brownian(mo*on:(( …school(curriculum(improving(digital(literacies((2 ......
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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((
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An(educaAonal(proposal(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
((
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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(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
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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(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
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(
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A(brief(history(of(Brownian(MoAon(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
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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(((((
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RelaAon(between(the(macroscopic(world(and(the(atomic(properAes(of(maher(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
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.((
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Random(walk(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
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.((
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The(stochasAc(concept(study(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
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indirectly(confirmed((
atomic(theory(
kineAc(theory((
the(origin(of(stochasAc(processes’(study(
And(BM(is(sCll(relevant(in(today's(physics((
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Works(on(Brownian(MoAon(have((
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
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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(
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Why(introduce(Brownian(MoAon((into(the(students’(curriculum?(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
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.((
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(Methodology(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
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“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(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
((
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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(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
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.(
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Web(Resources(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
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Random walk Simulation by Geogebra
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An(example(of(a(twondimensional(Brownian(moAon(simulaAon(created(using(Geogebra(soQware(
Random(walk(SimulaCon(by(Geogebra(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
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In(the(second(and(the(third(column(there(are(the(X(and(Y(parAcles(coordinates.((
hhps://tube.geogebra.org/material/simple/id/2294315(
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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”.(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
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((
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.(
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Physics(laboratory(A( simple( but( incisive( experiment( allows( students( to( observe(macroscopic( chaoAc( moAon( of( parAcles( in( a( fluid,( with( no( apparent(explanaAon(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
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• light!balls!“agitated”!by!air!flow,!are!moving!chao*cally!(
We(propose(building(a(simple(macroscopic(model(
achievable(with(basic(materials.((
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Exhibit(hands(non(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
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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.((
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An(«hands(–on»(Exhibit(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
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The(fascinaAon(of(Brownian(moAon(is:(
Its(connecAon(between(
macroscopic(scale(and(microscopic(
world(
It(facilitates(the(interdisciplinary(
teaching(
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Conclusion(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
Florence(2016(
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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(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
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(
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References(
Brownian(mo*on:(an(interdisciplinary(teaching(proposal((
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(
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