA was used for analysis controlling for age, time since diagnosis, income, marital status, years of education and body mass index. Results. Fear of recurrence Indexes between AA-BCS (mean 9.8) and C-BCS (mean 11.5) were not statistically different (p = .199). Health worries (AA- BCS mean 1.1, C-BCS mean 1.6, p= .018), Role worries (AA-BCS mean .8, C- BCS mean 1.2, p = .05), and Death worries (AA- BCS mean 1.3,C- BCS mean 2.2, p = .01) were significantly different between AA-BCS and C-BCS. Womanhood worries were not significantly different. Conclusions. AA-BCS and C-BCS were equally afraid of a recurrence. Except of womanhood worries, AA-BCS had lower mean health, role and death worries than C-BCS. Implications. Understanding the underlying worries related to overall fear of recurrence can lead to more focused and perhaps effective nursing intervention for AA-BCS and C-BCS

PySINDy: A Python package for the sparse identification of nonlinear dynamical systems from data

Authors of papers retaincopyright and release the workunder a Creative CommonsAttribution 4.0 InternationalLicense (CC-BY)Scientists have long quantified empirical observations by developing mathematical models that characterize the observations, have some measure of interpretability, and are capable of making predictions. Dynamical systems models in particular have been widely used to study, explain, and predict system behavior in a wide range of application areas, with examples ranging from Newton’s laws of classical mechanics to the Michaelis-Menten kinetics for modeling enzyme kinetics. While governing laws and equations were traditionally derived by hand, the current growth of available measurement data and resulting emphasis on data-driven modeling motivates algorithmic approaches for model discovery. A number of such approaches have been developed in recent years and have generated widespread interest, including Eureqa (Schmidt & Lipson, 2009), sure independence screening and sparsifying operator (Ouyang, Curtarolo, Ahmetcik, Scheffler, & Ghiringhelli, 2018), and the sparse identification of nonlinear dynamics (SINDy) (Brunton, Proctor, & Kutz, 2016). Maximizing the impact of these model discovery methods requires tools to make them widely accessible to scientists across domains and at various levels of mathematical expertise.This project is a fork of sparsereg( Quade, 2018). SLB acknowledges funding supportfrom the Air Force Office of Scientific Research (AFOSR FA9550-18-1-0200) and the ArmyResearch Office (ARO W911NF-19-1-0045). JNK acknowledges support from the Air ForceOffice of Scientific Research (AFOSR FA9550-17-1-0329). This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under GrantNumber DGE-1256082

The Relationship Between Depressive Symptoms and Social Cognitive Processing in Partners of Long-Term Breast Cancer Survivors

Purpose/Objectives: To determine 1) if depressive symptoms in partners of long-term breast cancer survivors (BCS) could be predicted by social cognitive processing theory, and 2) if partners of younger and older breast cancer survivors were differentially affected by the cancer experience. Design: A cross-sectional, descriptive study utilizing self-report questionnaires. Setting: Indiana University and 97 ECOG-ACRIN sites. Sample: Partners of breast cancer survivors (n=508) diagnosed 3-8 years prior. Methods: Secondary data mediation analyses were conducted to determine if cognitive processing mediated the relationship between social constraints and depressive symptoms. Age-related differences on all scales were tested. Main Research Variables: Depressive symptoms; secondary variables included social constraints, cognitive processing (avoidance and intrusive thoughts), and potentially confounding variables. Findings: Cognitive processing mediated the relationship between social constraints and depressive symptoms for partners (F(5,498)= 19.911, R2=.167, p<.001). Partners of young BCS reported worse outcomes on all measures than partners of older breast cancer survivors Conclusions: As predicted by the social cognitive processing theory, cognitive processing mediated the relationship between social constraints and depressive symptoms. Furthermore, partners of younger BCS fared worse on social constraints, intrusive thoughts and depressive symptoms than partners of older BCS. Implications for Nursing: Results provide support for using the social cognitive processing theory in intervention design with partners of long-term BCS to decrease depressive symptoms. Knowledge Translation: • Partners of long-term BCS report clinically significant depression. • Partners of younger BCS report higher levels of depressive symptoms than the national average and than partners of older survivors. • Addressing social constraints within the dyad may improve depressive symptoms.This study was coordinated by the ECOG-ACRIN Cancer Research Group (Robert L. Comis, MD and Mitchell D. Schnall, MD, PhD, Group Co-Chairs) and supported in part by Public Health Service Grants CA189828, CA180795, CA37403, CA35199, CA17145 and CA49883, and from the National Cancer Institute, National Institutes of Health and the Department of Health and Human Services. Its content is solely the responsibility of the authors and does not necessarily represent the official views of the National Cancer Institute. Research reported in this publication was supported by the National Institute of Nursing Research of the National Institutes of Health under Award Number F31NR013822, and by the National Cancer Institute of the National Institutes of Health under Award Numbers K05CA175048 and R25CA117865. Its content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health, including the National Cancer Institute or the National Institute of Nursing Research