Misconceptions or P-Prims: How May Alternative Perspectives of Cognitive Structure
Influence Instructional Perceptions and Intentions?
Author(s): David Hammer
Source: The Journal of the Learning Sciences, Vol. 5, No. 2 (1996), pp. 97-127
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THEJOURNAL
OFTHELEARNING
SCIENCES,
5(2),97-127
@ 1996,Lawrence
Erlbaum
Associates,Inc.
Copyright
Misconceptionsor P-Prims:How May
AlternativePerspectivesof Cognitive
StructureInfluenceInstructional
Perceptionsand Intentions?
David Hammer
Departmentof Education
TuftsUniversity
The notion that studentscome to science courses with misconceptionshas become
quite widely accepted by those who follow or participatein education research.
DiSessa and his colleagues (diSessa, 1988, 1993; Smith, diSessa, & Roschelle,
1993/1994) have challengedthe theoreticalandempiricalvalidityof this perspective
and offered an alternativeaccountof cognitive structurein phenomenologicalprimitives or p-prims.The purposeof this articleis to furtherclarifyand contrastthe two
accounts:in particular,to considertheirutility and generativityas conceptualtools
for teachers. How may each perspective influence instructionalperceptions and
intentions?The articlerecountsa discussion about forces and motion from a highschool physics class, analyzeshow a teachermay perceivestudents'participationin
that discussion from eitherperspective,and considerswhat, based on those perceptions, the teachermay see as tasks for instruction.
It has become widely accepted as a truth, among those who follow or participate in
science education research, that students come to science courses with conceptions
about the world that differ from scientists', and that these misconceptions need to
Requestsfor reprintsshould be sent to David Hammer,Departmentof Education,TuftsUniversity,
Medford,MA 02155.E-mail:[email protected]
98
HAMMER
be addressedin instruction.This view framesresearchdesignedto identifymisconceptions and instructiondesignedto reveal, confront,and replacethem.
The wide acceptance and application of this perspective warrantsconcern,
becausethereremaina numberof reasonsto questionits validityandcompleteness.
Smith, diSessa, andRoschelle (1993/1994) argued,on theoreticalgrounds,thatthe
misconceptionsperspectivecontradictsconstructivism:If studentconceptionsare
deeply and fundamentallydifferentfrom experts', then from what can they constructexpertconceptions?On empiricalgrounds,they arguedthatintuitivereasoning is not as consistentor stable as the misconceptionsperspectiveimplies.
Smith et al. (1993/1994) built their argumentsfrom diSessa's (1988, 1993)
earlierwork, andthey comparethe misconceptionsperspectiveto his "knowledgein-pieces" view of intuitive knowledge. In diSessa's model, intuitive physics is
made up of smaller,morefragmentarystructuresdiSessacalledphenomenological
primitives, or p-prims for short.The misconceptionsperspective,diSessa argued,
confuses emergentknowledge,acts of conceivingin particularsituations,for stable
cognitive structures.
As in Smith et al. (1993/1994), my purposeis to comparethe misconceptions
perspective to diSessa's p-prims account. However, rather than compare the
perspectiveson theoreticalor empiricalgrounds,I comparethem in regardto their
potentialutility and generativityas conceptualtools for teachers.How may each
of these perspectivesinfluenceteachers'perceptionsof studentsand intentionsfor
instruction?In otherwords,I am not askingwhich view is more valid;I am asking
what each view may do to shape a teacher'sawarenessand objectives.
The context for this comparisonis a class discussion about forces and motion
from a physics courseI taughtduringthe 1992 to 1993 school year at a public high
school in Massachusetts.In that discussion, the studentsexpressed a numberof
views inconsistentwith the standard,Newtonianaccount.I considertwo interpretationsof these views as (a) involving stablemisconceptionsor (b) situatedacts of
conceiving involving p-prims. In general, perceptionsof stable misconceptions
suggest tasksfor instructionof weakeningandreplacingelementsof students'prior
knowledge; perceptionsof acts of conceiving suggest tasks of modifying the use
of priorknowledge.
The article is organized in three sections. First, "AlternativePerspectiveson
Students'Knowledge"reviews misconceptionsandp-primsas models of cognitive
structures."AClass DiscussionAboutForcesandMotion"thenpresentsan account
of a physics class discussion, offers alternativeways in which a teacher may
perceive the students'views, andconsiderswhata teachermay supposeinstruction
should accomplish.The closing section, "ResearchPerspectivesand Instructional
Practice," summarizes the analyses and reflects on the contributionsof these
perspectivesfrom researchto instructionalpractice.
MISCONCEPTIONSOR P-PRIMS
99
ALTERNATIVE
PERSPECTIVESON STUDENTS'
KNOWLEDGE
Misconceptions'
As Smith et al. (1993/1994) noted, thereare many versions of the perspectivethat
students'conceptionsare differentfrom scientists'. The students'conceptionsare
referredto variously as preconceptions,alternativeconceptions,and misconceptions, but the core idea is of conceptionsthat
1. are stronglyheld, stablecognitive structures;
2. differ from expertconceptions;
3. affect in a fundamentalsense how studentsunderstandnaturalphenomena
and scientific explanations;and
4. must be overcome, avoided, or eliminatedfor studentsto achieve expert
understanding.
Not all authors would agree with this set of properties.In particular,some
consider the term misconceptionsto refer only to the phenomenologyof patterns
in students'responsesthatare inconsistentwith expertunderstanding.This use of
the termdoes notposit cognitivestructuresoranyotherexplanationforthe observed
patterns;it simply notes the patterns'existence (D. Hestenes,personalcommunication, January21, 1994). Following Smith et al. (1993/1994), I do not intendto
attributethe list to any particularauthors,butI suggestit is consistentwith common
usage of the variousterms(preconceptions,etc.) in the science educationcommunity. For the purposesof this article,I use the most commonterm,misconceptions,
and I take these four propertiesas its definition.
The misconceptions perspective reflects the constructivisttenet that people
perceive and interpretthe world throughtheir currentknowledge structures.It is
an alternativeto the naive, generally tacit view that studentsare "blankslates,"
accordingto which instructionconstitutesa transferof informationfromthe teacher
(or textbook,or demonstration,etc.) to the students.The core idea is thatstudents'
priorknowledge includesquitereasonableconceptionsthatarenot consistentwith
expert understanding.These misconceptions affect in a fundamentalway how
studentsperceive and interpretwhat they see and hear.For this reason,instruction
'Refer to Smith et al. (1993/1994) and Carey(1986) for more extensive discussionsof the misconceptions perspective.
100
HAMMER
cannot be a straightforward
exchangeof information.It is not sufficient simply to
tell studentsor to show them;teachersmust help studentschange or replacetheir
misconceptions.It is thus essential for educatorsto take seriously the alternative
and intelligentconceptionsthat underliestudents'"mistakes,"ratherthan simply
to convey scientists' knowledge.
AboutForcesandMotion
Misconceptions
By a Newtonian account, forces do not cause motion (velocity); they cause
change in motion (acceleration).If thereis no net force on an object, it moves at a
constant speed in a constantdirection;if there is a net force, the object's speed,
directionof motion,or both changes.Studentsoften have difficultyunderstanding
this account, due, from the misconceptionsperspective,to their misconceptions
aboutforces andmotion. I note severalthatarerelevantto the analysisof the class
discussion laterin the article.
McCloskey (1983) described students as having an intuitive impetus theory
similarto the impetustheoriesarticulatedby medievalphysicists.Studentssee the
motion of an objectas causedby an internallystoredimpetus,which they typically
callforce or energy.As the impetusrunsout, the object stops moving. McCloskey
identifiedtwo variationsof the impetustheory,one in which the impetusruns out
on its own andanotherin which the impetusis drainedby gravity,friction,or both.
Otherresearchershave identifiedsimilarmisconceptionswithoutattributingto
themthe coherenceof a theoreticalframework.Clement(1983) describedstudents'
use of a misconceptionthat"motionimplies a force"in a rangeof situations.This
is a misconceptionthatthemotionof anobjectindicatesthepresenceof a continuing
force causing thatmotion.
Hestenes and his colleagues (Halloun & Hestenes, 1985; Hestenes, Wells, &
Swackhamer,1992) haveprovidedthe mostcompletetaxonomyof misconceptions
relatedto mechanics.They use the termimpetusto describeseveralmisconceptions
relatedto an internallystoredcause of motion.Theirlist also includesthe misconceptionsthatmotionimplies an activeforce on an object,exertedby some external
agent,andthatmotionends when the activeforce "wearsout."Similarmisconceptions, of motion as caused by an externallyapplied force, have sometimes been
describedas Aristotelian(Champagne,Klopfer,& Anderson,1980;diSessa, 1982;
Whitacker,1983), althoughtheseauthorshavebeencarefulto notethatthe students'
conceptions do not have the coherenceor logical structureof Aristotle's account.
Othermisconceptionsin Hesteneset al.'s (1992) taxonomyincludethe conception
2Moreextensive accountsof misconceptionsin mechanicscan be found in Arons (1990), Campet
al. (1994), and Hallounand Hestenes (1985).
MISCONCEPTIONSOR P-PRIMS
101
that the strengthof gravity increasesas an object falls (Champagneet al., 1980),
that obstacles (e.g., a table) do not exert forces (Minstrell,1982), and thatmotion
occurs when the motive force is largerthanthe resistinginfluences.
Perspective
Challengesto theMisconceptions
The purposeof this article is not to debate the validity of the misconceptions
perspective. However, because of its wide acceptancein the science education
community, it may be importantto review some of the criticisms of the misconceptions perspectiveto motivatethe considerationof an alternative.
Some accountsof particularmisconceptionshave been criticizedas inappropriately framedwithin the scientists' position, using scientists' terms and meanings,
ratherthan within the students'(Viennot, 1985). For example, if a studentsays a
moving object "hasa force in it,"researchersmay interpreta misconceptionabout
force. It is a mistake,by this line of criticism,to interpretthe student'suse of the
wordforce as correspondingto a physicist's use of the term.Studentsmay have an
entirely differentschema for the wordforce (Carey, 1986), or several competing
schemas (Maloney & Siegler, 1993), or their concept of force may be vague in a
fundamentalsense (McDermott,1984). A similarcriticismholds that some of the
differences inferredbetween studentsand scientists are a matterof terminology.
Schuster(1993) showed thatchangingthe wordingof certainquestionscan have a
dramaticeffect: "Whichobject's speed is changing more quickly?"elicits very
different-and to a physicistmoreappropriate-responsesfrom"Whichobjecthas
a higheracceleration?"
Smith et al. (1993/1994) and diSessa (1988, 1993) challenged the idea of a
discontinuitybetween studentandexpertknowledge,arguingthatit conflicts with
the constructivistaccountof how we develop new understanding:
In focusingonlyon howstudentideasconflictwithexpertconcepts,themisconceptionsperspective
offersno accountof productive
ideasthatmightserveas resources
for learning.Becausethey are fundamentally
themselves
flawed,misconceptions
mustbe replaced.... An accountof usefulresourcesthataremarshaled
by learners
is anessentialcomponent
of a constructivist
theory,butthemisconceptions
perspectivefailsto provideone.(Smithet al., 1993/1994,p. 124)
That is, althoughthe misconceptionsperspectivepresentsa need for conceptual
change,fromthe students'misconceptionsto the expert'sappropriateconceptions,
it does not providean accountof how thatchange may take place.
Finally, a numberof researchershave questionedwhetherstudentreasoningis
as consistentas the misconceptionsperspectiveimplies. Most of this criticismhas
been directed at views of student reasoning as based on coherent, alternative
102
HAMMER
frameworks.A numberof authorstakethe position thatnaive reasoningin physics
lacks the coherenceof expertreasoning(Hesteneset al., 1992; Huffman& Heller,
1995; Minstrell, 1989, 1992; Viennot, 1985). Some of these accounts not only
challenge the view of students'having alternative,coherentframeworks,but also
questionthe view of incoherentcollectionsof stable,individualcognitive structures
(diSessa, 1988, 1993; McDermott,1984; Viennot, 1979). These authorspoint to a
malleability in the conceptions attributedto students,evident in the variationof
students'reasoningacross differentcontexts.
P-Prims
Not all thoughtsstudentsexpressneedto be understoodas directlyreflectingstable,
storedknowledgestructures.Whatthe misconceptionsperspectivetreatsas a stored
constructmay alternativelybe treatedas an act of construction.
For example, in one populardemonstrationof misconceptions,studentswere
askedto explain why it is hotterin the summerthanin the winter(Sadler,Schneps,
& Woll, 1989). Many respondedthatthis is because the earthis closer to the sun.
To see this responseas a misconceptionis to understandit as partof the students'
knowledge system: The question accessed that stored (and faulty) element of
knowledge about why it is hotterin the summer.Anotherinterpretationwould be
that the studentsconstructedthat idea at the moment.This constructionwould be
basedon otherknowledge,such as the (appropriate)knowledgethatmoving closer
to the sun would make the earthhotter,but it is not necessaryto assume that the
idea itself existed in some form in the students'mindspriorto the question.
DiSessa (1988, 1993) developed an alternativeaccount of students' intuitive
physics knowledge, positing the existence of more fundamental,more abstract
cognitive structureshe called phenomenologicalprimitives or p-prims. By this
view, how studentsrespondto a questiondependson which p-primsare activated.
For example, the question of why it is hotterin the summermay activatefor
them a p-prim connecting proximity and intensity: Closer means stronger. This
p-prim is an abstractionby which one may understanda range of phenomena:
Candlesarehotterandbrighterthe closer you get to them;musicis louderthe closer
you are to the speaker;the smell of garlic is moreintense the closer you bringit to
your nose. It may be throughthe activationof closer means strongerthat students
generatethe idea thatthe earthis closer to the sun in the summer.Thatmost people
would have this primitive in their knowledge system, and that it has a high
probabilityof being cued in the seasons question,is an alternativeexplanationfor
why many studentsgive such a response.
Moreover,becausecloser meansstrongeris encodedat an abstractlevel, in other
words because it is not directly linked to any surface features of experience,
different entrancesto the same topic would likely yield differentresponses. For
MISCONCEPTIONSOR P-PRIMS
103
example, if the question were to arise in the context of a discussion aboutthe tilt
of the earth,closer means stronger may never be activatedor the p-primmay be
activatedbut applied in a differentway, leading the studentto reason thatthe tilt
of the earth pushes one hemispherecloser to the sun. By the misconceptions
perspective,what is storedin some form is directlythe notion that "it is hotterin
the summerbecausethe earthis closerto the sun."By thatperspective,it is difficult
to understandhow any discussion aboutwhy it is hotterin the summerwould not
invoke the misconception.
In short,context sensitivity is easier to understandfrom a p-primsperspective
than it is to understandfrom a misconceptionsperspective,because p-prims are
encoded at a more abstractlevel. The p-prims perspective does not attributea
knowledge structureconcerningthe closeness of the sun and the earth;it attributes
a knowledge structureconcerningproximityand intensity.Moreover,the p-prim
closer means stronger is not incorrect.3Its activationin the situationof trying to
explain the seasons is incorrect,but the knowledge element itself is not. This
difference has practical relevance for instruction:A teacher would not try to
eliminatethe p-prim.
Similarly, ratherthan understandingstudentsas having a misconceptionthat
motionimpliesaforce, one mayunderstandthemas generatingsuchresponsesfrom
more fundamentalknowledge elements.DiSessa describeda p-prim,which I call
maintainingagency,4thatis relatedto the misconception,except againit is encoded
at a more abstractlevel. Maintainingagency is involved in an understandingof a
continuingcause thatmaintainsmotion,such as an engine maintainingthe motion
of a car, but it can also be involved in understandingthat a supply of energy is
necessary to keep a bulb lit or an oven hot, or thatcontinuousencouragementis
needed to keep a student motivated. Like closer means stronger, maintaining
agency is not incorrectin and of itself; its activationin certaincontextsis inappropriate.
Otherprimitivesin diSessa's frameworkincludeactuatingagency, dyingaway,
resistance,interference,andOhm'sp-prim.Actuatingagency is involved in understandingan initial cause of some effect, when the effect outlaststhe cause, in the
way thata toss causes the motion of a ball, the strikeof a hammercauses a bell to
ring, or, perhaps,a traumaticevent causes anxiety. Dying away is an abstraction
fromexperiences,suchas thefadingof thesoundof a bell, a decayin timeanalogous
to the decay with distance of closer means stronger. Dying away may underlie
students'understandingof why a tossedball returnsto earth,as the influenceof the
actuating agency fades over time. Resistance and interferenceare two p-prims
3I use correct and incorrectin this articleto describeconsistency and inconsistencywith accounts
that are establishedwithin the physics community.
4DiSessa (1993) called this p-prim continuingpush, but the word push in that name may be
misleading.I also use the name actuatingagency insteadof diSessa'sforce as mover.
104
HAMMER
pertainingto causes that impede an effect. Ohm'sp-prim5is an abstractionfrom
experiences involving an agency, an effect, and an impediment:The strongerthe
agency, the greaterthe effect; the strongerthe impediment,the weakerthe effect.
These two perspectiveson students' knowledge thus posit different kinds of
cognitive structures-misconceptions andp-prims-and these differentmodels of
knowledge point to differentinterpretationsof students'reasoning.The following
section presents a class discussion about forces and motion in which students
express a number of views that are inconsistent with the standard,Newtonian
account. In the subsequentanalysis of the discussion, I describe how one may
understandtheseviews eitheras indicatingmisconceptionsoras eventsof reasoning
thatinvolve the activationof more fundamentalknowledgeelements.
A CLASSDISCUSSIONABOUTFORCESAND MOTION
The purpose of this article, again, is to consider how alternativeperspectiveson
student knowledge may influence instructionalperceptionsand intentions.The
contextfor this comparisonis a class discussionaboutforces andmotion:How may
a teacher perceive the students'reasoning in this discussion, and what may the
teacherthen see as tasks for instruction?
I first give some backgroundaboutthe class, and then I presentan accountof
the discussion based on multipleviewings of the videotape,multiple readingsof
the transcript,and notes I recordedthatday.
Backgroundon the Class and Setting
There are about 2,000 studentsat the school, the single high school for a mostly
working-classcity in Massachusetts.I was thereas a guest, teachingone physics
class duringthe 1992 to 1993 academicyear.The class metdaily,for42 min,except
on Mondayswhen it met for a doubleperiod.I videotapedevery meetingfrom the
3rd week of school throughApril 1st, except for occasionaltechnicalproblems.In
addition,I recordeddaily, detailednotes and collected samplesof students'work.
Therewere 22 studentsin the class, dividedevenly by gender.Sixteenwere seniors,
and 6 werejuniors.
The discussion detailed later took place on Thursday,November 5th, about 2
months into the school year. With respect to the traditionalcontent of a physics
course, to this point in the year the studentshad been exploringvariousaspects of
5This name is due to the similaritybetween the p-primand intuitiveunderstandingsof Ohm's law
relatingelectricalpotentialdifference,resistance,and current.
MISCONCEPTIONS
ORP-PRIMS 105
one-dimensionalkinematics(see Hammer,1995a, for furtherdiscussion of activities early in the year). During the week that precededthis discussion, they used
microcomputer-basedlab materials(Thornton,1987). The final activity with that
equipmentwas to examine what happensto the speed of a cart when it is pushed
with a constant force, as measuredby a spring scale attachedto the cart. Most
studentspredictedthatthe cartwould move with constantspeed, but they all found
that the speed increased.We discussed these resultsfor the first partof the period
on Wednesday,November4th. Some studentssuggested that the accelerationof
the cartwas constant,underconstantforce,butatthattimewe only reacheda general
consensus thatthe speed increased.
With about 15 min remainingon Wednesday,I broughtout some metal tracks
androlleda steel ballon themto presenttwo argumentsby Galileothat"anyvelocity
once impartedto a body will be rigidly maintainedas long as thereare no causes
of accelerationor retardation."
The first argumentis as follows. If a balls roll down one ramp and then up
another,it will roll up the second rampuntil it reaches the height from which it
started,as long as the rampsand the ball are smooth enough so that the effect of
friction on the height the ball reaches is negligible. Thus, if the up ramp has a
shallowerslope thanthe down ramp,the ball travelsfartheron the up rampthanit
did on the down ramp.The more shallow the slope of the up ramp,the fartherthe
ball travelsto reachits originalheight(see Figure1). By thisreasoning,if the second
ramp were horizontal,the ball would have to roll forever,because it would never
reach its originalheight.
The second argumentstartsfrom the observationthata rolling ball gains speed
if it is rolling downhill and loses speed if it is rolling uphill. If uphill loses speed
FIGURE 1 As the slope of the rampbecomes more shallow, the ball must travel furtherto
reach its originalheight.
106
HAMMER
and downhill gains speed, then on a smooth, level surface the speed should be
constant.6
The studentsacceptedthese argumentsreadily;in fact, a few studentshelped
me complete the explanations.I assignedhomeworkfor the next day, first, for the
studentsto readthe textbook's(Haber-Schaim,Cross, Dodge, & Walter,1976, pp.
224-226) accountof Galileo's argumentsand, second, for them to come up with
argumentsagainst Galileo's view that a ball will roll forever at a constantspeed
unless thereis some force on it to makeit speed up or slow down. Severalstudents
protested, saying they could not argue against what they thought was true. I
explainedthatmy reasonsfor this assignmentwere thatI suspectedthey had other
ideas"lurkingaroundin [their]heads"andthatit is importantto consideralternative
positions thoroughly.
AnAccountof the Discussion
At the beginning of class on Thursday,I drew on current events for further
motivation, asking: "How many of you supportedfor presidentthe same person
your parentssupported?"I asked whetherthey supportedone or the otherbecause
they had thoughtcarefullyaboutboth sides of the issue or whetherit was just their
upbringing.7
Teacher: My parentsvoted for the same personI voted for for president.I have
to say, well wait a minute,did I just get it from them?I grew up in a
family that had certainideas that they think, and then I think them.
Does thatmean thatthose ideas areright,or does it just mean I grew
up in thatfamily. ... Ifyou're going to vote for Bill Clinton,you better
know why somebody would wantto vote for George Bush. Because
if you don't know why anybodycould ever vote for George Bush,
you haven't thought it through. ... I know yesterday I gave this
argumentaboutGalileo, and everybodysaid "Yeah,it makes sense.
Sure, it seems right."[But] if you don't seriouslyconsiderthe other
answer,how can you be confidentaboutthis answer?Maybeyoujust
haven't thoughtit through.
these
6GeorgeSmithhas calledto my attentionthe fact thatphysicists'practiceof attributing
becauseGalileohimselfdidnotbelievethem.Galileopresented
to Galileois misleading,
arguments
TwoNewSciences,buthe wentonto refutethem.Inthis
in hisDialoguesConcerning
thesearguments
theviewthattheball
article,as in theclassdiscussion,I continuethephysicists'practiceandattribute
arevalidmotivation
thesearguments
willcontinuemovingata constantspeedto Galileo.Tophysicists,
forNewton'sfirstlawof motion,thelawof inertia,thatanobjectwithno forceactingon it will move
in a straightlineat constantspeed.
deviatesfromdirect
7Inthe dialogueexcerpts,ellipsesandbracketsdenotewherethe transcript
All students'namesin thisarticlearepseudonyms.
dashesdenotepointsof interruption.
quotation;
ORP-PRIMS 107
MISCONCEPTIONS
I argued that it is importantnot only to know reasons for your side, but also to
understandand be able to respondto reasons for the other side. Tina helped me
make a comparisonbetweenwhat I was askingthemto do and what lawyers often
have to do: "Whetherthey believe it or not, they have to arguefor theirclient."
The students seemed convinced of the value of the exercise, so I solicited
argumentsagainstGalileo. Ning was the first to volunteer.She asked me to walk
acrosstheroomandlook atheras I spedupandslowed down.Frommy perspective,
she explained, she was speeding up and slowing down, but therewas no force on
her to make her speed up or slow down. This broughtan admiringmurmuraround
the room, and,fromthis pointon, therewas a high level of engagement,with many
side discussionsanddebates.No one hada responseto Ning's argument,so I asked
for otherarguments.We did not returnto Ning's until the next day.
Jack,referringto an experimentwe haddone earlier,said thata pendulumdoes
not swing back up to the same height from which it was released, so the ball in
Galileo's first argumentshould not come back up to the same height either.Other
students said they thoughtthe pendulumdid swing back to the same height, but
Scott convinced everyone by pointing out that the pendulumeventuallystops, so
it must lose a little height on each swing. Steve claimed that the pendulumlost
height in its swing becauseof friction,and, he said, Galileo was talkingabout"an
ideal environmentwith no friction."Jackassertedthata "pendulumhas no friction."
I wrote Jack's point, that the ball would not roll to the same height, on the
blackboard,and I asked for otherargumentsagainstGalileo. Penny was next.
For the pendulumthe reason it didn't go up to the same height
was becauseof gravity.So why can't you thinkof the ball rolling
on the flat surfacestoppingbecauseof gravitytoo. It's going to
slow down in a really small difference,so you can't even notice
the difference,but eventuallyit's going to stop because of that
little differenceaddingup.
2 Teacher: So your argumentis that the ball is slowing down, but it's just
slowing down slowly enoughthatyou can't really notice?
3 Penny:
Yeah becauseof gravity.
4 Teacher: Because of gravity.
1 Penny:
Several studentsresponded;Amelia's voice was the loudest.
Yeah, but Galileo was talkingaboutno gravity.
If there's no gravitythen how can the ball roll down the slope?
No he was talking about gravity, he was just talking about no
friction.
8 Nancy:
No friction,yeah.
9 Teacher: So Galileo was talkingaboutgravity.
5 Amelia:
6 Harry:
7 Steve:
108
HAMMER
10 Nancy: Gravity'sa kind of friction,though.
11 Teacher: Gravity'sa kind of friction?
12 Nancy: Yeah, because if you roll a ball down it speeds up because of
gravity.And if you roll a ball up, it slows down because of the
gravitationalpull. So if you're rolling a ball horizontallythe
gravitationalpull is pullingit downandit slows it down, youjust
can't notice, but eventuallyit will stop.
I intervenedat this point,tryingto curbthe idea that"Galileowas talkingabout'no
gravity.'"
13 Teacher: I don't thinkhe was thinkingof "nogravity."It's like Harrysaid,
how could it have rolled down the hill if there was no gravity?
Why would he even have it roll down the hill? So he wasn't
thinkingof "nogravity."
It wouldn'troll down the hill, it wouldjust float.
14 Scott:
I reiteratedPenny's argumentand wrote it on the board:"The ball slows down
gradually,so you don't notice, becauseof gravity."Steve contradictedthat view,
and Nancy and Jackcontradictedhis.
15 Steve:
Well see the ball's not slowing down because of gravity, it's
slowing down becauseof friction.So it-
Several voices, including:
16 Jack:
But gravityis there,gravitystops it.
17 Nancy: But the gravity'spulling it down18 Steve:
19 Jean:
But if there was no friction and there was still gravity then it
wouldn'tslow down,becausetheball wouldn'thaveanyfriction.
It doesn't matter,gravitydoesn't make it slow down. The thing
thatmakes it slow down is the friction,not the gravity.
Gravityis the same as friction.
There were a numberof voices at once, includingSusan saying somethingabout
gravity getting stronger"fartheraway from the ground."I quieted others to give
her the floor.
20 Susan: If you're fartheraway from the ground,the strongerthe pull.
21 Teacher: The strongerthe pull of gravity.
22 Nancy: It'sjust becauseyou'rerighton the groundyou can't feel it. You
can't notice it.
MISCONCEPTIONSOR P-PRIMS
109
23 Susan:
24
25
26
27
28
29
30
31
You can't feel it. You can't go any further.If you jump up in the
air, rightTeacher: Yeah?
Susan: It's gonna pull you rightdown. But if you'rejust standingthere
it's not going to pull you down.
Nancy: Because you don't fall. It's just so small you [unintelligible].
Susan: Because there's nowhereto go.
Teacher: Okay. So how does that [relateto] the thinggoing sideways and
slowing down?
Nancy: Because it's still, it's pulling, here's the ball, and gravity's still
pulling this, so eventuallyit's slowing it down.
Susan: You don't see it.
Steve: It's slowing down because of friction, if there was no friction
then it wouldn'tslow down.
Steve's comment led to anothereruptionof voices. I caught Amelia's saying
that"if gravitydoesn'tpull us down, why wouldn'tyou keep moving all the time?"
32 Teacher: [to Amelia, quieting other students] Why wouldn't we keep
moving all the time?
33 Joanne: It pulls us down, we're just saying it just doesn't you know34 Amelia: It does make us stop.
35 Joanne: -it doesn't say how fast and slow we're going to walk, [you're
not going to be] floating in the air.
36 Amelia: It's not friction,it's gravity.Whenyou throwa ball, it does come
down.
Amelia continuedto argueher position, and the debateintensified,with many
studentsspeaking at once. Sean managedto win the floor to argue:"If you use a
pendulum,does the stringslow down the pendulum?"Ricky answeredthat"there
is frictionin the stringwhereyou're holding it," and Sean clarifiedhis question.
Well does the string itself slow down the ball. Because it's
holding it at a certaindistance. Sort of like gravity does with
objects,holds it rightonto the surface.
38 Teacher: [gets a pendulumto help illustrateSean's point]
The string is the gravity. It's just keeping the pendulumwhere
39 Sean:
it's supposedto be.
40 Teacher: The stringis just keepingthe pendulumin this [drawsan arc on
the board].So the pendulumswings like this [gesturesalong the
37 Sean:
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HAMMER
arc on the board],and the reasonthe pendulumdoesn't go past
this is becausethe stringis holdingit along thatpath.Is thatwhat
you're saying?
41 Sean:
[Yes.]
42 Teacher: And so, you're saying if you roll a ball along a track,gravityis
just holding, makingit so it moves along the track.
Yeah.
43 Sean:
Susan asked why the two forces, gravitydown and the stringup, would not make
the ball slow down; Sean answeredthat"what'sslowing it down is the friction."
Ning came backinto the discussionto say that"theGalileotheorem"concerned
an "idealized"situationwith no forces,whichmustmeanno gravityandno friction.
This broughtus back to the questionof whethergravityis present,but Bruce took
the discussion in a new direction.
44 Bruce:
45
46
47
48
49
50
51
If there is no gravityand no friction, and there is a force that's
makingit move, it'sjust going to go in a straightline at a constant
speed.
Teacher: Okay. PennyPenny: If there's no gravitythe ball wouldn'tstay where it is.
Teacher: If there's no gravity, Penny says, if there's no gravity the ball
wouldn'tstay on the track.The ball wouldn'tstay whereit is. So
[to Bruce]do you have a, whatdo you say to that?
Bruce: What's makingthe ball move?
Amelia: [over severalothervoices] The forces behindit.
Susan: He said therewas no force.
Bruce: If there'sno force pullingit down, andno force slowing it down,
it wouldjust stay straight.
Several voices at once, including:
52 Harry: The ball wouldn'tmove.
There's no force that's makingit go.
53 Jack:
54 Steve: The force that'spushingit.
55 Bruce: The force that'spushingit will make it go
56 Jack:
57 Steve:
Where'dthatforcecome from,becauseyou don't have anyforce.
No there is force, the force that's pushingit, but no otherforce
that's slowing it down.
Sean gave the example of somethingmoving in "outerspace ... it's not going to
stop unless you stop it." Penny objected that the situation of the rolling ball is
MISCONCEPTIONSOR P-PRIMS
111
"nothinglike space." Amelia objectedfor anotherreason, saying that something
moving in space will still stop, because "even in space ... thereare ... gases."
I intervenedat this point to steer the discussion away from the question of
whetherthereare gases in space and towardan apparentinconsistency.
58 Teacher: Bruce, you were saying thereis the force on it thatis moving it.
So how can one side say thereare no forces on it, and the other
side say thereis a force that's moving it.
59 Bruce: Well therewas an initialforce.
60 Susan: There'san initialforce thatmakesit start,giving it the energyto
move.
61 Teacher: Therewas an initialforce.
62 Nancy: That initial force is gravity, because [if] there's no gravity it's
not going to roll down.
Jack talked about a puck on an air hockey table, arguingthat it will stop; he and
Bruce debatedwhetherit would stop becauseof frictionor because of gravity.
Steve explainedthat"gravityslows it down becauseof friction ... the reasonit
slows down is becausegravityis puttingfrictionon the ball ... by rubbingit against
the ground."This escalatedthe intensityof the debate.Penny's reactionwas that
Steve's explanationsupportedher position.
63 Penny:
If you're sayingthatthere'sfrictionbecauseof gravity,how can
you takeawayfrictionandleave gravitythere?If gravity'sthere,
there's going to be friction.
I highlightedas a key issue the question of whetherit is possible to think of
taking away friction without taking away gravity. Ning argued that "you can"
because"frictionandgravityaredifferentforces. Even theirdirectionis different."
She explained that "gravityis pointeddirectly down," but "frictiondepends"on
the motion. If a book is sliding to the left on a table,"thefrictiondirectionis to the
rightandthe gravitydirectionis [down],"and"wedon't haveto talkaboutgravity"
because the force of the table on the book cancels it. This broughta fresh burstof
discussion aroundthe room, but therewere only a few minutesleft in the period.I
stoppedthe discussionandassignedas homeworkfor studentsto supportor refute,
in writing,any of the argumentsthathad been presented.
The Discussion As Seen FromMisconceptionsand
P-PrimsPerspectives
There were a numberof ideas studentsexpressed in this discussion that were at
least technically inconsistentwith a Newtonian account of forces and motion. I
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consider five: (a) gravity makes the ball slow down; (b) no friction means no
gravity; (c) gravity is strongerfartherfrom the ground;(d) gravity holds objects
onto the ground;and(e) theball's motionis causedby a force.Thissectiondiscusses
these ideas, describinghow each may be seen either as indicatingstable misconceptionsor as situatedactsof conceivinginvolvingthe activationof p-prims.Again,
the purposeis not to argue which is the betteraccount,and I do not considerthe
classroomexcerptsas datathatcould validateor invalidateeitherperspective.
GravityMakestheBallSlowDown
Misconceptions. Duringtheclass discussion,severalstudentsarticulatedthe
idea thatgravitymakesthe ball slow down (Penny,line 1; Nancy, lines 10, 12, 29;
Jack,line 16; Susan,line 30; Amelia, line 36). Teachersfamiliarwith the literature
would anticipate the misconception that the downward force of gravity slows
horizontalmotion. McCloskey (1983), in particular,describedthis notion as part
of an impetustheoryof motion:Gravityandfrictiondrainimpetusfrom a moving
object.
The misconceptions perspectiveprovides, for example, an understandingof
Penny's reasoningin line 1. Jackhad comparedthe ball's rolling up and down the
ramps in Galileo's first argumentto the motion of a pendulum,noting that the
pendulumdid not returnto its originalheightandaskingwhy we shouldexpect the
ball to returnto its original height. Penny went beyond Jeff's phenomenological
point to suggest the cause: Gravitypreventsthe pendulumfrom rising back to its
originalheight, so, she claimed, it is reasonableto expect that gravitywould stop
a ball's motion on a horizontalplane.
Without an awareness of the misconception, Penny's reasoning may seem
strange:Why should whathappensto the pendulum,in which gravitycan be seen
as acting downwardagainstthe pendulum'srise, have any implicationfor what
happensto the ball rolling on a horizontalsurface?The misconceptionthatgravity
drainsimpetusmakes these two situationsexamples of the same phenomenon.
P-prims. Alternatively,one may understandthe idea that gravitymakes the
ball slow down as constructedby students in the context of the discussion. In
diSessa's account (1993), the motion of a ball on a horizontalplane is likely to
activatedying away: The ball's motionnaturallydecays. In manysituations,dying
away would have been sufficient. In this situation,however, the ball's slowing
neededfurtherexplanation,andthe studentsneededto identifya cause for thedying
away. The implicit question asking for a mechanismto explain dying away cued
the p-priminterference,so thatstudentsgeneratedthe idea thatgravitycauses the
MISCONCEPTIONS
ORP-PRIMS 113
ball to slow down. For Penny and others,the pendulumcued the same p-primsas
the ball, so they generatedthe same explanation.
No Friction
RequiresNo Gravity
Misconceptions. Nancy (line 10) and, momentslater,Jean (line 19) stated
this misconception,whichranthroughthe discussion:"Gravityis a kindof friction;
Gravityis the same as friction."Otherstudents,includingAmelia (line 5), Bruce
(line 44), andNing, confusedwhetherGalileo was neglectinggravity;Penny (line
63) said concisely what seemedto be a widely subscribedview: "Ifgravity'sthere,
there's going to be friction."
It is difficult to attributethis reasoningto any of the misconceptionsthathave
been described in the literature.Gravity and friction play a similar role in the
impetus theory (McCloskey, 1983), but thatdoes not entail the view that friction
must be presentif gravityis present.In this discussion,for example, Jack showed
very clearlythe misconceptionthatgravitymakesthe ball (andthe pendulum)slow
down, but he did not have a misconceptionthatno frictionmeans no gravity.
There is, however, no reason to expect that all misconceptions have been
catalogued,and it may be useful to thinkof this as a new one. It would be a way to
make sense of several students'persistencein claiming that Galileo was thinking
of no gravity,despitecompellingreasonsto the contrary(Galileo had a ball rolling
down a ramp)and despite the teacher'sattemptto stop this line of reasoning(line
13).
P-prims. From diSessa's (1993) perspective, the students' view that no
frictionrequiresno gravitywould be an exampleof the incoherenceandsensitivity
to the immediatesituationof the students'reasoning.When they were focused on
the ball rolling down the ramp,the studentsthoughtof gravityas causingthe ball's
motion, theirreasoningprobablymediatedby one or bothof the p-primsactuating
agency and maintainingagency. When they were focused on the ball rolling on a
level plane, they thought of gravity as interferingwith the ball's motion and
associatedit with friction,theirreasoningmediatedby interferenceanddyingaway.
It was possible for studentsto recognizegravityas necessaryfor the ball's motion
down the rampand then to insist thatGalileo was neglectinggravitybecausethese
were separateacts of conceiving thattook place in differentsituations.
The students'failureto comply with the teacher'ssuggestionto neglect friction
but not gravitymay be understoodnot as evidence of a misconceptionresistantto
change but as an example of regeneration.The teacher's suggestion may have
convinced studentsfor a moment,but it did not preventthem from reconstructing
the idea shortlylaterin the conversation.
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It is importantto note anotherplausible account not directly connected with
misconceptionsorp-prims.Some of the studentsmayhave intuiteda causalrelation
between gravity and friction as Steve articulatedlate in the discussion: "Gravity
puts friction on the ball ... by rubbingit against the ground."In fact, physicists
would agree in principlethat it is not possible to eliminatefriction between two
objectsthatarein contactandin relativemotion.It is correctthatno frictionbetween
the ball and the ground would requireno gravity (or no motion). Nevertheless,
physicistsalso considerit valid andproductivein such cases to supposeno friction.
This is whatsome of the studentsmay not have understood:the physicists'practice
of supposing ideal, unattainableconditions.Ning may have been expressingthis
epistemological point when she noted that Galileo was thinking of an idealized
situation.
GravityIs StrongerFartherFromthe Ground
Misconceptions. SusanandNancy's idea(lines 20-26) that"ifyou'refarther
away from the ground,the strongerthe pull" is also difficult to attributeto any
misconceptiondescribedin the literature.Therehave been accountsof a misconception that gravity is strongercloser to the ground (Champagneet al., 1980;
Hestenes et al., 1992), but not farther.Again, however,one may thinkof this as a
new misconception.
One may also thinkof thisas anideaSusanandNancyconstructedatthemoment
fromothermisconceptions.In fact, Champagneet al. (1980) presentedthe ideathat
gravitygets strongerthecloseranobjectis to theearth,notreallyas a misconception
in itself, but as a hypothesisstudentsgeneratein orderto remainconsistentwith a
misconceptionthatmotion is causedby an externalforce, the increasein speed as
an object falls indicatingto the studentsan increasingforce of gravity.
Susan and Nancy may have been doing somethingsimilarhere,generatingthe
idea that gravity is stronger fartherfrom the ground as an attempt to remain
consistent with a misconception that gravity drains impetus: Because impetus
appearsto drainmore slowly for a ball rolling on the groundthanfor a ball tossed
in the air, gravity must be weakeron the ground.Moreover,Susan's explanation
(lines 25, 27) that,on the ground,gravityis "notgoing to pull you down ... because
there'snowhereto go" implicatesa misconceptionthatobstaclesdo notexertforces
(Minstrell, 1982).8That misconceptionmay also have supportedthe construction
of the idea: Not recognizingan upwardforce, but recognizinga change in effect,
the studentsgeneratedthe idea thatthe downwardforce was weaker.
8The physicist's explainationwould be thatthe groundexertsan upwardforce equal and oppositeto
the downwardforce of gravity,resultingin no net verticalforce.
MISCONCEPTIONSOR P-PRIMS
115
P-prims. Similarly,the ideacouldbe understoodas an act of conceiving from
the activationof Ohm'sp-prim:A strongercause producesa greatereffect. Gravity
has a pronouncedeffect on objectsin the air,butits effect on objects on the ground
seems very small. Thatthe studentsdid not considerthe influenceof the groundis
an indicationthat, in this situation,the p-primssupportingand interferencetook a
low priorityin theirreasoning.
Holdsthe BallOntothe Ground
Gravity
Misconceptions. Sean's idea (lines 37, 39) that"gravityholds [theball]right
onto the surface"may indicatea misconceptionof gravityas a constraint,"holding
[the ball] at a certaindistance."Like Nancy andSusan,Sean was expressinga view
of the gravitationalpull on the ball as somehow relatedto the surfaceon which it
rests, andhis reasoningmay have involvedthe misconceptionthatobstaclesdo not
exert forces.
P-prims. If we think of Sean's idea, that "gravityholds [objects]right onto
the surface"as a storedpiece of knowledgehe may applygenerally,then we should
be concernedaboutit as a misconception.Alternatively,Sean's idea may be seen
as involving the activationof one or morep-primsfrom whatdiSessa (1993) called
the "constraintcluster,"includingsupporting,guiding, and clamping.If we think
of Sean's idea as an act of conceivingspecific to the situation,thenwe mayconsider
it an imaginativeandproductiveline of reasoning,because,in the situation,Sean's
idea was not inconsistentwith Newtonianreasoning.By a Newtonian account, a
force directedperpendicularto an objects' motion, such as the force of the string
on the pendulumbob or the gravitationalforce on the ball, cannotaffectthe object's
speed.
In fact, Sean's accountof the role of the stringor of gravity in these situations
may be seen as an intuitive version of the physicist's notion of an holonomic
constraint, which has the propertythat its influence can be taken into account
implicitly throughan appropriateselection of coordinates.Sean's reasoningabout
the stringandgravityas imposinga constrainton the motionon the bob or ball, but
as otherwise unimportant,is rigorously defensible. Thus, instead of being concerned about a misconception, we may see in Sean's reasoning the seeds of a
Newtonian understanding.9
9Note furtherthat Sean comparedgravity,in the situationof the ball, to the string,in the situationof
the pendulum;he could well have chosento comparethe stringto the tablesurfaceandgravityto gravity.
The lattercomparisonseems more direct:There is gravity in both situations;the string and the table
both preventthe objectfromfalling.However,the stringis always lateralto the pendulumbob's motion
and can thereforebe seen as a constraint;gravityis not always lateralto the bob's motion, and in the
case of the pendulum,it cannotbe seen as a constraint.
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TheBall'sMotionIs Causedby a Force
Misconceptions. Bruce's question (line 48), "What's making the ball
move?" was the first explicit mentionof the need for somethingto cause the ball
to move. Commentsby Amelia (line 49), Harry(line 52), Jack(line 53), and Steve
(lines 54, 57) all similarlyindicateda misconceptionthatmotionis causedby force,
althoughit would be difficult from these comments alone to distinguishwhether
studentsthoughtof the force as storedwithinthe ball or as externallyapplied.
Respondingto my question(line 58) of how to reconcilethe view thatthereare
no forces on the ball with the view thata force causes its motion, Bruce (line 59),
Susan (line 60), and Nancy (line 62) called the cause of motion an "initialforce,"
implying a force that initiated the ball's motion and suggesting that they were
thinkingof "force"as externallyapplied.Susan's version(line 60), thatthe "initial
force [gives the ball] the energy to move" may be seen as indicatingan impetus
misconception,in thatthe effect of the initialforce was to storeimpetus,"theenergy
to move," in the ball.'0
P-prims. Fromthe misconceptionsperspective,the students'commentspoint
to various misconceptionsthat motion is caused by force. One may alternatively
understandtheirviews as events of reasoninginvolving the activation-and deactivation-of variousp-prims.The situationof a ball rolling on a horizontalplane
has a high probabilityof cuing dying away: Moving objects slow down and stop.
Asked to explainthe motionof the ball, the studentsbeganto look for causes of its
motion and causes of its slowing, a situation likely to activate one or both of
actuating agency and maintainingagency, as well as interferenceor resistanceas
mentionedearlier.
The teacher'squestion(line 58), focusing attentionon the conflict between the
statementsthatthereis no force on the ball and thata force causes it to move, may
have favoredactuatingagency over maintainingagency, activatingthe formerand
deactivatingthe latter,so that some studentsbegan to distinguishan initial force
from a continuingforce. Priorto that,the studentshad felt no need to distinguish,
either in their reasoningor in their speech, a force that acts on the ball duringits
motion from a force thatacted in the past on the ball and set it in motion.
10Ifone were to attributethe physicist's meaningof energy andforce to Susan's use of the terms,
one could see her statementas correct(and thus revealinga correctconception):An initial force does
work on the ball, giving it kineticenergy. It would be difficultto supportsuch an attribution,however,
given Susan's other comments as well as the fact that this discussion was the students' first look at
dynamics.
MISCONCEPTIONS
ORP-PRIMS
117
On this view, much of the students'reasoningcould be seen as the beginnings
of a Newtonian understanding:Actuatingagency may be a useful resource for
building an understandingof the physicist's concepts of impulse,work, or both;
maintaining agency, for momentum,energy, or both. Thus, the students were
describingan initial agency impartingsomethingto the ball, and it is not unlikely
thatthis could develop into the idea of an impulseimpartingmomentumor of work
impartingenergy. Again, instead of being concernedabout a misconception,we
may see seeds of a physicist's understanding.
TasksforInstruction
How one conceptualizesthe tasksfor instructiondependssignificantlyon whatone
perceivesin students'knowledgeandreasoning.Theprecedinganalysisconsidered
how alternativeperspectivesmay influence a teacher's perceptionsof five ideas
technicallyinconsistentwith a Newtonianaccount:(a) gravitymakesthe ball slow
down; (b) no friction requiresno gravity;(c) gravity is strongerfartherfrom the
ground;(d) gravityholds objectsontothe ground;and(e) motionis causedby force.
This section considershow the differentperceptionsof these ideas may influence
a teacher'ssense of the consequenttasks for instruction.
In many ways, the misconceptionsand p-prims perspectives lead to similar
judgments about the tasks for instruction.Both suggest it would be ineffective
simply to explain the standardNewtonian account;both see students' incorrect
statementsas reflecting cognitive structureratherthan as individual,nonsensical
mistakes. Both suggest it is importantfor an instructorto explore the students'
knowledge and reasoning,to look for the sense behindtheirincorrectstatements.
The two perspectivesdiffer, however, with respect to what the instructormay
find in thatexploration.Fromone perspective,a teachersees conceptionsinherently
inconsistentwith expertknowledge;fromthe other,a teachersees p-prims,knowledge elementsthatcould contributeto expertunderstanding.Theprincipalpractical
significance for a teacheris that the formerimplies the tasks of dismantlingand
replacingprior knowledge, whereasthe lattersuggests the task of modifying the
organizationand use of priorknowledge.
Misconceptions
Froma misconceptionsperspective,one maysee animpetustheory(McCloskey,
1983) underlyingmuch of the students'reasoning.One may also see as misconceptionsthe ideasthatno frictionrequiresno gravity,thatgravityis strongerfarther
from the ground,and that gravityconstrainsobjects to move on the ground.The
misconceptionthat obstaclesdo not exert forces (Minstrell, 1982) also seemed to
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be involved. Still others,not evident in the discussion, may be expected based on
priorresearchand experience,such as the misconceptionthat air pressurecauses
gravity(Minstrell,1989).
A primarytaskfor instruction,basedon theseperceptions,wouldbe to eliminate
or at least weakenthese misconceptions.This could involve, first, drawingout any
misconceptionsthathad not been sufficientlyarticulated;second, confrontingand
confutingthose misconceptionswith argumentsor evidence;andthird,facilitating
the students'constructionof new, more appropriateconceptions(Strike& Posner,
1985). Withinthis perspective,one challengefor the teacheris to decide when the
studentshave sufficientlyarticulatedtheir variousmisconceptions.Thereis a risk
in confronting a misconception too soon, that the misconception has not been
sufficiently articulatedand the interventionwill be ineffective. On the otherhand,
there is a risk in waiting,thatthe discussionwill reinforcethe misconception.
A teacherwho sees the studentsas reasoningfrom an impetustheorywould not
believe this discussion had been successful in making that theory explicit. Only
Susan's comment, that an "initialforce [gives the ball] the energy to move" (line
60), could be interpretedas referringto an impetusstoredwithinthe ball. Between
the two versions of the impetustheory (McCloskey, 1983), by which impetus is
seen eitheras drainingon its own or becauseof an externalinfluence,only the latter
has been evident: In every instance, the studentsspoke of an externalinfluence
causing the ball to slow down, even in outerspace where,Amelia argued,the ball
would stop because "thereare still othergases."The teachermay choose to let the
discussioncontinueto drawoutimpetustheories;theteachermay intervenein some
way to facilitatetheirappearance.
On the otherhand,the view thatno frictionrequiresno gravityhas, at this point,
been expressed and debatedat some length, and it may be ripe for confrontation.
Ning alreadyinitiateda strongchallengeto thatmisconception,in herexplanation
thatthe forces of gravityand frictionact in differentdirections.The teachercould
build on her argumentor use Jack's example of air hockey to presenta series of
situationsthatlead towardan idealizedlimit of no friction.Recognizingthis view
as a deeply held misconception,the teachercould see it as necessaryto discuss and
confront,ratherthanas a passing notion thatcan be dismissedlightly.
Susan andNancy clearlyexpressedthe idea thatgravityis strongerfartherfrom
the ground,and if this is a misconception,it shouldnow be possible to confrontit.
For example, the teachercould ask why we do not feel heavieron the fourthfloor
of a buildingthanwe do on the first, ask whetherairplanesget heavieras they gain
altitude,or suggest that someone standingon the grounddoes exert a substantial
force on it. The earlier analysis, however, raised the possibility that gravity is
strongerfartherfrom the ground may be betterunderstoodas an idea the students
generatedfrom a misconceptionthatgravitydrainsimpetus.If thatis the case, then
it may not be importantor effective to confrontthe idea as a misconceptionitself.
ORP-PRIMS 119
MISCONCEPTIONS
Sean's misconception,thatgravityholds objectsonto the surface,may be more
difficultto address,andat thispointit probablyhas notbeen sufficientlyarticulated,
but eventuallythe teachercould ask whethergravity'sactiondependson the nature
of the surface, or what we should expect to happenif the surface were suddenly
removed. It may be appropriateto preparea lesson (Minstrell, 1982) specifically
to elicit and confrontthe misconceptionthatobstaclesdo not exert forces because
it appearedto have been involved in several of the students'reasoning.
P-Prims
From diSessa's (1993) perspective,the discussion pointed to the involvement
of a numberof p-prims in students'reasoning,including dying away, actuating
agency, maintainingagency, Ohm'sp-prim,interference,resistance,andconstraint
primitives.A primarytaskfor instructionwouldbe to exploittheseresourcestoward
students'constructionof a physicist's understanding.
With respect to the students'sense that the ball's motion is caused by a force,
the teacher may identify actuating agency and maintainingagency as resources
from which studentscould constructa physicist's understanding.Thus, a teacher
may never challenge the view that a force is necessary to maintain motion,
promoting instead its adaptationtoward a view that momentumis necessary to
maintainmotion (diSessa, 1980). In this discussion,a teacher'squestion (line 58)
created a situation that differentiatedthe activation of actuating agency and
maintainingagency, as Susan and others began to describethe force as "initial."
This could be seen as a step towardthe expertdistinctionbetweenappliedimpulse
and storedmomentum.
The p-primsaccountthusallows a differentorientationtowardstudentlearning:
The teacher may schematize instruction as promoting appropriateaspects of
students'knowledgeandreasoning.Ratherthanworkingto dismantlethe conceptions that gravity slows horizontalmotion, or that no frictionrequiresno gravity,
this perspectivesuggests using these acts of reasoningas steps towarda physicist's
understanding.Steve's argument,late in the discussion, providedone promising
option. He affirmedthat gravityslows horizontalmotion and that gravity causes
friction, but he added a specific causal mechanism:Gravity slows the ball by
pressing it against the ground, which results in friction. To give one plausible
account from the p-prims perspective,this argumentin effect uses the original
activationof interference,with gravityas the interference,to activatemaintaining
agency, with gravity as the agent that causes friction, and friction becomes the
interference.This would representprogresstowarda physicist's understanding.
Similarly,to perceivethe thoughtthatgravityis strongerfartherfromthe ground
as a passingact of reasoningwouldrelievetheteacherof theconcernfor eliminating
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HAMMER
it as a faulty element of the students'knowledge.Here, the teachermay focus on
Susan's and Nancy's contributionsas reflecting importantaspects of scientific
inquiry (Hammer, 1995b): They were reasoningfrom everyday experience, and
they were tryingto accountfor apparentdifferencesacross differentsituationsof
the effects of gravityon motion.
Finally,to understanda student'sview as specific to the situationmay affect the
teacher's assessmentof its consistency with respect to an expert account.Sean's
idea thatgravity"holds"the ball onto the groundis an example:Seen as a general
conceptualizationof gravity,this view is problematic;seen as an idea generatedin
the given situation,it is consistent with a physicist's understanding.Ratherthan
challenge it as a misconception,the teachercould choose to supportand build on
it as a creativeand productiveact of conceiving.
RESEARCHPERSPECTIVESAND INSTRUCTIONAL
PRACTICE
Misconceptionsand P-Prims
The notion that students come to science courses with misconceptions is now
routinein science educationdiscourse.Commonusage,if notall explicitconjecture,
attributesto misconceptionsthepropertyof existencewithinstudents'minds.Thus,
we speakof studentsas having,revealing,andhangingon to theirmisconceptions.
Misconceptions(or preconceptionsor alternativeconceptions)connotescognitive
structures,as opposed to events or patternsof behavior,thatare inconsistentwith
scientists' cognitive structures.They interfere with, rather than contributeto,
students'developmentof expertise.
DiSessa and his colleagues (diSessa, 1988, 1993; Smithet al., 1993/1994) have
challenged the misconceptionsperspectiveon theoreticalgrounds and offered a
differentaccountof cognitive structurein termsof phenomenologicalprimitives.
These p-primsare also structures,but they are both smallerand more generalthan
misconceptions,conceived of as involved in and contributingto both naive and
expert understanding.P-prims do not interfere with students' development of
expertise;they are essentialto it.
It is importantto acknowledgethatboth perspectivesare less thanprescriptive
with respectto instructionaltechnique.Of the two, the misconceptionsperspective
is more specific: It is difficult to see how instructioncould succeed without
confrontingin some way the students'misconceptions,and most authorstaking
this perspectivedescribe some form of confrontationas necessary (Smith et al.,
1993/1994). However,the misconceptionsperspectivedoes not rule out the possibility of useful resourcesin students'knowledge. Clement,Brown, and Zeitsman
(1989, see also Brown & Clement, 1989; Clement, 1991) noted that not all
MISCONCEPTIONSOR P-PRIMS
121
preconceptionsare misconceptionsand describedthe use of bridginganalogies to
help studentsgain access to theirappropriateconceptions.
The p-primsperspectivedoes not rule out confrontation.Fromthis perspective,
students need to build from their productiveresources,but if they have become
complacent,confrontationmay be an effective device to prompttheminto a process
of inquiry and construction.One may also think of confronting a robust but
inappropriatepatternof p-primactivation."
Proponentsof the two perspectives,in fact, drawmany similarimplicationsfor
instruction.From both perspectives, students and teachers should explore and
address students' existing ideas. Proponentsof both perspectivesargue that it is
importantto addresssimilarideas across a wide rangeof situations,althoughfor
differentreasons:From a misconceptionsperspective,this is because the misconceptionsareso deeply entrenchedthatthey needto be confrontedwith multipleand
variedevidence andarguments,whereasfromthe p-primsperspective,it is because
of the sensitivityto the situationof the p-prims'activation.
Thus, in many respects,differencesbetweenthe two perspectiveshave been of
greatertheoreticalthaninstructionalinterestin the science educationcommunity.
In at least one respect, however, the differenceis instructionallysignificant:The
misconceptionsperspectiveimplies the necessarytask of eliminatingunsuitable
cognitive structures.It may be useful to identify and build from students'useful
conceptions,but to constructfromuseful conceptionswithouteliminatingmisconceptions would leave in place knowledge inherently inconsistent with expert
understanding.
Multiple
PerspectivesandInstructional
Implications
The purposeof this articlehas been to help differentiatebetween two theoretical
perspectiveswith respectto how each may influence a teacher'sperceptionsand
intentions.The purposehas not, however,been to deriveinstructionalimplications
directly in terms of methods.Although I have noted various actual and possible
teacherinterventions,I do not intendto be makingany claims aboutinstructional
technique.In particular,I am not promotingmy own methodsas ideal or even as
appropriate.
There are three reasons for this emphasison perceptionsand intentionsrather
than on methods. First, as I noted earlier, neither perspective is specifically
11Thismay be a way to understandmisconceptionsfromwithinthe p-primperspective,as robustbut
inappropriatepatternsof p-prim activation. This would constitute a model with multiple levels of
cognitive structure(Brown, 1993), and it would representa shift from misconceptionsas commonly
understood.Withinsuch a unified model, with multiplelevels of cognitive structureand phenomenology, there would be alternativesfor how to conceptualizeany given studentidea.
122
HAMMER
prescriptivewith respectto method,andeithercould be invokedto supportsimilar
approaches.
Second, neitherperspectiveis sufficientlyreliable,norenjoys sufficientstability
and consensus in the community,to warrantcommitmentin educationalpractice.
I should note that I am not embracinghere a blanket"postmodern"position that
we should never treatany scientific perspectiveas if it describesreality.Thereare
a numberof constructsin the field of physics, for example, that have remained
stablefor decadesandarein essence unanimouslyaccepted.Electricians,scientists,
and lay people quite commonly applymetals conductelectricityas scientific fact;
physicists and solid-stateengineers treatCoulomb's law as an establishedtruth,
and in almost all situations,it has served them well to do so. In contrast,there is
not sufficient basis of experience, theoreticalcoherence, or consensus to justify
teachers' faithful adherenceto either a misconceptionsor a p-prims account of
studentknowledge.
Third,therearemany,manyotherperspectivesandconsiderationsthatcontribute to instructionaldecisions (Ball, 1993;Clark& Peterson,1986). Indeed,teachers
wouldfind it absurdto supposethateitherorbothof themisconceptionsandp-prims
perspectivescould be sufficient to determineappropriateintervention.Research,
moreover, provides strong theoreticaland empirical reasons to believe that an
adequatetheory of knowledge, reasoning,and learningmust include a range of
cognitive andaffectivestructuresandprocessesin a complexecology (Baron,1985;
Niedderer& Schecker, 1992; Schoenfeld, 1983). Elsewhere,I have discussed the
influenceon instructionalperceptionsandintentionsof anepistemologicalperspective (Hammer,1995a),thatis, a view of studentsas havingbeliefs aboutknowledge
and learning,and of an inquiry-orientedperspective(Hammer,1995b). Examples
of such considerationsappearin the precedinganalysis:One may understandthe
students' insistence that no friction requiresno gravity as reflecting a difference
betweentheirpracticeof inquiryandthe physicists' practice,in thatthe latteroften
involves supposing idealized, unattainableconditions. One may perceive, in the
students'argumentsthatgravityis strongerfartherfromthe ground,thatthey were
reasoningfrom everydayexperience.
There was much more. My objectives in assigning studentsto find arguments
against Galileo, and in planningto debatethe matterin class, were not limited to
students' progresstowardphysicists' understandingof forces and motion. I also
hoped to promote the notion that it is importantto consider alternativeviews
thoroughlybeforeacceptingone as correct,andI meantto raisestudents'awareness
and skepticismof theirhiddenassumptions.Moreover,I wantedthem to begin to
connect reasoningin physics with reasoningin everydaylife, such as in voting for
president,an example I chose because it was a currentevent, or in being a lawyer,
which I chose specifically for Joanne,who plannedto become a lawyer and who,
at this point in the year, remainedemphaticin her view that I shouldbe providing
informationratherthanasking studentsto reasonanddiscuss.
MISCONCEPTIONS
ORP-PRIMS 123
During the discussion, I was aware not only of the content of the students'
statementsbut also of theirengagementand interestboth for the class as a whole
and for individual students.For the class as a whole, this discussion markeda
qualitativechangein the generallevel of theirparticipationfromthe previousdays,
with well over half of the studentsactively contributingand most of the rest quite
attentive.This was progressI wanted very much to maintainand extend. Penny,
who had been all but silent since the beginningof the year, was one of the main
instigatorsof the debate.She and othersaroundthe room were frequentlytalking
out of turn,breakinginto heatedside discussions,always (as far as I could tell) on
topic;these side discussionsincludedsome of the studentswho nevertook the main
floor. Joanne, meanwhile, sitting in the front row, was checking her watch, and
Mona and Tim remainedpassive and uninvolved,perhapsuninterestedor perhaps
intimidated.
It would thus be misleadingto presentinstructionalimplicationsof misconceptions orp-primsperspectivesdirectlyin termsof intervention.Withor withoutthese
perspectives,teachers'perceptionsof studentsremainincompleteandambiguous,
and the practiceof instructionremainsuncertain.Such a stateof affairsis uncomfortablefor researchers,as the practiceof researchgenerallyinvolves a searchfor
definitive, principled understanding,but it is a fact of life for teachers. I am
suggesting a modestepistemologicalstancewith respectto the instructionalimplications of educationresearch:Both researchersandteachersshould,at least for the
present, understandresearchas supportingteachers' developmentof conceptual
tools, to broadenand supportteachers'awareness,judgment,and inquiry,rather
than as providingreliable findings and principlesor as prescribingmethods and
curricula(Richardson,1994; Schon, 1987).12
When I reflect on the respectivecontributionsof misconceptionsand p-prims
perspectivesto my perceptionsand intentionsas the teacherof this class, I discern
several roles. Both contributedto my sense of the students' conceptual understanding,in particularto my distrustof theirinitialacceptanceof Galileo's argument
andto my anticipationof variousideas.I consideredthemisconceptionsperspective
the more valuableresourcewith respectto my agendaof helping studentsbecome
awareof theirreasoning.Thus,I told the studentsthatpartof the purposeof having
this discussionwas to drawout conflictingknowledgeI suspectedthey had lurking
in their minds. (In subsequentdiscussions, I describedforce causes motion as a
"mentalmagnet,"an idea thatlives in our heads and to which we are drawn.)
The p-primsperspective,on the otherhand,motivatedmy decision to drawout
andbuildon the students'distinctionbetweenan initialandan ongoingforce,rather
than to draw out and then confrontthe idea thatmotion is caused by force. Over
12Minstrell's (1992) account of "facets,"influencedby both misconceptionsand p-primsperspectives, is an example of a construct of research designed more as a tool for instructorsthan as a
theoreticallyand empiricallydefensiblemodel.
124
HAMMER
the next severaldays, the class consideredvariousdefinitionsand names for these
two kinds of forces, eventually settling on innerforce, defined as a force stored
within a moving object, and outerforce, defined as caused by somethingexternal
to the object. These terms became part of the class vocabulary;we refined the
definitions,and eventuallyI offeredthatthese ideas of innerforce and outerforce
were similarto what physicists' call momentumand, simply, force.
More generally,the differencesbetween p-primsand misconceptionsperspectives on studentknowledge affected not only my sense of how to help students
progresstowardphysicists' knowledge but also of how to coordinatethis agenda
with others (Ball, 1993; Hammer,1995a, 1995b), including promotingstudents'
participationin inquiry, appropriatebeliefs about knowledge and learning, and
confidence in themselves as scientists.Often,these otheragendasprovidereasons
for caution with respect to confrontationas an instructionalstrategy.To contest
students' reasoning,for example, may dissuadethem from participatingor from
believing thattheirideas and experienceare relevant.
I am often aware of this tension between, on the one hand, as Perry (1970)
described,my intentionsto supportstudents'"sustainedgroping,explorationand
synthesis ... initiativeand scope in theirown thinking"(p. 211), and, on the other
hand, a sense thatI need to repair"errors"and "inexactnesses"(p. 211)1I perceive
in theirreasoning.I findthatit amplifiesthistensionto thinkof students'knowledge
in termsof misconceptions.Discussions with studentsinvariablypresenta myriad
of errorsand inexactnesses,andthe tasksof addressingthe underlyingmisconceptions, as well as the risks of inadvertentlycontributingto them, conflict in my
thinkingwith the importanceof establishingand promotingthe students'participation. In contrast,I find it alleviatesthis tension somewhatto think of students'
knowledge in termsof p-prims.The taskof supportingstudents'constructionfrom
useful cognitive resourcesgenerallyaligns in my thinkingwith the taskof promoting their participation.
This has not, however, been a studyof my thinking,and these reflectionsat the
end of the articleshouldbe distinguishedfromthe analysesearlier.With respectto
misconceptionsandp-primsperspectives,the analyseswentfarbeyondmy perceptions and intentionsas the teacherduringthe class, and in otherrespects,they fell
far short. As well, I do not claim to have faithfulaccess to my thoughtprocesses
during the class; I consider my reflectionsonly a plausibleaccount. Moreover,I
was not a typicalteacher:I was teachingone class, videotaping,keepinga journal,
and contemplatingthe influenceof researchperspectiveson my work.
This was a study of the two perspectivesand what they might in principlesay
about studentsin an authenticinstructionalcontext. Such hypotheticalanalysis is
useful, first, in promoting clarity and precision in researchers'and teachers'
understandingof the perspectivesand, second, as a step in understandingtheir
instructionalsignificance. Furtherstudy, however, must involve other teachers.
Informalconversationssuggestthatthe influenceof themisconceptionsperspective
MISCONCEPTIONSOR P-PRIMS
125
on teachers' thinkingvaries considerably.For some, it implies the importanceof
anticipatingand confrontingstudents' mistakenconcepts; for others, it suggests
whatseems to be the opposite,the importanceof validatingstudentideas as rational
and legitimate.
We need to learn more about how teachersare influenced by these and other
perspectives. The Cognitively Guided Instructionproject (Knapp & Peterson,
1995) is one exampleof suchresearch:Theypresentedteacherswith researchabout
elementarymathematicslearning(Carpenter,1985) and studiedthe influences on
the teachers'practices.McDonald(1986) describedanother,in the conversations
among a group of teacherswho, to theirsurprise,came to find useful new insights
in educationaltheory.Furtherwork in similardirectionswill informthe development of research perspectives, how and whether they should be presented to
teachers, and, more generally, how we should conceive of the relation between
researchand instruction.
ACKNOWLEDGMENTS
Supportfor this workwas providedby theNationalAcademyof Educationthrough
a Spencer FoundationPostdoctoralFellowship. I thankAndy Anzalone and Joe
Pignatiello for their help and hospitality; Sherry Cook, Andy diSessa, David
Hestenes, Janet Kolodner, Jim Minstrell, Ron Narode, BarbaraNelson, Jeremy
Roschelle, Michael Roth, Mary Budd Rowe, DeborahSchifter, and Bernie Zubrowski for theirsuggestions;andJayFogleman,Colleen Kozumplik,Hal Lefcourt,
AndrewNjaa,andDale Sweet fortheirreactionsto anearlydraftandfordiscussions
of relatedissues in the LabNetCommunityForum.
REFERENCES
Arons, A. B. (1990). A guide to introductoryphysics teaching.New York:Wiley.
Ball, D. (1993). With an eye on the mathematicalhorizon:Dilemmas of teachingelementaryschool
mathematics.ElementarySchool Journal,93, 373-397.
Baron, J. (1985). Rationalityand intelligence.New York:CambridgeUniversityPress.
Brown, D. E. (1993). Re-focusingcore intuitions:A concretizingrole for analogyin conceptualchange.
Journal of Research in Science Teaching,30, 1273-1290.
Brown, D. E., & Clement, J. (1989). Overcomingmisconceptionsvia analogicalreasoning:Abstract
transferversusexplanatorymodel construction.InstructionalScience, 18, 237-261.
Camp,C., Clement,J., Brown, D., Gonzalez,K., Kudukey,J., Minstrell,J., Schultz,K., Steinberg,M.,
Veneman,V., & Zietsman,A. (1994). Preconceptionsin mechanics:Lessonsdealing withstudents'
conceptualdifficulties.Dubuque,IA: Kendall/Hunt.
Carey, S. (1986). Cognitive science and science education.AmericanPsychologist,41, 1123-1130.
Carpenter,T. P. (1985). Learningto add and subtract:An exercise in problemsolving. In E. A. Silver
(Ed.), Teachingand learning mathematicalproblem solving: Multipleresearchperspectives (pp.
17-40). Hillsdale, NJ: LawrenceErlbaumAssociates, Inc.
126
HAMMER
Champagne,A. B., Klopfer,L. E., & Anderson,J. H. (1980). Factorsinfluencingthe learningof classical
mechanics.AmericanJournalof Physics, 48, 1074-1079.
Clark,C. M., & Peterson,P. L. (1986). Teachers'thoughtprocesses.In M. C. Wittrock(Ed.),Handbook
of research on teaching (pp. 255-296). New York:Macmillan.
Clement, J. (1983). A conceptualmodel discussedby Galileo and used intuitivelyby physics students.
In D. Gentner& A. Stevens(Eds.),Mentalmodels(pp. 345-362). Hillsdale,NJ:LawrenceErlbaum
Associates, Inc.
Clement, J. (1991). Nonformalreasoning in experts and in science students:The use of analogies,
extremecases, and physicalintuition.In J. Voss, D. Perkins,& J. Siegel (Eds.), Informalreasoning
and education(pp. 345-362). Hillsdale,NJ: LawrenceErlbaumAssociates, Inc.
Clement, J., Brown, D., & Zeitsman,A. (1989). Not all preconceptionsare misconceptions:Finding
"anchoringconceptions"for groundinginstructionon students'intuitions.InternationalJournalof
Science Education,11, 554-565.
diSessa, A. (1980). Momentumflow as an alternativeperspectivein elementarymechanics.American
Journal of Physics, 48, 365-369.
diSessa, A. (1982). UnlearningAristotelianphysics: A study of knowledge-basedlearning.Cognitive
Science, 6, 37-75.
diSessa, A. (1988). Knowledge in pieces. In G. Forman& P. Putall (Eds.), Constructivismin the
computerage (pp. 49-70). Hillsdale,NJ: LawrenceErlbaumAssociates, Inc.
diSessa, A. (1993). Towardan epistemologyof physics. Cognitionand Instruction,10, 105-225.
Haber-Schaim,U., Cross,J. B., Dodge, J. H., & Walter,J. A. (1976). PSSCphysics(4th ed.). Lexington,
MA: Heath.
Halloun,I. A., & Hestenes,D. (1985). The initialknowledgestateof college physics students.American
Journal of Physics, 53, 1043-1056.
Hammer,D. (1995a). Epistemologicalconsiderationsin teachingintroductoryphysics. Science Education, 79, 393-413.
Hammer, D. (1995b). Studentinquiry in a physics class discussion. Cognitionand Instruction,13,
401-430.
Hestenes, D., Wells, M., & Swackhamer,G. (1992). Force Concept Inventory.The Physics Teacher,
30, 141-158.
Huffman, D., & Heller, P. (1995). What does the Force Concept Inventoryactually measure?The
Physics Teacher,33, 138-143.
of "CGI"afterfouryears:Meaningsand
Knapp,N., & Peterson,P. L. (1995). Teachers'interpretations
practices.Journalfor Researchin MathematicsEducation,26, 40-65.
Maloney, D. P., & Siegler, R. S. (1993). Conceptualcompetitionin physics learning.International
Journal of Science Education,15, 283-296.
McCloskey, M. (1983). Naive theoriesof motion. In D. Gentner& A. Stevens (Eds.), Mentalmodels
(pp. 299-324). Hillsdale, NJ: LawrenceErlbaumAssociates, Inc.
McDermott, L. C. (1984). Researchon conceptualunderstandingin mechanics. Physics Today, 37,
24-32.
McDonald,J. P. (1986). Raisingthe teacher'svoice andthe ironicrole of theory.HarvardEducational
Review, 56, 355-378.
Minstrell,J. (1982). Explainingthe "atrest"conditionof an object. ThePhysics Teacher,20, 10-20.
Minstrell, J. (1989). Teaching science for understanding.In L. Resnick & L. Klopfer (Eds.), Toward
the thinkingcurriculum:Currentcognitive research (pp. 129-149). Alexandria,VA: Association
for Supervisionand CurriculumDevelopment.
Minstrell,J. (1992). Facets of students'knowledgeandrelevantinstruction.In R. Duit, F. Goldberg,&
H. Niedderer(Eds.), Research in physics learning: Theoreticalissues and empirical studies (pp.
110-128). Kiel, Germany:Institutfuirdie Pidagogik der Naturwissenschaftenan der Universitit
Kiel.
MISCONCEPTIONSOR P-PRIMS
127
Niedderer,H., & Schecker,H. (1992). Towardsan explicit descriptionof cognitive systems for research
in physics learning.In R. Duit, F. Goldberg,& H. Niedderer(Eds.), Researchin physics learning:
Theoreticalissues and empiricalstudies(pp. 74-98). Kiel, Germany:Institutfuirdie Pidagogik der
Naturwissenschaftenan der Universitit Kiel.
Perry,W. B. (1970). Formsof intellectualand ethicaldevelopmentin the college years:A scheme.New
York:Holt, Rinehart& Winston.
Richardson,V. (1994). Conductingresearchon practice.EducationalResearcher,23(5), 5-10.
Sadler,P. M., Schneps,M. H., & Woll, S. (1989). A private universe.SantaMonica,CA: PyramidFilm
and Video.
Schoenfeld, A. (1983). Beyond the purelycognitive:Belief systems, social cognitions andmetacognitions as drivingforces in intellectualperformance.CognitiveScience, 7, 329-363.
Schon, D. A. (1987). Educating the reflectivepractitioner: Towarda new designfor teaching and
learning in theprofessions. San Francisco:Jossey-Bass.
Schuster,D. (1993, August). Semanticsand students'conceptionsin science. Paperpresentedat the
summermeeting of the AmericanAssociationof Physics Teachers,Boise, ID.
Smith, J., diSessa, A., & Roschelle, J. (1993/1994). Misconceptionsreconceived: A constructivist
analysis of knowledge in transition.TheJournalof the LearningSciences, 3, 115-163.
Strike, K. A., & Posner,G. J. (1985). A conceptualchange view of learningand understanding.In L.
H. T. West & A. L. Pines (Eds.), Cognitivestructureand conceptualchange (pp. 211-231). New
York:Academic.
Thornton, R. (1987). Tools for scientific thinking: Microcomputer-basedlaboratoriesfor physics
teaching. Physics Education,22, 230-238.
Viennot, L. (1979). Spontaneousreasoning in elementarydynamics. European Journal of Science
Education,1, 205.
AmericanJournalof
Viennot, L. (1985). Analyzing students'reasoning:Tendenciesin interpretation.
Physics, 53, 432-436.
Whitaker,R. J. (1983). Aristotle is not dead: Studentunderstandingof trajectorymotion. American
Journal of Physics, 51, 352.