Implementation of inquiry-based learning in day-to-day teaching: a synthesis

This synthesis is designed to provide insight into the most important issues involved in a large-scale implementation of inquiry-based learning (IBL). We will first turn to IBL itself by reflecting on (1) the definition of IBL and (2) examining the current state of the art of its implementation. Afterwards, we will move on to the implementation of IBL and look at its dissemination through resources, professional development, and the involvement of the context. Based on these theoretical reflections, we will develop a conceptual framework for the analysis of dissemination activities before briefly analyzing four exemplary projects. The aim of our analysis is to reflect on the various implementation strategies and raise awareness of the different ways of using and combining them. This synthesis will end with considerations about the framework and conclusions regarding needed future actions.     

Inquiry-based learning in mathematics and science: a comparative baseline study of teachers’ beliefs and practices across 12 European countries

In the European educational context, reports by expert groups have identified the necessity of a renewed pedagogy in schools to overcome deficits in science and mathematics teaching and to raise the standards of scientific and mathematical literacy. Inquiry-based learning (IBL) is considered the method of choice. However, it remains open to what extent IBL is actually used in day-to-day teaching. In the study presented here we elaborate—from the perspective of teachers—the current status of IBL in day-to-day teaching. Further, we explore what problems teachers anticipate when implementing IBL. In order to gain insight into the wide spectrum of practices in mathematics and science teaching in relation to IBL, a baseline study using teacher questionnaires was carried out in the 12 participating countries. We present selected results from this study that for the first time provides an overview of teachers’ beliefs and their reports on the current use of IBL practices in a European context. The results facilitate a cross-cultural comparison on the potentials and challenges of implementing IBL from the perspective of practicing teachers. Furthermore, the study reveals considerable differences between the teaching of mathematics and science subjects. The findings of the baseline study can serve as a reference line against which the impact of interventions to improve the quality of teaching and learning can be evaluated.     

A US perspective on the implementation of inquiry-based learning in mathematics

This paper discusses issues related to the potential adoption of inquiry-based learning (IBL) projects in mathematics in the United States. To explain the challenges faced in making a place for IBL in the mathematics curriculum, we describe the historical demands of working with a diverse, highly distributed educational system (that is, a system that does not have a central educational decision-making agency with the authority to mandate nation-wide changes), the impact of high-stakes tests to either open or limit the potential for curricular changes, and the changing context in the United States owing to the emergence of the Common Core State Standards in Mathematics (CCSS-M) and nationwide high-stakes assessments designed to be consistent with the CCSS-M. We identify a number of dimensions along which there would be challenges for the implementation of IBL in US school mathematics, including: perceived societal needs; schooling traditions; the specific framing of CCSS-M goals pertaining to problem solving, communicating and reasoning, and modeling and data analysis; and the readiness of the US teaching force to implement IBL. We then consider the issue of scaling up interventions such as IBL, and the politics involved therein.     

Designing and using professional development resources for inquiry-based learning

This paper describes an attempt to design, analyse and refine professional development (PD) resources that encourage the implementation of inquiry-based learning (IBL). We describe the iterative development of the resources in England with over 100 mathematics teachers from secondary, tertiary and adult education and then analyse the impact these resources had on teachers’ beliefs and practices and the issues arising. This evaluation revealed that teachers had moved away from transmission-based orientations, encouraged by the use of less structured tasks and sample lesson plans, but some found it difficult to adopt IBL pedagogies. The most significant issues for teachers may be summarised as: confusing IBL with ‘discovery’ learning; developing and managing collaborative cultures within the classroom; and planning lessons that adapt to the emerging needs of learners.     

Inquiry-based learning for students, teachers, researchers, and representatives of educational administration and policy: reflections on a nation-wide initiative fostering educational innovations

International comparative studies such as TIMSS and PISA have had a considerable influence on the national educational policy in many countries. In Austria, as a reaction to the disappointing TIMSS 1995 results at the upper secondary level, a national initiative with the aim to foster mathematics and science education was launched in 1998: the IMST project. Due to specific challenges of the Austrian educational system, it has undergone several adaptations, but is still running. One of the project’s basic interventions is to promote teachers’ investigation into their own work. It is assumed that this supports the teachers’ critical stance towards innovation and inquiry, which in turn is an important basis for disseminating inquiry-based learning. A general look at the whole project and a specific look into one research project of IMST are used as opportunities to reflect on the complex interconnection and natural tension between the goal of promoting students’ IBL and its sustainable dissemination on a large scale. The paper introduces the project’s theoretical framework and genesis, provides exemplary research results, and reflects on its impact. The paper finishes with five “lessons learnt” from IMST.     

Research evidence on the benefits of IBL

This paper describes the current state of knowledge of empirical studies in the broader sense dealing with inquiry-based learning (IBL) of mathematics and science subjects in schools and universities. The advantages, disadvantages, and effects on relevant outcomes that students can achieve in IBL classrooms are discussed from the aspect of further developing teaching quality. First, the conceptual aspects of IBL are considered briefly to show the background of the studies and the results are categorized. Secondly, references are given with explanations or possible reasons for the results that are not always consistent and, at times, even contradictory. Finally, conclusions from current studies including this overview are drawn with respect to open scientific questions.     

Implementation and outcomes of inquiry-based learning in mathematics content courses for pre-service teachers

This mixed-methods study describes classroom characteristics and student outcomes from university mathematics courses that are based in mathematics departments, targeted to future pre-tertiary teachers, and taught with inquiry-based learning (IBL) approaches. The study focused on three two-term sequences taught at two research universities, separately targeting elementary and secondary pre-service teachers. Classroom observation established that the courses were taught with student-centred methods that were comparable to those used in IBL courses for students in mathematics-intensive fields at the same institutions. To measure pre-service teachers' gains in mathematical knowledge for teaching, we administered the Learning Mathematics for Teaching (LMT) instrument developed by Hill, Ball and Schilling for in-service teacher professional development. Results from the LMT show that pre-service teachers made significant score gains from beginning to end of their course, while data from interviews and from surveys of learning gains show that pre-service teachers viewed their gains as relevant to their future teaching work. Measured changes on pre-/post-surveys of attitudes and beliefs were generally supportive of learning mathematics but modest in magnitude. The study is distinctive in applying the LMT to document pre-service teachers' growth in mathematical knowledge for teaching. The study also suggests IBL is an approach well suited to mathematics departments seeking to strengthen their pre-service teacher preparation offerings in ways consistent with research-based recommendations.     

On deciding how to decide: Designing participatory budget processes

Participatory budgets are becoming increasingly popular in many municipalities all around the world. The underlying idea is to allow citizens to participate in the allocation of a municipal budget. Many advantages have been suggested for such experiences, including legitimization and more informed and transparent decisions. There are many conceivable variants of such processes. However, in most cases both its design and implementation are carried out in an informal way. In this paper we propose a methodology to design a participatory budget process based on a multicriteria decision making model.     

“一站式”远程开放实验平台的设计与实现

"一站式"远程开放实验平台需要集成和整合分别多个来自不同厂商的实践教学软件,而不同的实践教学软件又有各自不同的用户系统与管理平台.针对这一情况,阐述了"一站式"远程开放实验平台的设计思路,并论述了"一站式"远程开放实验平台通过单点登录解决跨平台接口技术,通过Web Service方法实现平台对实践教学软件的数据的采集以及平台的权限设计与实现等关键技术.     

The Prospect Award 1980: On-Line Mixture Calculation System for Stainless Steel Production by BSC Stainless: The Least Through Cost Mix System (LTCM)

A manufacturing industry with a raw materials bill of approximately £60 million per annum was faced with the problem of finding the best way of purchasing and using its raw materials to obtain operating and cost gains. This paper describes design and implementation of the system, which provides a 24 hour on-demand computer service that is run on a routine day-to-day basis as an integral part of the manufacturing process.     

Designing two-echelon supply networks

A modern distribution network design model needs to deal with the trade-offs between a variety of factors, including (1) location and associated (fixed) operating cost of distribution centers (DCs), (2) total transportation costs, and (3) storage holding and replenishment costs at DCs and retail outlets. In addition, network design models should account for factors such as (4) stockouts, by setting appropriate levels of safety stocks, or (5) capacity concerns, which may affect operating costs in the form of congestion costs. The difficulty of making such trade-offs is compounded by the fact that even finding the optimal two-echelon inventory policy in a fixed and uncapacitated distribution network is already a hard problem. In this paper, we propose a generic modeling framework to address these issues that continues and extends a recent stream of research aimed at integrating insights from modern inventory theory into the supply chain network design domain. Our approach is flexible and general enough to incorporate a variety of important side constraints into the problem.     

Learning to Solve Mathematical Application Problems: A Design Experiment With Fifth Graders

Recent research has shown that many upper elementary school children do not master the skill of solving mathematical application problems. In this design experiment, a learning environment for teaching and learning how to model and solve mathematical application problems was developed and tested in 4 classes of 5th graders. Pupils were taught a series of heuristics embedded in an overall metacognitive strategy for solving mathematical application problems. Meanwhile, pupils of 7 control classes followed regular mathematics classes. The implementation and effectiveness of the experimental learning environment were tested in a study with a pretest-posttest-retention test design with an experimental and a control group. The results indicate that the intervention had a positive effect on different aspects of pupils' mathematical modeling and problem-solving abilities.     

Learning to Solve Mathematical Application Problems: A Design Experiment With Fifth Graders

Recent research has shown that many upper elementary school children do not master the skill of solving mathematical application problems. In this design experiment, a learning environment for teaching and learning how to model and solve mathematical application problems was developed and tested in 4 classes of 5th graders. Pupils were taught a series of heuristics embedded in an overall metacognitive strategy for solving mathematical application problems. Meanwhile, pupils of 7 control classes followed regular mathematics classes. The implementation and effectiveness of the experimental learning environment were tested in a study with a pretest-posttest-retention test design with an experimental and a control group. The results indicate that the intervention had a positive effect on different aspects of pupils' mathematical modeling and problem-solving abilities.     

Tolerance interval for exponential distribution

Tolerance interval is a kind of interval that assures the probability of at least a given proportion of population falls into the interval attains to a fixed level. It is widely needed in various industrial practices and business activities, such as product design, reliability analysis, and quality inspection. However, comparing to its widely needs, the research on it is still quite limited. In this paper, we propose a numerical method to compute the tolerance interval for exponential distribution. As the simulation study illustrates, our method performs consistently well as the sample size varies. In particular, its good performance for small sample endows itself broadly potential usefulness in practice.     

A High‐Quality Professional Development for Teachers of Grades 3–6 for Implementing Engineering into Classrooms

With the increasing emphasis on integrating engineering into K‐12 classrooms to help meet the needs of our complex and multidisciplinary society, there is an urgent need to investigate teachers' engineering‐focused professional development experiences as they relate to teacher learning, implementation, and student achievement. This study addresses this need by examining the effects of a professional development program focused on engineering integration, and how teachers chose to implement engineering in their classrooms as a result of the professional development. 198 teachers in grades 3–6 from 43 schools in 17 districts participated in a yearlong professional development program designed to help integrate the new state science standards, with a focus on engineering, into their teaching. Posters including lesson plans and student artifacts were used to assess teachers' engineering practices and the implementation in their classrooms. Results indicated that the majority of the teachers who participated in the professional development were able to effectively implement engineering design lessons in their classrooms suggesting that the teachers' success in implementing engineering lessons in their classroom was closely related to the structure of the professional development program.     

An entire strategy for precise system tracking control of a revolving thin flexural link,part I: Finite element modeling and direct tuning controller design

An entire control strategy including a design based model, controller design, and system output modification for a distributed parameter system is illuminated by application to feedback control of a revolving thin flexural link. In Part I, a very realizable actuator and a sensor, which uses a motor and a tachometer, are applied to design the control system. The finite element modeling and the state space representation are obtained for the purpose of control system analysis and computer simulation. Instead of relying on parameter identification subroutines, a controller design based on directly tuning the parameter of the gain makes the closed-loop absolutely stable and good for system tracking control. This control system design scheme is robust, insensitive to system parameter changes, and this algorithm cannot depend on traditionally priori knowledge such as the system dimension, exact model, or observer design. The performance included in the presence of all the high frequency dynamics can be effectively shown through the computer simulation, and one is led to speculate that this design scheme may perform quite well in the real world implementation.     

工科微分方程课程的实践教学改革初探

国家中长期教育改革和发展规划纲要（2010—2020）在论述“提高人才培养质量”中明确提出：支持学生参与科学研究,强化实践教学环节．如何在本科数学公共课程中开展实践教学以适应创新型人才培养的需要,是数学教育教学改革中迫切需要解决的问题．微分方程是联系数学理论与实际问题的桥梁,本文以工科微分方程课程的实践教学为例,阐述实践教学的内容模块设计、教学方法等改革实践．     

The relevance of system dynamics to engineering systems design

With the recent advent of new technology using micro computers for the centralised monitoring of information, the scope for totally automatic, real time control of large engineering systems has been advanced. We are entering a period which, retrospectively, may well be seen as the era of control; where for the first time it is both feasible and necessary to design system in terms of the way in which they will be operated, as well as in the traditional terms of their capacity requirements. However, before such comprehensive design can be undertaken compatible advances are required in information usage technology.The purpose of this paper is to demonstrate how the subject of System Dynamics can be used to assist with this problem, though its capacity to model information feedback and hence to model and test alternative system control rules based on the information retrieved. This type of application in the hard system area of engineering provides a strong contrast to the more usual applications of System Dynamics in softer socio-economic systems.The problem described is taken from the coal mining industry and related to the design of large scale underground conveyor belt systems used for the clearance of coal from mines. The demonstration presented, therefore, concerns research in this field, but has considerable scope for application in the general area of large scale bulk handling system.Of particular importance in the results is an indication of the potential savings in physical capacity which can stem from the careful design and implementation of control in such systems.     

The virtual design team: A computational model of project organizations

Large scale and multidisciplinary engineering projects (e.g., design of a hospital building) are often complex. They usually involve many interdependent activities and require intensive coordination among actors (i.e., designers) to deal with activity interdependencies. To make such projects more effective and efficient, one needs to understand how coordination requirements are generated and what coordination mechanisms should be applied for given project situations. Our research on the Virtual Design Team (VDT) attempts to develop a computational model of project organizations to analyze how activity interdependencies raise coordination needs and how organization design and communication tools change team coordination capacity and project performance. The VDT model is built based on contingency theory (Galbraith, 1977) and our observations about collaborative and multidisciplinary work in large, complex projects. VDT explicitly models actors, activities, communication tools and organizations. Based on our extended information-processing view of organizations, VDT simulates the actions of, and interactions among actors as processes of attention allocation, capacity allocation, and communication. VDT evaluates organization performance by measuring emergent project duration, direct cost, and coordination quality. The VDT model has been tested internally, and evaluated externally through case-studies. We found three way qualitative consistency among predictions of the simulation model, of organization theory, and of experienced project managers. In this paper, we present the VDT model in detail and discuss some general issues involved in computational organization modeling, including level of abstraction of tasks and actors' reasoning, and model validation.     

Mathematics education research embracing arts and sciences

As a young field in its own right (unlike the ancient discipline of mathematics), mathematics education research has been eclectic in drawing upon the established knowledge bases and methodologies of other fields. Psychology served as an early model for a paradigm that valorized psychometric research, largely based in the theoretical frameworks of cognitive science. More recently, with the recognition of the need for sociocultural theories, because mathematics is generally learned in social groups, sociology and anthropology have contributed to methodologies that gradually moved away from psychometrics towards qualitative methods that sought a deeper understanding of issues involved. The emergent perspective struck a balance between research on individual learning (including learners’ beliefs and affect) and the dynamics of classroom mathematical practices. Now, as the field matures, the value of both quantitative and qualitative methods is acknowledged, and these are frequently combined in research that uses mixed methods, sometimes taking the form of design experiments or multi-tiered teaching experiments. Creativity and rigor are required in all mathematics education research, thus it is argued in this paper, using examples, that characteristics of both the arts and the sciences are implicated in this work.