Learning and teaching of calculus: performance analysis in a unified system

Parts I and II of the National Board of Medical Examiners (NBME) examination were first offered to graduates of foreign medical schools in 1989 as an alternative to the Foreign Medical Graduate Examination in the Medical Sciences (FMGEMS). This study was designed to determine whether differences in pass rates and scores were related to differences in the populations selecting one or the other examination. (1) Combined pass rates on the FMGEMS and NBME in 1989 and 1990 were compared with pass rates in previous years. (2) The proportion of NBME takers in 1989 was compared with the proportion in 1990. (3) Respective pass rates on the FMGEMS and NBME in the first NBME administration in 1989 were compared with pass rates in 1990. (4) The percentage of repeaters taking the FMGEMS was compared with the percentage taking the NBME in 1989 and 1990. (5) The distribution of repeaters by number of previous takes was compared between the FMGEMS and NBME in 1989 and 1990. (1) Combined pass rates were similar to the pass rates of previous years. (2) The proportion of NBME takers declined in 1990. (3) The pass rates for the FMGEMS were higher in both 1989 and 1990, but the difference in pass rates between the two examinations narrowed in 1990. (4) The percentage of repeaters taking the NBME was high in 1989 and declined in 1990. (5) The number of previous takes among repeaters was higher for the NBME than for the FMGEMS in 1989 and became equal in 1990. Some students probably opted to take the NBME in 1989 in the belief that it might be easier than the FMGEMS, resulting in lower pass rates for the NBME. The NBME pass rates rose in 1990 after the differential pass rates had become public.

Purpose Cognitive screening tools to identify patients at risk for cognitive deficits are frequently used by clinicians who work with aging populations in hearing health care. Although some studies show improvements in performance on cognitive screening exams when hearing loss intervention is provided in the form of a hearing aid or cochlear implant (CI), it is worth examining whether these improvements are attributable to increased auditory access to test items. This study aimed to examine whether performance and pass rate on a cognitive screening measure, the Montréal Cognitive Assessment (MoCA), improve as a result of CI, whether improved performance on auditory-based test items drives changes in MoCA performance, and whether postoperative MoCA performance relates to post-CI speech perception ability. Method Data were collected in adult CI candidates pre-implantation and 6 months postimplantation to examine the effect of intervention on MoCA performance. Participants were 77 CI users between the ages of 55 and 85 years. Participants completed the MoCA, administered audiovisually, and speech perception testing with monosyllabic (CNC) words at both intervals. Results Compared to 31 participants pre-operatively, 45 participants passed the MoCA postoperatively, which was a significant difference in pass rate. An improvement in MoCA scores could be attributed primarily to improvement in the "Delayed Recall" test domain, which was auditory based. Post-CI MoCA performance was related to post-CI CNC speech perception performance. Conclusions Improved performance and pass rates were demonstrated on the traditional MoCA test of cognitive screening from before to 6 months after CI. Improvements could primarily be attributed to better performance on a delayed recall task dependent on auditory access, and post-CI MoCA scores were related to post-CI speech perception abilities. Further studies are needed to investigate the application of cognitive screening tools in patients receiving hearing loss interventions, and these interventions' impact on patients' real-world functioning.

THE ACHIEVEMENT gap receives a lot of attention these days. It is, after all, alleged raison d'etre of No Child Left Behind. It is usually defined as difference between test scores of white students on one hand and those of black and Hispanic students on other. (Asian students almost always get ignored for some reason.) Unfortunately, educators and journalists alike have fallen into trap of reporting changes in pass rates on tests as if they were measures of achievement gap. They are not. At best, passing rates are poor proxies for real measures. The Massachusetts Department of Education; Michael Cohen and Matt Gandal of Achieve, Inc.; David Herszenhorn and Michael Winerip of New York Times; Mayor Michael Bloomberg of New York City; Chancellor Joel Klein of New York City Public Schools; and Achievement Alliance, a consortium of Education Trust, National Council of La Raza, Citizens' Commission on Civil Rights, Just for Kids, Inc., and Business Roundtable, have all reported passing rates as if they were scores. They are not. Consider data from Massachusetts Department of Education, reproduced in Cohen and Gandal's Do Graduation Tests Measure Up? Figure 1 shows passing rates for class of 2003 on Massachusetts Comprehensive Assessment System. On initial administration, when students were 10th-graders, blacks and Hispanics passed at rates far lower than whites: blacks, 37%; Hispanics, 29%; whites, 77%. By sixth retest, passing rates had become much more similar. Cohen and Gandal take these data as showing that the achievement gap closed dramatically. Probably not. Consider following hypothetical data. Hypothetical Data Score Needed to Pass = 60 Pass Average Rate Score Gap Black students, 2004 60% 62 White students, 2004 100% 78 16 Black students, 2005 70% 68 White students, 2005 100% 92 24 Between 2004 and 2005, black students improved both their passing rate (going from 60% to 70%) and their score (from 62 to 78). So far so good. But white students, while not improving their passing rate, improved their score even more, so much that black/white gap in scores (the proper metric) actually increased. There is another problem with conclusions in Massachusetts report. The 10th-graders and 12th-graders are not comparable. Somewhere between freshman and senior years, 18,000 students disappeared from Massachusetts' rolls. Some no doubt moved to other states. But others would have been retained in grade or would have dropped out, perhaps because of failing test. In either case, these low-scoring students are no longer part of class of 2003. Naturally, state officials, who like to brag about students rising to challenge of tests, don't like it when researchers call attention to such dishonest presentation of data, but when Anne Wheelock conducted appropriate analysis of data for Massachusetts for class of 2004, she concluded that state had little reason to brag. She found these passing rates: Class of 2004 Pass Rate All students 74%, not 96% White students 80%, not 98% Black students 59%, not 88% Hispanic students 54%, not 85% Asian students 89%, not 95% Note that gap for final pass rate for class of 2004 is nearly as large as 10th-grade gap was for class of 2003. This is not a trivial case of researchers making statistical mountains out of practical molehills. At least one of journalists cited above knows this. When I presented my hypothetical data to Times' Herszenhorn, he replied, Of course, that's exactly way it works.... We have done some analysis of mean scale scores, enough to know that strong gains in suburbs were masked by looking mostly at who crosses line. …

Operating room (OR) fires are rare but devastating events requiring immediate and effective response. Virtual Reality (VR) simulation training can provide a safe environment for practice of skills in such highly stressful situation. This study assessed interprofessional participants' ability to respond to VR-simulated OR fire scenarios, attitudes, numbers of attempt of the VR simulation do participants need to successfully respond to OR fires and does prior experience, confidence level, or professional role predict the number of attempts needed to demonstrate safety and pass the simulation. 180 surgical team members volunteered to participate in this study at Beth Israel Deaconess Medical Center, Boston, MA. Each participant completed five VR OR simulation trials; the final two trials incorporated AI assistance. Primary outcomes were performance scores, number of attempts needed to pass, and pre- and post-survey results describing participant confidence and experiences. Differences across professional or training role were assessed using chi-square tests and analyses of variance. Differences in pass rates over time were assessed using repeated measures logistic regression. One hundred eighty participants completed simulation testing; 170 (94.4%) completed surveys. Participants included surgeons (17.2%), anesthesiologists (10.0%), allied health professionals (41.7%), and medical trainees (31.1%). Prior to training, 45.4% of participants reported feeling moderately or very confident in their ability to respond to an OR fire. Eight participants (4.4%) responded safely on the first simulation attempt. Forty-three participants (23.9%) passed by the third attempt (VR only); an additional 97 participants (53.9%) passed within the 4-5th attempt (VR with AI assistance). Providers are unprepared to respond to OR fires. VR-based simulation training provides a practical platform for individuals to improve their knowledge and performance in the management of OR fires with a 79% pass rate in our study. A VR AI approach to teaching this essential skill is innovative, feasible, and effective.

To document the timings, frequencies, and outcomes of attempts at certification in internal medicine and the internal medicine subspecialties in the years following residency training for two cohorts of residents. Residents who had completed residency training and had been admitted to an American Board of Internal Medicine (ABIM) certifying examination in 1982 or 1983 were tracked through the ABIM database for five years. A total of 10,568 residents were studied. Of the cohort, 79% were men, 21% were women, 79% were graduates of U.S./Canadian medical schools (USMGs), and 21% were graduates of foreign medical schools (FMGs). Ultimately, 85% of the residents achieved certification in internal medicine. Cumulative pass rates were 87% for men, 81% for women, 92% for USMGs, and 60% for FMGs; rates increased minimally after the second attempt. Most (87%) residents first attempted the internal medicine examination in the year in which training had been completed. Delaying the first examination was associated with lower pass rates. Half of the candidates who had passed the internal medicine examination attempted subspecialty certification. Over all nine subspecialty examinations, the two-cycle cumulative pass rate was 87%. Higher percentages of FMGs than of any other subgroup attempted subspecialty certification. The detailed description extends the body of knowledge about certification in internal medicine and the nine internal medicine subspecialties. Questions are raised, such as why some candidates delay the first internal medicine examination and why some residents never seek certification. Future research could explore these issues as well as explanations for the observed differences in pass rates.

INVESTIGATING FORM COMPARABILITY IN THE IDAHO COMPREHENSIVE LITERACY ASSESSMENT: MATTERS OF FAIRNESS AND TRANSPARENCY

The purpose of the study is to determine the effectiveness of the metacognitive strategies as instructional approaches in teaching and learning of Basic Calculus. A number of 48 students consisting of 24 boys and 24 girls were purposively sampled in this study. Pretest-posttest quasi experimental research design was used which applied t-test and descriptive statistics. Both groups were subject to two instruments that were comprised of problem-solving test (pretest and posttest) and observation guide. Experimental group was taught Basic Calculus using metacognitive strategies while the control group was taught Basic Calculus using traditional teaching strategies. Both groups were subject to a pretest. Class observation was done while the two teaching strategies were applied. In the end, the posttest was administered to both groups to identify the effectiveness of the two teaching strategies. The data gathered were treated using paired sample t-test and independent sample t-test. The results of the study showed that the experimental group had significantly higher posttest scores as compared to control group which proved that metacognitive teaching strategies were more effective in improving the performance and problem-solving skills of the students than the traditional teaching strategies. It was also observed that students who taught using metacognitive strategies helped the students to be extremely engaged in Basic Calculus lessons cognitively, behaviorally, and affectively. The study reveals that the significant increase of the students' learning engagement in Basic Calculus lessons led the students to a corresponding increase in their posttest scores.

Objective IOI-HA response data are conventionally analysed assuming that the ordinal responses have interval-scale properties. This study critically considers this assumption and compares the conventional approach with a method using Item Response Theory (IRT). Design A Bayesian IRT analysis model was implemented and applied to several IOI-HA data sets. Study sample Anonymised IOI-HA responses from 13273 adult users of one or two hearing aids in 11 data sets using the Australian English, Dutch, German and Swedish versions of the IOI-HA. Results The raw ordinal responses to IOI-HA items do not represent values on interval scales. Using the conventional rating sum as an overall score introduces a scale error corresponding to about 10 − 15% of the true standard deviation in the population. Some interesting and statistically credible differences were demonstrated among the included data sets. Conclusions It is questionable to apply conventional statistical measures like mean, variance, t-tests, etc., on the raw IOI-HA ratings. It is recommended to apply only nonparametric statistical test methods for comparisons of IOI-HA results between groups. The scale error can sometimes cause incorrect conclusions when individual results are compared. The IRT approach is recommended for analysis of individual results.

A acelerada expansão do ensino superior no Brasil trouxe para o sistema de ensino indivíduos pertencentes a grupos de menor renda que frequentam cursos noturnos e arcam privadamente com os custos dos estudos. Uma boa parte deles tem idade mais avançada do que usualmente se imagina: não são, a rigor, estudantes que trabalham, mas trabalhadores que estudam. Neste artigo a suposição usual de que a educação superior deva conduzir os indivíduos a nichos ocupacionais de maior qualificação formal é invertida, em favor da ideia de que são as condições do mercado de trabalho e a inserção ocupacional já conquistada pelos indivíduos o que dá sustentação ao esforço de voltar a estudar em busca do diploma superior.

El presente trabajo constituye un resumen de la tesis doctoral, “Proceso de enseñanza – aprendizaje de la integral definida como el área bajo una curva en las asignaturas de Cálculo en las carreras de Ingeniería. Estudio realizado en la Facultad Regional Multidisciplinaria, Estelí. (FAREM – Estelí)”. El campo científico en el que está ubicado este estudio es la Didáctica de la Matemática, dentro de las líneas de investigación de la Calidad Educativa. El propósito de la investigación fue desarrollar el campo conceptual del Cálculo y su enseñanza aprendizaje, considerando dos aspectos principales: Un primer aspecto, de ámbito cognitivo mediante el cual se preparó material curricular con el objetivo de introducir previamente al estudio del cálculo de primitivas, el concepto de Integral Definida como área bajo una curva, desde una perspectiva gráfica y numérica. El segundo aspecto, de ámbito afectivo consistió en analizar las actitudes de los estudiantes en torno a confianza, seguridad, motivación, compromiso y uso de la computadora en el trabajo matemático. Los estudiantes fueron seleccionados de los cursantes de la asignatura Cálculo Diferencial e Integral en Ingeniería Ambiental e Ingeniería en Energías Renovables. Se concluye que, la elaboración de un compendio es un instrumento útil en la enseñanza y aprendizaje del Cálculo; y, en relación a las actitudes se tiene que, el uso de la computadora da confianza y seguridad, además de ser motivante y compromete al estudiante en la realización de actividades matemáticas.

We offer an analysis of calculus assessment items that highlights ways to evaluate students’ application of important meanings and support their engagement in generative ways of reasoning. Our central aim is to identify characteristics of items that require students to apply their understanding of key ideas. We coordinate this analysis of assessment items with a discussion of relevant findings from research on the teaching and learning of calculus, emphasizing the importance of promoting students’ engagement in quantitative and covariational reasoning. We conclude with a broader commentary on the importance of instructors attending to students’ meanings in their teaching, and offer suggestions for flexibly introducing these items as part of formative assessments throughout the life of a calculus course.

Advantages and disadvantages of the use of Digital Technologies (DT) and especially of Computer Algebra Systems (CAS) in mathematics lessons are worldwide discussed controversially. Many empirical studies show the benefit of the use of DT in classrooms and there are also many useful examples concerning their use. However, despite these inspiring results and the countless ideas, classroom suggestions, lesson plans and research reports, the use of DT—and especially CAS—has not succeeded, as many had expected during the last decades see Hoyles & Lagrange, (2010). The thesis of this article is that we have not been able to convince teachers, lecturers at university and parents of the benefit of CAS in the classrooms in a sufficient way. What are the arguments that justify the use of CAS in the classroom? The article gives examples of a fruitful use of CAS with regard to the generally accepted goals or standards of mathematics education—like fostering students’ abilities in problem solving, modelling, proving or communicating—and to the subjects taught in high school. The basis of the argumentation is a competence model which classifies the relation between contents or topics: sequences and limits, functions and equations; representations of DT or CAS: static isolated, static multiple, dynamic isolated and dynamic multiple representations; and classroom activities: calculate, consult, control, communicate and discover.

The study investigated detecting differential item functioning using item response theory in West African Senior School Certificate English language test in south-south Nigeria. 2 research questions were formulated to guide the study. Using descriptive research survey design for the study, study population was 117845 Senior Secondary 3 students in Edo, Delta, Rivers and Bayelsa state. A sample of 1309 (604 males, 705 females) drawn through multi stage sampling technique was used for the study. Two valid instruments titled: Socio-economic status questionnaire (SSQ) and WASSCE/SSCE English language objective test (ELOT) were used to collect data for the study. The reliability indices of the instruments were estimated using the Cronbach Alpha method of internal consistency and Richard Kuderson 20 with coefficient values of .84 for the English Language objective test and .71 for the socio-economic status questionnaire respectively. Chi-square and Lord Wald test statistics statistical technique employed by Item Response Theory for Patient Reported Outcome (IRTPRO) was the technique used in data analysis which provided answers to the research questions at.05 level of significance. On analysis, the result revealed that 13 items functioned differently significant between the male and female group and significantly 23 items differentially functioned between High and low socio-economic status group. Thus, this shows 18% DIF based on gender and 32% based on socio-economic status indicating large DIF and items that are potentially biased. Based on the findings, recommendation were made and one among others was that Item Response theory should be used as DIF detection method by large scale public examination and test developers.

11.1 Toward an Optimized Version of the Positive and Negative Syndrome Scale (PANSS) for Pediatric Trials

The experimental design was conducted to investigate the use of Microsoft Mathematics, free software made by Microsoft Corporation, in teaching and learning Calculus. This paper reports results from experimental study details on implementation of Microsoft Mathematics in Calculus, students’ achievement and the effects of the use of Microsoft Mathematics on students’ attitudes in relation to such experience. Two classes of the students from the first year student in Universitas Serang Raya were participated in the study. This study found that students who taught by using Microsoft Mathematics had higher achievement and has a positive effect on students’ confidence of mathematics.Keywords: Calculus, Educational Technology, Mathematics Education, Microsoft Mathematics, Technology Application DOI: dx.doi.org/10.22342/jme.61.63