digital competence in physics in the frame of the national

Digital competence in physics in the frame of the

national project Development of Natural Science

Competences

Marko Gosak

Faculty of Natural Sciences and Mathematics

University of Maribor

Koro²ka cesta 160, SI-2000 Maribor, Slovenia

[email protected]

Robert Repnik

Faculty of Natural Sciences and Mathematics &

Faculty of Education



[email protected]

Vladimir Grubelnik

Faculty of Natural Sciences and Mathematics &

Faculty of Electrical Engineering and Computer Science



[email protected]

Marjan Kra²na

Faculty of Education



[email protected]

Milan Ambroºi£

Joºef Stefan International Postgraduate School &

Faculty of Natural Sciences and Mathematics,


Jamova 39, SI-1000 Ljubljana, Slovenia

[email protected]

Abstract. The national project Developmentof Natural Science Competences which startedin October 2008 is now in full swing. Learningmaterials are being prepared periodically, and thenthey are tested in schools and revised afterwards.The main goal of these materials is to indicatebetter didactics strategies for systematic develop-ment of students' natural science competences.One of these competences, taken from the wideframe of eight key competences � Key Competencesfor Lifelong Learning from the EU Legislation(Education, Training, Youth) � is the digitalcompetence. Several of our materials in the projectwritten so far include this competence in di�erentways: e-learning materials, use of the computerin experiments and measurements, numericalmodelling, graphic tools, etc. Here we focus on

particular cases from our physics materials. Thetests have shown indubitably that students areprone to acquiring digital competence.

Keywords. key competences, natural sciencecompetences, digital competence, education

1 Introduction

There are di�erent de�nitions of competences andtheir classi�cations. For instance, Coolahan pro-posed the following de�nition on symposium of theEuropean Council in 1996: Competences are gen-eral operational abilities which are based on knowl-edge, experience, ethic principles and dispositionsdeveloped by a person during his/her education

Proceedings of the 21st Central European Conference on Information and Intelligent Systems 141

Varazdin, Croatia Faculty of Organization and Informatics September 22-24 2010

mailto:[email protected]





[3]. On the other hand, on the same symposiumWeinert interpreted competences as rather special-ized system of abilities, experience and skills whichare necessary to achieve speci�c goals [3]. In theEU Legislation � Education, Training, Youth (Keycompetences for Lifelong Learning) eight key com-petences are de�ned [4]:

1. Communication in the mother tongue

2. Communication in foreign languages

3. Mathematical competence and basic compe-tences in science and technology

4. Digital competence

5. Learning to learn

6. Social and civic competences

7. Sense of initiative and entrepreneurship

8. Cultural awareness and expression

The third competence refers to science and morespeci�cally to natural sciences, but also other keycompetences are interconnected with science. Forinstance, in regard to science the �rst competencein the upper list could be translated into Commu-nication in the mother tongue in the area of natu-ral sciences, and so on. Here we focus on the sig-ni�cance of digital competence for natural sciencesand on its implementation in the education of sci-ence. This competence includes the use of com-puter and other Information Communication Tech-nology (ICT) tools in natural sciences. More gen-erally (not only in science) its de�nition in EU Leg-islation is: "Digital competence involves the con�-dent and critical use of information society technol-ogy (IST) and thus basic skills in information andcommunication technology (ICT)."

In October 2008 the National project Develop-ment of Natural Science Competences began and itwill �nish at the end of 2011 [6]. Its main purposeis to indicate better didactics strategies for system-atic development of students' natural science com-petences. Learning & testing materials are beingprepared periodically, and then they are tested inschools and revised afterwards. Typical materialsinclude instructions for teachers and for students,

materials with the topic contents, exercises, pre-tests and post-tests, etc. Authors of these mate-rials in the project closely cooperate with teacherswho test them in school. All educational levels fromthe �rst year of 9-year primary school to the endof various secondary schools are considered; somematerials are prepared even for preschool children(in kindergartens). Besides the three basic natu-ral science subjects in school � biology, chemistryand physics (or their topics in wider subjects atthe lower educational level), also some supportingsubjects are included in the project: mathematics,technics and computer science.

In addition to key competences listed above, wefocused in the project also on a speci�c set ofgeneric competences de�ned by the Mayer commit-tee, Australia, which are also related to natural sci-ences [2]. Each of these generic competences hasa narrower meaning as compared the key compe-tences above; a few examples of these competencesare: 1) ability of collecting information, 2) abil-ity to synthesize conclusions, 3) implementation oftheory in practice, 4) care for quality, 5) ability ofindividual work, 6) verbal communication, etc.

Since we are aware of the ever growing impor-tance of digital competence in life and science, thiscompetence has been considered in many preparedmaterials in all natural science subjects and sup-porting subjects. In this paper we focus on materi-als in physics which include digital competence indi�erent ways: e-learning materials, use of the com-puter in experiments and measurements, numericalmodelling, graphic tools, etc. Digital competenceis interconnected with some generic competencesmentioned above, e.g., with the ability of collectinginformation (from the web), etc.

2 Examples of physics materi-

als with digital competence

We give the examples of the physics materials withtraining digital competence written so far. In thenext materials we plan even larger extent of usingICT.



2.1 Success of traditional learning

techniques in incorporation of

modern scienti�c achievements

in primary school physics

Two authors prepared a series of materials wherethey tested three di�erent didactic methods forintroducing some actual physics topics in school:1) frontal work, 2) individual work with hardcopylearning materials, and 3) frontal work with thehelp of ICT. The topics prepared (and most of themalready tested) so far are quite interesting [7]: 1)Nuclear Power Plant Kr²ko in Slovenia, 2) Photo-voltaic cells, 3) Optical �bres, 4) Nuclear waste, 5)Colour Perception, 6) Weather Forecast. The ma-terials are intended for the 8th and 9th grade of9-year primary school. The three methods weretested in parallel classes of the same level (andusually by the same teacher who teaches at leastin three parallel classes). Using ICT was usuallymeant as searching for speci�c information on webpages by individual students. The pre-tests andpost-test were short � they contained 7 questionsof increasing cognitive degree, where the correctanswer from the four had to be selected. The �rstquestion is asking for the pupil's relation to physics(pre-test) and the treated subject (post-test). Toavoid memorizing the solutions from the pre-test,the questions in the post-test were di�erent butwere actually asking for the same level of knowl-edge (or competence). Preliminary results of theschool tests showed that the combination of thefrontal work and ICT is preferable when the un-familiar topics are learned.

2.2 Web textbook about Galileo

One of the materials was dedicated to Galileo's lifeand work. The year 2009 was declared as the In-ternational year of astronomy (brie�y IYA 2009) byUnesco and the International Astronomical Unionsince this year was the 400th anniversary of the�rst Galileo's important and revolutionary contri-butions to the further development of astronomy.In 1609 Galileo made key observations of Moonsurface through his improved telescope, and in thenext year some of his further discoveries followed(e.g., the moons of Jupiter). In addition, his bookStarry Messenger was published in 1610. Galileo'swork �nally discarded the geocentric view of the

Universe and accelerated the development of thescience and scienti�c concepts as we accept today.IYA 2009 stimulated us to write a short web text-book (e-book) with the title Galileo and Interna-tional Year of Astronomy 2009 in Slovene [1]. Theaim of this e-book was also encouraging students touse ICT and develop digital competence. In addi-tion, the learning material appropriate for testingin the 9th year of primary school (topic Astron-omy within physics for this level) or in secondaryschools (for instance, for optics topics in physics)was written. The structure and philosophy of oure-book as well as preliminary testing results have al-ready been described elsewhere [1, 8], thus we onlybrie�y mention key points about training digitalcompetence in education. Depending on teacher'splanning the physics lesson about Galileo and as-tronomy (or other topics in the e-book) and his cor-responding instructions, either one student in theclass or a few of them or all the students get the taskof reading the part of the e-book. Reading the e-book is a good exercise of the student's navigationthrough this material and other e-materials withsimilar design; our e-book contains also a searchingkey by using the keywords. There are also manyexternal links in this e-book.

It should be mentioned that a large fraction ofstudents are relatively inert (or to be said moresincerely � lazy) and dislike reading of any kind.Teachers' experiences in using our material in con-nection with Galileo e-book in school tests only con-�rmed this general �nding. But perhaps at leastsome of students may be encouraged to read a lit-tle more with the help of user-friendly e-books ifthey are not willing to read printed books. Usinge-materials helps the student to develop a genericcompetence ability of collecting information andtheir organization. In addition, a part of the e-book, for instance, the section Development of as-tronomy, should be presented as a seminar lectureby one or more students to their schoolmates. Thismeans training of the use of the program Pow-erpoint. This material is appropriate for train-ing teacher's digital competence, too. The teachershould read the Galileo e-book before his/her stu-dents do. Some other addresses of e-materialsabout Galileo are suggested for further reading.



2.3 An introduction to percolation

theory at elementary level

Percolation is involved in a broad range of phys-ical phenomena including forest �res, propagationof epidemics, oil �elds, transport through porousmedia, ferromagnetism, communication in an un-reliable network etc [9]. One of the easiest andmost interesting percolation-related phenomena tostudy is the electrical behaviour of a system of con-ducting particles dispersed in an insulating ma-trix. When the fraction of the conducting ma-terial, p, is lower than a critical fraction pc, nomacroscopic conducting pathway exists, and thecomposite remains in the insulating phase. Onlyif the fraction of conducting material is greaterthan the critical fraction, the system becomes elec-trically conducting. The value of pc is the crit-ical threshold, in which the properties of a per-colation system suddenly change; the percolationphase transition is a second-order phase transitionpoint. Due to its straightforwardness, these disor-dered conductor-insulator composites represent ane�cient way to introduce the theory of percolationand the general ideas of critical phenomena to highschool or perhaps even to elementary school stu-dents.

Figure 1: A snap-shot of the user-friendly programfor an introductory overview of the percolation the-ory at the elementary level.

In view of that we prepared an experiment, wherethe students randomly arrange conducting and in-sulating cubes between capacitor plates. Then, theconductivity of the setup is being tested in depen-

dence on the ration between conducting and in-sulating elements, thus providing an introductoryoverview of the �eld at elementary level. Alongwith that we also developed two computer pro-grams, which can nicely supplement or even substi-tute the experiment. The �rst program is very user-friendly and is meant to acquaint the students withthe basic idea of the functioning of the conductor-insulator composites. The students are allowed tochange the fraction of conducing elements and thesize of the lattice, whereby for each setup the pro-gram indicates if the lattice is conducting. Becauseof the graphical interface on can easily observe theparticular arrangements at di�erent parameter val-ues. A characteristic snap-shot of the program isshown in Fig. 1. The second program enables amore quantitative insight into the percolation phe-nomenon. It gives the students the opportunity toperform calculations on larger lattices and it calcu-lates the statistics of the probability of conductionin dependence on fraction of the conducting mate-rial p. Consequently, the students are able to quiteprecisely estimate the critical fraction pc and forinstance observe the behaviour near the transitionpoint for di�erent lattice sizes.Nevertheless, the percolation theory surely repre-

sents a topic where the concept of interdisciplinar-ity is emphasized. First, in this manner studentsimprove not only their knowledge in physics, butalso in mathematics and computer science. Sec-ond, students realize that approaches and discov-eries ascertained during a physics lesson can be ofgreat importance in various disciplines, thus givingrise to the development in specialized competencies,which are characteristic for physics and other nat-ural sciences. Furthermore, with this kind of workgeneric competencies are being evolved as well. Inparticular, students certainly improve their skillsconsidering the usage of mathematical ideas andtechniques.

2.4 Refraction of light

We prepared materials for the realization of a phys-ical experiment in which refraction of light is beingstudied. Our main objective was the elaboration ofa material in which students develop several genericand specialized competencies with special empha-sis on digital competencies. The main idea is thatthe students perform an experiment, in which the



refraction index of water is being measured. Forthe analysis and the subsequent calculations theymake use of a digital photo camera, a computerprogram enabling the representation and manipu-lation of image data, a spreadsheet application andat last they prepare the �nal report using a wordprocessor.

The refraction index is a measure of the bendingof a ray of light when passing from one mediuminto another. The relationship between the anglesof incidence and refraction and the refraction in-dexes of both mediums is given by the Snell's lawsin α1sin α2

= n2n1, where α1 and α2 are the refraction an-

gle and the angle of incidence, respectively, whereasthe quotient n2

n1gives the ratio between the refrac-

tion indexes of both media.

Figure 2: Scheme of the experiment indicating thebending of a ray of light as it enters the water.

The course of the experiment is as follows: Stu-dents draw two right-angled lines on a white sheetof paper, whereby the horizontal line indicates thewater level and the vertical line speci�es the rightangle on the water surface. The scheme is shownin Fig. 2. After that, they glue up the paper be-hind a glass container, which is half full of water,so that the horizontal line is even with the watersurface. By using a laser pointer they light alongthe paper, whereat the beam must enter into thewater at the point of intersection (see Fig. 2). Us-ing a proper photography technique, the studentstake a picture of the arrangement. This procedureis then repeated for di�erent angles of incidence.All the photos must then be copied to a hard driveand imported in an image editing software. Thesubsequent graphical manipulation allows then thestudents to measure the angles of interest from the

photographs (see Fig. 3). Afterwards, studentsenter the measured angles into a spreadsheet appli-cation, which enables them to graphically presentthe results and to calculate the refraction index ofwater for di�erent realizations of the experiment.Finally, the students have to write a report aboutthe experiment and their �ndings using a word pro-cessor.

The proposed material represents a good exam-ple of how students can develop various competen-cies during a physics lesson. In particular, a lecturebased on our materials encourages the students toimprove their abilities in collecting of informationas well as in organizing and planning of work. Fur-thermore, the students develop several other com-petencies, such as handling of mathematical ideasand techniques, the ability of individual and teamwork and they improve their skills for oral and writ-ing communication. Nevertheless, the most impor-tant aspect of our proposed material is the devel-opment of the digital competence, which is withoutdoubt expressed at every step of the lesson.

2.5 Measurement and presentation

of the results with tables and di-

agrams

This material is intended for the 9th year of pri-mary school, the physics topic Accelerated move-ment, more exactly, the rolling of balls down theslope. The realization strategy is interesting. Inthe �rst lesson students perform experiments insmall groups where the inclined desk represents theslope (Fig. 4). They measure the time dependenceof the small steel ball's distance from the startingpoint, s(t), and write the results in the form of ta-bles. They are encouraged to use the timer on theirmobile phones. Finally, they draw manually thes(t) diagram on paper with millimetre grid and no-tice that the functional dependence s(t) is not lin-ear. In the next school lesson the teacher performsthe computer-aided demonstration experiment ofrolling the ball down the slope (the playing ball isused, Fig. 5). The ultrasonic distance detector isused and it is connected with the USB computerinput. The software package Logger Pro (Vernier)[11] is used to manipulate the information from thedetector and to draw the corresponding s(t) andv(t) diagrams. Students compare the correspond-



Figure 3: Photography of the experiment and the corresponding procedure of measuring of the angles.

Figure 4: Setup of the experiment with rolling steelballs.

ing s(t) diagram on computer with their former di-agrams. Among generic competences, the care forquality should be emphasised.

2.6 Heat conduction

This material has been written for secondary schoolphysics. The experimental work in groups is sug-gested where the non-stationary heat-conductionproblem is tackled. Hot water is poured into thepot from the material of known heat conductivity.The water is cooling down and the time depen-dence of its temperature, T (t), is measured. Re-sistivity thermometers connected to the computercan be used. The graphs T (t) can be drawn man-ually or with some computer programme, such asexcel. The main challenge of the task is an e�ortto make a suitable interpretation and quantitativeanalysis of experimental results, so that the math-

Figure 5: Setup of the computer-aided experimentwith rolling playing balls.

ematical competence is crucial here. The studentsare o�ered three mathematical models (functions)for the T (t) dependence: 1) C/t, 2) C/t2, and 3)C1e

−C2t, where C (or Ci) is an appropriate con-stant. They are asked to decide which of the threefunctions correctly describes the time dependenceof the temperature of water. They are expectedto guess the right answer � exponential decrease ofthe temperature since the algebraic solutions givea senseless in�nite temperature at time zero.Nevertheless, they can make a semi-quantitative

checking that exponential function is the right one.First, the �rst two functions can be discarded inthe following way. If the T (t) dependence is T (t) =Ct−m, where m = 1 or 2, the corresponding log-log dependence is linear: ln T = −m ln t + ln C.The student can use excel to insert the pairs of themeasured values (t, T ) in two columns, calculatethe natural logarithms of these values and drawthe corresponding diagram. He/she can see that



Figure 6: Graphic base of computer programBerkely Madonna. Illustration of the variable bythe reservoir is shown. The �uid �ux is regulatedby valves which can be in�uenced by constants orvariables.

the graph ln T (ln t) is not a straight line and con-cludes that the dependence T (t) = Ct−m does not�t the experiment. Second, to check that the ex-ponential dependence is true the logarithm of onlythe temperature (and not of time) is to be taken,so that ln T = −C2t+ ln C1. The diagram ln T (t)thus yields the straight line.

2.7 Dynamical models

Understanding natural phenomena generally re-quires the description with appropriate mathemat-ical models [5, 10]. Such modelling proved to bea successful scienti�c method in combination withexperimental work. Mathematical models are sig-ni�cant in dynamical systems where they can beused to predict the time evolution of the system.There arises a question of the transfer of mathemat-ical modelling into educational area. Study of therelations between quantities (variables) determin-ing the system state usually demands solving thesystem of di�erential equations and this representsone of the key di�culties of the system modelling ineducation. Therefore, simpli�ed systems are gener-ally considered which often fail to agree with realexperiments what results in poor understanding ofphysical systems.

In this paper, we present the possibility of treat-ing dynamical systems in primary school withthe help of graphic oriented programmes, such asBerkeley Madonna, Dynasys and Stella. These pro-grammes enable an easy and evident connectionof graphical symbols for parameters, variables andtheir �uxes into composed mathematical model thesimulation of which is handled by computer. In pre-pared learning materials we considered some study

cases of �uid �ow where pupils discover the rela-tions between variables and their �uxes (Fig. 6).Next, we illustrated the movement of objects un-der the in�uence of forces: we took an example offree-falling objects in the air where air resistancehad to be taken into account. After the input ofmathematical relations and the initial values of cor-responding variables the computer programme sim-ulates and illustrates the time evolution of relevantvariables.

Using such programmes o�ers the pupil the op-portunity to use the minimal model for a givenphysical problem and start acquiring basic scien-ti�c principles together with digital competence.

3 Conclusions

In the materials described above the following com-puter programmes and tools were trained by teach-ers and students: Excel, Powerpoint, word proces-sors (such as MS Word), web pages, programmesfor reading documents (such as Adobe Reader),image editing software (such as Paint Shop Pro),some executable numerical programs (commercialprogrammes and our own programmes), etc.

ICT competences at school can be classi�ed intothree levels:

1. ICT fundamentals

2. ICT theory and practice

3. ICT application

Of course the third level of knowledge is desir-able. We think that the application of preparedmaterials in schools within the National project�Development of Natural Science Competences� en-hances the second and partially the third level ofICT competences.



Acknowledgements

We greatly acknowledge the support of the Min-istry of Education and Sport of Republic of Sloveniaand European Social Fund in the frame of �Project:Development of Natural Science Competences� onFaculty of Natural Sciences of University of Mari-bor.

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digital competence in physics in the frame of the national

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