Active learning: a case study of student engagement in college Calculus

This paper presents a case study for strategic engagement of students in a Calculus course in order to produce increased learning in the classroom. Since it has been shown that active learning can promote greater comprehension for students in science, technology, engineering, and mathematics (STEM) courses, the researcher utilized many types of active learning techniques to enhance classroom instruction. The key components implemented are presented as a model of enhanced learning through developed classroom engagement. This course redesign model entitled, Strategic Engagement for Increased Learning (SEIL), has the potential to (1) contribute to the body of knowledge on ways to improve mathematics skills for college students, (2) identify successful teaching strategies and technologies that will promote the retention of STEM students, (3) increase the success rate of students taking Calculus, and (4) help produce more STEM graduates needed for the STEM workforce in the United States of America.     

Students as toolmakers: refining the results in the accuracy and precision of a trigonometric activity

Smartphones used as tools provide opportunities for the teaching of the concepts of accuracy and precision and the mathematical concept of arctan. The accuracy and precision of a trigonometric experiment using entirely mechanical tools is compared to one using electronic tools, such as a smartphone clinometer application and a laser pointer. This research has demonstrated how two classroom activities based on tool-making can enhance student measurement and application of accuracy and precision considerations through a trigonometric activity investigating arctan.     

Peer interactions in a computer lab: reflections on results of a case study involving web-based dynamic geometry sketches

A case study, originally set up to identify and describe some benefits and limitations of using dynamic web-based geometry sketches, provided an opportunity to examine peer interactions in a lab. Since classes were held in a computer lab, teachers and pairs faced the challenges of working and communicating in a lab environment.Research has shown that particular teacher interventions provide motivation for the consideration of new ideas, and help uncover misunderstandings that may interfere with student progress [Towers, J. (1999). In what ways do teachers interventions interact with and occasion the growth of students’ mathematical understanding. Doctoral Dissertation, University of British Columbia, Unpublished]. Examples of student discourse presented here suggest that certain peer interactions act in similar ways—helping propel students towards new understanding. On the other hand, they also show that some peer interactions, although superficially similar to teacher interventions, may hamper student progress.     

Opportunities for learning: the use of variation to analyse examples of a paradigm shift in teaching primary mathematics in England

We demonstrate the power of Variation Theory as an analytical tool used to understand the underlying conceptual structure of mathematics lessons taught by English primary school teachers. We study excerpts of three lessons that are posted on a professional website. We show how lesson analysis using variation allows us to focus on what is made available to be learnt in the lesson excerpts. We identify some differences in their use of dimensions of variation and the associated ranges of change and discuss how suitable patterns of variation and invariance might differ according to the nature of the learning focus. We reflect on the value of our analytical approach.     

Available-To-Promise modeling for multi-plant manufacturing characterized by lack of homogeneity in the product: An illustration of a ceramic case

Lack of homogeneity in the product (LHP) appears in some production processes which incorporate raw materials that originate directly from nature and/or production processes with operations that confer heterogeneity to the characteristics of the outputs obtained, even when the inputs used are homogeneous. Poor LHP management may have a very negative impact on the customer service level and on the supply chains’ operation costs, especially when the customer needs to be served with homogeneous units of one same product. One of the key processes for suitable LHP management is the order-promising process. This work presents a mathematical programming order-promising model for make-to-stock environments with LHP. The model considers two objectives placed within a single objective by the weighted sum method. For the purpose of testing the validity of the proposed model and to evaluate the characteristics of the solutions obtained in different scenarios, numerical experiments based on realistic data from a ceramic tile company have been conducted. The results show that better results are obtained for the defined performance measures if multiple objectives are considered when promising orders than the single objective of maximizing profits. Furthermore, the superiority of the results obtained from the proposed model, if compared with current company practice, proves the model’s utility.     

Using the Knowledge Quartet to quantify mathematical knowledge in teaching: the development of a protocol for Initial Teacher Education

This study examined trainee teachers' mathematical knowledge in teaching (MKiT) over their final year in a US Initial Teacher Education (ITE) programme. This paper reports on an exploratory methodological approach taken to use the Knowledge Quartet to quantify MKiT through the development of a new protocol to code trainees' teaching of mathematics lessons. This approach extends Rowland's et al. work on the Knowledge Quartet (KQ). Justification for using the KQ to quantify MKiT, and the potential benefits such an attempt might provide those involved with ITE, are discussed. It is suggested that quantified MKiT data based on the Knowledge Quartet can be used to consider MKiT development in novice teachers in order to inform ITE programmes and form new theoretical loops between theory and practice in teacher education.     

On the convergence rate and optimization of a numerical method with splitting of boundary conditions for the stokes system in a spherical layer in the axisymmetric case: Modification for thick layers

The convergence rate of a fast-converging second-order accurate iterative method with splitting of boundary conditions constructed by the authors for solving an axisymmetric Dirichlet boundary value problem for the Stokes system in a spherical gap is studied numerically. For R/r exceeding about 30, where r and R are the radii of the inner and outer boundary spheres, it is established that the convergence rate of the method is lower (and considerably lower for large R/r) than the convergence rate of its differential version. For this reason, a really simpler, more slowly converging modification of the original method is constructed on the differential level and a finite-element implementation of this modification is built. Numerical experiments have revealed that this modification has the same convergence rate as its differential counterpart for R/r of up to 5 × 10³. When the multigrid method is used to solve the split and auxiliary boundary value problems arising at iterations, the modification is more efficient than the original method starting from R/r ～ 30 and is considerably more efficient for large values of R/r. It is also established that the convergence rates of both methods depend little on the stretching coefficient η of circularly rectangular mesh cells in a range of η that is well sufficient for effective use of the multigrid method for arbitrary values of R/r smaller than ～ 5 × 10³.     

A methodology for supporting strategy implementation based on the VSM: A case study in a Latin-American multi-national

Soft OR tools have increasingly been used to support the strategic development of companies at operational and managerial levels. However, we still lack OR applications that can be useful in dealing with the “implementation gap”, understood as the scarcity of resources available to organizations seeking to align their existing processes and structures with a new strategy. In this paper we contribute to filling that gap, describing an action research case study where we supported strategy implementation in a Latin American multinational corporation through a soft OR methodology. We enhanced the ‘Methodology to support organizational self-transformation’, inspired by the Viable System Model, with substantive improvements in data collection and analyses. Those adjustments became necessary to facilitate second order learning and agreements on required structural changes among a large number of participants. This case study contributes to the soft OR and strategy literature with insights about the promise and constraints of this soft OR methodology to collectively structure complex decisions that support organizational redesign and strategy implementation.     

On the application of a transportation model for revenue optimization in waste management: a case study

This paper describes an interactive decision support system called Opti-Link which has been developed for a company operating in the area of waste and raw material management. Built around a specific transportation problem, the system is used to maximize the revenue generated by selling waste paper to paper mills. Furthermore, the dual variables of the linear program allow the planner to identify upper bounds for setting bid prices to buy waste paper from waste collection companies. First operational results indicate a significant increase in profit while at the same time the duration of the planning process could be cut by more than half.     

Weierstrass points and their impact in the study of algebraic curves: a historical account from the “Lückensatz” to the 1970s

In this note we give a historical account of the origin and the development of the concept of Weierstrass point. We also explain how Weierstrass points have contributed to the study of compact Riemann surfaces and algebraic curves in the century from Weierstrass’ statement of the gap theorem to the 1970s. In particular, we focus on the seminal work of Hürwitz that raised questions which are at the center of contemporary research on this topic.      

基于StoNED和动态SPDM模型的绿色创新效率分异趋势及其驱动机制分析——以长江中游城市群为例

文章构建StoNED模型测度2005~2019年长江中游城市群绿色创新效率值,并引入动态SPDM模型从收敛速度的角度探究绿色创新效率时空分异的驱动机制,其目的在于解决传统效率测度模型无法兼顾多产出及投入产出松弛性、难以合理量化绿色创新效率分异趋势及其作用机制的问题。研究发现:(1)长江中游城市群绿色创新效率形成了以武汉、长沙、南昌、宜昌、襄阳等城市为多中心的空间格局,省域内绿色创新效率值的绝对差异基本固化、相对差异有较大程度缩小,东西地区和南北地区绿色创新效率的分异度呈现缩小趋势。(2)绿色创新效率分异趋势的差异性是通过收敛速度不同表现出来,江西省域收敛速度最快,湖南省域次之,湖北省域最慢,而这种差异主要由于经济发展水平、政府科技支出、环境规制、教育水平、产业结构、金融支持水平等因素和影响机制共同作用驱动。最后,提出了相应的对策建议。     

A regularity result for a minimum problem in orlicz-sobolev spaces with applications in the study of the dirichlet problem for the operator of hencky-nadai theory

The existence and uniqueness of the solution to the problem of minimum for functionals generated by N- functions are obtained in Orlicz-Sobolev spaces. Applications for some functionals dealing with Hencky theory are given.     

Analytical solutions for ore fluid transport in fractured rocks: a case study on ore-forming processes of the stratabound skarn copper deposits in China

The Dongguashan skarn copper deposit can be considered as theproduct of the transport-chemical reaction coupling processof ore-forming materials (for example, complexes of copper)in discrete, parallel fractures in a porous medium system. Amathematical model of metallogenesis has been established andthe accurate analytical solutions for depicting the transportof ore-forming materials have been worked out. In establishingthe model of metallogenesis and working out the analytical solutions,the following aspects have been taken into consideration: (1)advective transport along fractures; (2) diffusion and longitudinalmechanical dispersion of ore-forming materials (solutes) alongthe fracture axis; (3) diffusion of ore-forming materials fromthe fractures to the wall media; (4) adsorption of ore-formingmaterials on the surface of wall-rock matrices; (5) adsorptionof ore-forming materials within the wall-rock matrices; (6)reduction of the concentrations of solutes due to the chemicalreactions between ore fluids and wall-rock matrices and theprecipitation of ore-forming materials. The general transient solution takes the form of a double integral,which can be evaluated using the Gauss–Legendre quadrature.By comparing the steady-state solutions in the special caseof D = 0 (without dispersion) and of D 0 (with dispersion),a simple criterion can be established, with which one can assessthe importance of longitudinal dispersion along the fracturesystem. Case studies showed that the developing extent of fracturesin the system would exert a great influence on the transportrate and distance of ore-forming materials. In case that fracturesare developed at small intervals, ore-forming materials willbe transported along the fracture system over larger distancebecause of the limited capability of the wall rocks to storeore-forming materials. That is to say, larger orebodies wouldbe formed. In the case of higher transport rates of ore fluidsalong the fracture system the longitudinal mechanical dispersionis negligible, but in the reversed case, the longitudinal mechanicaldispersion would exert a great influence on fluid transport.Under such circumstances, the longitudinal mechanical dispersioncould not be neglected. In the normal case of D 0, the steady-statesolutions could provide a potential approach to predicting theultimate distance over which ore fluids of a certain concentrationlevel penetrate along the fracture system, that is, how longan orebody would extend. Analytical solutions can rationallyinterpret the spatial distribution characteristics of strata-boundskarn copper deposits, the rules governing spatial variationsin ore texture and ore grade, as well as other important geologicalcharacteristics of the ore deposits. This work will providea better understanding of the metallogenic mechanism of strata-boundskarn copper deposits widely spread along the Middle-Lower Reachesof the Yangtze River Valley and its adjacent areas in China.     

The role of computer simulations in learning analytic mechanics towards chaos theory: a course experimentation

We present the results of an experimental project, made at the University of Calabria, which uses computer simulations and scientific computational systems in teaching and learning the fundamentals of analytic mechanics, in particular the classical Lagrangian and Hamiltonian formulation of the matter. Starting with examples of classical dynamical systems we also introduced students to appreciate chaos concepts going step by step to more complex settings. The success obtained with the use of computer-based methodologies has been very clear and the final students' tests confirm it. In this paper, in particular, we compare the results obtained by four groups of students: the first two attended such an experimental course and employed computer support for their individual work at home, while the learning environment of the second two groups (the control ones) was based only on traditional classroom lectures with paper and pencil home activities. If on the one hand a better overall performance of the first two groups was evident, it is very interesting (and not so easy) to investigate how much in quantity and quality, the learning of the experimental groups differs from that of the other groups, and why. For example, we illustrate some relevant differences between them in the comprehension of the studied phenomena, in dealing with and solving the proposed problems, and also in the individual development of further personal ideas.