The difference in the descriptions of motion phenomena made by pupils in the first grades of secondary school and physicists is quite evident. Conceptual metaphors hidden in language suggest that there is continuity between the conceptual structure involved in the description and the interpretation of motion of experts and laypersons. In this paper the presence of such a continuity is shown through a metaphor analysis of linguistic expressions from both groups

Ascari, Alessandro

Ceroni, Gabriele

Corni, Federico

Fuchs, Hans U.

The difference in the descriptions of motion phenomena made by pupils in the first grades of secondary school and physicists is quite evident. Conceptual metaphors hidden in language suggest that there is continuity between the

conceptual structure involved in the description and the interpretation of motion of experts and laypersons. In this paper the presence of such a continuity is shown through a metaphor analysis of linguistic expressions from both groups

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2015-15085-2Colloquia: GIREP/MPTL 2014IL NUOVO CIMENTO 38 C (2015) 85From naive to scientific understanding of motion and its causesAlessandro Ascari(1)(∗), Federico Corni(1)(∗∗), Gabriele Ceroni(2)(∗∗∗)and Hans U. Fuchs(3)( ∗∗∗)(1) University of Modena and Reggio Emilia - Reggio Emilia, Italy(2) University of Bologna - Bologna, Italy(3) Zurich University of Applied Sciences - Winterthur, Switzerlandreceived 26 October 2015Summary. — The difference in the descriptions of motion phenomena made bypupils in the first grades of secondary school and physicists is quite evident. Con-ceptual metaphors hidden in language suggest that there is continuity between theconceptual structure involved in the description and the interpretation of motion ofexperts and laypersons. In this paper the presence of such a continuity is shownthrough a metaphor analysis of linguistic expressions from both groups.1. – IntroductionWe know from literature (DiSessa, 1993; McCloskey, Caramazza, and Green, 1980)that students face difficulties in studying motion and its causes. We argue that if wewant to address these problems, we have to investigate the conceptualization of motion.We are going to investigate the conceptual structure involved in the description ofmotion of laypersons, i.e. students, and of experts, i.e. teachers, scientists, physicists.We argue that some kind of continuity should be present between these two kinds ofconceptualization and that physics education should be built upon it.In the first part of this article we are going to illustrate how it is possible to understandhow the concept of motion is constructed in the human mind. A theory that relatesmind and language is presented starting from the works of Lakoff, Johnson, Turner andFauconnier.In the second part we will show the analyses carried out of two different sources oflanguage, the first representing the scientific conceptualization, the second the lay one.In the last part the evidence and the results of the analyses are presented anddiscussed.(∗) E-mail: alessandro.ascari@unimore.it(∗∗) E-mail: federico.corni@unimore.it(∗∗∗) E-mail: gabriele.ceroni3@unibo.it( ∗∗∗) E-mail: hans.fuchs@zhaw.chCreative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 ALESSANDRO ASCARI et al.2. – A theory of mindIn cognitive linguistics, conceptual metaphor is defined as understanding one concep-tual domain (target domain) in terms of another conceptual domain (source domain).Lakoff, Johnson and Turner underline the deep and strong connection between languageand mind. According to these authors, the nature of the conceptual structure that weuse to think, speak and act is figurative. As a consequence, conceptual metaphors playan important role in structuring knowledge. They are systematic in that there is a fixedcorrespondence between the structure of the domain to be understood (e.g., death) andthe structure of the domain in terms of which we are understanding it (e.g., departure).We usually understand them in terms of common experiences. They are largely uncon-scious, though attention may be drawn to them. Their operation in cognition is almostautomatic. And they are widely conventionalized in language, that is, there are a greatnumber of words and idiomatic expressions in our language whose meanings depend uponthose conceptual metaphors (Lakoff and Turner, 1989). Metaphor is no longer seen asa mere linguistic and aesthetic feature: the cognitive role of metaphor emerges in theprocess of structuring and acquiring new knowledge. In synthesis, a concept is constitutedby the metaphor (Lakoff and Johnson, 1980).Moreover, according to Fauconnier and Turner, in the human mind there are entirenetworks of projections between conceptual spaces leading to what have been known asconceptual integration networks (Fauconnier and Turner, 1998, 2002; Fauconnier, 1994,1997).As a consequence, we can understand the way we think about our conceptualization ofmotion, looking at the way we speak, in particular at the conceptual metaphors impliedin the language we use to talk and describe motion.We have to make a distinction between metaphor and metaphoric linguistic expres-sion: the latter is what we hear or read when somebody uses a metaphor, the former is afigure of the mind, we might say the actual concept. We will show an example in orderto evidence the difference.Heat flows through the walls of the buildingis the metaphorical expression of the metaphor:Heat Is A Fluid SubstanceWe will use small caps in order to distinguish between the conceptual metaphors and themetaphorical expressions.3. – Language analysesIn order to compare the two forms of conceptualization of motion we selected twosources of sentences about motion: the first volume of “The Feynman lectures on Physics”(Feynman, 1965) as a source of scientific language, and recordings of college students en-rolled in physics courses collected in the paper “Common sense concepts about mo-tion” by Halloun and Hestenes as a source of lay language (Halloun and Hestenes,1985).We looked for the sentences containing the word “force” and we tried to see the un-derlying conceptual metaphor. We constructed the categories of conceptual metaphors ina recursive way in order to have the most general and encompassing ones. We developedthe conceptual metaphor categorization starting from the Force Dynamic Gestalt theory(Fuchs, 2007), image schemas (Johnson, 1990) and event structures (Lakoff and Johnson,1999).FROM NAIVE TO SCIENTIFIC UNDERSTANDING OF MOTION AND ITS CAUSES 3Here we present the list of metaphors involved in the description of the word “force”.• Force Is A Substance-Like Quantity◦ Force Is A Product◦ Force Is A Quantity◦ Force Is A Possession• Force Is An Agent◦ Force Is A Compulsion◦ Force Is A Resistance• Force Is A Medium• Force Is A Path◦ Force Is A Line◦ Force Is A Connection• Force Is A Scale• Force Is BalanceThe complete list of categorized sentences is presented in the following tables I–VI. Thefirst observation is that sentences from both expert and lay language are metaphoricalexpressions contained in all these categories.Table I. – Force Is A Substance-Like Quantity expressions.Conceptualmetaphor sub-categoryFeynman expressions Students expressionsForce Is AProductThis potentiality for producing aforce is called an electric field.A source of the force.The speed creates a force. Theforce behind it. . .coming fromthe throw.Force Is AQuantityHow much force would there beMore or less force is required.There is very little force at anyappreciable distance.As it goes down, the force ofgravity increases. . . and that’swhy the speed increases until[gravity] equals this amount offorce. It provides the ball withmore and more force as it goesdown.Force Is APossessionA spinning top has the sameweight as a still one. The weightof the atom. These forces arewithin the nuclei of atoms.If the mass of block X is grea-ter than the force [of pull] of Y ,block X stays in place. . .it couldnot be moved. [The moving body]has still got some force inside.4 ALESSANDRO ASCARI et al.Table II. – Force Is An Agent expressions.Conceptualmetaphor sub-categoryFeynman expressions Students expressions(unsorted) The first charge will feel a certainreaction force.There is not a force [acting] on theball. Gravity means the same forcepulls on different objects.Force Is ACompulsionBecause of the action of a force,the velocity changes. The forcewhich controls, let us say, Jupiterin going around the sun.A force only starts the motion. Aforce is just changing the directionof motion.Force Is AResistanceIt is a question of electrical forcesagainst which we are working. Notangential force is needed to keepa planet in its orbit.A force has nothing to do with thespeed, it only has to keep the ballmoving.Table III. – Force Is A Medium expressions.Feynman expressions Students expressionsWe shall have to hold the pis-ton down by a certain force.The gas exerts a jittery force.That maximum speed isalways equal to the forceyou apply.Table IV. – Force Is A Path expressions.Conceptualmetaphor sub-categoryFeynman expressions Students expressionsForce Is ALineThe force in the vertical directiondue to gravity. The force isdirected along the line joining theplanet to the sun.The ball goes out in the directionof the resultant [of the forces].Force Is AConnectionThe true nature of the forcesbetween the atoms.noneTable V. – Force Is A Scale expressions.Feynman expressions Students expressionsThe force weakens as we go higher.The more massive a thing is, the stronger theforce required to produce a given acceleration.noneFROM NAIVE TO SCIENTIFIC UNDERSTANDING OF MOTION AND ITS CAUSES 5Table VI. – Force Is Balance expressions.Feynman expressions Students expressionsIf the force between them were not balanced.Talk only about excess forces.All the internal forces will balance out.noneBesides that, we also found some differences in the metaphorical expressions from thetwo sources.The Force Is A Product conceptual metaphor (table I) tells us that force couldbe “produced”. The possible “producers” in Feynman’s expressions are the basic inter-actions between objects, i.e. electrical and gravitational, while in students’ expressionsthe “producers” are speed and aspects of motion.In Force Is A Quantity metaphorical expressions (table I), Feynman only speaksabout the intensity of force, while in students’ language we find expressions that arerelated to the concept of momentum or energy of a moving object.Finally, the metaphorical expressions of Force Is A Possession (table I) in Feyn-man are only about weight, while in laypersons we have expressions involving movingobjects, devices that produce movement (i.e. a cannon), and more abstract concepts aspower, inertia and velocity.Some metaphorical expressions found in Feynman are not present in students’ ex-pressions, but we think this could be due to the set of data chosen for this purpose. Weare almost sure that similar sentences could be found in students’ expressions if only wecould have a larger collection.The metaphorical sentences in lay language often involved the terms “speed” or“velocity”. In order to deepen our investigations we repeated the same analysis forthe sentences containing these two words.The conceptual metaphors we found are listed below.• Speed Is A Substance-like quantity◦ Speed Is A Possession◦ Speed Is A Quantity• Speed Is A Location◦ Speed Is A Level◦ Speed Is A Scale• Speed Is An Agent◦ Speed Is A Force◦ Speed Is A MakerTable VII collects the categorization of the metaphorical sentences found in both setsof data.All the expressions belonging to the two sources fitted all these categories with onlyone exception. Metaphorical expressions belonging to Speed Is An Agent can only befound in students’ language.6 ALESSANDRO ASCARI et al.Table VII. – Speed and Velocity metaphors and metaphorical expressions.ConceptualmetaphorcategoryConceptualmetaphor sub-categoryFeynman expressions Students expressionsSpeed Is ASubstance-like quan-titySpeed Is APossessionMotion of a body. If she keptgoing with the same speed.The velocity of the fallingball.Its speed remains con-stant. Their speed getsgreater and greater. Bothshould have the samespeed.Speed Is AQuantity[. . .] if we increase the speedof the atoms.Its velocity keepsincreasing. The speed issmaller. A new speedbigger than the one ithad before.Speed Is ALocationSpeed Is ALevelAt what speed is the radius in-creasing She is going at thatspeed. Some car can get fromrest to 60 miles an hour.The ball must go at con-stant speed. They canreach a speed limit.Speed Is AScaleIt speeds up. The car wasslowing down. High speeds.It speeds up for a shortwhile. It slows down.Speed IsAn AgentSpeed Is AForcenone The force due to theair overcomes the ini-tial velocity. The forceof velocity.Speed Is AMakernone The speed creates aforce.4. – Results and conclusionsThis metaphor analysis is a powerful and sensible tool that allows us to investigate theconceptual structure that both scientists and students use to understand and to explainphenomena.The first important result is that the metaphorical expressions coming from both layand expert language share the majority of the metaphors. This allows us to claim thatthere is continuity between the two kinds of language.We also revealed a metaphorical and conceptual mismatch involving velocity andspeed. In the analysis we discovered that Speed Is An Agent is a conceptual metaphoronly present in lay language (students). Therefore we could say that speed (and velocity)is perceived and conceptualized as an agent only by laypersons (students), while this isnot true for scientists and experts (Feynman, 1965).Another important result is that some aspects coming from the Force Dynamic Gestalttheory, such as quantity, quality, intensity (Fuchs, 2007) are present in the metaphoricalexpressions. Moreover they are not completely differentiated in lay language.The presence of continuity tells us that it is possible to teach starting from the knowl-edge pupils have already developed during their previous experience: we could use con-ceptual metaphor as a basis for developing a physics curriculum.FROM NAIVE TO SCIENTIFIC UNDERSTANDING OF MOTION AND ITS CAUSES 7Physics teachers should be aware of the conceptual metaphors and how they relateand overlap in order to create comprehension (i.e. conceptual integration networks). Inthis sense we could say that an education based on conceptual metaphors could helpstudents to be aware of them in order to understand and relate the aspects involved inthe interpretation of motion and its causes.In order to do so, further analysis should be done to reveal the logical connections andthe dependencies between concepts involved in the description of motion (momentum,energy). A refined analysis should be done taking different language sources, both oraland written.REFERENCES[1] DiSessa A. A., Cogn. Instruc., 10 (1993) 105.[2] Fauconnier G., Mental Spaces: Aspects of Meaning Construction in Natural Language(Cambridge University Press, Cambridge, UK) 1994.[3] Fauconnier G., Mappings in Thought and Language (Cambridge University Press,Cambridge, UK) 1997.[4] Fauconnier G. and Turner M., Cognitive Sci., 22 (1998) 133 DOI:10.1016/S0364-0213(99)80038-X.[5] Fauconnier G. and Turner M., The way we think (Basic Books, New York) 2002.[6] Feynman R. P., The Feynman Lectures on Physics, Vol. I (Addison Wesley) 1965; Am.J. Phys., 33 (1965) 750, DOI:10.1119/1.1972241.[7] Fuchs H. U., From Image Schemas to Dynamical Models in Fluids, Electricity, Heat,and Motion. An Essay on Physics Education Research (Winterthur, Switzerland) 2007.Retrieved from https://home.zhaw.ch/fuh/LITERATURE/Literature.html.[8] Halloun I. A. and Hestenes D., Am. J. Phys., 53 (1985) 1056 Doi:10.1119/1.14031.[9] Johnson M., The Body in the Mind (University of Chicago Press) 1990.[10] Lakoff G. and Johnson M., Metaphors We Live By (University of Chicago Press) 1980.[11] Lakoff G. and Johnson M., Philosophy in the flesh: The embodied mind and its challengeto western thought (Basic Books) 1999.[12] Lakoff G. and Turner M., More Than Cool Reason: A Field Guide to Poetic Metaphor,(University of Chicago Press) 1989 Retrieved fromhttp://books.google.it/books?id=pz9TveJ5N5QC.[13] McCloskey M., Caramazza A. and Green B., Science (New York), 210 (1980) 1139DOI:10.1126/science.210.4474.1139.

English

From naive to scientific understanding of motion and its causes

ASCARI, ALESSANDRO

CORNI, Federico

Archivio istituzionale della ricerca - Università di Modena e Reggio Emilia

DOI 10.1393/ncc/i2015-15085-2Colloquia: GIREP/MPTL 2014IL NUOVO CIMENTO 38 C (2015) 85From naive to scientiﬁc understanding of motion and its causesAlessandro Ascari(1)(∗), Federico Corni(1)(∗∗), Gabriele Ceroni(2)(∗∗∗)and Hans U. Fuchs(3)( ∗∗∗)(1) University of Modena and Reggio Emilia - Reggio Emilia, Italy(2) University of Bologna - Bologna, Italy(3) Zurich University of Applied Sciences - Winterthur, Switzerlandreceived 26 October 2015Summary. — The diﬀerence in the descriptions of motion phenomena made bypupils in the ﬁrst grades of secondary school and physicists is quite evident. Con-ceptual metaphors hidden in language suggest that there is continuity between theconceptual structure involved in the description and the interpretation of motion ofexperts and laypersons. In this paper the presence of such a continuity is shownthrough a metaphor analysis of linguistic expressions from both groups.1. – IntroductionWe know from literature (DiSessa, 1993; McCloskey, Caramazza, and Green, 1980)that students face diﬃculties in studying motion and its causes. We argue that if wewant to address these problems, we have to investigate the conceptualization of motion.We are going to investigate the conceptual structure involved in the description ofmotion of laypersons, i.e. students, and of experts, i.e. teachers, scientists, physicists.We argue that some kind of continuity should be present between these two kinds ofconceptualization and that physics education should be built upon it.In the ﬁrst part of this article we are going to illustrate how it is possible to understandhow the concept of motion is constructed in the human mind. A theory that relatesmind and language is presented starting from the works of Lakoﬀ, Johnson, Turner andFauconnier.In the second part we will show the analyses carried out of two diﬀerent sources oflanguage, the ﬁrst representing the scientiﬁc conceptualization, the second the lay one.In the last part the evidence and the results of the analyses are presented anddiscussed.(∗) E-mail: alessandro.ascari@unimore.it(∗∗) E-mail: federico.corni@unimore.it(∗∗∗) E-mail: gabriele.ceroni3@unibo.it( ∗∗∗) E-mail: hans.fuchs@zhaw.chCreative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 ALESSANDRO ASCARI et al.2. – A theory of mindIn cognitive linguistics, conceptual metaphor is deﬁned as understanding one concep-tual domain (target domain) in terms of another conceptual domain (source domain).Lakoﬀ, Johnson and Turner underline the deep and strong connection between languageand mind. According to these authors, the nature of the conceptual structure that weuse to think, speak and act is ﬁgurative. As a consequence, conceptual metaphors playan important role in structuring knowledge. They are systematic in that there is a ﬁxedcorrespondence between the structure of the domain to be understood (e.g., death) andthe structure of the domain in terms of which we are understanding it (e.g., departure).We usually understand them in terms of common experiences. They are largely uncon-scious, though attention may be drawn to them. Their operation in cognition is almostautomatic. And they are widely conventionalized in language, that is, there are a greatnumber of words and idiomatic expressions in our language whose meanings depend uponthose conceptual metaphors (Lakoﬀ and Turner, 1989). Metaphor is no longer seen asa mere linguistic and aesthetic feature: the cognitive role of metaphor emerges in theprocess of structuring and acquiring new knowledge. In synthesis, a concept is constitutedby the metaphor (Lakoﬀ and Johnson, 1980).Moreover, according to Fauconnier and Turner, in the human mind there are entirenetworks of projections between conceptual spaces leading to what have been known asconceptual integration networks (Fauconnier and Turner, 1998, 2002; Fauconnier, 1994,1997).As a consequence, we can understand the way we think about our conceptualization ofmotion, looking at the way we speak, in particular at the conceptual metaphors impliedin the language we use to talk and describe motion.We have to make a distinction between metaphor and metaphoric linguistic expres-sion: the latter is what we hear or read when somebody uses a metaphor, the former is aﬁgure of the mind, we might say the actual concept. We will show an example in orderto evidence the diﬀerence.Heat ﬂows through the walls of the buildingis the metaphorical expression of the metaphor:Heat Is A Fluid SubstanceWe will use small caps in order to distinguish between the conceptual metaphors and themetaphorical expressions.3. – Language analysesIn order to compare the two forms of conceptualization of motion we selected twosources of sentences about motion: the ﬁrst volume of “The Feynman lectures on Physics”(Feynman, 1965) as a source of scientiﬁc language, and recordings of college students en-rolled in physics courses collected in the paper “Common sense concepts about mo-tion” by Halloun and Hestenes as a source of lay language (Halloun and Hestenes,1985).We looked for the sentences containing the word “force” and we tried to see the un-derlying conceptual metaphor. We constructed the categories of conceptual metaphors ina recursive way in order to have the most general and encompassing ones. We developedthe conceptual metaphor categorization starting from the Force Dynamic Gestalt theory(Fuchs, 2007), image schemas (Johnson, 1990) and event structures (Lakoﬀ and Johnson,1999).FROM NAIVE TO SCIENTIFIC UNDERSTANDING OF MOTION AND ITS CAUSES 3Here we present the list of metaphors involved in the description of the word “force”.• Force Is A Substance-Like Quantity◦ Force Is A Product◦ Force Is A Quantity◦ Force Is A Possession• Force Is An Agent◦ Force Is A Compulsion◦ Force Is A Resistance• Force Is A Medium• Force Is A Path◦ Force Is A Line◦ Force Is A Connection• Force Is A Scale• Force Is BalanceThe complete list of categorized sentences is presented in the following tables I–VI. Theﬁrst observation is that sentences from both expert and lay language are metaphoricalexpressions contained in all these categories.Table I. – Force Is A Substance-Like Quantity expressions.Conceptualmetaphor sub-categoryFeynman expressions Students expressionsForce Is AProductThis potentiality for producing aforce is called an electric ﬁeld.A source of the force.The speed creates a force. Theforce behind it. . .coming fromthe throw.Force Is AQuantityHow much force would there beMore or less force is required.There is very little force at anyappreciable distance.As it goes down, the force ofgravity increases. . . and that’swhy the speed increases until[gravity] equals this amount offorce. It provides the ball withmore and more force as it goesdown.Force Is APossessionA spinning top has the sameweight as a still one. The weightof the atom. These forces arewithin the nuclei of atoms.If the mass of block X is grea-ter than the force [of pull] of Y ,block X stays in place. . .it couldnot be moved. [The moving body]has still got some force inside.4 ALESSANDRO ASCARI et al.Table II. – Force Is An Agent expressions.Conceptualmetaphor sub-categoryFeynman expressions Students expressions(unsorted) The ﬁrst charge will feel a certainreaction force.There is not a force [acting] on theball. Gravity means the same forcepulls on diﬀerent objects.Force Is ACompulsionBecause of the action of a force,the velocity changes. The forcewhich controls, let us say, Jupiterin going around the sun.A force only starts the motion. Aforce is just changing the directionof motion.Force Is AResistanceIt is a question of electrical forcesagainst which we are working. Notangential force is needed to keepa planet in its orbit.A force has nothing to do with thespeed, it only has to keep the ballmoving.Table III. – Force Is A Medium expressions.Feynman expressions Students expressionsWe shall have to hold the pis-ton down by a certain force.The gas exerts a jittery force.That maximum speed isalways equal to the forceyou apply.Table IV. – Force Is A Path expressions.Conceptualmetaphor sub-categoryFeynman expressions Students expressionsForce Is ALineThe force in the vertical directiondue to gravity. The force isdirected along the line joining theplanet to the sun.The ball goes out in the directionof the resultant [of the forces].Force Is AConnectionThe true nature of the forcesbetween the atoms.noneTable V. – Force Is A Scale expressions.Feynman expressions Students expressionsThe force weakens as we go higher.The more massive a thing is, the stronger theforce required to produce a given acceleration.noneFROM NAIVE TO SCIENTIFIC UNDERSTANDING OF MOTION AND ITS CAUSES 5Table VI. – Force Is Balance expressions.Feynman expressions Students expressionsIf the force between them were not balanced.Talk only about excess forces.All the internal forces will balance out.noneBesides that, we also found some diﬀerences in the metaphorical expressions from thetwo sources.The Force Is A Product conceptual metaphor (table I) tells us that force couldbe “produced”. The possible “producers” in Feynman’s expressions are the basic inter-actions between objects, i.e. electrical and gravitational, while in students’ expressionsthe “producers” are speed and aspects of motion.In Force Is A Quantity metaphorical expressions (table I), Feynman only speaksabout the intensity of force, while in students’ language we ﬁnd expressions that arerelated to the concept of momentum or energy of a moving object.Finally, the metaphorical expressions of Force Is A Possession (table I) in Feyn-man are only about weight, while in laypersons we have expressions involving movingobjects, devices that produce movement (i.e. a cannon), and more abstract concepts aspower, inertia and velocity.Some metaphorical expressions found in Feynman are not present in students’ ex-pressions, but we think this could be due to the set of data chosen for this purpose. Weare almost sure that similar sentences could be found in students’ expressions if only wecould have a larger collection.The metaphorical sentences in lay language often involved the terms “speed” or“velocity”. In order to deepen our investigations we repeated the same analysis forthe sentences containing these two words.The conceptual metaphors we found are listed below.• Speed Is A Substance-like quantity◦ Speed Is A Possession◦ Speed Is A Quantity• Speed Is A Location◦ Speed Is A Level◦ Speed Is A Scale• Speed Is An Agent◦ Speed Is A Force◦ Speed Is A MakerTable VII collects the categorization of the metaphorical sentences found in both setsof data.All the expressions belonging to the two sources ﬁtted all these categories with onlyone exception. Metaphorical expressions belonging to Speed Is An Agent can only befound in students’ language.6 ALESSANDRO ASCARI et al.Table VII. – Speed and Velocity metaphors and metaphorical expressions.ConceptualmetaphorcategoryConceptualmetaphor sub-categoryFeynman expressions Students expressionsSpeed Is ASubstance-like quan-titySpeed Is APossessionMotion of a body. If she keptgoing with the same speed.The velocity of the fallingball.Its speed remains con-stant. Their speed getsgreater and greater. Bothshould have the samespeed.Speed Is AQuantity[. . .] if we increase the speedof the atoms.Its velocity keepsincreasing. The speed issmaller. A new speedbigger than the one ithad before.Speed Is ALocationSpeed Is ALevelAt what speed is the radius in-creasing She is going at thatspeed. Some car can get fromrest to 60 miles an hour.The ball must go at con-stant speed. They canreach a speed limit.Speed Is AScaleIt speeds up. The car wasslowing down. High speeds.It speeds up for a shortwhile. It slows down.Speed IsAn AgentSpeed Is AForcenone The force due to theair overcomes the ini-tial velocity. The forceof velocity.Speed Is AMakernone The speed creates aforce.4. – Results and conclusionsThis metaphor analysis is a powerful and sensible tool that allows us to investigate theconceptual structure that both scientists and students use to understand and to explainphenomena.The ﬁrst important result is that the metaphorical expressions coming from both layand expert language share the majority of the metaphors. This allows us to claim thatthere is continuity between the two kinds of language.We also revealed a metaphorical and conceptual mismatch involving velocity andspeed. In the analysis we discovered that Speed Is An Agent is a conceptual metaphoronly present in lay language (students). Therefore we could say that speed (and velocity)is perceived and conceptualized as an agent only by laypersons (students), while this isnot true for scientists and experts (Feynman, 1965).Another important result is that some aspects coming from the Force Dynamic Gestalttheory, such as quantity, quality, intensity (Fuchs, 2007) are present in the metaphoricalexpressions. Moreover they are not completely diﬀerentiated in lay language.The presence of continuity tells us that it is possible to teach starting from the knowl-edge pupils have already developed during their previous experience: we could use con-ceptual metaphor as a basis for developing a physics curriculum.FROM NAIVE TO SCIENTIFIC UNDERSTANDING OF MOTION AND ITS CAUSES 7Physics teachers should be aware of the conceptual metaphors and how they relateand overlap in order to create comprehension (i.e. conceptual integration networks). Inthis sense we could say that an education based on conceptual metaphors could helpstudents to be aware of them in order to understand and relate the aspects involved inthe interpretation of motion and its causes.In order to do so, further analysis should be done to reveal the logical connections andthe dependencies between concepts involved in the description of motion (momentum,energy). A reﬁned analysis should be done taking diﬀerent language sources, both oraland written.REFERENCES[1] DiSessa A. A., Cogn. Instruc., 10 (1993) 105.[2] Fauconnier G., Mental Spaces: Aspects of Meaning Construction in Natural Language(Cambridge University Press, Cambridge, UK) 1994.[3] Fauconnier G., Mappings in Thought and Language (Cambridge University Press,Cambridge, UK) 1997.[4] Fauconnier G. and Turner M., Cognitive Sci., 22 (1998) 133 DOI:10.1016/S0364-0213(99)80038-X.[5] Fauconnier G. and Turner M., The way we think (Basic Books, New York) 2002.[6] Feynman R. P., The Feynman Lectures on Physics, Vol. I (Addison Wesley) 1965; Am.J. Phys., 33 (1965) 750, DOI:10.1119/1.1972241.[7] Fuchs H. U., From Image Schemas to Dynamical Models in Fluids, Electricity, Heat,and Motion. An Essay on Physics Education Research (Winterthur, Switzerland) 2007.Retrieved from https://home.zhaw.ch/fuh/LITERATURE/Literature.html.[8] Halloun I. A. and Hestenes D., Am. J. Phys., 53 (1985) 1056 Doi:10.1119/1.14031.[9] Johnson M., The Body in the Mind (University of Chicago Press) 1990.[10] Lakoff G. and Johnson M., Metaphors We Live By (University of Chicago Press) 1980.[11] Lakoff G. and Johnson M., Philosophy in the ﬂesh: The embodied mind and its challengeto western thought (Basic Books) 1999.[12] Lakoff G. and Turner M., More Than Cool Reason: A Field Guide to Poetic Metaphor,(University of Chicago Press) 1989 Retrieved fromhttp://books.google.it/books?id=pz9TveJ5N5QC.[13] McCloskey M., Caramazza A. and Green B., Science (New York), 210 (1980) 1139DOI:10.1126/science.210.4474.1139.

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From naive to scientific understanding of motion and its causes

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