Search

As calculus instruction moves further from lecture-based instruction toward student-centered pedagogy, support services must align with the changing goals for the course. This paper describes the work of a department as they collectively design and redesign a co-requisite Calculus I course, in an effort to better promote students' academic and social integration into active, student-centered calculus classrooms. We highlight the inclusion of more cognitively demanding and group-worthy tasks, re-negotiation of support for procedures and fundamental concepts, and promotion of collaborative participation. Our discussion is supplemented with reflections from faculty, graduate student instructors, and students. [ABSTRACT FROM AUTHOR]

This case study examines how online mathematics homework impacts student learning, attitude, and efficacy in a college Calculus I class. This research is important because it provides data on student perceptions for how to effectively implement online homework. Participants for this study completed homework using a blend of online and paper formats. We use a mixed methods approach to analyze quantitative survey data and qualitative data collected in focus groups and interviews. Our findings indicate students benefited from using a combination of paper homework and online homework. Recommendations are made for how instructors can utilize the benefits of both approaches to support student learning, attitude, and efficacy. [ABSTRACT FROM AUTHOR]

In the article 'How long is my toilet roll-a simple exercise in mathematical modelling' several models of increasing complexity are introduced and solved to calculate indirectly the length of paper on a toilet-roll. All these results are presented without errors. The authors of this comment believe the error analysis of measurements made in a laboratory is an important part of the experiment. The calculation of the absolute errors in indirect measurements provides us with information about the confidence that we must have in our experimental results. For that reason, the error calculation for all approximations has been made. [ABSTRACT FROM AUTHOR]

This editorial provides an introduction to the special issue, Infusing active learning into precalculus and calculus courses: Insights and lessons learned from mathematics departments in the process of change. We begin with providing the background for the special issue, including an overview of the current status of active learning in precalculus through calculus, what many of the papers in this issue mean by the term "active learning" (inquiry based mathematics education), and a brief overview of the literature on institutional change. We then offer an overview of each of the three issues, explaining how various papers relate to each other within each issue. We conclude the editorial with some reflections on the institutional changes efforts in light of the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to recognize a continuous function from its graph. To help mitigate this problem, these visuals can be used alongside the definitions in analysis courses, and in calculus courses where the same definitions are used. The content is arranged into a series of pictures accompanied by questions, with suggestions for the instructor on how to guide students in their learning. The design allows students to make their own discoveries and connections. The investigations crescendo to a surprising fact: that almost all continuous functions are differentiable nowhere! [ABSTRACT FROM AUTHOR]

Texas A&M University-Commerce has implemented supplemental instruction (SI) for Calculus since the fall of 2013. A direct display of the ABC rates from fall 2005 to spring 2021 only presents fluctuation from semester to semester, and one can hardly deduce that the ABC rates are increasing. In this paper, the "moving average" technique is used to reveal the effectiveness of SI in improving the percentage of students earning a grade of A, B, or C (ABC rates) in Calculus. Our longitudinal data under the "moving average" also shows that the SI implementation increased the ABC rates of major ethnic groups. [ABSTRACT FROM AUTHOR]

In this note we describe the mathematics that emerges from the construction of an origami box. We first construct a simple origami box from two rectangular sheets and then discuss some of the mathematical questions that arise in the context of algebra, geometry and calculus. [ABSTRACT FROM AUTHOR]

George Berkeley is known as "The Good Bishop," a name celebrating his faith, pastoral ministry and earnest commitment to his philosophical views. To mathematicians, he is known for his agitated performance in his 1734 critique of fluxions, The Analyst. That work and its petulant tone were occasioned by (i) his "philo-mathematical" opponents' alleged admonitions on religious mysteries' lack of logical respectability and (ii) what Berkeley saw as a related public appetite for reformist and deist religious movements. This paper questions Berkeley's saintly reputation by outlining the hostility and flippancy in his handling of Jacob Walton's contributions to the debate. Berkeley's interactions with Walton bear many of the hallmarks of contemporary "trolling" culture and this paper emphasises and explains these parallels. Finally, given Berkeley's theological and political agenda in his mathematical interactions, I argue that we should not read his mathematical rhetoric as straightforwardly representing his philosophical views. [ABSTRACT FROM AUTHOR]

This study is framed within the anthropological theory of the didactic. The first part is a comparative study of the mathematical organisation of concave/convex functions on the one hand at university, and on the other hand in secondary education. Data for this analysis are from a university textbook on calculus and a secondary school textbook. The analytic results show how the mathematics (to be) taught at secondary level consists of a largely demathematised logos block. The corresponding institutional fragmentation of knowledge reveals a missing praxeological organisation from which the organisations of knowledge we consider in this paper could be derived by transposition. Responding to this insight, in the second part of the paper, we have outlined what we call an archeorganisation for concave/convex functions, a framework that teacher education institutions could refer to when trying to satisfy the specific constraints they are subjected to (notably because of its publics), without for that matter isolating themselves epistemically from other academic institutions. Formulating an archeorganisation represents a meta-curricular study, with the objective of transforming the institutional conditions and constraints that guide mathematics educators and curriculum designers in their deliberations about the concept of concave/convex functions. [ABSTRACT FROM AUTHOR]

In this paper, we present the analysis of the students' achievements in learning calculus in a dynamic software environment during the Covid19 crisis. Two groups of students, the experimental and the control one, were monitored. Blended learning was applied to the students in the experimental group, with the help of Microsoft Teams and dynamic software GeoGebra, in autumn 2020. All students in the control group learned in the classroom without using GeoGebra in 2019. The comparison between these two groups of first-year students, regarding their calculus test results, is described in this paper. It is interesting that the results of the experimental group were significantly better than the results of students in the control group, despite the fact that the students from the experimental group learned during the Covid19 crisis. [ABSTRACT FROM AUTHOR]

As educational systems move from onsite to online due to the COVID-19 pandemic, teachers face the difficulty of designing online examination formats which minimize opportunities for dishonesty. In this paper, we expose our design of such a format: a protected Microsoft Excel spreadsheet containing short-answer questions, which was implemented in a calculus module taught by us. This format allows examiners to randomize questions with the aim that each student receives each question with different numerical details, making plagiarism impossible, while keeping the marking effort very low. [ABSTRACT FROM AUTHOR]

Quasi-Nelson logic (QNL) was recently introduced as a common generalisation of intuitionistic logic and Nelson's constructive logic with strong negation. Viewed as a substructural logic, QNL is the axiomatic extension of the Full Lambek Calculus with Exchange and Weakening by the Nelson axiom, and its algebraic counterpart is a variety of residuated lattices called quasi-Nelson algebras. Nelson's logic, in turn, may be obtained as the axiomatic extension of QNL by the double negation (or involutivity) axiom, and intuitionistic logic as the extension of QNL by the contraction axiom. A recent series of papers by the author and collaborators initiated the study of fragments of QNL, which correspond to subreducts of quasi-Nelson algebras. In the present paper we focus on fragments that contain the connectives forming a residuated pair (the monoid conjunction and the so-called strong Nelson implication), these being the most interesting ones from a substructural logic perspective. We provide quasi-equational (whenever possible, equational) axiomatisations for the corresponding classes of algebras, obtain twist representations for them, study their congruence properties and take a look at a few notable subvarieties. Our results specialise to the involutive case, yielding characterisations of the corresponding fragments of Nelson's logic and their algebraic counterparts. [ABSTRACT FROM AUTHOR]

Given a structural set ψ ⊂ H , some papers [M. Shapiro, V. Vasilevski, (Complex Var Theory Appl. 1995;27:17–46 and 1995;27:67–96)] study the quaternionic ψ-Fueter operator calculus, where the Fueter-type operator is ψ D = ∑ i = 0 3 ψ i ∂ ∂ x i . The aim of this paper is to present the function theory and the Bergman theory induced by the ψ-Fueter-type operator: α ψ D [ f ] = α f + ψ D [ f ] , where a is a quaternionic constant and f is a continuously differentiable function. Particularly, this work shows the Stokes and Borel–Pompieu formulas associated to α ψ D and presents several results of the Bergman theory such as the existence of the Bergman kernel, Bergman projection and their conformal covariant properties. [ABSTRACT FROM AUTHOR]

Given a set H of functions defined on a set X, á function f : X ↦ R ¯ is called abstract H -convex if it is the upper envelope of its H -minorants, i.e. such its minorants which belong to the set H ; and f is called regularly abstract H -convex if it is the upper envelope of its maximal (with respect to the pointwise ordering) H -minorants. In the paper we first present the basic notions of (regular) H -convexity for the case when H is an abstract set of functions. For this abstract case a general sufficient condition based on Zorn's lemma for a H -convex function to be regularly H -convex is formulated. The goal of the paper is to study the particular class of regularly H -convex functions, when H is the set L C ˆ (X , R) of real-valued Lipschitz continuous classically concave functions defined on a real normed space X. For an extended-real-valued function f : X ↦ R ¯ to be L C ˆ -convex it is necessary and sufficient that f be lower semicontinuous and bounded from below by a Lipschitz continuous function; moreover, each L C ˆ -convex function is regularly L C ˆ -convex as well. We focus on L C ˆ -subdifferentiability of functions at a given point. We prove that the set of points at which an L C ˆ -convex function is L C ˆ -subdifferentiable is dense in its effective domain. This result extends the well-known classical Brøndsted-Rockafellar theorem on the existence of the subdifferential for convex lower semicontinuous functions to the more wide class of lower semicontinuous functions. Using the subset L C ˆ θ of the set L C ˆ consisting of such Lipschitz continuous concave functions that vanish at the origin we introduce the notions of L C ˆ θ -subgradient and L C ˆ θ -subdifferential of a function at a point which generalize the corresponding notions of the classical convex analysis. Some properties and simple calculus rules for L C ˆ θ -subdifferentials as well as L C ˆ θ -subdifferential conditions for global extremum points are established. Symmetric notions of abstract L C ˇ -concavity and L C ˇ -superdifferentiability of functions where L C ˇ := L C ˇ (X , R) is the set of Lipschitz continuous convex functions are also considered. [ABSTRACT FROM AUTHOR]

Competence in fractions is important in achieving advanced mathematics such as algebra and calculus. To foster students' understanding of fractions, intervention studies have found number lines to be an effective representational tool. Yet, it is unclear whether or not number lines are equally effective regardless of the ways in which they are implemented. The present study compared two ways in which number lines were used to teach fourth graders fraction magnitudes. One was an iPad digital game and the other was a paper-and-pencil workbook. The students in the digital-game condition played the game on their own whereas those in the workbook condition received one-on-one tutoring. Taking part in just four lessons, both groups improved their fraction knowledge compared to the control group. The current findings confirm that number lines are an effective representational tool. The results further suggest that number lines – when implemented as a digital game or in a workbook – are on the average equally effective in improving students' fraction knowledge. Implications for classroom instruction are discussed. [ABSTRACT FROM AUTHOR]

Contributions of the present paper consist of two parts. In the first one, we contribute to the theory of stochastic calculus for signed measures. For instance, we provide some results permitting to characterize martingales and Brownian motion both defined under a signed measure. We also prove that the uniformly integrable martingales (defined with respect to a signed measure) can be expressed as relative martingales and we provide some new results to the study of the class Σ (H) . The second part is devoted to the construction of solutions for the homogeneous skew Brownian motion equation and for the inhomogeneous skew Brownian motion equation. To do this, our ingredients are the techniques and results developed in the first part that we apply on some stochastic processes borrowed from the theory of stochastic calculus for signed measures. Our methods are inspired by those used by Bouhadou and Ouknine in [2013]. Moreover, their solution of the inhomogeneous skew Brownian motion equation is a particular case of those we propose in this paper. [ABSTRACT FROM AUTHOR]

A productive understanding of rate of change concept is essential for constructing a robust understanding of derivatives. There is substantial evidence in the research that students enter and leave their Calculus courses with naive understandings of rate of change. Implementing a short unit on "what is rate of change" can address these issues and better support students in understanding the fundamental ideas of Calculus. This paper provides a short teaching intervention that instructors can utilize to help students build a productive understanding of rate of change that will aid them in understanding derivatives as instantaneous rates of change. [ABSTRACT FROM AUTHOR]

In this study, we redesigned paper-and-pencil activities and adapted them to an introductory multivariate calculus course supported by 3D dynamic geometry software. We used semi-structured interviews and students’ written productions during the semester to analyse the use of technology in supporting students’ learning. Considering the work of two students, we find that the software has transformative potential but that it did not promote students’ learning as expected. We discuss possible reasons for this. [ABSTRACT FROM AUTHOR]

Differential operators and integral operators are linked together by the first fundamental theorem of calculus. Based on this principle, the notion of a differential Rota-Baxter algebra was proposed by Guo and Keigher. Recently, the subject has attracted more attention since it is associated with many areas in mathematics, such as integro-differential algebras. This paper considers differential Rota-Baxter algebras in the quasi-idempotent operator context. We establish a Gröbner-Shirshov basis for free commutative quasi-idempotent differential algebras (resp. Rota-Baxter algebras, resp. differential Rota-Baxter algebras). This provides a linear basis of a free object in each of the three corresponding categories by the Composition-Diamond lemma. Communicated by P. Kolesnikov [ABSTRACT FROM AUTHOR]

In this paper, we provide a report of preliminary findings of the Morgan State University (MSU) Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL) project and its focus on culturally responsive teaching (CRT) as an active learning framework for pre-calculus instruction. The paper concludes with a summary of wins and challenges faced by MSU's Mathematics Department. Lessons learned by MSU SEMINAL will help inform other departments on implementing CRT in a pre-calculus course. [ABSTRACT FROM AUTHOR]

Over the past 10 years, the authors of this paper have implemented a series of project-based and inquiry-based learning initiatives in the calculus sequence at our institution. These initiatives took place in a department with an existing strong culture supporting teaching innovation and improvement. In this paper, we describe three initiatives in detail. We describe how in one, a syllabus redesign allowed for more instructor autonomy. In another, we were able to significantly improve student buy-in. We describe key support we received from our department and institutional leadership at each stage, as well as from working in community with each other. Finally, by looking at the long arc of change in our department, we hope to encourage others who are encountering roadblocks. By working in community, we have created an environment where active learning can flourish. [ABSTRACT FROM AUTHOR]

In summer 2013, Manhattan College introduced an online summer "bridge to calculus" course for incoming first-year students in science, engineering, and mathematics education who marginally did not receive a calculus recommendation based on a mathematics placement test. In this paper, we describe the development of the bridge course and demonstrate statistically that this course continues to prepare its students for Calculus at a level comparable to those who took a full semester of Precalculus, yet at a significantly lower cost in terms of both time and money. [ABSTRACT FROM AUTHOR]

In this paper, we briefly introduce three theoretical frameworks for mathematical identity and why they matter to practitioners teaching undergraduate mathematics courses. These frameworks are narrative identities, communities of practice, and figured worlds. After briefly describing each theory, we provide examples of how each framework can be used to interpret or inform classroom discourses by applying the framework to a selected transcript from a student-centered mathematics project called the Catwalk problem. We summarize how an awareness of students' forming mathematical identities can be used positively in the undergraduate classroom to help educators support students to form productive mathematical identities. [ABSTRACT FROM AUTHOR]

A significant portion of mathematics education research has focused on factors that impact student pursuit of science, technology, engineering and mathematics (STEM). Low rates of STEM student enrollment combined with high drop-out rates have consistently drawn attention from educators, administrators and policy-makers at all levels. Many studies have been dedicated to the investigation of the influential factors that exacerbate this problem, and one factor that has been cited consistently is the learning experience in a specific introductory mathematics course – first-semester calculus. Research has shown strong relationships between STEM persistence and student affect in this context including their attitudes, beliefs, confidence and enjoyment related to mathematics, and between persistence and student perceptions of pedagogy in these courses. In this paper, we extend prior work by the authors by investigating the impact of three different Calculus I course settings on these relationships and find that some course structures have a moderating effect on these relationships. We present those results and indicate some possible ways to leverage pedagogical structures to improve student persistence in pursuing a STEM major. [ABSTRACT FROM AUTHOR]

A growing body of research supports writing as a means to learn mathematics. Although introductory courses have benefited the most from the spread of this mode of learning, writing may be promoted in advanced courses. This paper reports on writing tasks in a complex analysis course where the primary goal was for students to investigate similarities and differences between key concepts in complex analysis and their counterparts in real analysis (or in single and multi-variable calculus). Results show that not only the project's outcomes were met, but the exercise increased also students' curiosity for expanding knowledge to material not discussed in class. [ABSTRACT FROM AUTHOR]

In this paper, we will discuss a type of activity that lets the mathematics classroom become a place where students can learn more than mathematical content. Specifically, students can learn interdisciplinary skills in the area of communication (both verbal and non-verbal) and debate skills that are often taught in communication or English classes. This paper discusses activities, which we call TACTivities, that can be added into any mathematics course to make the course more interdisciplinary, merging the arts and the sciences. They are best fit in mathematics courses where skills are to be learned and practiced, but modifications can be made for a variety of mathematics courses. [ABSTRACT FROM AUTHOR]

This article is a follow-up to an earlier paper on the mathematics support learning tutorial programme (SLT), an intervention programme at The University of Queensland that targets students considered to be at risk of failing Calculus and Linear Algebra I, the first tertiary level mathematics subject at The University of Queensland. The first paper (Hillock, P., Jennings, M., Roberts, A., & Scharaschkin, V. (2013). Amathematics support programme for first-year engineering students. International Journal of Mathematical Education in Science and Technology, 44(7), 1030–1044) reported on the inaugural programme implemented in 2012. This article provides an update of the progress of the SLT since 2012. We provide statistics for the subsequent 12 semesters to Semester 2, 2018 and describe the evolution of the SLT since its implementation. Statistical analysis of the additional data and student feedback indicate that the SLT continues to have a positive impact on student learning, with weak students making significant gains from attending the programme. [ABSTRACT FROM AUTHOR]

In this paper, a general formula concerning the multi-composition rule of convex subdifferential calculus is provided in the setting of Banach spaces under an appropriate regularity condition. As an application, this calculus rule is applied to obtain necessary and sufficient Karush–Kuhn–Tucker type optimality conditions for constrained convex minmax location problems with perturbed minimal time functions and set-up costs. [ABSTRACT FROM AUTHOR]

In the 3rd century B.C.E., Archimedes wrote his treatise on the quadrature of the parabola, in which he laid out his solution to the problem of finding the area of a parabolic segment. Archimedes attacks the problem from two sides; first, he uses classical mechanics to derive an area formula, and then he uses pure geometry to prove his formula is correct. In this paper, we will present two modern approaches to this problem using calculus. The first approach can be presented to a calculus class that has learned about optimization methods and convergent geometric sequences, and the second can be presented after they have learned the Fundamental Theorem of Calculus. [ABSTRACT FROM AUTHOR]

This paper extends work in the areas of quantitative reasoning and covariational reasoning at the undergraduate level. Task-based interviews were used to examine third-semester calculus students' reasoning about partial derivatives in five tasks, two of which are situated in a mathematics context. The other three tasks are situated in real-world contexts (i.e. weight, revenue, and mortgage). There are three main findings from this study. First, interpreting quantities representing partial derivatives in real-world contexts was problematic for most of the students. Second, students' interpretations of partial derivatives were not consistent across tasks. Third, all the students engaged in several levels of covariational reasoning when interpreting quantities representing partial derivatives in the context of weight, revenue, and mortgage. Implications for calculus instruction and directions for future research are included. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the higher-order optimality conditions for strict efficient solutions to a nonsmooth optimization problem subject to inclusion constraint. A concept of higher-order contingent derivative type for set-valued maps, some main calculus rules of which are obtained, is proposed and employed with the Robinson–Ursescu open mapping theorem to get a Karush–Kuhn–Tucker condition under assumptions of Hölder direction metric subregularity. Sufficient conditions for these solutions are established without convexity assumptions and possibly without the existence of derivatives. As an application, we extend some optimality conditions for a nonsmooth optimization problem subject to generalized inequality constraint. Another application is presented for necessary and sufficient conditions for robust local strict efficient solutions in uncertain vector optimization. Some examples are provided to illustrate our theorems as well. Our results are new and improve the existing ones in the literature substantially. [ABSTRACT FROM AUTHOR]

In this paper, we introduce provability multilattice logic P M L n and multilattice arithmetic M P A n which extends first-order multilattice logic with equality by multilattice versions of Peano axioms. We show that P M L n has the provability interpretation with respect to M P A n and prove the arithmetic completeness theorem for it. We formulate P M L n in the form of a nested sequent calculus and show that cut is admissible in it. We introduce the notion of a provability multilattice and develop algebraic semantics for P M L n on its basis, by the method of Lindenbaum-Tarski algebras we prove the algebraic completeness theorem. We present Kripke semantics for P M L n and establish the Kripke completeness theorem via syntactical and semantic embeddings from P M L n into G L and vice versa. Last but not least, the decidability of P M L n is shown. [ABSTRACT FROM AUTHOR]

In this paper, six interviews with course coordinators from two mathematics departments are analysed to better understand the relationship between course coordination and local data in the Precalculus to Calculus 2 sequence with respect to online grading platforms. We highlight several potential coordinator decisions and present illustrative examples to show how the coordinators may be affected by the data available from an online grading platform. Three themes emerged as being most important to the coordinators at both institutions: (a) affordances and constraints related to time, (b) informing instruction and content and (c) data informing grading practices. We argue that attention to these themes by coordinators can result in a more substantial, efficient, and consistent experience affecting all stakeholders involved. [ABSTRACT FROM AUTHOR]

We are interested in the existence and asymptotic behavior of smooth solutions to the hydrodynamic model of semiconductors with non-zero doping profile. Within the insulating boundary conditions, recently, a steady state for any doping profile with large amplitude was obtained by using the calculus of variations. In this paper, the obtained steady state is regarded as the background solution. Utilizing energy methods and entropy analysis, we prove the existence of smooth solutions to the hydrodynamic model. As a by-product, we show the smooth solution convergent to the background solution with exponential decay rate. [ABSTRACT FROM AUTHOR]

This paper seeks to explore the nature of dialogue within calculus lecture rooms. This paper reports on part of a larger study, in which the participants were two lecturers lecturing to 198 third year pre-service teachers at a University in South Africa. This qualitative interpretive study was framed within the ambits of social constructivism and aspects of Mortimer and Scott's framework were used to analyse dialogue in the lecture room. Data for this paper were generated through video-recorded lecture observations. Subsequently, a qualitative data analysis of the generated data revealed that dialogue within the calculus lecture rooms under study may be in the form of explanations and questioning. Questioning included questions that assess students' prior knowledge, probing, follow-up and guiding questions. The findings of this study are of value to both lecturers and students within higher education with implications for teaching and learning mathematics within higher education are presented. [ABSTRACT FROM AUTHOR]

The complexity in understanding the ϵ–δ definition has motivated research into the teaching and learning of the topic. In this paper I share my design of an instructional analogy called the Pancake Story and four different questions to explore the logical relationship between ϵ and δ that structures the definition. I designed the story from an anti-deficit perspective on students' mathematical thinking. I leverage students' intuitions about quality control, and explicitly build on students' prior knowledge that I gathered from student interviews. I illustrate the utility of the story in supporting students' sense-making of the formal definition by sharing changes in students' claims and justifications about the relationship between ϵ and δ. Students' justifications also provide examples of the kind of thinking an instructor might expect to see in the classroom when using the story. I end the paper with some classroom implications and a teaching episode illustrating how students might use the story to make sense of limit more broadly. [ABSTRACT FROM AUTHOR]

This curated collection covers a selection of PRIMUS articles published over a roughly 12-year period that focus on modeling and applications. The collection includes sections on individual projects, courses with a significant modeling component, and modeling and applications in extracurricular settings and throughout the curriculum. [ABSTRACT FROM AUTHOR]

Why do rebels leave rebellions? Although much scholarly attention has been devoted to understanding why individuals join rebellions, relatively little is known about why they leave. This paper seeks to fill this deficit by exploring the decision-making process that rebels undertake when determining whether to stay or leave. Based on interview data collected from ten active rebels and four former rebels all engaged (or previously engaged) in conflicts in East Africa, we find that the reason why rebels joined the group influences their decision to leave or stay. Rebels who joined due to grievances are far less likely to escape opportunistically, while rebels who joined due to "greed" display a higher sensitivity to the hardships of rebel life and the pull of alternative options. Understanding why a person joins a rebellion helps predict the factors that will drive them to leave. [ABSTRACT FROM AUTHOR]

Textbooks have been the subject of research within and across disciplines, but have not yet been widely studied from a disciplinary literacy perspective. Readerly agency is also understudied in disciplinary literacy. The present paper aims to illuminate both of these areas by examining facets of agency that readers demonstrated during think-aloud interviews with a college calculus textbook, thus exploring the disciplinary literacies that are involved in reading this didactical text. Authors have drawn on the recently forwarded theory of "didactical disciplinary literacy," as well as definitions of agency in both literacy and math fields, to reveal how agency was enacted by readers using the textbook to negotiate unknowns in calculus. Findings show participants exhibiting agency in a range of ways, but not always in direct relationship to themselves as agents within the field of mathematics. This study invites college instructors and secondary teachers to consider ways they might foster didactical disciplinary literacy skills to support student learners in mathematics, and other disciplines. [ABSTRACT FROM AUTHOR]

In this paper, the authors question the value of a required calculus class for undergraduate business students. We use the tenets of Transfer of Learning theory along with the Theory of Formal Discipline to evaluate whether the value of calculus may be overstated. Using data from business faculty, students, and alumni, we look at the degree to which these constituents believe that taking a calculus class is important to their future success. Findings indicate that while some groups believe calculus is important to business students, most results suggest that the value of a required calculus class to business student success is limited. [ABSTRACT FROM AUTHOR]

This paper considers the global synchronisation and finite-time synchronisation for a class of delayed fractional-order complex neural networks (DFOCNNs). Based on the properties of fractional-order calculus and the Razumikhin-type Lyapunov theorem of a fractional-order system, two new lemmas are proved. These lemmas are employed to formulate a couple of novel criteria for both finite-time synchronisation and global synchronisation of DFOCNNs. Moreover, the upper bound of the setting time for synchronisation is given. Three examples are provided to verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and calculus. [ABSTRACT FROM PUBLISHER]

Large lecture halls are a common feature of many undergraduate mathematics programs. However, teaching effectively in a large lecture hall can be challenging. This paper discusses the use of personal whiteboards for students as a way to make large lecture halls a more productive learning environment. I discuss the logistics of using whiteboards, setting up norms, and provide examples of supporting instructional techniques. These techniques are: warmup problems, think-pair-share, group work, and student presentations. To support this exposition, I draw on personal reflections as an instructor and report from a brief student survey on their experiences using the whiteboards. [ABSTRACT FROM AUTHOR]

In this paper, we derive some formulas for higher order derivatives ofr-Lambert functions. Moreover, an integration formula involving powers ofr-Lambert function is obtained. [ABSTRACT FROM PUBLISHER]

In this paper the authors described the influence of the computer-based environment on students' learning achievement of the multidimensional calculus, in particular double integrals. The research was conducted with the second year students at the University of Kragujevac, Serbia, with two groups of students: the experimental and the control one. During the learning process of the experimental group, the materials made in Wolfram Mathematica were used for visualization. Students from the experimental group used these materials in order to successfully solve their double integral tasks. In the control group, students did not use a computer. The students in both groups got the identical tasks in their learning process and for the exam. During the exam, the students from both groups were not allowed to use computers. The results of the students' exam tasks were analyzed, with the emphasis on influence of visualization using computer environment, in determining the domain and integration bounds within solving double integrals. It was shown that the students from the experimental group had better results in all the exam tasks and that the software application for the visualization of multivariate functions contributed to better students' achievements in determining the domain of integration and the integration bounds in order to solve double integrals. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate through the use of matrix calculus a transparent analysis of fractional inhomogeneous Markov models for life insurance where transition matrices commute. The resulting formulae are intuitive matrix generalizations of their single-state counterparts, and the absorption times are matrix versions of well-known scalar distributions. A further advantage of this approach is that it allows extending the analysis to the non-Markovian case where sojourns are Mittag-Leffler distributed, and where the absorption times are fractional phase-type distributed. Considering deterministic time transforms gives rise to fractional inhomogeneous phase-type distributions as absorption times. The latter underlying processes are an example of a regime where not only the present but also the history of a policyholder influences its future evolution. The sub-exponential nature of stable distributions translates into the multi-state insurance model as a random longevity risk at any given state of the chain. [ABSTRACT FROM AUTHOR]

My aim in this paper is to present a pluralist thesis about the inferential role of logical constants, which embraces classical, relevant, linear and ordered logic. That is, I defend that a logical constant c has more than one correct inferential role. The thesis depends on a particular interpretation of substructural logics' vocabulary, according to which classical logic captures the literal meaning of logical constants and substructural logics encode a pragmatically enriched sense of those connectives. The paper is divided into four parts: first, I introduce the motivation for the pluralist thesis of the paper; second I introduce the calculus for the different logics endorsed in the pluralist thesis; third, I motivate how the different behaviors of the logical vocabulary of these logics can be pragmatically interpreted, and fourth, I motivate how the different inferential roles that each substructural logic attribute to logical constants can coexist, and how we should reason with a logical constant c given this plurality. [ABSTRACT FROM AUTHOR]

'The mathematisation of time has limits,' writes Derrida in 'Ousia and Gramme.' Taking this quote in all possible senses, this paper considers Derrida's definition of limit as gramme, trace, and aporia, and develops the 'mathematisation' of all three. I will consider the structure of mathematical limit in Fregean arithmetics, calculus, and topology. I argue that a topological approach to the concept of gramme creates a new 'limit' that illustrates the map of our 'commute' to the unknown, and therefore avoids the aporetic act of crossing the impassible limit between life and death. This new 'limit,' often referred to by mathematicians as a 'cone,' is a shapeless shape that offers us knowledge about time and space that we otherwise cannot gain. By redefining the 'limit' of time through three mathematical systems – arithmetic, calculus, and topology – this paper offers new perspectives to couple mathematics with philosophy. [ABSTRACT FROM AUTHOR]

In this paper we present two simulations designed with GeoGebra that illustrate dynamically a key concept in Vector Calculus: line integrals of vector fields, along with other associated mathematical properties and applications. Students are not required to know the GeoGebra environment: a user-friendly interface with buttons, functionalities and online help and exemplar problems allows immediate use of the simulations. The goal of the simulations is to enhance student insight, in the spirit of learning by experimentation, by analysing the dynamic representations provided by the simulations and by dragging objects and changing the parameters involved. The numerical results can be confirmed for special cases by standard undergraduate calculations. [ABSTRACT FROM AUTHOR]

Every application of integration by parts can be done with a tabular method. The trick is to identify and consider each new integral in the table before deciding how to proceed. This paper supplements a classic introduction to integration by parts with a particular tabular method called Row Integration by Parts (RIP). Approaches to tabular methods found online and in the literature often fail to clearly identify new integrals since the focus is on constructing columns, thus new integrals are ignored. With RIP, each integral is identified with a row and tables are built one row at a time. This allows RIP to be an efficient bookkeeping method and to apply to a much wider range of functions than those typically considered with other tabular methods. [ABSTRACT FROM AUTHOR]