Differentiation of teaching and learning mathematics: an action research study in tertiary education

Diversity and differentiation within our classrooms, at all levels of education, is nowadays a fact. It has been one of the biggest challenges for educators to respond to the needs of all students in such a mixed-ability classroom. Teachers’ inability to deal with students with different levels of readiness in a different way leads to school failure and all the negative outcomes that come with it. Differentiation of teaching and learning helps addressing this problem by respecting the different levels that exist in the classroom, and by responding to the needs of each learner. This article presents an action research study where a team of mathematics instructors and an expert in curriculum development developed and implemented a differentiated instruction learning environment in a first-year engineering calculus class at a university in Cyprus. This study provides evidence that differentiated instruction has a positive effect on student engagement and motivation and improves students’ understanding of difficult calculus concepts.     

Integrating transportation and production: an international study case

The problem we study is inspired by the real case of Mesdan S.p.A., an Italian company worldwide leader in the textile machinery sector, which has two production units with two warehouses, one located in Italy (Brescia) and the other in China (Foshan). The critical point in this logistic system is the integration between production and transportation management, given the long distance between Brescia and Foshan. Shipments are performed by the means of different types of vehicles with different unit costs and significantly different lead times. Variable production costs, variable and fixed transportation costs and, possibly, inventory costs are charged in the objective function. Different production policies are compared. Our aim is to determine integrated policies that minimize the total cost of the system. We formulate integer linear programming models for the solution of these problems, and we solve the real instance and carry out a sensitivity analysis of the optimal solution.     

Enhancing elementary-school mathematics teachers' efficacy beliefs: a qualitative action research

Individuals and societies that can use mathematics effectively in this period of rapid changes will have a voice on increasing the opportunities and potentials which can shape their future. This has brought affective characteristics, such as self-efficacy, that affect mathematics achievement into focus of the research. Teacher efficacy refers to the extent to which a teacher feels capable to help students learn, influence students’ performance and commitment, and thus plays a crucial role in developing the student in all aspects. In this study, we used two sources of efficacy beliefs, mastery experiences and physiological and emotional states, in an interesting and challenging seven month workshop, as tools to foster teacher efficacy for six elementary-school teachers who were frustrated and wanted to leave their job. Our aim was to study the nature of these teachers’ efficacy in order to change it. In this qualitative action research, we used open interviews, non-participant observations and field notes. Results show that these teachers became efficacious, their students’ achievements and motivation were enhanced, and the school climate was changed. Qualitative inquiry of this construct sheds light on efficacy beliefs of mathematics teachers. Nurturing teacher efficacy has borne much fruit in the field of mathematics in school.     

Integrating accounting and multiplicative calculus: an effective estimation of learning curve

Numerical interpolation methods are essential for the estimation of nonlinear functions and they have a wide range of applications in economics and accounting. In this regard, the idea of using interpolation methods based on multiplicative calculus for suitable accounting problems is self-evident. The purpose of this study, therefore, is to develop a way to better estimate the learning curve, which is an exponentially decreasing function, based on multiplicative Lagrange interpolation. The results of this study show that the proposed multiplicative method of learning curve provides more accurate estimates of labour costs when compared to the conventional methods. This is because the exponential functions are linear in multiplicative calculus. Furthermore, the results reveal that using the proposed method enables cost and managerial accountants to better calculate both cost of unused capacity and product cost in a cumulative production represented by a nonlinear function. The results of this study are also expected to help researchers, practitioners, economists, business managers, and cost and managerial accountants to understand how to construct a multiplicative based learning curve to improve such decisions as pricing, profit planning, capacity management, and budgeting.     

QML-Morven: A novel framework for learning qualitative differential equation models using both symbolic and evolutionary approaches

In this paper, a novel qualitative differential equation model learning (QML) framework named QML-Morven is presented. QML-Morven employs both symbolic and evolutionary approaches as its learning strategies to deal with models of different complexity. Based on this framework, a series of experiments were designed and carried out to: (1) investigate factors that influence the learning precision and minimum data requirement for successful learning; (2) address the scalability issue of QML systems.     

An experimental comparison of several approaches to the discriminant problem with both qualitative and quantitative variables

This paper reports the results of an experimental comparison between a linear programming approach and the well known statistical procedure by Fisher for solving discriminant analysis problems. This work represents an extension of the work of Bajgier and Hill as we incorporate qualitative variables into our design as well as enlarge the estimation sample from 30 to 90. Our results indicate that both methods are enhanced by the inclusion of the qualitative variables, but that the Fisher approach seems preferable. Lastly, we discuss the effect of the different experimental factors on the relative performance of the two methods.     

Integrating design problems in mathematics curriculum: an architecture college case study

This paper reports an attempt to improve results in the mathematics course in one of the architecture colleges in Israel through practise in applications. The effect of integrating structure design problems in the calculus curriculum on students' achievements and attitudes was examined. The applied topics in the curriculum were connected to calculus topics and studied through problembased learning activities. The integrated curriculum was implemented and the learning results in experimental and control groups were assessed by means of achievement tests, attitude questionnaires and student interviews. The learning achievements in the experimental group proved to be significantly higher than in the control group. The positive impact of learning applications on motivation, understanding, creativity and interest in mathematics is indicated.     

Volatility forecasting for interbank offered rate using grey extreme learning machine: The case of China

Interbank Offered rate is the only direct market rate in China’s currency market. Volatility forecasting of China Interbank Offered Rate (IBOR) has a very important theoretical and practical significance for financial asset pricing and financial risk measure or management. However, IBOR is a dynamics and non-steady time series whose developmental changes have stronger random fluctuation, so it is difficult to forecast the volatility of IBOR. This paper offers a hybrid algorithm using grey model and extreme learning machine (ELM) to forecast volatility of IBOR. The proposed algorithm is composed of three phases. In the first, grey model is used to deal with the original IBOR time series by accumulated generating operation (AGO) and weaken the stochastic volatility in original series. And then, a forecasting model is founded by using ELM to analyze the new IBOR series. Lastly, the predictive value of the original IBOR series can be obtained by inverse accumulated generating operation (IAGO). The new model is applied to forecasting Interbank Offered Rate of China. Compared with the forecasting results of BP and classical ELM, the new model is more efficient to forecasting short- and middle-term volatility of IBOR.     

Pairs trading and outranking: The multi-step-ahead forecasting case

Pairs trading is a popular speculation strategy. Several implementation methods are proposed in the literature: they can be based on a distance criterion or on co-integration. This article extends previous research in another direction: the combination of forecasting techniques (Neural Networks) and multi-criteria decision making methods (Electre III). The key contribution of this paper is the introduction of multi-step-ahead forecasts. It leads to major changes in the trading system and raises new empirical and methodological questions. The results of an application based on S&P 100 Index stocks are promising: this methodology could be a powerful tool for pairs selection in a highly non-linear environment.     

Classification for forecasting and stock control: a case study

Different stock keeping units (SKUs) are associated with different underlying demand structures, which in turn require different methods for forecasting and stock control. Consequently, there is a need to categorize SKUs and apply the most appropriate methods in each category. The way this task is performed has significant implications in terms of stock and customer satisfaction. Therefore, categorization rules constitute a vital element of intelligent inventory management systems. Very little work has been conducted in this area and, from the limited research to date, it is not clear how managers should classify demand patterns for forecasting and inventory management. A previous research project was concerned with the development of a theoretically coherent demand categorization scheme for forecasting only. In this paper, the stock control implications of such an approach are assessed by experimentation on an inventory system developed by a UK-based software manufacturer. The experimental database consists of the individual demand histories of almost 16?000 SKUs. The empirical results from this study demonstrate considerable scope for improving real-world systems.     

Integrating learning theories and application-based modules in teaching linear algebra

The research team of The Linear Algebra Project developed and implemented a curriculum and a pedagogy for parallel courses in (a) linear algebra and (b) learning theory as applied to the study of mathematics with an emphasis on linear algebra. The purpose of the ongoing research, partially funded by the National Science Foundation, is to investigate how the parallel study of learning theories and advanced mathematics influences the development of thinking of individuals in both domains. The researchers found that the particular synergy afforded by the parallel study of math and learning theory promoted, in some students, a rich understanding of both domains and that had a mutually reinforcing effect. Furthermore, there is evidence that the deeper insights will contribute to more effective instruction by those who become high school math teachers and, consequently, better learning by their students. The courses developed were appropriate for mathematics majors, pre-service secondary mathematics teachers, and practicing mathematics teachers. The learning seminar focused most heavily on constructivist theories, although it also examined socio-cultural and historical perspectives. A particular theory, Action-Process-Object-Schema (APOS) [10], was emphasized and examined through the lens of studying linear algebra. APOS has been used in a variety of studies focusing on student understanding of undergraduate mathematics. The linear algebra courses include the standard set of undergraduate topics. This paper reports the results of the learning theory seminar and its effects on students who were simultaneously enrolled in linear algebra and students who had previously completed linear algebra and outlines how prior research has influenced the future direction of the project.     

Computational organizational network modeling: Strategies and an example

This paper articulates the logic of computational organizational modeling as a strategy for theory construction and testing in the field of organizational communication networks. The paper introduces, Blanche, and objectoriented simulation environment that supports quantitative modeling and analysis of the evolution of organizational networks. Blanche relies on the conceptual primitives of attributes that describe network nodes and links that connect these nodes. Difference equations are used to model the dynamic properties of the network as it changes over time. This paper describes the design of Blanche and how it supports both the process of theory construction, model building and analysis of results. The paper concludes with an empirical example, to test the predictions of a network-based social influence model for the adoption of a new communication technology in the workplace.     

Operational risk modelling and organizational learning in structured finance operations: a Bayesian network approach

This paper describes the development of a tool, based on a Bayesian network model, that provides posteriori predictions of operational risk events, aggregate operational loss distributions, and Operational Value-at-Risk, for a structured finance operations unit located within one of Australia's major banks. The Bayesian network, based on a previously developed causal framework, has been designed to model the smaller and more frequent, attritional operational loss events. Given the limited availability of risk factor event information and operational loss data, we rely on the elicitation of subjective probabilities, sourced from domain experts. Parameter sensitivity analysis is performed to validate and check the model's robustness against the beliefs of risk management and operational staff. To ensure that the domain's evolving risk profile is captured through time, a formal approach to organizational learning is investigated that employs the automatic parameter adaption features of the Bayesian network model. A hypothetical case study is then described to demonstrate model adaption and the application of the tool to operational loss forecasting by a business unit risk manager.     

How are theoretical approaches expressed in research practices? A report on an experience in comparing theoretical approaches with respect to the construction of research problems

This article explores the idea that theoretical approaches might be usefully compared in terms of the ways in which they lead researchers to construe commonsense classroom problems. It reports an experience when one such problem was posed to a range of researchers with different theoretical backgrounds. They were invited to propose an answer, and to reframe the classroom problem as a research problem. As anticipated, responses adopted particular theoretical perspectives that “privileged” certain objects of study and modes of explanation. Nevertheless, where responses did appeal to a common theoretical perspective, sometimes used in combination with others, there could be quite sharp differences in conceptualisation, proposed action, and research intention.     

Computationally modeling organizational learning and adaptability as resource allocation: An artificial adaptive systems approach

A framework for and a computational model of organizational behavior based on an artificial adaptive system (AAS) is presented. An AAS, a modeling approach based on genetic algorithms, enables the modeling of organizational learning and adaptability. This learning can be represented as decisions to allocate resources to the higher performing organizational agents (i.e., individuals, groups, departments, or processes, depending on the level of analysis) critical to the organization's survival in different environments. Adaptability results from the learning function enabling the organizations to change as the environment changes. An AAS models organizational behavior from a micro-unit perspective, where organizational behavior is a function of the aggregate actions and interactions of each of the individual agents of which the organization is composed. An AAS enables organizational decision making in a dynamic environment to be modeled as a satisficing process and not as a maximization process. To demonstrate the feasibility and usefulness of such an approach, a financial trading adaptive system (FTAS) organization is computationally modeled based on the AAS framework. An FTAS is an example of how the learning mechanism in an AAS can be used to allocate resources to critical individuals, processes, functions, or departments within an organization.     

On the influence of theory on research in mathematics education: the case of teaching and learning limits of functions

After an introduction on approaches, research frameworks and theories in mathematics education research, three didactical research studies on limits of functions with different research frameworks are analysed and compared with respect to their theoretical perspectives. It is shown how a chosen research framework defines the world in which the research lives, pointing to the difficult but necessary task to compare research results within a common field of study but conducted within different frameworks.     

New research directions in learning and cognition

Research in learning and cognition continues to extend the boundaries of possibilities for theoretical frameworks, research designs, and questions interrogated. This overview captures a snapshot of recent research for the purpose of drawing attention to new directions. It includes: types of theoretical frameworks employed to study student learning, the reciprocity of teaching and learning, and identifying underpinning conceptual understanding that can contribute to curriculum development, including a discussion paper on possible roles of algorithms. Future directions for research are then discussed. The papers in this special issue are briefly introduced in relevant sections. This paper draws attention to the increased use of multi-theoretical perspectives and what they have enabled us to learn about the complexities of teaching and learning in classrooms. It also draws attention to some of the innovative research designs and analysis techniques that have been employed to enable the answering of various research questions.