Secondary Calculus Research Articles

Presenting a New Model to Support the Secondary-Tertiary Transition to College Calculus

Although the secondary-tertiary transition has been investigated in mathematics education research with different focuses and theoretical approaches, it remains a major issue for students in the transition. With success in a science, technology, engineering, or mathematics (STEM) major at stake, we investigated a novel approach to support the transition from secondary precalculus or calculus to tertiary calculus. Using the Four Component Instructional Design (4C/ID) model and empirical data from the United States (US) nationally representative FICSMath project, we mapped instructional experiences of students in the transition to theoretical components of the 4C/ID model. From exploratory factor analysis (n=6,140), we found six factors that mapped to the 4C/ID model components and created the new Secondary Precalculus Calculus (SPC) 4C/ID model. In this model, the Learning Task Component represents tasks to engage learners in meaningful problem solving; the Support Component grounds instruction in reasoning and understanding; the Procedure Component integrates group work and graphing calculators to connect concepts to procedures; and the Part-Task Component represents instruction to develop automaticity. The SPC 4C/ID model presents a unique support for precalculus and calculus teachers in the quest of teaching for learning and transfer of learning across the transition.

Intravesical Migration of the Longest Forgotten Intrauterine Contraceptive Device with Secondary Vesicolithiasis in a 70-Year-Old Female: A Rare Case Report

Intrauterine Contraceptive Device (IUCD) is the most common method of contraception due to its low cost and reversibility. Longstanding IUCD’s can cause complications like menorrhagia, chronic pelvic pain, perforation of uterus and migration into adjacent structures as pouch of douglas, rectum or bladder. The Copper T acts as a foreign body and its presence for a long time causes secondary stone formation in bladder. Most of the cases in literature have been managed with open surgery. The author reports a case of a 70-year-old female presenting with transmigration of a forgotten Copper T into bladder with secondary calculus formation. The unique features of the presented case were the age of the patient, the longest duration of the forgotten Copper T (31 years) and the successful removal of both the calculi and Copper T device using an endoscopic approach.

Various Foreign Bodies Causing Bladder Stones in Females: The Lessons Learnt

Background: Bladder stones are common in males but not so common in females. They account for nearly 5% of the urinary system stone disease. We here share our journey of bladder calculi in female patients and will let you know various foreign bodies that can cause bladder calculus, various treatment modalities that exist to treat them and the lessons that we learnt. Methods: We did a retrospective study from August 2016 to July 2020 at SMBT IMS & RC, Nashik. A total nine patients were included out of the total twentythree bladder stone patients. Diagnostic investigations included X-ray of kidney, ureter and bladder region, ultrasonography of abdomen and pelvis, computed tomography and if needed, cystoscopy before every planned surgical procedure. Results: Nine patients of complicated bladder stone with or without foreign body were treated in the study. Two patients required open surgery. Six patients underwent per urethral cystolithotripsy for their stones and one patient underwent suprapubic percutaneous cystolithotripsy. Psychiatric evaluation was done for one patient. Clean intermittent catheterisation was advised for the neurogenic bladder patient. Conclusion: To find and treat a bladder stone in a female patient is much easy as compared to find out the cause of that stone. The reason being the rarity of bladder calculus in females, more so the secondary calculus. Therefore, whenever you find a bladder calculus in female patient you should find out the cause by taking prior proper history, doing proper clinical examination, ordering relevant investigations and treating them as per the current strategies. Keywords: Bladder calculus females; Foreign body; Calculus over foreign body; Giant bladder calculus; Fragmented D J stent.

PEDAGOGY OF CALCULUS IN INDIA: AN EMPIRICAL INVESTIGATION

When students learn a calculus construct, both a concept image as well as a concept definition is imprinted in their mind, and because of it, concrete and real-life examples become a prerequisite for a contextually rich learning environment for the abstractions inherently present in calculus. In the light of aforementioned propositions, the current study focusses on delving into several issues, few of the prominent ones include the epistemological nature of calculus curriculum in India’s senior-secondary schools, role of Indian calculus teachers in students’ cognition, possibility of enumeration of characteristics of a successful calculus teacher with regards to India’s socio-cultural milieu, challenges regarding complete immersion of calculus in manipulation of symbols that eventually give rise to cognitive obstacles, interrelationship between teachers’ calculus content knowledge and their pedagogical practices, effect of secondary school calculus on performance of Indian students’ college calculus, and the nature of effect on Indian learners having calculus in school on their procedural and conceptual performance. For this extensive study, data were collected from PGTs and Assistant/Associate Professors having more than 8 years of calculus teaching experience drawn from 76 different schools, colleges and universities belonging to 23 different states and union territories of India. A total of 323 teachers took part in this study. Multiple methods of data collection were used including naturalistic observation, structured interviews, classroom observations, focussed group interviews, and informal discussions, and these were done both before and after the classroom teaching. The researcher transcribed the interviews, identified emerging and repeated themes, and used NVivo and Concordance software to conduct content and classroom discourse analysis, with simple counting methods and applied grounded theory approach using which empirical data were thematically categorized and in the process of it, employed the induction approach. The researcher analyzed the transcripts using N5 (NUD*IST 5.0; QSR International, Melbourne) with the grounded theory approach. This research study is purely qualitative in nature and its framework lies within the interpretative paradigm. The current study was carried out between June 2016 and March 2019. Findings indicate that there are lots of cognitive obstacles in understanding the concepts inbuilt in calculus: two of the prominent ones that came out from the study include the one related to intuitions and the other related to linguistic/representational aspects.

Secondary Vesical Calculus caused by Transmigration of Intrauterine Device: A Case Report

Secondary Vesical Calculus caused by Transmigration of Intrauterine Device: A Case Report

Congenital Diverticulum at the Proximal Part of Penile Urethra with Secondary Calculus

Voiding dysfunction and lower urinary tract symptoms (LUTS) in children due to congenital anomalies of urogenital system is common, but congenital anterior urethral diverticulum (CAUD) in male is very rare. Sometimes the problem is associated with anterior urethral valve. CAUD with secondary stone is rare. Here we report a case of a 12-year-old male child with obstructive symptoms. It was treated by excision of diverticulum, removal of stone and primary repair.J Enam Med Col 2017; 7(3): 162-164

Intravesical Migration of an Intrauterine Contraceptive Device with Secondary Calculus Formation.

Intrauterine contraceptive devices (IUCDs) are a common form of reversible contraception owing to fewer systemic side effects and low cost, especially in a developing country like India. However, IUCDs are not without complications. Migration of a device into adjacent organs is the most morbid of all the documented complications. A patient who presents with a history that suggests loss or disappearance of an IUCD thread associated with urinary symptoms should raise suspicions that a device may have migrated into the bladder. Physicians should also be aware of possible secondary vesical calculus formation. Further radiological investigations and appropriate management are warranted. We present a case report describing the migration of an IUCD into the bladder with secondary calculus formation.

Unusual Complication of Intrauterine Contraceptive Device

ABSTRACT Intrauterine foreign bodies have been used in animals as a contraceptive since times immemorial. The use of pebbles in camels as a contraceptive has been reported in Arabs. Intrauterine contraceptive devices (IUCDs) have been used since 1962 when the first International Conference of Population Council, New York reported encouraging data on Margulies coil and Lippes loop as IUCDs. According to the World Health Organization, IUCDs are the second most widely used reversible contraceptive method after voluntary female sterilization. Intrauterine contraceptive devices have undergone extensive evolution from Grafenberg ring to Ota ring, Margulies coil, Lippes loop, Birnberg bows, Saf T-coil followed by Cu T 200, Cu 7, Multiload Cu 250/375, Cu T 380 Ag, Cu T 380 S [slimline]. Hormonereleasing IUCDs were developed in 1973. Ombrelle 250/380 and FlexiGard are the latest in this series. The common complications encountered with IUCD insertion are pelvic infections, infertility, the risk of both intrauterine and extrauterine pregnancy, pain, altered bleeding pattern, expulsion of the device, and its migration. Migration of IUCD into the bladder has been rarely reported in the literature. The authors report an unusual case of a secondary vesical calculus formed around a migrated IUCD. How to cite this article Agarwal N, Agarwal BK. Unusual Complication of Intrauterine Contraceptive Device. J South Asian Feder Obst Gynae 2016;8(3):243-245.

Bladder calculus resulting from an intravesical translocation of intrauterine contraceptive device in a postmenopausal woman

Although perforation of the uterus by an intrauterine contraceptive device (IUCD) is commonly encountered, intravesical translocation and secondary calculus formation is a very rare complication. We report a case of a 60-year old multiparous woman in whom an intrauterine contraceptive Copper-T device inserted 12 years earlier translocated from the uterus to the bladder and resulted in formation of a calculus. Diagnosis was established with pelvic ultrasonography and plain abdominal radiograph. The cystoscopic removal was not successful due to the large size of the calculus. The patient later underwent cystolithotomy. Sonographic follow-up immediately after the insertion and at six month intervals will go a long way in early detection of any possible complications.

A female patient with urethral calculus presenting with bladder distention: A case report

Urethral calculi are extremely rare, especially in female patients, and usually associated with genitourinary tract abnormalities such as urethral stricture or diverticulum. Primary calculus of the urethra is very rare and usually associated with congenital diverticulum. Secondary urethral calculus, often originate from the kidney or bladder. However, primary calculus of the urethra is very rare and is usually associated with congenital diverticulum. Diagnosis of urethral calculus is difficult due to location, and failure of the diagnosis may cause urethral injury, incontinence or renal insufficiency. Herein, we report the computed tomography, clinical and surgical findings of a urethral calculus in a female patient without any urogenital anomaly.

Enhancing Students’ Understanding in Integral Calculus through the Integration of Maple in Learning

Students entering engineering and engineering technology courses at the university are expected to be competent in mathematics. This is due to the fact that mathematics, including calculus is a primary gateway to an engineering and engineering technology careers. However, the issue of under preparedness of students with diversity in mathematics background enrolling these two courses is at an alarming rate. One factor which can be improved to minimize this gap is to enhance the teaching technique of the subject. With the evolution of various forms of technology, a new approach of teaching integral calculus was developed in this study. Accordingly, this paper discusses the process of integrating Maple software in the teaching of the first year integral calculus topic. In addition, this paper also discusses how this approach can help to deepen the engineering technology students’ understanding in integral calculus topic at the university. Two groups of Technical Mathematics 2 with various mathematics backgrounds were randomly chosen to undergo the treatment. As an initial measurement, a pre-test on integral calculus was administered to these students to check their integral calculus background. The highest mark for the test was far below the passing mark, indicates that students involved in this study have a minimum understanding in secondary school integral calculus. These students were exposed to the treatment for five weeks. At the end of the treatment a post-test was administered to see the effect of the treatment on students’ understanding in integral calculus. Students in the experimental group were found to outperform their peers in the control group in both constructs investigated in this study. The effectiveness of the use of the technology in learning this topic may be enhanced further if its prerequisite topics were also exposed to the same strategy.

Bladder Calculus Secondary to Migrated Intra-Uterine Contraceptive Device

Intrauterine contraceptive device (IUCD) is currently one of the most popular reversible contraception method used world wide. Since its introduction, many complications have been reported with IUCD which include dysmenorrhoea, menorrhagia, pelvic infection, pregnancy, uterine perforation and migration into adjacent organs [1]. Migration of the IUCD into the bladder has been rarely reported in the literature [2–4]. The authors report an unusual case of a secondary vesical calculus formed around a migrated IUCD found 22 years following insertion of IUCD.

Secondary Vesical Calculus Resulting from Migration of an Intrauterine Contraceptive Device

Intrauterine contraceptive device (IUCD) is the commonest form of contraception used in view of less systemic side effects. However, there are a multitude of local complications caused by it. Of all the local complications described, migration of the device into adjacent organs is the most morbid of all complications. A patient presenting with history of loss or disappearance of the intrauterine contraceptive device accompanied by urinary symptoms should raise the doubt of a migrated device with the formation of a secondary calculus. This prompts further radiological investigations and merits surgical intervention either endourologically or by open surgery depending upon the merits of the case. A case report elucidating this fact is presented.

Histories and observables in covariant field theory

Motivated by DeWitt’s viewpoint of covariant field theory, we define a general notion of a non-local classical observable that applies to many physical Lagrangian systems (with bosonic and fermionic variables), by using methods that are now standard in algebraic geometry. We review the methods of local functional calculus, as they are presented by Beilinson and Drinfeld, and relate them to our construction. We partially explain the relation of these with Vinogradov’s secondary calculus. The methods present here are all necessary to understand mathematically properly, and with simple notions, the full renormalization of the standard model, based on functional integral methods. Our approach is close in spirit to non-perturbative methods since we work with actual functions on spaces of fields, and not only formal power series. This article can be seen as an introduction to well-grounded classical physical mathematics, and as a good starting point to study quantum physical mathematics, which make frequent use of non-local functionals, like for example in the computation of Wilson’s effective action. We finish by describing briefly a coordinate-free approach to the classical Batalin–Vilkovisky formalism for general gauge theories, in the language of homotopical geometry.

Assessment on Previous Course Work in Calculus and Subsequent Achievement in Calculus at the Post-Secondary Level

Abstract There is limited research examining the effect of antecedent work in calculus and subsequent achievement in post-secondary calculus. This study examines the effects of prior coursework in calculus, often a locally developed secondary school calculus class, and ensuing achievement in a first-year university calculus class. Analysis of covariance confirms that students who had successfully completed antecedent course work in calculus are achieving higher final grades than their equally capable peers, even after gender differences and prior achievement are accounted for in the ANCOVA model. Sequential linear regression results substantiate the significance of antecedent coursework as a predictor of final grades.

Secondary calculus and the covariant phase space

The covariant phase space of a lagrangian field theory is the solution space of the associated Euler–Lagrange equations. It is, in principle, a nice environment for covariant quantization of a lagrangian field theory. Indeed, it is manifestly covariant and possesses a canonical (functional) “presymplectic structure” ω (as first noticed by Zuckerman in 1986) whose degeneracy (functional) distribution is naturally interpreted as the Lie algebra of gauge transformations. We propose a fully rigorous approach to the covariant phase space in the framework of jet spaces and (A. M. Vinogradov’s) secondary calculus. In particular, we describe the degeneracy distribution of ω . As a byproduct we rederive the existence of a Lie bracket among gauge invariant functions on the covariant phase space.

Secondary Ureteropelvic Junction Obstruction and Renal Calculus after Failed Open Pyeloplasty: Laparoscopic Management

Secondary Ureteropelvic Junction Obstruction and Renal Calculus after Failed Open Pyeloplasty: Laparoscopic Management

Migrated Urethral Catheter In The Urinary Bladder Forming A Stone And Presenting As Recurrent Urinary Tract Infections

A secondary vesical calculus develops in the presence of outflow obstruction, infection or in the presence of a foreign body. A 19-year-old Hindu male, manual laborer by occupation and resident of an urban slum, presented to the surgery OPD with one year old complaints of suprapubic pain, frequency of passing urine, low grade hematuria, fever and passage of foul smelling urine with pus for the past 6 months. History revealed retention of urine one year before. The patient went to seek the advice of a local practitioner, who inserted a hollow tube transurethrally. Urine culture revealed E.coli in significant levels sensitive to Cefotaxime and Norfloxacin. A plain X-ray KUB showed a mass suggestive of a single bladder calculus. On detailed examination of the stone, a secondary calculus appeared developed over a mass of coiled tube. The stone was removed via suprapubic cystostomy. INTRODUCTION A secondary vesical calculus develops in the presence of outflow obstruction, infection or in the presence of a foreign body. Presenting features include suprapubic pain, dysuria, frequency of micturition and hematuria. Diagnosis is by a plain X-ray KUB or an ultrasonography, which shows a radiolucent shadow changing position with patient movement. Treatment is by endourological procedures or a suprapubic cystotomy if the stone is large (size greater than 3 cm).1 CASE REPORT A 19-year-old Hindu male, manual labor by occupation and resident of an urban slum, presented to the surgery OPD with complaints of Suprapubic pain for the past 1 year Frequency of passing urine for the past 1 year Hematuria for the past 1 year Fever, low grade, off and on for the past 1 year Passage of foul smelling urine with pus for the past 6 months On taking a detailed history, it was recorded that the patient had an episode of severe suprapubic pain, dysuria and a sudden onset of retention of urine 1 year before. The patient went to seek the advice of a local practitioner, who inserted a hollow tube transurethrally by which urine was drained. The patient was also given oral medication. The patient did not pay heed to the hollow tube and did not have any other episode of retention. He did not note what happened to the tube after that. There is no history suggestive of tuberculosis or diabetes mellitus. Since then the patient had the above symptoms repeatedly and was treated by a local practitioner. A general physical examination did not reveal any abnormality except pallor. On per abdomen examination there was suprapubic tenderness. Urine culture revealed E.coli in significant levels sensitive to Cefotaxime and Norfloxacin. Hemoglobin was 8.6gm% and TLC was 12500/cu mm. A plain X-ray KUB revealed a mass suggestive of a single bladder calculus. Blood sugar, blood urea and serum creatinine were normal. Preanesthetic investigations were done and the stone was removed via suprapubic cystotomy. Intravenous Cefotaxime was given to the patient for 5 days. Postoperatively, the patient was also given Norfloxacin for 5 days. The stitches were removed on day 8 and the patient was discharged. When the patient reported for follow-up 3 months later, he was asymptomatic Migrated Urethral Catheter In The Urinary Bladder Forming A Stone And Presenting As Recurrent Urinary Tract Infections 2 of 3 and urine culture was sterile. On detailed examination, the stone appeared as a secondary calculus developing over a mass of coiled tube shown in figure 1. Figure 1 Figure 1: Photograph of specimen removed from the bladder DISCUSSION Recurrent urinary tract infection is uncommon in males and usually occurs due to an abnormality of the urinary tract, stricture or foreign body1. In our case, a hollow tube was inserted which migrated into the bladder, with the patient unaware. A foreign body in the bladder has been documented as a cause of recurrent urinary tract infection2. A detailed history and a high index of suspicion help to arrive at the diagnosis. Plain X-ray KUB and ultrasonography confirm diagnosis. Antibiotic therapy should be guided by culture and sensitivity.

Operational calculus in differential algebras*

Outlines of operational calculus i.e., techniques, reducing the solution of linear differential equations with constant coefficients to the solution of appropriate algebraic systems of linear equations, in differential algebras are described. It is shown that in the classical differential algebra such techniques cannot be realized, because of the lack of non-trivial exponentials. At the same time, the differential Lie algebra of vertical derivations, possesses a full spectrum of exponentials, and the corresponding operational calculus (secondary operational calculus )is developed.*

From symmetries of partial differential equations towards secondary (“quantized”) calculus

Diffieties are analogues of algebraic varieties for partial differential equations. They are a kind of (generally, infinite-dimensional) manifolds supplied with an infinite-order contact structure. Secondary, or more speculatively, “quantized” calculus arises as a sort of differential calculus over filtered smooth function algebras on diffieties that respects the contact structure. This paper, written as an informal introduction and invitation to Secondary Calculus, is an account of the author's attempt to understand what should be the analogue of the Schrödinger equation for quantum field theory. So, more attention is paid to motivations than to exact constructions and formulas.