The application of prediction capability and adaptive target control to the newspaper business

A newspaper wholesaler determines the optimal supply of newspapers, which minimises costs or maximises profit when demand is uncertain. Targets concerning the mean number of unsold newspapers and the probability of not stocking out are commonly used in the absence of known costs. These targets help to strike a balance between excessive wastage (overage) and increased stock-outs (underage). Wholesalers also use various methods of predicting demand, some of which achieve one of the targets while others achieve both. We investigate the relationship between these targets and the prediction method. We say that a prediction method is ‘capable’ if both targets can be achieved when using that method. We introduce a technique for adapting targets, which renders the prediction method capable. We show how optimality is achieved while preserving prediction capability. We use a case study drawn from the newspaper business to illustrate the automatic allocation of newspapers.     

'Model your genes the mathematical way'--a mathematical biology workshop for secondary school teachers

This article describes a mathematical biology workshop givento secondary school teachers of the Danville area in Virginia,USA. The goal of the workshop was to enable teams of teacherswith biology and mathematics expertise to incorporate lessonplans in mathematical modelling into the curriculum. The biologicalfocus of the activities is the lactose operon in Escherichiacoli, one of the first known intracellular regulatory networks.The modelling approach utilizes Boolean networks and tools fromdiscrete mathematics for model simulation and analysis. Theworkshop structure simulated the team science approach commonin today's practice in computational molecular biology and thusrepresents a social case study in collaborative research. Theworkshop provided all the necessary background in molecularbiology and discrete mathematics required to complete the project.The activities developed in the workshop show students the valueof mathematical modelling in understanding biochemical networkmechanisms and dynamics. The use of Boolean networks, ratherthan the more common systems of differential equations, makesthe material accessible to students with a minimal mathematicalbackground. High school students can be exposed to the excitement of mathematicalbiology from both the biological and mathematical point of view.Through the development of instructional modules, high schoolbiology and mathematics courses can be joined without havingto restructure the curriculum for either subject. The relevanceof an early introduction to mathematical biology allows studentsnot only to learn curriculum material in a innovative setting,but also creates an awareness of new educational and careeropportunities that are arising from the interconnections betweenbiological and mathematical sciences. The materials used in this workshop are available at a websitecreated by the directors: http://polymath.vbi.vt.edu/mathbio2006/.     

Characterization of curriculum materials to support NGSS-aligned engineering instruction in chemistry teaching

Curriculum materials can play a major role in shaping teachers’ thinking about instruction and content as well as serve as a support for teachers’ learning. With the inclusion of engineering in NGSS, many teachers may be turning to existing curriculum materials to help them infuse engineering into their science classroom, especially when they do not have the time or opportunity for professional development sessions. In this study, we identified a sample of curriculum materials freely available online to chemistry teachers trying to incorporate engineering in the topics of stoichiometry and/or energy, common topics in secondary chemistry curricula. Using qualitative coding methods, we examined what this sample had to offer the chemistry teachers in the way of developing their understanding of engineering and teaching it. Our findings indicate that within our sample there are limited existing curriculum materials to support teachers’ engineering incorporation into secondary chemistry, and the support for teachers varied in terms of content and usefulness across the materials. The materials provided procedural information for activities but lacked in supports for teacher learning and student development beyond the procedure. Implications for the enactment of NGSS in secondary science along with needs for curriculum development and teacher learning are discussed.     

The Indiana Science Initiative: Lessons from a Classroom Observation Study

The Indiana Science Initiative (ISI) is a systemic effort to reform K–8 science education. The program provides teachers with professional development, reform‐oriented science modules, and materials support. To examine the impact of the initiative's professional development, a participant observation study was conducted in the program's pilot year. Five teachers in grades 3–6 were observed and interviewed as they implemented the ISI‐provided modules. Analysis of the observation data revealed that the teachers incorporated each of the features of inquiry science instruction. However, they did not consistently teach in a way that was aligned with the intent of the ISI. Examination of interview data provided insight into influences on teachers' use of inquiry with the ISI‐provided modules. These data revealed that teachers were aware of the intent of the ISI and attempted to align their instruction. However, teachers were influenced by their perceptions of students' behavior and abilities as well as timing and the appropriate level of teacher control needed to facilitate science instruction. The research suggests that professional development activities should prepare teachers to help learners evaluate explanations against alternatives, connect explanations to scientific knowledge, and provide strategies to address teachers' perceptions of students, timing, and teacher control.     

Mathematics teaching practices with technology that support conceptual understanding for Latino/a students

We analyze how three seventh grade mathematics teachers from a majority Latino/a, linguistically diverse region of Texas taught the same lesson on interpreting graphs of motion as part of the Scaling Up SimCalc study (Roschelle et al., 2010). The students of two of the teachers made strong learning gains as measured by a curriculum-aligned assessment, while the students of the third teacher were less successful. To investigate these different outcomes, we compare the teaching practices in each classroom, focusing on the teachers’ use of class time and instructional format, their use of mathematical discourse practices in whole-class discussions, and their responses to student contributions. We show that the more successful teachers allowed time for students to use the curriculum and software and discuss it with peers, that they used formal mathematical discourse along with less formal language, and that they responded to student errors using higher-level moves. We conclude by discussing implications for teachers and mathematics educators, with special attention to issues related to the mathematics education of Latinos/as.     

The Virginia mathematics specialist initiative: Collaborative effort among all components of the VA mathematics community

The Virginia Mathematics Specialist Initiative (VMSI) is an ongoing collaborative effort among all components of the mathematics and mathematics education community of Virginia spanning more than two and a half decades. This paper describes the use of extensive collaborations to reach shared beliefs about teaching and learning mathematics with the goal of improving student learning; accomplished by preparing and supporting school-based mathematics specialists to coach K-8 teachers. A foundation built on shared beliefs enabled community members to reach consensus on this goal and continues to fuel the accomplishments of the VMSI. Several accomplishments are discussed including identification of the role of K-8 mathematics specialists, the attainment of a Virginia licensure add-on endorsement; and development of a model for a Virginia Mathematics Specialist Preparation Program (VMSPP). Also discussed are the annotated syllabi for core mathematics content and leadership courses in the VMSPP and tools to sustain and extend the VMSI.     

Japanese and American teachers' evaluations of mathematics lessons: A new technique for exploring beliefs

In our study, we use a novel technique to explore the beliefs of Japanese and American elementary school teachers. Four American and four Japanese teachers watched a mathematics lesson—videotaped in either Nagano, Japan or Chicago, Illinois—and commented on the lesson's strengths and weaknesses. The major pedagogical issues that differentiated the teachers' comments were: what students should do during a lesson, how instructors should use language, how instructors should pace lessons and address ability differences, and how instructional materials should be used. The specific beliefs of the American and Japanese teachers in this study mapped easily onto common instructional practices in elementary school mathematics classes in the United States and Japan. We conclude that, at least for the teachers in this sample, beliefs are linked to practices and they may help to tie teachers to their culturally preferred method of mathematics instruction.     

The Zoo Connection: A Cooperative Project Between Formal and Informal Educational Institutions

This project was a cooperative effort between university faculty, elementary school teachers, and members of the Education Department at the Indianapolis Zoo. The purpose of this project was to develop, evaluate, and disseminate a set of fourteen K-6 science lessons that could be used in conjunction with field trips to the zoo. These lessons, titled The Zoo Connection, follow the Learning Cycle teaching model. In addition to following the model, the development of the lessons was based on the premise that teachers should focus on a specific science concept or set of related concepts when visiting a zoo. Workshop sessions were conducted to introduce teachers to the materials and to provide them with strategies for implementing the materials in their science instruction. An evaluation was conducted for each workshop session to determine teachers' perceptions of the materials and to determine whether they felt prepared to use them with their students. The materials were also field-tested in several elementary schools to assess their effectiveness for presenting science concepts to elementary school children. Results indicate that teachers felt the workshops adequately prepared them to use the materials and that the materials were effective for presenting science concepts.     

A heuristic algorithm for the free newspaper delivery problem

This paper addresses the problem of finding an effective distribution plan to deliver free newspapers from a production plant to subway, bus, or tram stations. The overall goal is to combine two factors: first, the free newspaper producing company wants to minimize the number of vehicle trips needed to distribute all newspapers produced at the production plant. Second, the company is interested in minimizing the time needed to consume all newspapers, i.e., the time needed to get all the newspapers taken by the final readers. The resulting routing problem combines aspects of the vehicle routing problem with time windows, the inventory routing problem, and additional constraints related to the production schedule. We propose a formulation and different heuristic approaches, as well as a hybrid method. Computational tests with real world data show that the hybrid method is the best in various problem settings.     

School mathematics curriculum materials for teachers’ learning: future elementary teachers’ interactions with curriculum materials in a mathematics course in the United States

This report describes ways that five preservice teachers in the United States viewed and interacted with the rhetorical components (Valverde et al. in According to the book: using TIMSS to investigate the translation of policy into practice through the world of textbooks, Kluwer, 2002) of the innovative school mathematics curriculum materials used in a mathematics course for future elementary teachers. The preservice teachers’ comments reflected general agreement that the innovative curriculum materials contained fewer narrative elements and worked examples, as well as more (and different) exercises and question sets and activity elements, than the mathematics textbooks to which the teachers were accustomed. However, variation emerged when considering the ways in which the teachers interacted with the materials for their learning of mathematics. Whereas some teachers accepted and even embraced changes to the teaching–learning process that accompanied use of the curriculum materials, other teachers experienced discomfort and frustration at times. Nonetheless, each teacher considered that use of the curriculum materials improved her mathematical understandings in significant ways. Implications of these results for mathematics teacher education are discussed.     

Researching the enacted mathematics curriculum: learning from various perspectives on enactment

This issue of ZDM focuses on research related to the enacted curriculum from various perspectives within the context of the US educational system. In this editorial, we describe the broad view of curriculum enactment taken in this issue, highlighting that we mean more than just how instruction plays out within a classroom. For instance, enactment can occur at a national level as educational goals are enacted into a set of national objectives or standards. Enactment can occur as goals or standards are embedded into written curriculum materials or textbooks, both in terms of teacher guides and materials for students. Enactment can occur as teachers make decisions about how to use their written curriculum materials. Finally, enactment can occur as teachers and students engage and interact with written materials during classroom instruction. We elaborate briefly on these views and then outline the structure of this ZDM issue.     

Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching

This paper sets the scene for a special issue of ZDM—The International Journal on Mathematics Education—by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers’ and didacticians’ engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice.     

A Survey of Job Opportunities and Job Requirements and their Effect on the Mathematics Teaching for Early Leavers in Secondary Schools

A questionnaire survey was used to gauge the opinions of mathematics teachers about some history of mathematics material recently developed for use in the classroom. Teachers' opinions of the materials were generally favourable, but a sizeable proportion responded that they would not be prepared to actually use such material in their own teaching.

     

Integrating Science and Mathematics: Perceptions of Preservice and Practicing Elementary Teachers

One hundred and sixty-one undergraduate elementary education majors and sixty elementary teachers completed an eight-item questionnaire designed to assess their perceptions toward integrating science and mathematics in the elementary grades. The two groups of subjects differed significantly on their responses to five of the eight items. Chi square analyses suggest that practicing elementary teachers felt they had more background in mathematics and science, were more aware of curriculum materials in this area, did not think that integration was currently a common practice, and were more likely to indicate that there was not sufficient time in the school day to integrate the subjects. Preservice teachers were more likely to indicate that integrating the disciplines was preferred to teaching them separately. In addition to the analyses of data, a list of recommendations are provided for teachers, curriculum developers, and policy makers interested in advancing the concept of integrating science and mathematics in instruction.     

A Telecommunications Project to Empower Kansas Elementary/Middle Level Teachers as Change Agents for Integrated Science and Mathematics Education

Nineteen elementary and 5 middle school in-service teachers served as regional lead teachers to provide 13 two- and four-day workshops for 235 in-service teachers. The lead teachers attended 100 hours of inservice training on national science/math reform curricula, cognitive theory, pedagogical strategies for enhancing problem solving, and authentic assessment procedures. The lead teachers then selected $30,000 worth of instructional materials for use in their classrooms. Subsequently, they developed four hands-on-manipulative-based workshops through extensive use of video-teleconferencing technology. The lead teachers strongly believe that this extensive project has made a permanent positive impact on the quality and quantity of integrated science and math instruction in Kansas.     

Multilevel programming,rational reaction sets,and efficient solutions

The prime concern in this paper is the interface between efficient solutions and rational reaction sets in multilevel programming. It is shown that there need be no rational reaction solution which is also efficient, although in the bilevel case such a solution always exists, and in the generalK-level case such a solution exists if certain conditions hold. Some theoretical properties of an extension of known methods for generating efficient solutions are given, which are important algorithmically.This work was carried out under the auspices of the University of Manchester, Manchester, England and the University of Virginia, Charlottesville, Virginia, USA. The author thanks the referees for their helpful comments on the original version.     

The “Problem” of Experience in Mathematics Teaching

Prior research has established that teachers' use of curriculum materials is affected by a range of factors, such as teachers' conceptions of mathematics teaching, and the nature and extent of their teaching experience. What is less clear, and far less examined, in prior research is the role that the teacher guide (TG) may play in mediating the influence of these and other factors on teachers' decisions and actions. Accordingly, this study examines how two 6th grade teachers use the TG from Connected Mathematics Project as a resource in making planning and enactment decisions, and factors associated with patterns of TG use. Through cross‐case analysis, the author found that these teachers seemed to draw largely from their previous experiences and their own conceptions of mathematics teaching and learning when making planning and enactment decisions related to mathematical tasks, and not particularly from the TG. For example, when faced with certain planning and instructional challenges, such as students struggling with the content, teachers tended to rely on their particular conceptions of mathematics teaching to address these challenges. Despite the fact that the TG provided suggestions for teachers as to how address such challenges, it was not extensively used as a resource by the teachers in this study in their planning and enactment of lessons.     

The examination of a vignette activity sequence in a secondary mathematics methods course

Because of their brief nature, vignettes are a strategic way to highlight or explore complex instructional practices. Using a qualitative approach, we examined how the use of vignettes in a Vignette Activity Sequence contributed to secondary mathematics preservice teachers’ understanding of the Mathematical Practices and the Mathematics Teaching Practices. By examining three vignettes used in two iterations of a secondary mathematics methods course, the researchers found that preservice teachers were able to draw connections between the vignettes and their own teaching experiences. However, some misconceptions or incomplete understandings related to the practices were revealed. Preservice teachers sometimes provided vague evidence when identifying particular practices in the vignettes that did not clearly indicate if they understood the practices. Taken together, the researchers found the Vignette Activity Sequence to be a valuable formative assessment that could be used to inform instruction in a secondary mathematics methods course. These findings have implications for teacher preparation programs and mathematics teacher educators.