Tijdschrift voor Didactiek der B-wetenschappen 8 (1990) nr.1 3
Students' reasoning in thermodynamics
S . R o z i e r & L . V i e n n o t L . D . P . E . S .
U n i v e r s i t y o f Paris 7
Toelichting
Dit artikel is een weergave van de voordracht die door Viennot gehouden is op het seminar "Relating macroscopic phenomena to microscopie particles: a central problem in secondary science education", dat plaats heeft gevonden in Conferentieoord Woud- schoten te Zeist van 22-26 oktober 1989.
1. Introduction
T h e r m o d y n a m i c s is a subject w h i c h involves m u l t i v a r i a b l e p r o - blems. T h e b e h a v i o u r o f a huge number o f particles is described using a s m a l l number o f variables, w h i c h are mean values or macroscopic quantities. These variables can be l i n k e d , at t h e r - m o d y n a m i c e q u i l i b r i u m , by certain relationships, f o r example PV=NRT for perfect gases. In any transformation, such r e l a t i o n - ships h o l d f o r i n i t i a l a n d f i n a l e q u i l i b r i u m states. In transforma- tions considered as "quasistatic", these relationships h o l d as w e l l for any intermediate state, then also considered as e q u i l i b r i u m states. T h a t is to say that we have to consider several variables, most o f the time more than t w o , changing simultaneously under the constraint o f one or several relationships.
S u c h a m e n t a l a c t i v i t y a p r i o r i raises obvious d i f f i c u l t i e s . Piaget a n d I n h e l d e r (1941) have shown that c h i l d r e n , d e a l i n g w i t h three k i n e m a t i c variables (s,v,t), i n fact consider one o f these quantities as l i n k e d to a single other one: "the faster, the further". O t h e r studies ( V i e n n o t , 1982; M a u r i n e s , 1986) show s i m i l a r d i f f i c u l t i e s .
In this paper, we w i l l illustrate, i n the d o m a i n o f t h e r m o - d y n a m i c s , h o w students, a n d others, c o m m o n l y reduce the i n t r i n - s i c c o m p l e x i t y o f s u c h p r o b l e m s . These tendencies t o w a r d s
"functional reduction" i n c o m m o n reasoning, w i l l be s h o w n to range f r o m a simple r e d u c t i o n i n the number o f variables c o n - sidered to a more elaborate procedure where a l l the variables are t a k e n i n t o a c c o u n t , b u t i n a s i m p l i f i e d w a y : the "linear causal reasoning".
T h e e x p e r i m e n t a l facts s u p p o r t i n g o u r analysis come f r o m a study b y S . R o z i e r (1987). T h e students i n the study ( N ^ 2 0 0 0 ) were d r a w n f r o m three types o f courses: one o f the f o u r first y e a r s at u n i v e r s i t y o f P a r i s 7, a s e l e c t i v e course p r e p a r i n g f r e n c h "grandes é c o l e s d ' i n g é n i e u r s " ( t w o years af ter b a c c a - laureat) a n d teachers (N=29) i n i n - s e r v i c e t r a i n i n g sessions.
A f t e r u n d e r t a k i n g exploratory i n t e r v i e w s (N=9), this study was c o n d u c t e d m a i n l y o n the basis o f w r i t t e n questionnaires (14, o n l y 4 o f them are quoted here, many results b e i n g left aside for the sake o f b r e v i t y ) . Because o f the s i m i l a r i t y o f results f o r the d i f f e r e n t sub-samples we do not report the results f o r each separately. We w i l l also quote excerpts f r o m textbooks, p o p u l a r science books a n d research papers i n science e d u c a t i o n , as w e l l as teachers' reactions i n t r a i n i n g sessions, i n order to show to w h i c h extent a n d a c c o r d i n g to w h i c h modalities students' c o m - m o n w a y s o f r e a s o n i n g are shared b y d i f f e r e n t categories o f professionals i n science.
T h e p e d a g o g i c a l i m p l i c a t i o n s f i n a l l y d i s c u s s e d w i l l relate m a i n l y to o u r teaching goals.
2. Reducing the number of variables a) Forgetting some of them
A f i r s t q u e s t i o n w i l l i l l u s t r a t e s t u d e n t s ' m o s t g e n e r a l a n d obvious tendency i n c o p i n g w i t h m u l t i v a r i a b l e p r o b l e m s , w h i c h is to forget some r e l e v a n t v a r i a b l e s . T a b l e I summarizes the question posed (a w r i t t e n test) and the most frequent response.
A s k e d to e x p l a i n i n molecular terms w h y pressure increases i n an adiabatic compression o f a perfect gas, 43% students say, f o r instance:
" V o l u m e decreases, t h e r e f o r e m o l e c u l e s are closer to ea ch o t h e r , t h e r e f o r e t h e r e a r e m o r e c o l l i s i o n s , t h e n pressure increases".
" V o l u m e decreases, t h e r e f o r e there are more molecules per u n i t v o l u m e , then pressure increases".
These responses m a y be o u t l i n e d i n the f o l l o w i n g way:
" V \ ^ n f ^ p f "
In these comments, an increase i n pressure is ascribed o n l y to an increase i n the "number" (per unit v o l u m e , w h i c h is o f ten i m p l i c i t ) o r "density" o f p a r t i c l e s . N o t h i n g is said about the
Rozier & Viennot 5
T a b l e 1: Questions about an adiabatic compression (see R o z i e r , 1987), correct and typical responses
An adiabatic compression of a perfect gas:
pressure and temperature both increase.
Can you e>:plain why in terms of particles?
notations used below: volume of gas:V, number of particles per unit volume: n, pressure of gas: p, temperature of gas: T, mean speed of particles: v, mean kinetic energy of particles: e^, heat :Q,/:"increases",\ :"decreases", l:"is produced", ^-^"therefore* (see text)
„.common explanation:
V \ n ^ — - number of collisions ^ — - P - - "
T outlines of ....
_ correct explanation:
V \ — - v , - - e c - T - '
common explanation:
V \ —-number of collisions Q —1 —
other r e l e v a n t aspect, f r o m a k i n e t i c p o i n t o f v i e w , i.e. the mean speed o f particles (see correct answer o u t l i n e d i n table 1).
O t h e r questions i n this study c o n f i r m this p r e f e r e n t i a l l i n k between pressure and "number o f particles". In what f o l l o w s , we w i l l refer to s u c h l i n k s as "preferential associations" between two variables.
Such a tendency i n reasoning is not l i m i t e d to students. A s an e x a m p l e , let us quote an excerpt f r o m a book o f popular science ( M a u r y , 1989) considered as very good b y many physics u n i v e r s i t y teachers ( i n f o r m a l evaluation, i n France): " Planes f l y very h i g h , at an altitude where molecules o f a i r are m u c h less numerous, and therefore the pressure o f the external a i r o n the
QUESTION:
p outlines of ...correct explanation:
~ n / ~
and — ("number of collisions Lper...
and v
w i n d o w is m u c h l o w e r than at sea level." T h i s e x p l a n a t i o n may be s u m m e d up i n the f o l l o w i n g way: n \ —>p \ , n o t h i n g b e i n g said about temperature. T h e same single variable dependency as i n students' comments is observed, despite the fact that at the a l t i t u d e c o n s i d e r e d , (=10 k m ) , the temperature is m u c h l o w e r than at sea level ( = 7 0 ° C , i.e. a decrease o f about 25% i n t e m p e - r a t u r e ) w h i c h also c o n t r i b u t e s to the l o w e r i n g o f pressure.
Teachers i n d i f f e r e n t t r a i n i n g sessions ( N - - 5 5 )1 have been i n v i t e d to c r i t i c i z e this c o m m e n t . I n e v e r y session, m o r e t h a n 9 5 % accepted it w i t h o u t any m o d i f i c a t i o n , and w h e n the change i n t e m p e r a t u r e was p o i n t e d o u t , the great m a j o r i r y o f teachers said that it was "not the i m p o r t a n t phenomenon", so it was not necessary to specify what happened to this q u a n t i t y . F i v e pages further i n the same book, the hot air balloon is presented and
"explained" using the fact that w h e n the temperature increases, it contains "less and less air". So the "number o f particles ..."
decreases. Y e t i n the hot air b a l l o o n , the pressure inside is not lower than that outside, due to temperature. N o c o n n e c t i o n is made w i t h the explanation p r e v i o u s l y proposed f o r l o w pressure outside the aircrafts.
Such ad hoe variations on the equation o f state f o r perfect gases, PV=NRT, are t y p i c a l o f the inconsistencies i n t r o d u c e d b y the c o m m o n tendency towards "functional reduction" a n d a call on preferential associations w i t h no m e n t i o n o f other relevant variables.
b) Combining together two variables
R e d u c i n g the n u m b e r o f variables may be obtained b y another process also observed i n other domains ( V i e n n o t , 1989a): two p h y s i c a l quantities seem to be "stuck together". T h i s is the case, f o r i n s t a n c e , f o r mean d i s t a n c e b e t w e e n p a r t i c l e s a n d mean k i n e t i c energy o f particles ( R o z i e r , 1987). T h e name frequently used f o r this c o m p o u n d n o t i o n is " t h e r m a l m o t i o n " , a n d its cement is the idea o f disorder. In fact, o n l y one o f these q u a n - t i t i e s is d e t e r m i n e d o n l y b y t e m p e r a t u r e , n a m e l y the m e a n k i n e t i c energy o f particles. T h e other is also l i n k e d w i t h other aspects: pressure, shape o f p o t e n t i a l o f i n t e r a c t i o n b e t w e e n p a r t i c l e s f o r solids and l i q u i d s . Students' reasoning and c o m - ments i n this respect w i l l be analysed i n detail i n what f o l l o w s . L e t us start, this t i m e , w i t h teachers' a n d researchers' q u o t a - tions.
Rozier & Viennot 7
In the book p r e v i o u s l y mentioned, one may read: "particles need more room to move faster". In research reports, so called
" a c c e p t e d ideas" o f ten g i v e the i m p r e s s i o n o f an a d h e r e n c e b e t w e e n these t w o - k i n e t i c a n d g e o m e t r i c a l - aspects. F o r instance, about thermal expansion ( L e e , e.a., 1989):
"When a substance is heated, the molecules o f the substance move faster a n d , therefore, move faster apart, w h i c h causes the substance to e x p a n d . In contrast, w h e n the substance is c o o l e d , the m o l e c u l e s m o v e m o r e s l o w l y a n d m o v e c l o s e r together, so the substance contracts."
O r , still more s i m p l y , a very c o m m o n l y accepted idea is that thermal m o t i o n is m u c h higher i n gases (larger mean distance b e t w e e n p a r t i c l e s ) than i n l i q u i d s (smaller mean distance b e - tween p a r t i c l e s ) , and larger i n l i q u i d s than i n solids. See for instance these excerpts f r o m french textbooks or w r i t t e n mate- rials at university:
"In some solids, such as glass, and many plastics, molecules are squashed against each other and cannot move" (Sciences Physiques, 1980).
" w h e n , c o o l i n g d o w n a l i q u i d , p a r t i c l e s become motionless without any order, it is an a m o r p h i c solid" ( D E U G S S M , 1985).
H o w e v e r , as said before, thermal m o t i o n , i f meant as mean k i n e - tic energy o f particles, is o n l y a matter o f temperature. It is therefore the same for the water i n the sea, the air just above, and a stone on the beach, i n as m u c h as they are at same t e m - perature.
c) Lack of symmetry in implications
A s t r i k i n g feature i n the w a y s i n g l e - v a r i a b l e dependencies are c o m m o n l y handled is a lack o f s y m m e t r y i n i m p l i c a t i o n s . Indeed, i n the accepted theory o f quasistatic transformations, variations are simultaneous and therefore, the i m p l i c a t i o n s are s y m m e t r i c a l ( p r o v i d e d that the variables w h i c h are kept constant are s p e c i - fied).
A t y p i c a l example is the f o l l o w i n g : the c o m m o n l y accepted i m p l i c a t i o n V \ -*p f , which was discussed above, seldom ap- pears to be a p p l i e d i n reverse: p f —>V \ (see below section 3).
This. lack o f symmetry may even occur i n i m p l i c a t i o n s c o n - c e r n i n g some variables w h i c h are, most o f the t i m e , s i m p l y stuck together and therefore interchangeable i n a s y m m e t r i e r e l a t i o n - ship. T h i s is the case for two variables evoked about the c o m -
p o u n d n o t i o n o f "thermal motion": temperature and v o l u m e . A s s h o w n further i n the paper, students are f a m i l i a r w i t h the T f
—>V f implication for a heated gas. But it is not so frequent at a l l , as c l a s s r o o m practice shows, to say that e x p a n d i n g a gas results i n an increase i n temperature.
A n o t h e r result also suggests, although i n d i r e c t l y , that s t u - dents w o u l d not u n c o n d i t i o n a l l y reverse the p r e c e d i n g i m p l i c a - t i o n . A question proposed to students i n R o z i e r ' s i n q u i r y (see table 2) presents the f o l l o w i n g situation: an equal amount o f heat is transferred to two systems consisting o f same numbers o f particles o f perfect gases at same temperature, but i n vessels o f d i f f e r e n t volumes. 22% o f students (N=255) or teachers (N=28) g i v e responses e q u i v a l e n t to this one: "the amount o f heat is more d i l u t e d i n the larger vessel, so the temperature does not increase as m u c h as i n the smaller vessel", w h i c h can be s u m - marised by "larger v o l u m e —» smaller increase i n temperature"
T a b l e 2: A question f r o m ( R o z i e r , 1987) and c o r r e s p o n d i n g rates o f response
(N,V,T) (1)
(H2V.T)
(2) Two rigid vessels (1) and (2) are filled with a perfect gas. in respective states (N.V.T) and (N.2V.T)
N= number of moles in each vessel V= volume of vessel 1
T- temperature of each vessel
(2)
( D The two vessels are heated up for the same time with idenlical heat sources, then one measures their respective temperature.
Ix> you Üünk that Ra te af response (N-283)
T p T2
T1-T2 T i < T2
37X 48X 5%
22X: ~because Vj<V2~
30X correct justification
I don't know 8X Why?
Rozier Sc Viennot 9
In conclusion to this first section we suggest that c o m m o n types o f reasoning observed i n students and teachers are characterised i n the f o l l o w i n g way:
In the implications used, $x —• $2' refers to a phenome- non specified with only one variable, for instance: "p increases", or " i n p u t o f heat". When several variables are mentioned (see table 1), this is done t h r o u g h an a r g u m e n t w h i c h l i n k s the variables i n a linear chain:
$1 - » *2 - $n - •••
E a c h specific i m p l i c a t i o n $n $n + 1 does not i m p l y that the reverse i m p l i c a t i o n w o u l d be accepted b y the same person.
Students' responses to other questions w i l l n o w i n t r o d u c é a new feature i n the interpretation o f such chains, w h i c h gives some coherence to these p r e l i m i n a r y conclusions.
3 . Causality and chronology: linear causal reasoning
A v e r y c o m m o n (43%, N=120 students) " e x p l a n a t i o n " o f the increase i n volume resulting f r o m the.heating o f a perfect gas at constant pressure is o f the f o l l o w i n g type (see question i n table 3):
T a b l e 3: A q u e s t i o n about an i r o b a t i c h e a t i n g o f a gas (see R o z i e r , 1987), correct and t y p i c a l responses
QUESTION
i n A perfecl gas is heated at constant pressure...lts volume and temperature both increase. Can you explain why?
Notationp used below: see table 8, and: Cp: molar spedfic heat at constant pressure, R:
constant, N): total number of moles. A: alRCbraic increment of..
Outlines of....
correct explanation:
Q (supplied to gas)=cp AT and Q>0
and cp>0
— |AT>0 and PV=NRT and
p,N,R, all constant common explanation:
supply of Q — • T ^ — - p ^ 'V
-AV>0
"The temperature o f the gas increases. K n o w i n g that i n a p e r - fect gas PV=NRT, therefore at constant v o l u m e , pressure i n - creases: the p i s t o n is free to s l i d e , therefore it moves a n d volume increases".
T h i s response c a n be o u t l i n e d i n the f o l l o w i n g w a y : s u p p l y o f heat -*Tf—*pf-*Vf ( w i t h o b v i o u s notations).
In such comments, one o f the evoked events, p f , c o n t r a - diets data presented i n the p r o b l e m , n a m e l y that p is k e p t constant.
Such a contradictio», and others as we will see, disappears if one admits that this form of argument is interpreted tempora- rily. A n a r r o w , then, does not mean o n l y "therefore", but also
"later". T a b l e 4 shows h o w , i n three a n d p r o b a b l y many other languages, these l o g i c a l a n d c h r o n o l o g i c a l levels melt into a single w o r d , totally a m b i v a l e n t , i n english: "then".
T a b l e 4 Shift i n meanings from l o g i c a l to c h r o n o l o g i c a l levels
level l french english spanish
l o g i c a l intermediate c h r o n o l o g i c a l
donc alors ensuite
therefore then later
por eso entonces despues
F r o m this p o i n t o f v i e w , the previous c h a i n s u b d i v i d e s into t w o steps:
- first step: "Supply o f heat —>T f—*pfn, v o l u m e b e i n g i m p l i c i - tely o r e x p l i c i t e l y kept constant. N o t i c e that such a constancy o f v o l u m e is a s u f f i c i ë n t c o n d i t i o n f o r the t w o first i m p l i c a t i o n s to be s t r a i g h t f o r w a r d . A t constant v o l u m e , an i n p u t o f heat, i n the accepted theory, necessarily results i n an increase o f t e m p e - rature (no w o r k being transferred to the e x t e r i o r o f the gas).
T h e same c o n d i t i o n also allows the otherwise not o b v i o u s c o n - c l u s i o n that i f temperature increases, then pressure increases.
- second step: "p f —>V f". T h e piston is n o w released (this is said e x p l i c i t e l y b y some students) a n d moves u n t i l the i n t e r n a l pressure equals the external one. In such a c h r o n o l o g i c a l v i e w , the seemingly c o n t r a d i c t o r y argument "p f ( d u r i n g i s o b a r i c heat- ing)" becomes acceptable, as w e l l as the statement "at constant V", f o l l o w e d b y this other: " V o l u m e increases". These events indeed are understood as successive, a n d therefore as temporary.
So they seem no longer c o n t r a d i c t o r y .
Rozier & Viennot 11
T o s u m up: this k i n d o f response supports the hypothesis (see R o z i e r , 1987) that a linear type o f reasoning is used:
* 1 - * 2 $n —
i n w h i c h , as said earlier, each phenomenon $ is s p e c i f i e d w i t h o n l y one p h y s i c a l quantity, and where the causality referred to by the arrow has a both logical a n d c h r o n o l o g i c a l content. T h e t e m p o r a l c o n n o t a t i o n o f such an i m p l i c a t i o n accounts f o r the lack o f symmetry described i n section Ic. T h i s w a y o f reasoning c o n t r a d i c t s the a c c e p t e d theory o f quasistatic phenomena, i n w h i c h a l l the c h a n g i n g p h y s i c a l q u a n t i t i e s are s u p p o s e d to change simultaneously under the permanent constraint o f one or several relationships. B u t this enables variables to be coped w i t h two b y t w o , and to say d i f f e r e n t things about one o f them at different stages o f the argument.
O t h e r inconsistencies become acceptable i n this l i n e a r causal reasoning, as we w i l l see n o w .
4. Linear causal reasoning and the problem of steady states A n o t h e r question from this study ( R o z i e r , 1987) puts i n evidence how the features o f linear causal reasoning just described f i t i n w i t h students' most c o m m o n responses a n d a l l o w c o m m e n t s w h i c h i n the accepted theory lead to contradictions. A s k e d to e x p l a i n i n molecular terms w h y an adiabatic compression o f a perfect gas results i n an increase o f temperature (see question i n table 1), 42% o f students (N=140) give comments o f this type:
"When the piston is pushed d o w n , v o l u m e decreases, therefore p a r t i c l e s are closer to each o t h e r , w h e n c e m o r e c o l l i s i o n s occur between them.. and there is an increase i n tempera- ture"
"Same number o f particles i n smaller v o l u m e , then particles more squashed, more c o l l i s i o n s , more heat produced"
" M o r e collisions between particles, more energy p r o d u c e d due to f r i c t i o n "
These responses can be o u t l i n e d as follows: V \ —* n f —• number o f collisions f -* Q is produced —• T f, the fourth statement being j u s t i f i e d b y the fact that "collisions produce heat".
A g a i n a linear f o r m is observed. L e t us see n o w h o w the h y p o t h e s i s o f a t e m p o r a l c o n t e n t is s u p p o r t e d b y this last comment: "collisions produce heat".
In such a c o m m e n t , one can see an emergence o f the w e l l k n o w n p r e f e r e n t i a l association between temperature a n d heat, an increase i n temperature being necessarily a s c r i b e d , i n c o m m o n reasoning, to a supply o f heat. O n e can also say that m a c r o s - c o p i c properties o f bodies c o l l i d i n g inelastically are ascribed to microscopie particles.
V a l i d as they may be, these interpretations do not e x p l a i n h o w it is that none o f these students r e a ü s e the i n c o m p a t i b i l i t y between this statement: "collisions produce heat" and the idea o f steady state. Indeed, i f i n an adiabatic vessel, collisions between particles were c o n t i n u o u s l y p r o d u c i n g heat, an e x p l o s i o n w o u l d soon o c c u r . B u t i f the statement: "collisions produce heat", or
"there is some heat produced", refer to a temporary p h e n o m e - n o n , as i n the "chronological" interpretation o f students' reason- i n g , then there is no longer any i n c o m p a t i b i l i t y w i t h the idea o f steady state. I n t e r e s t i n g l y , some students i n this i n q u i r y , and others i n f o r m a l l y questionned in a class r o o m , said that more c o l l i s i o n s p r o d u c e d more heat, during the transformation, but that at the e n d o f the t r a n s f o r m a t i o n , the heat p r o d u c t i o n stopped: the end o f the argument is also the end o f the story...
So, it seems that seeing the evoked p h e n o m e n o n as temporary avoids the d i f f i c u l t i e s inherent to the analysis o f steady states.
Such states are not envisaged for themselves, but as the result o f t r a n s i t o r y phases, themselves a n a l y s e d as step b y step - variable" b y v a r i a b l e processes. A l l this is d o n e , i n c o m m o n reasoning, w i t h o u t saying it, and p r o b a b l y w i t h o u t being aware o f it.
M o s t p r o b a b l y , teachers share to a large extent this t o l e - rance towards explanations i n c o m p a t i b l e (according to accepted l o g i c ) w i t h steady states. Some teachers were a s k e d , d u r i n g t r a i n i n g sessions ( N = 4 5 )2 , to consider what answer they w o u l d give to a student who says "collisions between particles produce heat". None o f them proposed a counter argument i n terms o f steady states O t h e r examples o f this teachers' tolerance are g i v e n i n R o z i e r ' s study (1987, see also V i e n n o t , 1989b).
5. Interpreting a common idea in terms of linear causal reason- ing: changes of states and thermal motion
A s s a i d b e f o r e , an i d e a w i d e l y spread a m o n g students a n d teachers, is that thermal m o t i o n is more intense f o l l o w i n g the order: so'lid, l i q u i d , gas. A t first sight, this m i g h t be s i m p l y a
Roeier & Viennot 13
manifestation o f the adherence between mean k i n e t i c energy a n d mean distance between particles c o m m o n l y referred to b y the expression "thermal motion" and cemented b y the idea o f d i s - order.
A n experiment ( R o z i e r , 1987) has been done w i t h students at u n i v e r s i t y to refine this point o f v i e w a n d to see i f the linear causal reasoning was an help i n interpreting c o m m o n ideas i n this f i e l d .
A n excerpt f r o m a textbook ( V a l e n t i n , 1983) was first g i v e n to students, w h o were asked to read it carefully:
" T h e r m a l energy possessed b y each molecule is large enough to prevent the molecules o f the gas f r o m being bound: i n a gas, molecules are continuously h i t t i n g each other and b o u n c i n g . B u t i f t e m p e r a t u r e is l o w e r e d , the system w i l l be able to become l i q u i d and even s o l i d . Such p h y s i c a l phenomena o c c u r w h e n , w i t h decreasing temperature, molecules have so l o w a mean k i n e t i c e n e r g y that they cannot any longer resist the electromagnetic interaction. T h e y first gather i n l i q u i d state and f i n a l l y get b o u n d i n solid states"
T h e subsequent questions are:
I. D o y o u t h i n k that this text suggests the f o l l o w i n g statements:
Statement 1: A t a g i v e n t i m e d u r i n g the l i q u e f a c t i o n , mean k i n e t i c energy o f a molecule o f gas is larger than mean k i n e t i c energy o f a molecule o f l i q u i d ( l i q u i d and vapor are i n thermal e q u i l i b r i u m at the time considered).
Statement 2: A t a g i v e n time d u r i n g the l i q u e f a c t i o n , the mean d i s t a n c e b e t w e e n p a r t i c l e s is l a r g e r i n the gas than i n the l i q u i d .
II. D o y o u t h i n k that
Statement 1 is true false w h y ? Statement 2 is true false w h y ?
A m o n g 181 students i n the three first years at U n i v e r s i t y , 77%
t h i n k that the text suggests statement 1 a n d 69% t h i n k that this statement is true. T h e corresponding percentages f o r state- ment 2 are 80% ("the text suggests statement 2") and 85% ("sta- tement 2 is true").
A s recalled earlier i n the paper, mean k i n e t i c energy depends o n l y , in classical t h e r m o d y n a m i c s , o n temperature a n d is there- fore the same f o r systems at same temperature, f o r instance two
phases o f a substance at thermal e q u i l i b r i u m . T h i s is recalled b y the author o f this text one page further (not r e p r o d u c e d i n the test).
In i n t e r p r e t i n g these facts, one may first notice the strong i n p u t o f temporal connotations i n the text: " i f ... the system w i l l be, .... they cannot resist any longer, ... first .... f i n a l l y
T h i s suggested c h r o n o l o g y superimposes on the logical c h a i n , as follows: T —» ec \ —• electromagnetic interactions w i n —•
l i q u i d state —»..—» solid state.
L i n e a r and c h r o n o l o g i c a l , this text seems i n perfect resonan- ce w i t h the features characterising the "linear causal reasoning".
T h e idea subtly i n d u c e d by such a c h r o n o l o g y is that the story begins w i t h h i g h t e m p e r a t u r e a n d gaseous state and finishes w i t h l o w k i n e t i c a l energy and l i q u i d state, no r o o m being left to envisage simultaneously gaseous and l i q u i d states at same t e m p e - rature. A l l these students, however, k n o w that at thermal e q u i - l i b r i u m the two phases are at same temperature.
T h e very h i g h percentage o f students who accept statement 1 as true supports the h y p o t h e s i s that they share the t y p e o f r e a s o n i n g d e s c r i b e d e a r l i e r ( l i n e a r c a u s a l r e a s o n i n g ) , a n d seemingly encouraged b y the text.
6. Discussing our teaching goals: some remarks in conclusion T h e r e are various points w h i c h can be discussed at length about the greater or lesser correctness o f some o f the excerpts quoted above. One m i g h t then ask whether comments s u c h as : "at h i g h altitude, there is less molecules, so pressure is lower", or "ther- m a l m o t i o n is h i g h e r i n gases than i n s o l i d s " , or "molecules have so l o w a k i n e t i c energy that they cannot resist any longer the electromagnetic interactions..." should be banished or not.
T h i s is not the point o f interest here. R a t h e r than discussing the correctness o f these statements, let us just note that such
"soft qualitative reasonings" gloss over the d i f f i c u l t i e s o f m u l t i - variable reasoning, that this is, most o f the t i m e , not p o i n t e d out, a n d that the contradictions w h i c h may arise f r o m a careless e x t e n s i o n o f these s i m p l e a n d evocative explanations are not c o n f r o n t e d . These facts deserve attention and b r i n g us back to the c r u c i a l question: what are our teaching goals,
- to make students f a m i l i a r w i t h particulate, or atomic structure o f matter, or w i t h other ideas or phenomena
- or to teach them how to reason i n a coherent way (in p a r -
Rozier & Viennot 15
ticular w i t h several variables), a n d to show them the l i m i t s o f each level o f explanation?
T h i s a l t e r n a t i v e is p u t i n a p r o v o c a t i v e w a y . In fact, i n the constructivist v i e w so w i d e l y shared n o w among researchers i n science education, f a m i l i a r i t y w i t h ideas is o f no real value i f a personal construction o f concepts b y c h i l d r e n has not o c c u r r e d . In other words, there cannot be any conceptual learning w i t h o u t any reasoning. So we can d r o p our first alternative and replace it b y this question:
- w h i c h k i n d o f reasoning do we a i m at f o r our pupils or s t u -
• dents when i n t r o d u c i n g such and such ideas or phenomena?
T h i s question is d o u b l é faced:
- w h i c h (available) k i n d o f reasoning w i l l help them to grasp new concepts (for example i n an i n d u c t i v e progression)
- w h i c h k i n d o f reasoning w i l l they learn?
It seems to us that it is important to be extremely careful i n such a s p e c i f i c a t i o n . F o r instance, i n d u c t i v e procedures a i m e d at i n t r o d u c i n g particulate ideas raise the f o l l o w i n g questions:
w h i c h e x p e r i m e n t s i n p h y s i c s , a n d according to which logic, s u p p o r t a p a r t i c u l a t e model rather than a continuous one? A classical theory, h y d r o d y n a m i c s , accounts f o r changes o f v o l u m e and flows w i t h a continuous model w h i c h , o f course, respects a l l the necessary c o n s e r v a t i o n s , d y n a m i c a l ones i n c l u d e d . N o t to speak o f q u a n t u m m e c h a n i c s w h i c h is also c o n t i n u o u s w i t h respect to space. M a n y teachers are not aware o f this lack o f evidence. In a w o r k s h o p i n a recent international c o n f e r e n c e3, participants were asked w h i c h experiment(s), among the f o l l o w - ing, were the most appropriate to i n t r o d u c é particulate ideas:
- change o f state - dissolution
- difference i n color f o r different concentrations - expansion and compression o f a gas
- d i f f u s i o n
- non a d d i t i v i t y o f volume in the m i x i n g o f water a n d a l c o h o l , about a t h i r d o f participants chose expansion a n d compression o f a gas. So, there is a danger o f pseudo demonstrations.
T h i s w o u l d support the choice made, f o r example, b y M e h e u t and a l . (1987), i.e. i n t r o d u c é ex cathedra the basis o f a p a r t i c u - late m o d e l , then ask c h i l d r e n to w o r k on it.
T h i s h o w e v e r leads us to ask the q u e s t i o n : what k i n d o f w o r k , should the students be i n v o l v e d i n the learning a c t i v i t y ?
A w o r k about c o n s e r v a t i o n o f mass and n u m b e r o f particles through changes o f v o l u m e or changes o f state has been p r o - posed by several authors (for instance M e h e u t e.a.), a goal v e r y appropriate to pave the way for learning the basis o f c h e m i s t r y . T h e n the d i f f i c u l t y is again to specify what k i n d o f w o r k it is possible to do i n a consistent way. One may envisage activities o f a d e s c r i p t i v e type: c h i l d r e n or students have to describe i n terms o f a particulate model changes o f v o l u m e or changes o f state. T h i s may also be consistent w i t h goals w h i c h emphasise explanations. T h e d i f f i c u l t i e s stressed in this paper suggest that, at any level o f teaching, o n l y two attitudes are self-consistent.
- One is to be extremely careful about the degree o f "explana- tion" actually expected, and to specify what cannot be a c c o u n - ted f o r i n the frame o f the p r o p o s e d d e s c r i p t i o n . T h u s , f o r instance, the f o l l o w i n g levels o f understanding may be envisaged:
"Gases can change their v o l u m e to a large extent but ( w i t h o u t the b e g i n n i n g o f a k i n e t i c theory) we cannot e x p l a i n w h y they resist a compression before molecules are in contact"
"Solids e x p a n d w h e n heated (contract when cooled), we cannot (yet) e x p l a i n w h y . K n o w i n g that thermal m o t i o n increases (de- creases) i n such a case is not enough to e x p l a i n w h y this makes the solid expand. Indeed, the particles might vibrate more i n t e n - sely, and stay around the same place w i t h o u t d r i f t i n g (a matter o f a n h a r m o n i c i t y o f the potential o f interaction between p a r - ticles!)."4
" A t e q u i l i b r i u m between, say, l i q u i d and gas, thermal m o t i o n (mean k i n e t i c energy) is the same i n the two phases, and we cannot (yet) e x p l a i n this s u r p r i s i n g t h i n g . In other w o r d s , we cannot e x p l a i n w h y , w i t h the same thermal m o t i o n , some m o l e - cules are l i n k e d to each other and others are free. We cannot e x p l a i n w h y thermal m o t i o n keeps the same d u r i n g the change o f state. We k n o w indeed that an input o f heat is used to break the l i n k s between particles i n the l i q u i d . B u t we do not k n o w w h y it is used o n l y for this and not also to increase thermal motion."
- A n o t h e r possible teaching strategy is to w o r k w i t h some "soft"
e x p l a n a t i o n s , b u t w i t h o u t h i d i n g the dangers o f a careless extension o f such explanations to other cases. F o r instance, to w o r k w i t h the f o l l o w i n g ideas:
" A t an a l t i t u d e , there are fewer molecules, therefore pressure
Rozier & Viennot 17
is lower"... adding: "this reasoning works o n l y i f the molecules have (more or less, admittedly) the same v e l o c i t y i n the two compared cases.
"When a tyre is heated up, it becomes harder because the m o l e - cules have a larger mean speed"... a d d i n g "this reasoning w o r k s o n l y i f the same number o f molecules is still i n the same v o l u - me" ( o b v i o u s l y not the case since the tyre is harder, but an approximate constancy o f v o l u m e may be i n v o k e d ) . •
T h i s k i n d o f harder qualitative reasoning may be considered too d e m a n d i n g , but it is the price to pay for consistency i n d e a l i n g w i t h such phenomena.
O f course, i f one is interested i n fostering the m u l t i v a r i a b l e reasoning for itself, rather than illustrate phenomena connected w i t h p a r t i c u l a t e structure o f matter, one may choose s i m p l e r e x a m p l e s f i r s t ; T h e area o f a rectangle is a f u n c t i o n o f two variables: hard qualitative reasoning may be trained on s i m i l a r simple examples.
H o w e v e r such teaching goals, l i n k e d w i t h general features o f reasoning, are not m u c h i n favour at the moment, overshadowed as they are by more c o n t e n t - s p e c i f i c objectives. H o w e v e r , one p o i n t at least must be made c l e a r l y : i n o u r students, l i n e a r causal r e a s o n i n g w i l l be the most l i k e l y outcome o f teaching w h i c h never confronts it.
It seems therefore that we cannot a v o i d a debate about our teaching goals, w h i c h should more e x p l i c i t e l y consider the k i n d s o f reasoning we expect our pupils or students to learn.
A c k n o w l e d g e m e n t
T h e help received f r o m R o s a l i n d D r i v e r i n the preparation o f the english version o f this paper is gratefully a c k n o w l e d g e d .
Notes
1. L.Viennot, Paris 1986-7, first cycle in secondary education (grades 6 to 9), N=30, training in physics; Milan 1989, all levels of teaching, N=25, training in didactics
2. L.Viennot, 1989, all levels of teaching, Paris N=20, Milan N=25, training in didactics
3. I l l r d International Conference on Research in Science and Mathematic Education, Santiago de Compostela, 1989, Workshop by Enciso, E . Llorens, J . A . , Sebadra, F .
4. It happens even that they vibrate more intensely being closer to each other, for instance when ice melts and the resulting liquid water is subse- quently heated.
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