Internationalizing College Algebra

Over the last decade, the pedagogical approach known as mathematical modeling has received increased interest in college algebra classes in the United States. Math modeling assignments ask students to develop their own problem-solving tools to address non-routine, realistic scenarios. The open-ended quality of modeling activities creates dilemmas for teachers who design the assignments and convey grading expectations to students. This article provides a critical review of our own approach to task design for modeling as well as the extensive contributions in the United Kingdom (UK) and elsewhere in Europe dating from the 1980s and 1990s. Each approach attends differently to several competing needs: modeling as a process, modeling competencies, and developing clarity in academic writing. These resources provide substantial support for instructors of college algebra and other early undergraduate mathematics classes in the U.S. who may be embarking for the first time on task design and grading in a modeling framework.

This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students’ conceptual understanding.

Michigan Technological University had a collective 28% drop, fail, or withdraw rate in four predominantly first-year mathematics classes for the fall semesters from 2011 to 2015, with 58% of students dropping, failing, or withdrawing from College Algebra I in the fall of 2013. A survey was distributed via email to the 2015-2016 first year class of Michigan Tech in an attempt to determine why students struggle in making the transition from high school to undergraduate mathematics class, and what instructors can do to make this transition easier for students. It was found that the time between a student’s last high school mathematics course and their first at the university was not influential on student struggles. The first mathematics class taken at Michigan Tech was related to some differences in struggle, but the student’s highest level of mathematics before arriving at the university and the grade a student received in their first mathematics class at Michigan Tech were fairly significant factors. Over all students surveyed, the factors found to be most difficult included the clarity of lectures, the students’ ability to study for tests and exams, and working with an online mathematics homework system.

Students from small rural schools (class 1A, 2A, and 3A) historically have not had access to dual credit courses for several reasons including distance from a college campus, affordability, and district teaching strength. In an effort to address these problems and to begin the college experience sooner, a new program was developed by the Mathematics Department at Stephen F. Austin State University. This program is based on the creation and delivery of two online courses in mathematics, College Algebra and Plane Trigonometry.

This Complete Research paper details XXX University's summer math bridge program designed to support at-risk students transitioning into engineering and technology programs. We present two years of longitudinal data on the outcomes of these students. Math bridge programs are becoming more common as higher education institutions are adapting to changing student demographics, including an increase in minority and non-traditional student enrollments. The changing demographics of college students offer both promising opportunities and unique challenges for educators as they strive to connect with these underserved populations. Shifting demographics are compounded by declining ACT scores, exacerbated by the pandemic, and financial constraints, particularly among underrepresented groups. XXX engineering college has seen a rise in students needing math remediation. In the 2020 incoming engineering freshman class of XXX University, 42% required at least one math remediation course, of which 43% were Hispanic, 26% were Caucasian, 13% were African American, 13% were Asian, and 17% were female. Underrepresented groups, oftentimes carrying a larger debt burden and financial constraints, comprise a majority of students needing remedial math courses in their degree programs. These challenges place underserved students at high risk of dropping out of their degree programs or even from college altogether, as remedial math courses often prolong graduation timelines. We aim to address this issue through a 1-week math bridge program, offering one session in 2021 and two consecutive sessions in 2022, with a total of 48 students served. The program targets public high school transition students, and non-traditional students (veterans and returning learners) with over a year gap in the last math course they have taken. This bridge program provides individualized math plans, rigorous math review, and hands-on project-based learning with math faculty, engineering faculty and tutors with engineering or mathematics post-secondary degrees. An online math platform was used to assess each student's current mathematical ability, diagnose weaknesses, and provide guided practice to address those areas of weakness. There were five tests covering basic geometry, standard high school algebra, advanced algebra, and trigonometry. Students would take a test, work the study plan generated if performance was below 80%, retake that test and then move on to the next section of material. A university math professor and two tutors were always available for help. The math faculty would dedicate time daily to a group review session for a target objective followed by a hands-on activity reinforcing that objective. Target objectives included factoring, the relationship between a factor and a zero of a polynomial and developing a deep understanding of sine and cosine functions. Engineering PBLs were designed in an interdisciplinary approach leveraging the unique XXX University engineering missions program. Engineering mission programs have been shown to engage a larger percentage of underrepresented students in engineering and provide unique opportunities to engage students with engineering problems. We've used the strengths of the engineering missions program to create project-based learning (PBL) activities in Electrical, Civil, and Mechanical engineering. These PBLs centered around providing clean water access and involve students in addressing the needs of a fictional global partner with a remote clinic. Students explore technical and social challenges and work on solutions while learning fundamental concepts in Electrical, Civil, and Mechanical engineering, including algebra, trigonometry, and precalculus. At the end of the week a culminating final pump prototype system was designed. Results show that over 80% of students placed at least one math course higher after the program. We also compare retention rates and math performance with their peers. At-risk students in the program show significant persistence and better math performance. The data reveals a substantial increase in first-semester math course success for program participants. Students placed into College Algebra, Pre-Calculus, or Trigonometry through the program outperform historical data for engineering students in these courses. Those who continue to Calculus 1 earn about 0.8 higher letter grades than the control group. Ongoing data collection will help assess progress in higher-level math courses like Calculus III and Differential Equations.

Recently Published Dissertations on Community and Junior Colleges

BackgroundMany Indigenous communities in Canada live with high-risk drinking water systems and drinking water advisories and experience health status and water quality below that of the general population. A scoping review of research examining drinking water quality and its relationship to Indigenous health was conducted.ObjectiveThe study was undertaken to identify the extent of the literature, summarize current reports and identify research needs.DesignA scoping review was designed to identify peer-reviewed literature that examined challenges related to drinking water and health in Indigenous communities in Canada. Key search terms were developed and mapped on five bibliographic databases (MEDLINE/PubMED, Web of Knowledge, SciVerse Scopus, Taylor and Francis online journal and Google Scholar). Online searches for grey literature using relevant government websites were completed.ResultsSixteen articles (of 518; 156 bibliographic search engines, 362 grey literature) met criteria for inclusion (contained keywords; publication year 2000–2015; peer-reviewed and from Canada). Studies were quantitative (8), qualitative (5) or mixed (3) and included case, cohort, cross-sectional and participatory designs. In most articles, no definition of “health” was given (14/16), and the primary health issue described was gastrointestinal illness (12/16). Challenges to the study of health and well-being with respect to drinking water in Indigenous communities included irregular funding, remote locations, ethical approval processes, small sample sizes and missing data.ConclusionsResearch on drinking water and health outcomes in Indigenous communities in Canada is limited and occurs on an opportunistic basis. There is a need for more research funding, and inquiry to inform policy decisions for improvements of water quality and health-related outcomes in Indigenous communities. A coordinated network looking at First Nations water and health outcomes, a database to store and create access to research findings, increased funding and time frames for funding, and more decolonizing and community-based participatory research aimed at understanding the relationship between drinking water quality and health outcomes in First Nations communities in Canada are needed.

Access to clean drinking water is crucial for human health, but there are concerns that consumption levels of particular solutes may be linked to negative health outcomes. Many studies use data aggregated to area-level to assess consumption-health associations, but these do not account for differences in behaviour between individuals. Therefore, we combined publicly reported tap water chemistry from compliance data with estimated drinking water consumption within the home calculated from a water habits survey for 1970 UK adults from the TwinsUK cohort. The resulting average daily dose (ADD) estimate of key solutes (including nitrate, hardness, chlorine, selenium), multiple solutes dimensionally reduced to k-means clusters, and ingestion rate (IngR) were used as predictors in nested regression analysis, including stratification for employment status (as a proxy for time spent and home) and adjustment for age. Health outcomes included cardiovascular disease (CVD), CVD risk factors, eczema, sarcopenia, frailty, gastrointestinal disease and cancer. We found estimation of ADD significantly changed the distribution of solutes (ks-tests p<0.001). Overall, we identified few associations with health outcomes, with mixed or inconsistent signals across nested models. There were some exceptions, including increased odds of hardness predicting CVD risk factors in our employment strata (Hardness ADD OR:1.25, 1.09-1.48, p<0.002; age-adjusted OR: 1.22, 1.05-1.4, p<0.002) and eczema negatively associated with IngR in non-stratified models (IngR OR: 0.86, 0.77-0.96, p<0.01). We found no evidence of difference in ADD in twins discordant for health outcome. The lack of significant findings in solute-health pairings could be inferred as a positive result that supports UK drinking water as a safe source of hydration and therefore our results represent a positive public health outcome. Our study demonstrates an effective approach to estimate personalised exposure to water solutes that can inform researchers designing similar studies.

Given the number of chemicals in the environment and people’s variability in exposure and susceptibility to harm, it’s a daunting challenge to catalog all possible drinking water contaminants and assess their associated health risks. But after reviewing the state of the science and the data gaps surrounding drinking water contaminants, a team of authors presents in this issue of EHP an ambitious roadmap to help future studies identify and elucidate risks presented by specific contaminants.1 Although microbial agents are the largest cause of waterborne diseases worldwide,1 chemical contaminants in drinking water have been associated with a broad array of adverse health effects, including cancer, cardiovascular disease, neurological disease, and miscarriage.2 Some contaminants enter water through leaching, accidental spills, runoff, and atmospheric deposition. Others, such as disinfection by-products and lead, are introduced during treatment or even at the tap.3 Contaminants may occur naturally, or they may derive from human-related activities, such as industry, agriculture, and mining. Not only have the prevalence and uses of chemicals escalated in the last century, but the analytical techniques to detect them have become exquisitely sensitive.4,5 Consequently, it is possible to define vanishingly small levels of both well-studied and emerging contaminants in drinking water. The presence of a contaminant does not necessarily translate to an adverse impact on human health; the levels may be unimportant, exposure is not a given, and toxicity may depend on individual susceptibility. Assessing the human health effect of any given chemical requires careful epidemiological and toxicological study, which has not been conducted for most drinking water contaminants.1 Longitudinal cohort studies can help address drinking water data gaps by incorporating water consumption in their design. “The amount that we know about chemicals is really very little,” says Herman Gibb, president of research consultancy Tetra Tech Sciences, who was not involved with the review. “We keep hammering on the same chemicals like arsenic, cadmium, and so forth, but there are so many chemicals that we don’t know much about. And even for the chemicals for which we have relatively good information, we still don’t know enough.” To address the knowledge gaps, the Centre for Research in Environmental Epidemiology (CREAL) in Barcelona organized a workshop in 2012 to discuss the state of the science vis-a-vis chemical contaminants in drinking water and make recommendations for future research. “Having the workshop and writing [this review] has led to some ideas for future collaborations,” says lead author Cristina Villanueva, an associate research professor at CREAL. Ultimately, the authors’ recommendations are intended to provide a template for researching any type of chemical contaminant occurring in drinking water.1 The U.S. Environmental Protection Agency, World Health Organization, and European Union Council together currently regulate more than 120 drinking water contaminants.1 But even regulated chemicals carry some uncertainty because new information requires questioning and possibly revising limits. Emerging chemical contaminants also generate concern because little to nothing is known about their potential health effects, much less the levels at which those would occur. Likewise, contaminant mixtures may pose greater threats than their individual components. The review authors call for specific steps to address the many unknowns. In addition to determining the identity and level of individual contaminants, which will help to prioritize research topics, investigators need information on human exposures, which could be gained through epidemiological study as well as statistical modeling. Ideally, ongoing longitudinal cohort studies would incorporate drinking water consumption in their design, and particular attention would be focused on vulnerable populations, such as children and pregnant women. Information on contaminants’ mechanisms of toxicity and biomarkers of exposure could potentially link exposure with health outcomes.1 Villanueva and her colleagues cite climate change as a major future challenge projected to affect drinking water quality through more frequent extreme weather events and increased growth of toxin-producing cyanobacteria.1 Gibb, who coauthored a 2014 review of data needs related to health effects of chemicals,6 adds that current trends point to increased chemical contamination of the environment, particularly in developing countries. “It’s quite a wish list of things to do,” Gibb says of the Villanueva review. “The focus here is on drinking water, but this really applies to the chemical world in general because there’s so much that we don’t know about how it affects the burden of disease.”

Drinking water quality was investigated at source and corresponding point-of-use in 2 peri-urban areas receiving drinking water either by communal water tanker or by delivery directly from the distribution system to household-based groundtanks with taps. Water quality variables measured were heterotrophic bacteria, total coliforms, E. coli, conductivity, turbidity, pH, and total and residual chlorine. Water quality data were analysed together with an existing epidemiological database to investigate links between microbial quality of drinking water, household demographics, health outcomes, socio-economic status, hygiene and sanitation practices. Groundtank households had better quality drinking water than households using storage containers filled from communal tankers. Uncovered storage containers had the poorest microbial water quality among all storage containers. All stored water did not meet drinking water standards, although mains water did. Households with children under 5 years and using open-topped containers had the poorest water quality overall. Households with groundtanks had the best water quality at point-of-use, but did not have the lowest occurrence of health effects. Although groundtanks were supplied together with urine diversion (UD) toilets and hygiene education, groundtank households showed overall poorer hygiene practices than tanker-supplied households, and some groundtank households with UD toilets preferred to continue using open defecation. Households that practised open defecation had higher levels of E. coli in their drinking water and higher rates of adverse health outcomes. Poorer socio-economic standing and lower educational standard were associated with poorer water quality, poorer hygiene practices and higher rates of diarrhoea and vomiting.Keywords: drinking water; point of use; water quality; water quantity; hygiene; sanitation

Educational institutions face unrelenting pressure to incorporate the latest technology into their classrooms. U.S. higher education has been adopting computers to augment the in-class learning experience. Anecdotally, computers (PC and Mac architectures) and tablet devices (iPads, smartphones, and tablet PCs) have been used in a myriad of settings for interactive polling as means to increase student participation and engagement. To date, other uses of computers and tablet devices have taken hold in project-focused or problem solving-oriented small classes rather than in large lecture classes. Undergraduate mathematics classes seem to be a natural fit for introducing tablet devices as many students find it easier to handwrite mathematical notation than to use a keyboard. This study investigates the impact of a tablet PC implementation in undergraduate college algebra and trigonometry (CAT) on student performance and retention in science, technology, engineering, and mathematics (STEM) majors. This longitudinal project explores the effect of Tablet PC use in an important gateway course for freshmen who intend to major in a STEM field. Five important metrics were assessed: class attendance, class performance, instructor evaluation, retention in STEM, and persistence to graduation. The CAT course was taught by the same instructor as a conventional CAT lecture class from 2005 to 2007 using the same textbook, secure exams, and grading rubric. This structure provides a reasonably well-controlled setting in which to assess the impact of tablet PCs on retention in STEM.

Humanitarian crises, particularly in conflict zones, create cascading disruptions that impact every aspect of daily life, including health and disease outcomes. While international humanitarian frameworks categorize these crises into discrete operational clusters, affected populations experience them as interwoven, systemic failures. This study examines how conflict-induced disruptions transform a preventable and typically self-limiting disease— Hepatitis A—into a fatal outcome in North Gaza. Using a systems approach, we seek to characterize the architecture of interconnected disruptions leading to preventable deaths.This study employed the FAIR (Fairness, Agency, Inclusion, and Representation) Framework, a participatory methodology centering community epistemes, to analyze four pediatric cases of Hepatitis A that progressed to fulminant liver failure. Data were obtained through interviews with healthcare providers, caregivers, and community members, supplemented by medical chart reviews. A network-based Architecture of Systems (AoS) map was constructed to visualize the interconnections between war-induced systemic disruptions and health outcomes. Network analysis was performed to identify key nodes, bottlenecks, and pathways within this system.The findings of this study reveal a complex system of war-driven factors—displacement, destruction of healthcare infrastructure, water scarcity, food deprivation, and fuel blockades— that collectively reshaped disease trajectories. Network analysis of the AoS map identified 138 nodes and 231 edges, generating 41,444 pathways linking conflict-related disruptions to health outcomes. Women’s health emerged as a central mediator, with 95% of pathways intersecting with 13 key nodes related to women’s roles in caregiving, resource acquisition, and psychological stability. The lack of access to food and clean water, combined with the destruction of healthcare facilities and restrictions on medical evacuation, created conditions where a preventable disease became fatal.This study highlights how conflict restructures health determinants, shaping survival strategies that paradoxically increase morbidity and mortality. By documenting the lived experiences of affected communities, our findings underscore the necessity of a systems-based humanitarian response that accounts for the interconnected nature of crises. Recognizing the pivotal role of women in mediating health outcomes is crucial to designing effective interventions in conflict settings.

Review objective The review objective is to synthesise the best available evidence on exposure to chlorinated water and risk of cancer. Risks associated with colorectal or bladder cancers have already been established and therefore will not be considered in this systematic review. Inclusion criteria Types of participants This review will consider studies that include males and females of all ages. Types of intervention(s)/phenomena of interest This review will consider studies that evaluate exposure to chlorine disinfection by-products by drinking (ingesting), bathing, showering, swimming, cooking, cleaning and dishwashing (dermal and inhalation) and identify incidence and mortality outcomes of cancer (excluding colorectal and bladder) compared with exposure without chemical disinfection (chlorine) or alternative disinfection processes. Types of outcomes This review will consider studies that include the following outcome measures. Incidence, mortality and specifically measures of risk between exposure and outcome of cancers with the exception of bowel and bladder. For example the following cancers have been associated with chlorine disinfection by products, kidney/adrenal, liver, thyroid, pituitary, lymphoma and leukaemia, pancreatic, gastrointestinal (other than colorectal), testicular, breast and lung cancer. These and any other cancers identified as relevant eg. skin cancers will be included.

Focuses on the fundamental needs of providing safe drinking water, sanitation, and hygiene (WASH) for poor and vulnerable populations. Globally, the use of improved drinking water sources increased from 1990’s 76 percent to 2015’s 91 percent, and four of five people in urban areas use piped water. Unlike water supply which met its Millennium Development Goal (MDG) in 2010, sanitation as of 2015 has failed to meet its MDG target. Data on handwashing practice globally has become more frequently collected and indicates low usage of soap and water after contact with excreta. Health consequences list diarrheal disease, helminth infections, and undernutrition. Effective interventions include water filtration or disinfection, use of sanitation services and handwashing places, but they rely on behavioral change within a community for full adoption. Cash transfer programs, community-driven development programs, and safety-net programs enhance implementation, and cost-effective results show the benefit of targeting poorer households which find themselves at increased health risk due to lack of clean water and sanitation.

The majority of organizations are competing to survive in this volatile and fierce market environment. Motivation and performance of the employees are essential tools for the success of any organization in the long run. On the one hand, measuring performance is critical to organization's management, as it highlights the evolution and achievement of the organization. On the other hand, there is a positive relationship between employee motivation and organizational effectiveness, reflected in numerous studies. This paper aims to analyze the drivers of employee motivation to high levels of organizational performance. The literature shows that factors such as empowerment and recognition increase employee motivation. If the empowerment and recognition of employees is increased, their motivation to work will also improve, as well as their accomplishments and the organizational performance. Nevertheless, employee dissatisfactions caused by monotonous jobs and pressure from clients, might weaken the organizational performance. Therefore, jobs absenteeism rates may increase and employees might leave the organization to joint competitors that offer better work conditions and higher incentives. Not all individuals are the same, so each one should be motivated using different strategies. For example, one employee may be motivated by higher commission, while another might be motivated by job satisfaction or a better work environment.