brownian(mo*on:(( …school(curriculum(improving(digital(literacies((2 ......

Brownian(mo*on:((an(interdisciplinary(teaching(proposal(Capone.(R.,(D’Acunto(I.,(Dello(Iacono(U.,(Del(Regno(F.(Department(of(Physics,(University(of(Salerno((Italy)(

(

Historical(aspects(

The(transdisciplinary(and(interdisciplinary(aspects(

Teaching((through(Discovery(Learning((construcAon(of(the("knowledge(society(“)((

Choosing(the(required(level(

Revitalizing(school(curriculum(

Improving(digital(literacies((

2(

An(educaAonal(proposal(

Brownian(mo*on:(an(interdisciplinary(teaching(proposal((

Florence(2016(

((

3(

Alongside(the(Brown’s(historical(experience(and(some(other(classical(experiments,(real(or(virtual((

•  a(“random(walk”(simulaAon(made(using(the(soQware(“Geogebra”(

•  a( simple( macroscopic( model( of(chaoAc(moAon(

We(propose((

Both(experiences(are(easily(implementable(in(a(classroom(acAvity((

An(educaAonal(LAB(proposal(


Florence(2016(

((

1827(observaAon(Robert(Brown(

1905(ExplanaAon(Albert(Einstein(

1908(Experimental(confirmaAon(Jean(Perrin(

1908(IntroducAon(of(stochasAc(concept(Paul(Langevin(

1975(ConnecAon(to(quantum(mechanics(Richard(Feynman(

(InteresAng(phenomenon,(easily(observable(but(not(so(simply(

explainable!(

4(

A(brief(history(of(Brownian(MoAon(


Florence(2016(

((

Robert(Brown(

Any( m i nu t e( p a r A c l e(suspended(in(a(fluid(moves(chaoAcal ly( under( the(acAon( of( collisions( with(surrounding(molecules.((

The( intensity( of( th is(chaoAc(moAon(is(increased(with(a(rise(in(temperature.((

This(experimental( fact(was(highlighted( by( the( BriAsh(biologist(R.(Brown(in(1827.(

Brownian(moAon:((an(interdisciplinary(teaching(proposal(

5(

A(brief(history(of(Brownian(MoAon(


Florence(2016(

((

relaAon(between(the(macroscopic(

diffusion(constant(D(and(the(atomic(

properCes(of(maEer.(

D=kT/6πηa(((

the(average(of(parAcle(

displacement(in(the(space(during(Ame(

<x(t)2(>�6Dt(((((

6(

RelaAon(between(the(macroscopic(world(and(the(atomic(properAes(of(maher(


Florence(2016(

((

Explain(Brownian(moAon(using(a(probabilisAc(model:(

•  if(the(kineAc(energy(of(fluids(was(adequate,(its(molecules(moved(with(“random(walk”.((

•  The(“random(bombardment”(by(the(molecules(of(the(fluid(would(cause(a(sufficiently(small(parAcle(to(move(exactly(as(Brown(observed(and(described.((

7(

Random(walk(


Florence(2016(

((

The(theory(of(Brownian(moAon(has(been(extended(to( situaAons(where( the( fluctuaAng( object( is( not( a(real( parAcle( at( all,( but( instead( some( collecAve(property(of(a(macroscopic(system.((

In( 1908,( Langevin( ( introduced( stochasAc( concept(into(the(explanaAon(of(Brownian(moAon,( founding(an( equaAon( containing( both( fricAonal( forces( and(random(forces.((

8(

The(stochasAc(concept(study(


Florence(2016(

((

indirectly(confirmed((

atomic(theory(

kineAc(theory((

the(origin(of(stochasAc(processes’(study(

And(BM(is(sCll(relevant(in(today's(physics((

9(

Works(on(Brownian(MoAon(have((


Florence(2016(

((

Large!educa*onal!poten*al!into!STEM!educa*on(

It!links!the!microscopic!world!and!the!macroscopic!world(

It!integrates!many!disciplines(

Adaptability(to(different(didacAc(levels(

10(

Why(introduce(Brownian(MoAon((into(the(students’(curriculum?(


Florence(2016(

((

The(implementaAon(of(research(methodology.(

The(implementaAon(of(“laboratory(teaching”.(

The(topics(are(proposed(emphasizing(their(historical(importance.(

Students(are(placed(in(the(core(of(the(whole(process(of(teaching(and(learning.((

11(

(Methodology(


Florence(2016(

((

12(

“Lab”(is(not(necessarily(a(physical(space((

The( laboratory( is( a( place(for(discovery,(observaAon(and( a cAon n r e sea r ch(around(cultural(facts((

(“Lab"(as(cogniAve(context(


Florence(2016(

((

13(

Experimental(pracAce(is(necessary(alongside(theoreAcal(acAviAes(

The(teaching(content(covers(a(variety(of(topics(in(mathemaAcs,(probability(and(staAsAcs,(classical(and(modern(physics(

The(main(educaAonal(power(of(the(chosen(argument(is(its(adaptability(to(different(didacAc(levels(

EducaConal(AcCviCes(


Florence(2016(

((

Videos(of(lectures(and(experiments(on(Brownian(moAon.(

Videos(of(experiments(and(lessons(on(fluids’(diffusion.(

Use(of(applets(on(Brownian(moAon(

SoQware(–TRAKERn(to(describe(and(quanAfy(Brownian(moAon.(

14(

Web(Resources(


Florence(2016(

((

Random walk Simulation by Geogebra

15(

An(example(of(a(twondimensional(Brownian(moAon(simulaAon(created(using(Geogebra(soQware(

Random(walk(SimulaCon(by(Geogebra(


Florence(2016(

((

In(the(second(and(the(third(column(there(are(the(X(and(Y(parAcles(coordinates.((

hhps://tube.geogebra.org/material/simple/id/2294315(

16(

Random(walk(SimulaCon(by(Geogebra(

This(Geogebra( construcAon( allows( students( to( observe( graphically( a(random(moAon(and(so,(to(create(a(Brownian’s(moAon(simulaAon.((

The( creaAon( of( computer( applicaAon( allows( students( to( work( out(skills(that(are(the(bases(for(“digital(literacy”.(


Florence(2016(

((

((

R e p r o d u c A o n ( o f(B r own ’ s( h i s t o r i c a l(exper iment( (po l len(grains’(moAon(in(water).(

Diffusion(experiments(in(fluids.(

17(

Physics(laboratory(A( simple( but( incisive( experiment( allows( students( to( observe(macroscopic( chaoAc( moAon( of( parAcles( in( a( fluid,( with( no( apparent(explanaAon(


Florence(2016(

((

• light!balls!“agitated”!by!air!flow,!are!moving!chao*cally!(

We(propose(building(a(simple(macroscopic(model(

achievable(with(basic(materials.((

18(

Exhibit(hands(non(


Florence(2016(

((

light(balls(of(different(colors(are(separated(by(a(grid.(((

when(the(internal((grid(is(removed,(the(orange(balls(are(diffused(by(air(flow.((The(moAon(obtained(is(not(determinisAc,(but(occurs(due(to(the(casual(collision(between(balls.((

19(

An(«hands(–on»(Exhibit(


Florence(2016(

((

The(fascinaAon(of(Brownian(moAon(is:(

Its(connecAon(between(

macroscopic(scale(and(microscopic(

world(

It(facilitates(the(interdisciplinary(

teaching(

20(

Conclusion(


Florence(2016(

((

21(

History(of(Brownian(moAon(aQer(nearly(200(years(remains(perAnent(today(

((

Our(proposal(is(

to(introduce(students(to(the(microscopic(

world(and(some(physical,(

mathemaAcal,(staAsAcal(theories((

Through(

simple(experiments((

soQware(simulaAons(

Alongside(theoreAcal(

study(


Florence(2016(

((

•  Brown,(R.((1987).(A(brief(account(of(microscopical(observaAons(made(in(the(months(of(June,(July(and(August,(1827,(on(the(parAcles(contained(in(the(pollen(of(plants;(and(on(the(general(existence(of(acAve(molecules(in(organic(and(inorganic(bodies.(Philosophical!Magazine(N.(S.(4,(161n173,(1828.(

•  Ministero(dell’Istruzione,(dell’Università(e(della(Ricerca( (MIUR)( (2010),( “Indicazioni(nazionali(riguardanA( gli( obie{vi( specifici( di( apprendimento( concernenA( le( a{vità( e( gli( insegnamenA(compresi(nei(piani(degli(studi(previsA(per(i(percorsi(liceali(di(cui(all’arAcolo(10,(comma(3,(del(DPR(15(marzo(2010,(n.(89."(

•  Dore((Romagnino(C,((Loy(L.((1988).(Lo(studio(del(moto(browniano:(un(esame(della(prima(teoria(di(Einstein(sull'argomento.(Sezione!A.I.F.!di!Cagliari(

•  Einstein,( A.( (1906).( On( the( theory( of( the( Brownian( movement.( Annalen! der! physik( 4.19:(371n381.(

•  Fosnot,(C.(T.,((2005).(Construc*vism:!Theory,!Perspec*ves!and!Prac*ces,(Columbia(University,(New(York(and(London(2005.((

•  Gilster,(P.((1997).(Digital(Literacy.(John!Wiley!&!Sons,(New(York.((•  ( Langevin,( P,( (1908).( On( the( Theory( of( Brownian(MoAon.( [“Sur( la( théorie( du( mouvement(

brownien.(C.!R.!Acad.!Sci.!(Paris)(146,(530–533.(•  Lavenda,( B.(H.( (1983).( Il(moto(browniano(da( Einstein( a( oggi.(Scien*fic!American( n.( 174( vol.(

XXX.(•  Perrin,( J.( (1908).( L’agitaAon(moléculaire( et( le(mouvement( brownien.( Comptes! rendus,( 146:(

967n970.(

•  Resnick,(Lauren(B.((1987).(EducaAon(and(learning(to(think.(Na*onal!Academies.(•  hhp://tnt.phys.uniroma1.it/twiki/pub/TNTgroup/AngeloVulpiani/brown.pdf(

22(

References(


Florence(2016(

((

((Capone(R.,(D'Acunto(I.,(

Dello(Iacono(U.,(Del(Regno(F.((

Department(of(Physics,(University(of(Salerno(n(Italy(

[email protected],([email protected],!

[email protected],([email protected](

23(Brownian(mo*on:(an(interdisciplinary(teaching(proposal((

Florence(2016(

((

brownian(mo*on:(( …school(curriculum(improving(digital(literacies((2 ......

Documents