Project Descpition

Project Description Research and Development Project World-Class Maths and Science Learning Lab in the Copenhagen Region April 2000 The Joint Business Development Program for the Copenhagen Region Copenhagen City Municipality of Frederiksberg County of Copenhagen County of Frederiksborg County of Roskilde World-Class Maths and Science - Learning Lab in the Copenhagen Region Contents Introduction Background and aim Objectives and resources Initial target areas Common denominator Mathematical and scientific literacy Motivating tuition Practical assignments Target areas A. High level mathematics, physics and chemistry 10 ICT in mathematics and science subjects Practical assignments in mathematics, physics and chemistry Cooperation with universities, institutional and commercial enterprises B. Transition from Grade school to High school 14 Mathematics in final year Grade school and first year High school Introductory physics classes in High school Robolab in final year Grade school and first year High school C. Mathematics, science and technology in lower Grade school 17 Team-building and local curricula Mathematics, modeling skills and problem solving Learning through manipulation with Robolab Practical information Information Developing literacy Funding Application for project enrollment Additions: project and management committee membership 3 5 10 20 22 Preface In October 1999, following a motion proposed by the five (county) mayors constituting the Copenhagen Region Forum of Commerce and the Joint Business Development Program for the Copenhagen Region, a project committee was established with the task of developing a framework for implementation of World-Class Maths and Science in a number of schools across the Copenhagen region. Project committee members include Carl P. Knudsen (project manager), Niels Hartling, Allan Jørgensen, Erik Pawlik, H.C. Thomsen, Søren Thorborg and Anne Winther Petersen. We would like to take this opportunity to thank the many people who each in their own way contributed ideas and constructive proposals to the project at various meetings and seminars during development of the project description. Special thanks must also go to the authors whose contributions can be read on the project’s home page. These discussions have proved extremely inspiring for us, and hopefully many people will be able to recognize specific sections of the project specification. We apologize for not always referring directly to original sources. Carl P. Knudsen 2 World-Class Maths and Science - Learning Lab in the Copenhagen Region Introduction Background and aim World-Class Maths and Science is born of the proposal for the creation of Learning Lab Denmark, where top international experience on teaching and learning methods can be developed, tested and applied to a joint project set up between Danish schools, commercial enterprises and various forms of knowledge environment. It is a regrettable fact that far too many young people express little or no interest in mathematics and science. This has resulted in significant numbers of the adult population lacking basic literacy in mathematics, physics and chemistry, presumably due to a failure of current teaching methods. Enrollment procedures for entry into technical and scientific disciplines are inadequate, meaning that in future it will be extremely difficult to satisfy demand for employees with technical and scientific backgrounds. The objective of World-Class Maths and Science is to:    increase interest in mathematics and science focus on mathematical and scientific literacy encourage young people to enter technical or scientific courses of higher education The project intends to establish a network of schools in the Copenhagen region, forming the basis for cooperation between didactic researchers and practitioners in schools. Universities, institutions and commercial enterprises can be connected to the network via active involvement in particular research and development projects. Objectives and resources The project intends to identify new concepts in education and greater flexibility in teaching methods aimed at improving general education standards so all students are capable of understanding and participating in mathematics and science subjects at a higher proficiency level than before. The teaching methods applied must at the same time give particularly interested and talented students the opportunity of further improvement within the mathematics and science field. The project will focus primarily on the development of teaching technique. This predisposes that circumstances are as normal as possible and means, for example, that no restructuring of teaching time or subject content is planned, but rather an improvement in economic resources and organizational flexibility of classes. This does not mean subject content is without 3 World-Class Maths and Science - Learning Lab in the Copenhagen Region interest. On the contrary, interest in cohesion and progression in teaching curricula concerning mathematics and science in the joint educational system is to a high degree a requirement. The project committee has identified the following research and development fields:       Increased emphasis on motivating teaching New teaching methods Revised thinking on practical assignments Application of ICT with special emphasis on mathematics and science subjects Cohesion and progression in teaching, in particular the transition from Grade school to High school and from High school to further education Application of alternative learning environments via cooperation with business enterprises, educational institutions, etc. Initial target areas The initial project comprises 15-20 schools in the Copenhagen region, and action will focus on three areas: A. High level mathematics, physics and chemistry B. The transition from Grade school to High school C. Mathematics, science and technology subjects in Grade school It is intended that within each target area a specific number of High schools and/or Grade schools will participate in the project. The plan is for classes or groups involved in the project to take part in trials in both mathematics and science subjects (which at different class levels are termed science and technology, physics/chemistry, physics and chemistry, respectively). The project as such will attain a higher profile and a synergy effect may be generated. Research expertise will be assigned to sub-projects for each target area for development, completion and evaluation. Teachers participating in the project will receive training through the provision of courses, seminars and conferences. 4 World-Class Maths and Science - Learning Lab in the Copenhagen Region Common denominator General education standards, motivating teaching forms encouraging student improvement and practical assignments are three central areas of research and development within mathematics and science. The concepts described below, and the opinions referred to, constitute a common denominator for sub-projects under World-Class Maths and Science. Mogens Niss1 contends (albeit only in reference to general education and mathematical literacy) that, "The reappraisal of existing High school (and Grade school) subjects with application of the described ideas would in itself be a great step forward, without thereby requiring significant modification of the general system or framework". It goes without saying that this view is one the project should expand upon. Mathematical and scientific literacy A forthcoming OECD's investigation2 into school pupil benefit of mathematics and science subjects places most emphasis on mathematical and scientific literacy. The PISA-project3 definitions of literacy confirm the significance of functional knowledge and proficiency in ensuring individuals the opportunity of playing an active role in society4. It is this concept of literacy which provides much of the basis for World-Class Maths and Science. Mathematical literacy is an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded mathematical judgments and to engage in mathematics, in ways that meet the needs of that individual’s current and future life as a constructive, concerned and reflective citizen. Scientific literacy is the capacity to use scientific knowledge to identify questions and to draw evidence-based conclusions in order to understand and help make decisions about the natural world and the changes made to it through human activity. In the PISA project, teaching is characterized with the help of the competencies it is to avail to recipients. 1 2 Mogens Niss: Gymnasiets opgave, almen dannelse og kompetencer, Uddannelse 2/2000. OECD Program for International Student Assessment (PISA). See e.g. www.pisa.oecd.org. 3 Measuring Student Knowledge and Skills - A New Framework for Assessment. OECD 1999. 4 See also: Svein Sjøberg: Naturfag som allmenndannelse, Ad. Notam Gyldendal 1998 5 World-Class Maths and Science - Learning Lab in the Copenhagen Region Mathematical competencies5: Being capable of:  Mathematical thinking  Mathematical argumentation  Modeling  Problem posing and solving  Representation  Symbolic, formal and technical skills  Communication skills  Making use of various aids and tools, including ICT Scientific competencies: Being capable of:  Recognizing scientifically investigable questions  Identifying evidence needed in a scientific investigation  Drawing or evaluating conclusions  Communicating valid conclusions  Demonstrating understanding of scientific concepts The above competencies should naturally be applied in relation to subject content in tuition. The processes described by these competencies can only occur in conjunction with specific circumstances. The intention of the detailed PISA project description, which more traditionally could be termed "mathematical/scientific thought and methodology", is that competencies should be prioritized in relation to specific teaching content in the classroom. According to Mogens Niss6, the important thing is that a main consideration for selection of teaching material should be the competencies the given material best suits. Motivating tuition A new survey7 on physics teaching in High school shows that classes are characterized by a very restricted selection of assignment types and activity. The daily routine comprises mostly teacher monologue or teacher-controlled discussion, arithmetic or practical assignments 5 6 See also: Mogens Niss: 'Kompetencer og uddannelsesbeskrivelse' , Uddannelse 9/1999 Mogens Niss: 'Gymnasiets opgave, almen dannelse og kompetencer'. Uddannelse 2/2000. 7 Lars B. Krogh and Poul V. Thomsen: GFII report no.1: 'Undervisningsstil og læringsudbytte – en undersøgelse af fysikundervisningen i 1.g. Århus Universitet marts 2000'. 6 World-Class Maths and Science - Learning Lab in the Copenhagen Region containing little or no level of freedom for students. The survey is based on two styles of teaching:   A subject-centered teaching style, with subject structure providing the hub around which teaching evolves and where the teacher acts as a kind of 'sculptor', forming and shaping this structure for students. A constructivist teaching style, with teaching focusing on student learning processes and where the teacher establishes a learning environment which supports and naturally encourages students to become involved in the physical subject matters. Not surprisingly, the survey reveals that subject-centered teaching is the prevalent teaching form and that the overriding conclusion is thus: Students get a better impression of teaching when classes are provided a greater constructivist element. It is, however, interesting to note that classes containing an affirmative equal mix of subject-centered and constructivist styles are very positively thought of by students. Therefore it is not considered beneficial to completely remove the element of subject-centralization, but rather to supplement this with sufficient constructivist content. It is only natural to assume that a study of mathematics and chemistry lessons would come to a similar conclusion. World-Class Maths and Science intends to investigate whether teaching styles which are more pro-active to student involvement in the learning process by placing greater demands of independent activity on the individual actually contribute to increased interest whilst at the same time supporting development of relevant literacy. An increased element of practical assignments immediately springs to mind because of the manner in which this form of study allows for greater student involvement and increased personal responsibility in the actual learning process8. Practical assignments are considered a way of structuring a working process9. It is "an on-going, coherent working process, eventually taking material form, for example as a report". This broad definition allows for dialogue on ideal placement in various connotations on a range of continuous scales, for example in connection with:  range of freedom (teacher or student-controlled)  orientation (subject-oriented or problem-oriented)  realness (internal professional problem solving or modeling)  social interaction (individual work or teamwork) 8 Jens Dolin: 'Projektorienteret arbejde set i et læringsteoretisk og fysikfagligt perspektiv'. See www.matnatverdensklasse.dk 9 Tomas Højgård Jensen: 'Projektarbejde: Navigering i et skitseret mulighedsrum ifm. en samtænkning af matematik- og fysikundervisningen' . See www.matnatverdensklasse.dk 7 World-Class Maths and Science - Learning Lab in the Copenhagen Region Practical assignments Practical assignments undertaken by students of science subjects come from a long and somewhat old-fashioned tradition10. In High school physics classes this tradition can be traced all the way back to 1903, whilst titles for practical assignments in the classical department can be found on a list of 40 experiments students had to have undertaken prior to enrollment at Harvard College in 1887. Typical reasoning for the necessity of these experiments is that students must:  familiarize themselves with phenomena at first hand  learn elemental experimental techniques  learn to apply natural science processes and methodology  develop their understanding of scientific concepts Experiments are further expected to encourage active class involvement and motivate students. Whether this type of practical assignment work actually contributes to expected learning results11, however, is in question. In particular, use of "cook-book" practices provides a distorted image of how theory and experiment go hand in hand, and of how experimental work is performed outside the realms of school. A study12 of student experiments in High school indicates that students have little opportunity for independent activity, judged on three possible ranges of freedom:  The problem the experiment is designed to affirm or solve  The actual carrying out of the experiment  The findings, either in tabular form, a theory to be demonstrated or singular valued problem solving There is a need for the rethinking of experiment work in general, mirrored in significant current interest in the field. As such the Danish Ministry of Education has launched the Nordic research and development project, NORDLAB13, where Denmark is charged with examining practical and experimental work in the natural sciences. With the introduction of experimental projects, etc. into classroom education, the first step has been taken to change the current outlook. There is a need, however, to further develop a practice that departs from otherwise inaccessible, closely monitored lab work and moves towards more open and explorative experimental activity. 10 Karin Beyer: 'Fysiske øvelser - det store fremskridt eller den store illusion'. Fysiklærerforeningen 1921-1996. Fysikforlaget 1996 11 NORDLAB-DK. See e.g. www.nordlab.u-net.dk. 12 See: GFII-rapport nr.1. 13 NORDLAB. See e.g. www.nordlab.u-net.dk. 8 World-Class Maths and Science - Learning Lab in the Copenhagen Region In order to provide students with an impression of authentic lab work, recent years have seen the creation of a joint project between schools and laboratories of individual business enterprises and universities. In the Copenhagen region for example, the Technical University of Denmark (DTU)14 and Copenhagen University (KU) offer experimental activities to schools, just as a small number of schools and business enterprises work together on project development in business enterprises15. 14 15 Ny viden – øvelser og foredrag for gymnasieklasser. DTU 1999. Dansk Industri (DI): Skole, teknik og industri. See e.g. www.di-gym.dk. 9 World-Class Maths and Science - Learning Lab in the Copenhagen Region Target areas A. High level mathematics, physics and chemistry The intention is to pay extra attention to those students expressing particular interest in mathematics and science subjects by opting for a so-called "subject-combo", either mathematics and physics or mathematics and chemistry at high proficiency levels. There is a need to study just why students choose these subjects at a high level. It would be no less interesting to discover whether increased effort could create greater interest in choosing a course of higher education within the technical and science disciplines. ICT in mathematics and science subjects Use of information and communication technology (ICT) in mathematics and science classes involves two primary areas. The first concerns experience, research findings and new concepts associated with communication and information search mediums, for example electronic networks, discussion forums, electronic conferences, home pages, databases and other similar resources. The second concerns application of modern technology in a specific subject connotation, for example data collection and processing, use of computer algebra systems (CAS), mathematical modeling and problem solving. Students will be provided with laptop computers with remote line access to the school network and as such to the intranet and Internet. Equipment will have standard software such as Windows and Internet Explorer installed, as well as Office programs like Word, Excel and Powerpoint. The market for PCs as a tool in mathematics and science classes is growing steadily. New products, versions and prices appear all the time, so selection of class equipment will be an on-going process. For use in high schools, DERIVE16 currently offers a very viable option as a CAS program. It is Windows-based, cheap, easy to use and Word-compatible. For data collection for use with physics and chemistry, FPro17 is also a good tool. Again, like DERIVE, this is Windows-based, cheap, easy to use and Word-compatible. All students involved in the project will be provided with DERIVE and FPro. 16 Nils Fruensgaard: 'EDB programmer i matematikundervisningen'. See www.matnatverdensklasse.dk 17 Ole Bakander: 'Dataopsamlingssystemer – en oversigt'. See www.matnatverdensklasse.dk 10 World-Class Maths and Science - Learning Lab in the Copenhagen Region A program of further education for teachers will be developed directed at both technical knowledge of applied computer tools and subject didactics concerning just how these tools can best be exploited in order to create optimal subject challenge for students. Cooperative dialogue must be established for subject-specific programs used, so that material produced in connection with the development project may be made available to teachers and students through discussion and Web site mediums. The written High school exam in these subjects is expected to be restructured so that special ICT aspects for students are taken into account. Exam specifications will be set as soon as possible and no later than the end of the second year of High school. ICT in mathematics A number of surveys18 suggest that the introduction of ICT into mathematics classes appears to be of great significance to the way students approach mathematical thinking and methodology. The intention is to investigate whether, with the assistance of mathematical programs, it is possible to acquire knowledge in such a way that it allows for greater conceptual assimilation, and thereby easier application in other subject areas. Groups opting for mathematics/physics or mathematics/chemistry subject-combos for example are better suited for analyzing conceptual assimilation of infinitesimal calculus. The research project is founded on addressing the following questions:  How good is the association between student work with standard formulae and their understanding of mathematical concepts?  How can the application of ICT assist student conceptual assimilation?  What is the role of ICT in working with mathematical models and modeling?  What is the role played by ICT for teaching norms and for the interaction between teacher and student? ICT in physics and chemistry Computers are often used today in experimental physics and chemistry teaching. Computer-based data collection19 involves three principal components:  Sensor  Measurement box, converting the signal from the sensor into numerical form 18 Morten Blomhøj: 'Integration af ICT i gymnasiets matematikundervisning – en didaktisk udfordring', Ministry of Education, 1999. 19 Ole Bakander: 'Dataopsamlingssystemer – en oversigt'. See www.matnatverdensklasse.dk 11 World-Class Maths and Science - Learning Lab in the Copenhagen Region  Computers for receiving, saving and processing collated data The development of cost-effective sensors and measurement boxes (e.g. CBL, Robolab RCX) for use with PCs makes it very relevant to investigate the possibilities which access to laptop data collection makes available. The research and development project is based on addressing the following questions:  How can data collection, processing and management be integrated with the application of computers in experimental work?  How can the possibility of laptop data collection with use of CBL, etc. support investigative and experimental teaching forms?  What problems – and solutions – arise from extensive use of ICT? Use of Internet, intranet, databases, home pages, etc. Current use of ICT – except in connection with word-processing – is limited in teaching today, and the use of Internet, intranet, databases, home pages, etc. has until now been driven by a relatively small group of enthusiastic pioneers. The project will see the development of examples of this type of ICT use in classes. There is a need for subject related didactic research to be initiated in this field of ICT as well, thereby creating a sound foundation for the exploitation of new opportunities, including: Databases and information retrieval The Internet can be a valuable source of information acquisition. This, however, must not be confused with knowledge. Information is a specific answer to a specific question. Knowledge, on the other hand, is the ability to generalize and anticipate based on, albeit a normally incomplete, given pool of information or intelligence. Partial resolution of this could be the use of subject matter listings as a set of relevant links, for example the subject info-guide, (URL:http://www.infoguide.dk) and the physics, mathematics and chemistry home pages on the Intranet.. Visualization Interactive visualization would most likely prove a positive contribution to increased understanding of a multitude of concepts. At the moment only a few examples of such material exist, and development of illustrations would necessitate concerted effort from teachers involved, although it is presumably one of the most obvious areas where ICT can promote learning. Under the name VisionQuest, UNI-C are developing computer-based, supplementary materials, which with the aid of 3D visualization techniques and a high level of interactivity provide classes with a whole new perspective compared with traditional teaching resources. http://www.visionquest.dk/ 12 World-Class Maths and Science - Learning Lab in the Copenhagen Region Simulation By using computer-generated models the findings of an experiment can be calculated based on a given set of initial conditions and a more or less idealized theoretical model. If the actual experiment is not discussed or performed, then simulation is considered a “virtual” exercise. Electronic documents on WWW Written products are delivered as HTML documents. ICT would be used as a tool in a differentiated teaching and writing process. Electronic logbooks of classes are kept. Practical assignments in mathematics, physics and chemistry A series of studies, including a research project undertaken at DTU, reveal that many students learn to "pass the exam", yet still lack the basic conceptual understanding teachers would like. It is the intention to investigate project work forms in mathematics, physics and chemistry at high proficiency levels. The objective is to document whether students working on project-organized work attain greater involvement and understanding; whether students hereby are more motivated and whether the practical assignment form positively influences the type of literacy demanded from the commercial business world, for example, problem solving, independence, initiative, ability to work in a team, etc. As experiment organizers are in possession of computer equipment it is possible to work with more authentic examples in each of the three subjects. Objectives include students realizing their own ability to formulate problems; to gather relevant information; to carry out a modeling process and to work independently in groups. It will be investigated whether or not the practical assignment process also contributes to an understanding of internal subject matter problem identification. The intention is to work with projects in individual subjects, while some projects may involve more than one subject. Specific examples include the 10-hour physics project, configuration in mathematics and projects created from cooperation between commercial enterprises and educational institutions. Theoretical problem posing is an additional working subject20 possibility. Cooperation with universities, institutions and commercial enterprises The objective of the project is to develop a model for cooperation between High schools and institutes of higher education and business enterprises. Cooperation will assist in:  improving the quality of mathematics and science lessons  increased entry into higher education in these subjects. 20 Examples found e.g. in Tomas Højgård Jensen's study (www.matnatverdensklasse.dk ) and in "Projektorganiseret undervisning i fysik", Uddannelsesstyrelsens temahæfte no. 24/1999. 13 World-Class Maths and Science - Learning Lab in the Copenhagen Region It is important for young people to learn that technology and science are exciting and can offer a life of content and challenge. Therefore it is vital to maintain contact between young people and those within the technical and scientific professions. There is currently a wide range of material available offering opportunities and inspiration on cooperation, for example the “New Knowledge” catalogue from DTU; listings from the Institute for Mathematical Sciences at Copenhagen University and the "science and mathematics initiative" listings of the Copenhagen City21. In addition to this material, development includes:  bilateral cooperation between a number of High schools and establishments of higher education (DTU).  a concept involving a field-trip for advance-level (subject-combo group) students at physics and chemistry sites located at Copenhagen University/Pharmaceutical High School for the performing of experiments. A work-group at Copenhagen University will make a presentation during the spring of the year 2000.  a system of industrial grants in the Copenhagen region whereby individual students are employed for a week at a local company where they work on a specific task.  a home page under the Confederation of Danish Industries including potential sites of interest and good descriptions of enterprise offers.  an evaluation methodology for analyzing which projects influence student attitudes. It is extremely demanding on resources for enterprises and institutions to have high school students visit and at the same time put on activities relevant for the advanced-level group. Therefore it is important to establish a set routine for each activity, allowing planning and organization of the trip to be kept to a minimum. B. Transition from Grade school to High school Many of the problems associated with mathematics and science lessons are known phenomena in other Western countries, although some are unique to the Danish school system. As such, it is a well known fact that in Denmark a gulf exists between different sections of the educational system, especially between Grade school and High school. The intention is to reveal which problems students associate with the transition between Grade school and High school – especially regarding the subject of mathematics – and to investigate just how these problems can be diminished. 21 See www.efeu.dk 14 World-Class Maths and Science - Learning Lab in the Copenhagen Region Mathematics in final year Grade school and first year High school The primary objective is to apply Mogens Niss’ theory on literacy to a problematic discontinuity in mathematics teaching – the transition from one type of school to another. The objective is to first improve mathematics teaching for students in their last year of Grade school and the first year of High school – and secondly to improve opportunities for mathematics teachers to bridge-build between the two school types; to develop understanding and respect for the considerations and methods favored by "the other type of school" – without getting in the way of normal teaching. Thirdly the objective is – with the assistance of external supervision, ideally research-based – to investigate and describe precisely what differences exist between the two types of school, describing the possibilities teachers have for learning from each other and documenting a number of case examples for use in World-Class Maths and Science. A number of examples can be cited of subjects provided during both the last year of grade school and the introductory term of high school. For example, linear functions, square roots and numbers, classical geometry, analytical geometry, solving equations, reading mathematical text, communicating mathematics, finites and denumerables, prime numbers and denominations, functions (representation), modeling (computation of interest), use of ICT. The research project is founded on addressing the following questions:  What difference is there between the way the two types of school teach the same mathematical subjects, for example linear cohesion?  How can classes in the last year of Grade school and the first year in High school be arranged such that the transition between the two is made easier for students? The plan is to study 2-3 representative teaching programs. Introductory physics classes in High school It is the primary objective of the experiment to improve introductory physics education in the first year of high school whilst at the same time increasing student motivation. It is the direct aim of the experiment that students quickly learn to live up to the requirements of abstraction, which is a precondition for understanding materials taught in physics at High school. This will ease the transition from the last year in Grade school. The experiment is inspired by the approximately 15-year old British CASE project. Planning in Denmark is coordinated by P.V .Thomsen and Jens Holbech22, and includes as mentioned, introductory physics education in High school. The project will answer the question of whether it is possible to accelerate students’ cognitive development through physics education. 22 Poul V. Thomsen and Jens Holbech: 'Bedre Tænkning gennem Fysikundervisning'. See www.matnatverdensklasse.dk Also see: Leif Henriksen and Ejnar Hobolth: 'TAFAT – Træning Af Folkeskoleelevers Abstrakte Tænkeevne'. See www.matnatverdensklasse.dk 15 World-Class Maths and Science - Learning Lab in the Copenhagen Region This builds amongst other things on Piaget’s theories concerning child development occurring in stages:  The sensory-motor stage (0-2 years old)  The pre-operational stage (2-7 years old)  The specific-operational stage (7-11 years old)  The formal-operational stage (11 or older ) The project also builds upon Piaget’s theory that new knowledge is constructed - in particular during a "cognitive conflict" - meaning how people acquire new experiences which conflict with the construction already acquired. This forces the student into "reprogramming" or "restructuring" knowledge in order to incorporate new insight. If newly-acquired knowledge is not to be lost then it is important that simultaneous metacognition occurs, meaning realization of newly-acquired knowledge23. In the British project children are subject to a (closely) controlled program containing a number of tasks of experimental character. These tasks are founded to address different stages and they are structured to bring the children into cognitive conflict and thereby accelerate natural development. British findings have proved very positive, and opinion is that those children taking part in the experiment perform significantly better in tests compared to other children. It must be assumed that students at High school have reached the "specific-operational stage", despite experience indicating they most likely have not progressed any further. Therefore the majority of the British texts, structured to a different age group, will be left out, changed or replaced by other projects. Scheduled projects are carried out for participating classes during the course of the school year, parallel to regular tuition. As projects are experimental in character it is likely that they can be incorporated as part of regular practical assignment work in the classroom. Robolab in final year Grade school and first year High school The intention is to investigate how to approach projects concentrating on problem solving and construction in relation to final year Grade school and first year High school. The project will be interdisciplinary. In Grade school this means mathematics and physics/chemistry - in High school, physics and mathematics. Robolab/LEGO provides the experimental equipment24. LEGO bricks can be used to build programmable models. Students decide how their models will behave and formulate a program to be installed into the model. 23 24 Also see: "Undervisning i fysik - den konstruktivistiske idé". Gyldendal 1992 Bjarne Thams: 'Robolab i gymnasiets indledende fysikundervisning'. See www.matnatverdensklasse.dk 16 World-Class Maths and Science - Learning Lab in the Copenhagen Region Often the model/program does not work according to plan. The challenge is in turning ideas into reality. In order for ideas to be realized, students must undergo a working process which typically consists of reviewing what needs to be done, acquiring ideas, analyzing, formulating problems, designing, planning, organizing, constructing, cooperating, making on-going evaluation, reevaluating, testing, correction, overcoming crises, controlling, describing, estimating and presenting. The research task is to highlight the project work form in the two school cultures and assess whether this type of cooperation between teachers in the two school systems can ease student transition from Grade school to High school and give some ideas for how students can ease this transition via initiatives proposed by the respective schooling systems. C. Mathematics, science and technology in lower Grade school The objective is to strengthen general education in mathematics and science subjects in a school dominated by the Humanities. The project is founded on supporting teams at individual schools teaching mathematics, science and technology subjects and aims at developing local curricula in these subjects, thereby increasing cohesion and progress in education25. Team-building and local curricula In Grade school, two main routes have dominated educational structure until now; specialist-teaching and comprehensive teaching. Now a third route is beginning to emerge: Team-teaching. Specialist teaching has the advantage of containing high professional content – often with an assigned subject matter didactic. Teachers have a professional identity and form part of a specialist group where experience is shared and new thinking encouraged. Specialist teaching has the disadvantage that the daily curriculum is divided into small time-periods with changing subjects, teachers and often classrooms. Children must relate to many different teachers, and none of the teachers are part of the daily routine or possess full pedagogic or social insight in relation to the class as a whole or to the individual child. Comprehensive teaching provides a safe, manageable framework with children only having to relate to a small number of people. Work time scales fit in with actual assignments and given situations, thus promoting continuity, unity and the possibility for greater depth. Comprehensive teaching is in part built on the somewhat dubious assumption that anybody can teach anything. This occasionally results in insufficient professional ability and subject didactic experience. Teaching has unity and breadth, yet only partially suitable depth. 25 See reports from LUNT project, Danmarks Lærerhøjskole (DLH) 1997 17 World-Class Maths and Science - Learning Lab in the Copenhagen Region The reason the project is team-structured is that this form of working allows for a combination of positive elements from both specialist and comprehensive teaching structures. The team structures its own planning and division of labor. Planning is undertaken periodically, allowing teacher strengths to be highlighted in turn. The teachers themselves are also undergoing a learning process. The Primary Education Act – and not least the new agreement on working hours – favors the team concept, encompassing both science and technology as well as mathematics education in the same class. The project objective will be to support a form of science and technology teaching that fulfills the criteria of the teaching guidelines concerning building upon constructivist thinking, whilst at the same time placing emphasis on the teacher as professional, contributing to overall cohesion and professional unity to the recipient students’ experience of the experimental process. We will contribute to change which addresses a situation whereby many students are performing practical/experimental assignments, but where many conclusions, findings of common characteristics or rules or the association between student work and supporting theory often leave much to be desired. We want to encourage teacher professionalism and specialist knowledge in order that they may better meet the professional challenge of bringing the experimenting student closer to professional, systematic enlightenment. Mathematics, modeling skills and problem solving. It is the general opinion that many students in the upper years of Grade school and those in High school currently find it difficult to solve the more abstract tasks. It is often maintained it would be preferable to start very early on, working for example with the significance of reason. World-Class Maths and Science will investigate how the mathematical curriculum can be organized in lower Grade school, focusing on the ability of generalization and abstraction, and which takes into account the most motivated students of this age group. During the course of the experiment, certain elements will be developed targeted at a specific mathematical topic. This can take the form of a specific everyday problem, where students initially work on a set item but where they work towards the establishment of a general theory, such that this theory may be applied to new problems26. A beneficial form of working would be with basic mathematical models, putting forward general mathematical rules and working with actual mathematical language. In the work on arithmetic and algebra within this age group it is possible to work from the specific to the abstract and for many students it would be an advantage in future work if the level of general knowledge were increased. One example is with surveying. For this material resources will be available. Large and small measurements and calculations will be worked on during the course of the project, by the end 26 Lisser Rye Ejersbo and Michael Wahl Andersen: 'Problemhåndtering'. See www.matnatverdensklasse.dk 18 World-Class Maths and Science - Learning Lab in the Copenhagen Region of which it will be clear to students which mathematical theory they have actually been working on. Another example is distance and dimension in space. Tangible work can be performed in this connection, for example with the construction of proportionally dimensioned planet models, as well as abstractly, for example how distance to the sun is judged. These topics allow for good interdisciplinary cooperation with science and technology. A third example is equations. This allows for special focus on student proficiency in arithmetic. Learning through manipulation with Robolab27 Science and technology curricula for lower Grade school denote: "On the basis of their own ideas and hypotheses, students now to a higher degree design and perform experiments, tests and studies. The computer is used for measurement and management, simulation and systematization of data." World-Class Maths and Science intends to investigate whether the above is achieved through working with LEGO MindStorms at schools (Robolab), as well as the extent to which students assimilate problem solving strategies by working with Robolab. The core of the Robolab concept is LEGO’s yellow microcomputer, RCX. RCX is programmed via an icon-based programming language. Robolab combines learning with laughter and theory with practice. The idea is that the students learn a problem solving strategy or learning strategy, whilst they inquisitively and experimentally construct something which works in reality, based upon their own ideas. A successful manual construction process thereby has a retroactive positive effect on thought structures28. The project involves students working in groups of 3-4 on tasks requiring the construction of a "robot", programming of this robot and subsequent testing. Students must keep a running log of events detailing progress and how they have overcome problems. Groups can work on projects whereby the individual robot comprises part of a larger entity, for example in a theme park. 27 Mitchel Resnick, MIT Media Lab: 'Technologies for Lifelong Kindergarten'. ETR&D, Vol. 46, No. 4, 1998 28 See e.g. http://www.mikrov.dk/robloab og http://www.dlh.dk/mat/fys/robolab//index.html 19 World-Class Maths and Science - Learning Lab in the Copenhagen Region Practical information Information An electronic conference (inside SkoleKom) is established for all participants in the project, with subconferences for individual working groups. A Web site for World-Class Maths and Science with the address www.matnatverdensklasse.dk will also be created for the dissemination of new ideas, experiences and research findings. An annual conference on World-Class Maths and Science and smaller seminars will be held according to demand. Courses Participants in the project will be offered courses in a number of specialist areas. Courses are currently expected on DERIVE, FPro, the fundamental principles of CASE and use of Robolab. Funding Each participant teacher will be allocated 50 working hours as a general test allowance, and each participant school will be allocated DKK 10,000 to cover increased operational expenditure. The purchase of computers, program licensing, Robolab, etc. will be administered by the project committee and the expenses covered by the project. Application for project enrollment 15-20 schools across the Copenhagen region may participate in the project. The duration of the project is expected to be between 2-4 years. Applications for enrollment to the project must be received no later than May 10, 2000. Applications should be sent to the project manager: Mr. Carl P. Knudsen, Principal, Helsingør Gymnasium Borgm. P. Christensensvej 3, 3000 Helsingør 20 World-Class Maths and Science - Learning Lab in the Copenhagen Region Tel + 45 49 22 41 00 e-mail: Carl.P.Knudsen@skolekom.dk A copy of the application should be forwarded to your own Local Education Authority. Schools selected for participation in the project will be chosen by the project’s steering committee before May 20, 2000. Schools decide themselves which teachers and classes are to participate in the project. Participants in the three primary target areas include: A. High level mathematics, physics and chemistry Schools: High schools with subject-combos in mathematics-physics and/or mathematics-chemistry. Classes: In the academic year 2000/2001, starting with subject combos in 2nd year High school mathematics and physics (and/or mathematics and chemistry). The experiment continues in the following academic year in 3rd year High school with an expected new subject-combo in 2nd year High school Teachers: The class teachers for mathematics and physics (and/or mathematics and chemistry). B. Transition from final year Grade school to High school Schools: Partner-schools (e.g. a Grade school and a High school submit a joint application). Classes: Two final year Grade school classes and one first year High school class in mathematics. Teachers: Final year Grade school teachers of mathematics and physics/chemistry (4 in total) and first year High school teachers of mathematics and physics (4 in total). C. Mathematics, science and technology in lower Grade school Schools: Grade schools primarily from the Copenhagen City or Municipality of Frederiksberg districts. Classes: In the academic year 2000/2001 starting with two 5th year Grade school classes. The experiment continues the following academic year in the 6th year of Grade school, with additional expected start of two new 5th year Grade school classes. Teachers: Class teaching team of mathematics and science/technology (4-6 in total during the academic year 2000/2001). Any questions concerning the above may be directed to the project manager. 21 World-Class Maths and Science - Learning Lab in the Copenhagen Region ADDITIONS PROJECT GROUP Copenhagen City Senior Lecturer Erik Pawlik Rysensteens Gymnasium Educational Adviser Søren Thorborg Administration of Education & Youth Municipality of Frederiksberg Senior Lecturer H.C. Thomsen Frederiksberg Gymnasium Senior Lecturer Allan Jørgensen Virum Gymnasium Principal Carl P. Knudsen (project manager) Helsingør Gymnasium Senior Lecturer Niels Hartling Birkerød Gymnasium County of Roskilde Senior Lecturer Anne Winther Petersen Himmelev Gymnasium. County of Copenhagen County of Frederiksborg COMMITTEE Copenhagen City Chief Executive Peter Rasmussen Administration of Education & Youth Director of Culture Ivar Koed Directorate for Cultural Affairs Director of Culture Henning Thomsen Board of Cultural Affairs Director Jan Magnussen (Chairman) Education, Commerce & Cultural Affairs Director Ole Hvidesten Rasmussen Board of Education & Cultural Affairs Municipality of Frederiksberg County of Copenhagen County of Frederiksborg County of Roskilde 22 World-Class Maths and Science - Learning Lab in the Copenhagen Region Translations of footnote titles originally in Danish: Footnote: 1. Mogens Niss, 'The High School Mission, General Curriculum and Literacy', Uddannelse 2/2000. 4. Svein Sjoberg, 'Science and the General Curriculum', Ad Notam Gyldendal 1998. 5. Mogens Niss, 'Literacy and the Nature of Education', Uddannelse 9/1999. 6. Mogens Niss, 'The High School Mission, General Curriculum and Literacy', Uddannelse 2/2000. 7. Lars B. Krogh and Poul V. Thomsen: GFII report no. 1: ‘Teaching style and learning curves – a study of physics education in first year High school’, Aarhus University March 2000. 8. Jens Dolin, ‘Project-oriented work in a theoretical learning and physics teaching perspective’. 9. Tomas Hojgard Jensen, ‘Project work: Navigating mapped territory in appraising maths and physics classes’. 10. Karin Beyer, ‘Exercises in Physics – vision or delusion?’, Assoc. of Physics Teachers 1921-1996, Fysikforlaget 1996. 14. ‘New Knowledge – exercises and seminars for High schools’, DTU 1999. 15. Confederation of Danish Industry (DI): ‘School, technology and industry’. 16. Nils Fruensgaard, ‘Computer programs in mathmematics education’. 17. Ole Bakander, ‘Data collation – taking stock’. 18. Morten Blomhoj, ‘Integration of ICT in High school mathematics teaching – a didactic challenge’, Ministry of Education, 1999. 19. Ole Bakander, ‘Data collation – taking stock’. 20. Examples found e.g. in Tomas Hojgard Jensen’s study and in ‘Project-oriented physics teaching’, Uddannelsesstyrelsens temahæfte no. 24/1999. 22. Poul V. Thomsen and Jens Holbech, ‘Improved Thought Through Physics Education’. See also Leif Henriksen and Ejnar Hobolth: ‘TAFAT – Teaching of Folkeskole (Grade school) Student Abstract Thought’. 23. See also, ‘Education in Physics – the Constructivist Approach’, Gyldendal 1992. 24. Bjarne Thams, ‘Robolab in Introductory High School Physics Teaching’. 26. Lisser Rye Ejersbo and Michael Wahl Andersen, ‘Tackling Problems’. 23