Skip to main content
SpringerLink
Log in

Could HPS Improve Problem-Solving?

  • Published:
Science & Education Aims and scope Submit manuscript

Abstract

It is generally accepted nowadays that History and Philosophy of Science (HPS) is useful in understanding scientific concepts, theories and even some experiments. Problem-solving strategies are a significant topic, since students’ careers depend on their skill to solve problems. These are the reasons for addressing the question of whether problem solving could be improved by means of HPS. Three typical problems in introductory courses of mechanics—the inclined plane, the simple pendulum and the Atwood machine—are taken as the object of the present study. The solving strategies of these problems in the eighteenth and nineteenth century constitute the historical component of the study. Its philosophical component stems from the foundations of mechanics research literature. The use of HPS leads us to see those problems in a different way. These different ways can be tested, for which experiments are proposed. The traditional solving strategies for the incline and pendulum problems are adequate for some situations but not in general. The recourse to apparent weights in the Atwood machine problem leads us to a new insight and a solving strategy for composed Atwood machines. Educational implications also concern the development of logical thinking by means of the variety of lines of thought provided by HPS.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Notes

  1. The incline, pendulum and Atwood machine problems are dealt with in a very similar way in contemporary textbooks (see for example Alonso and Finn 1992; Cutnell and Johnson 1992; Knudsen and Hjorth 1996; Daniel 1997; Young, Freedman and Sears 2004; Nolting 2005; Faughn et al. 2006; Fließbach 2007; Greiner 2008; Kuypers 2010). Hence, to take a problem from a textbook is not to make of it a particular problem.

  2. This equation is usually called ‘Newton’s second law’. However, it does not appear anywhere in Newton’s Principia (Newton 1972 [1726]). Moreover, Euler (1750) presented this equation as a new principle of mechanics. On the other hand, historians of science do not agree with each other concerning an equation for Newton’s second law (Maltese 1992, p. 26).

  3. Helmholtz (1911) had already pointed out that “nothing can be stated about force, which is not already known from acceleration” (“Man kann daher von der Kraft nichts aussagen, was man nicht bereits von der Beschleunigung weiss”) (Helmholtz 1911, p. 24). Bergmann and Schaefer (1998) also express a similar point of view: “acceleration is the only sign we have for force” (Bergmann and Schaefer 1998, p. 114).

  4. “From the point D draw DE parallel to AB, and take DE to represent the force of gravity; from E draw EF perpendicular to AC. Then the whole force DE is equivalent to the two DF, FE, of which FE is perpendicular to the plane, and consequently, is supported by the plane’s reaction (Art. 116); the other force DF, not being affected by the plane, is wholly employed in accelerating or retarding the motion of the body in the direction of the plane; therefore, the accelerating force: the force of gravity :: DF : DE :: ([…]) AB : AC” (Wood 1796, p. 147).

    Similar presentation of the problem can be found in Gravesande (1747, pp. 56–57), Rutherforth (1748, pp. 106–108), Rowning (1779, pp. 28–29), Helsham (1793, p. 148 et seq.), Adams (1794, pp. 154–157), Emerson (1800, p. 45 et seq.). Some authors show the connection between free falling and incline through the terminology: the accelerating force on the incline is called ‘relative gravity’ and the accelerating force in free falling ‘absolute gravity’ (see for example Desaguliers 1719, p. 21 and Adams 1794, p. 157).

  5. See for example Lodge (1885, p. 135) and Crew (1900, pp. 81–82). Lommel uses the common representation at that time as well as the currently common one. Using g′ for the acceleration on the incline, he writes \( g^{\prime} = g\frac{h}{l} = g\sin a \) (Lommel 1899, p. 33). In this form, these two equations can still be found nowadays (Bergmann and Schaefer 1998, p. 103).

  6. Kater and Lardner use the parallelogram of forces to deal with the incline problem (Kater and Lardner 1830, p. 93 et seq.); Avery (1885, p. 59) speaks of force and uses the same geometrical strategy as those who speak of acceleration; Lommel (1899, pp. 32–33) solves the incline problem as an application of the parallelogram of forces; Henderson and Woodhull (1901, pp. 81–83) presents two methods of solving the problem: virtual velocities and decomposition of weight. On incline experiments in textbooks, see Turner (2012).

  7. The connection between inclined plane and pendulum problems in textbooks of the early eighteenth century is addressed by Gauld (2004, pp. 322–330).

  8. “a Body acquires the same Velocity, in falling from a certain Height, whether it falls directly or comes down along an inclin’d Plane. But a Body may also run down along several Planes differently inclin’d, and even along a Curve ([…]) and the Celerity will be the same when the Height is equal” (Gravesande 1747, p. 86, § 393). In the case that a body runs down along several planes the following remark is made: “we must observe, that the passing from one Plane to another must be without a Shock, for by it the Velocity of the Body would be diminished” (Gravesande 1747, p. 86, § 394).

    Similar approaches can be found in Rutherforth (1748, pp. 117–125), Gibson (1755, pp. 54–59), Rowning (1779, pp. 43–44, see also p. 31), Helsham (1793, pp. 153–154, 161), Adams (1794, pp. 206–213), Emerson (1800, p. 45 et seq.), Kater and Lardner (1830, pp. 145–159).

  9. This equation is also similar to that of the incline. Authors presented the following sequence in justifying the pendulum: free falling, inclined plane and pendulum. In all these cases, height is what matters. Similar results based on the same approach or on a slightly different one can be found towards the end of the nineteenth century. The presentation of the results concerning the pendulum by equations represents the main difference between textbooks of this time and earlier ones (see for example Adams 1794; Kater and Lardner 1830; Lommel 1899; Henderson and Woodhull 1901).

  10. According to Dransfeld et al. (2001) the fact that the period of the pendulum is independent of the bob is only understandable if the equivalence principle holds (Dransfeld et al. 2001, p. 94). See also Fishbane et al. (1996, pp. 130–131) and Nolting (2005, p. 144).

  11. Poggendorff’s paper was also published in the Annalen der Physik und Chemie, 1854. Neither in this nor in the 1853 paper is there any picture of the apparatus described. Mach’s picture agrees with the description of the instrument given by Poggendorff (1854, pp. 181–182).

  12. Atwood’s machine was used to determine local acceleration. In order to achieve this goal, the acceleration of the bodies in the machine was determined. For this, the machine was equipped with a ruler and a clock. Later on, local acceleration was determined by other means and the machine appeared in a simplified form (Kater and Lardner 1830, plate to p. 104; Lodge 1885, p. 69). This was however not general in the nineteenth century (see Avery 1885, pp. 59–62).

  13. Bueche and Jerde, for instance, write: “The two masses […] are tied to opposite ends of a massless rope, and the rope is hung over a massless and frictionless pulley”. They explain: “We specify that the rope and pulley be massless so that we can neglect their inertias. Because the pulley is both massless and frictionless, the tension in the rope is the same on both sides of the pulley” (Bueche and Jerde 1995, p. 85). Serway and Jewett write: “In problems such as this in which the pulley is modeled as massless and frictionless, the tension in the string on both sides of the pulley is the same” (Serway and Jewett 2004, p. 129).

    The equality of tensions T 1 and T 2 can be justified by the apparent weights. In comparing Eqs. (12) and (13) with Eqs. (5) and (6), it follows that \( T_{1} = W^{\prime}_{m} \) and \( T_{2} = W^{\prime}_{M} \). Therefore, if \( W^{\prime}_{m} = W^{\prime}_{M} \), then \( T_{1} = T_{2} \).

  14. This is the most common definition of force (Planck 1916, p. 10; Westphall 1959, p. 7; Blatt 1989, p. 53; Knudsen and Hjorth 1996, p. 28; Nolting 2005, p. 109, among many others).

  15. See for example Galili and Bar (1992), Galili (1993, 1995, 2001), Bliss and Ogborn (1994), Hijs and Bosch (1995), Jammer (1997 [1961], 1999 [1957], 2001), Carson and Rowlands (2005), Roche (2005), Hecht (2006), Rowlands et al. (2007), Gönen 2008, Coelho (2010, 2012) and Kalman (2011a). Discussion on the concepts of mass and weight also appears in textbooks. See for instance French (1971), Kleppner and Kolenkow (1976), Hestenes (1987), Halliday et al. (1993), Ohanian (1994) and Greiner (2008).

  16.   "Quand on dit que la force est la cause d'un mouvement, on fait de la métaphysique, et cette définition, si on devait s'en contenter, serait absolument stérile. Pour qu'une définition puisse servir à quelque chose, il faut qu'elle nous apprenne à mesurer la force; cela suffit d'ailleurs, il n'est nullement nécessaire qu'elle nous apprenne ce que c'est que la force en soi, ni si elle est la cause ou l'effet du mouvement" (Poincaré 1897, p. 734). This passage also appears in Poincaré’s Science and Hypothesis (Poincaré 1952, p. 98).

  17. See for example Hodson (1992), Bailin (2002), Kalman (2002, 2011), Zemplén (2007), Doménech et al. (2007), Galili (2009), Malamitsa et al. (2009).

  18. In a very recent paper, Ha et al. (2012) pointed out the problem: “Most science senior-level teaching consists of transmitting de-contextualized abstract knowledge along with a ‘‘template’’ (solely numerical) problem-solving approach. Only one dominant interpretation of nature is presented, which comes from the instructor and the textbook” (Ha et al. 2012, p. 2).

References

  • Adams, G. (1794). Lectures on natural and experimental philosophy (Vol. III). London: Hindmarsh.

    Google Scholar 

  • Alonso, M., & Finn, E. J. (1992). Physics. Wokingham: Addison-Wesley.

    Google Scholar 

  • Atwood, G. (1784). A treatise on rectilinear motion and rotation of bodies: With description of original experiments relative to the subject. Cambridge: Merril and Deighton.

    Google Scholar 

  • Avery, E. M. (1885). Elements of natural philosophy. New York, Chicago: Sheldon and Company.

    Google Scholar 

  • Bailin, S. (2002). Critical thinking and science education. Science & Education, 11, 361–375.

    Article  Google Scholar 

  • Bergmann, L., & Schaefer, C. (1998). Lehrbuch der Experimentalphysik I: Mechanik, Akustik, Wärme (11th ed.). Berlin, New York: de Gruyter.

    Google Scholar 

  • Blatt, F. J. (1989). Principles of physics (3rd ed.). Boston, London: Allyn and Bacon.

    Google Scholar 

  • Bliss, J., & Ogborn, J. (1994). Force and motion from the beginning. Learning and Instruction, 4, 7–25.

    Article  Google Scholar 

  • Bueche, F. J., & Jerde, D. (1995). Principles of physics. New York: McGraw-Hill.

    Google Scholar 

  • Carson, R., & Rowlands, S. (2005). Mechanics as the logical point of entry for the enculturation into scientific thinking. Science & Education, 14, 473–493.

    Article  Google Scholar 

  • Coelho, R. L. (2010). On the concept of force: How understanding its history can improve physics teaching. Science & Education, 19, 91–113.

    Article  Google Scholar 

  • Coelho, R. L. (2011). Conceptual problems in the foundations of mechanics. Science & Education. doi:10.1007/s11191-010-9336-x.

  • Coelho, R. L. (2012). On the definition of mass in mechanics: Why is it so difficult? The Physics Teacher, 50, 304–306.

    Article  Google Scholar 

  • Crew, H. (1900). The elements of physics. New York, London: The Macmillan Compony.

    Google Scholar 

  • Cutnell, J. D., & Johnson, K. W. (1992). Physics. New York: Wiley.

    Google Scholar 

  • Daniel, H. (1997). Physik I: Mechanik, Wellen, Wärme. Berlin, New York: de Gruyter.

    Book  Google Scholar 

  • Desaguliers, J. T. (1719). Lectures of experimental philosophy. London: printed for W. Mears, B. Creake and J. Sackfield.

    Google Scholar 

  • Doménech, J. L., Gil-Pérez, D., Gras-Marti, A., Guisasola, J., Martínez-Torregrosa, J., Salinas, J., et al. (2007). Teaching energy issues: A debate proposal for a global reorientation. Science & Education, 16, 43–64.

    Article  Google Scholar 

  • Dransfeld, K., Kienle, P., & Kalvius, G. M. (2001). Physik I: Mechanik und Wärme (9th ed.). München: Oldenbourg.

    Google Scholar 

  • Emerson, W. (1800). The principles of mechanics. London: G.G. and J. Robinson.

    Google Scholar 

  • Euler, L. (1750 (1752)). Découverte d’un Nouveau Principe de Mecanique. Mémoires de l’académie des sciences de Berlin, 6, 185–217. Opera Omnia, serie II (Vol. 5, pp. 81–108).

  • Faughn, J., Serway, R., Vuille, C., & Bennett, C. (2006). Serway’s college physics. Belmont, CA: Thomson.

    Google Scholar 

  • Fishbane, P. M., Gasiorowicz, S., & Thornton, S. T. (1996). Physics for scientists and engineers. Upper Saddle River, NJ: Prentice Hall.

    Google Scholar 

  • Fließbach, T. (2007). Lehrbuch zur theoretischen Mechanik 1: Mechanik (5th ed.). Heidelberg, Berlin, Oxford: Spektrum Akademischer Verlag.

    Google Scholar 

  • French, A. P. (1971). Newtonian mechanics. New York, London: W. W. Norton.

    Google Scholar 

  • French, A. P. (1983). Is g really the acceleration due to gravity? The Physics Teacher, 21, 528–529.

    Article  Google Scholar 

  • Galili, I. (1993). Weight and gravity: Teachers’ ambiguity and students’ confusion about the concepts. International Journal of Science Education, 15, 149–162.

    Article  Google Scholar 

  • Galili, I. (1995). Interpretation of students’ understanding of the concept of weightlessness. Research in Science Education, 25, 51–74.

    Article  Google Scholar 

  • Galili, I. (2001). Weight versus gravitational force: Historical and educational perspectives. International Journal of Science Education, 23, 1073–1093.

    Article  Google Scholar 

  • Galili, I. (2009). Thought experiments: Determining their meaning. Science & Education, 18, 1–23.

    Article  Google Scholar 

  • Galili, I., & Bar, V. (1992). Motion implies force: Where to expect vestiges of the misconception? International Journal of Science Education, 14, 63–81.

    Article  Google Scholar 

  • Galili, I., & Sela, D. (2004). Pendulum activities in the Israeli physics curriculum: Used and missed opportunities. Science & Education, 13, 459–472.

    Article  Google Scholar 

  • Galili, I., & Tseitlin, M. (2010). Excurse to the history of weight concept: From Aristotle to Newton and then to Einstein (online: http://hipst.eled.auth.gr/hipst_docs/weight.pdf).

  • Gauld, C. (2004). The treatment of the motion of a simple pendulum in some early 18th century Newtonian textbooks. Science & Education, 13, 321–332.

    Article  Google Scholar 

  • Gibson, R. (1755). A course of experimental philosophy; being an introduction to the true philosophy of Sir Isaac Newton. Dublin: printed for R. Gibson and O. Nelson.

    Google Scholar 

  • Gönen, S. (2008). A study on student teachers’ misconceptions and scientifically acceptable conceptions about mass and gravity. Journal of Science Education and Technology, 17, 70–81.

    Article  Google Scholar 

  • Graneau, P., & Graneau, N. (2006). In the grip of the distant universe: The science of inertia. New Jersey: World Scientific.

    Book  Google Scholar 

  • Gravesande, J. W. (1747). Mathematical elements of natural philosophy confirm’d by experiments: or, an introduction to Sir Isaac Newton’s philosophy (Vol. 1, 6th ed.) (J. T. Desaguliers, Trans.). London: printed for W. Innys, T. Longman and T. Shewell.

  • Greiner, W. (2008). Klassische Mechanik I: Kinematik und Dynamik der Punktteilchen Relativität (8th ed.). Frankfurt am Main: Harry Deutsch.

    Google Scholar 

  • Ha, S., Lee, G., & Kalman, C. (2012). Workshop on friction: Understanding and addressing students’ difficulties in learning science through a hermeneutical perspective. Science & Education.doi:10.1007/s11191-012-9465-5.

  • Halliday, D., Resnick, R., & Walker, J. (1993). Fundamentals of physics (4th ed.). New York: Wiley.

    Google Scholar 

  • Hecht, E. (1994). Physics. Pacific Grove, CA: Brooks/Cole Publishing Company.

    Google Scholar 

  • Hecht, E. (2006). There is no really good definition of mass. The Physics Teacher, 44, 40–45.

    Article  Google Scholar 

  • Helmholtz, H. (1911). Vorlesungen über die Dynamik discreter Massenpunkte. Leipzig: J. A. Barth.

    Google Scholar 

  • Helsham, R. (1793). A course of lectures in natural philosophy (6th ed.). Dublin: Bryan Robinson.

    Google Scholar 

  • Henderson, C. H., & Woodhull, J. F. (1901). Elements of physics. New York: A Appleton and Company.

    Google Scholar 

  • Hestenes, D. (1987). New foundations for classical mechanics. Dordrecht, Boston, Lancaster: D. Reidel Pub. Co.

    Google Scholar 

  • Hijs, T., & Bosch, G. M. (1995). Cognitive effects of science experiments focusing on students’ preconceptions of force: A comparison of demonstrations and small-group praticals’. International Journal of Science Education, 17, 311–323.

    Article  Google Scholar 

  • Hodson, D. (1992). In search of a meaningful relationship: An exploration of some issues relating to integration in science and science education. International Journal of Science Education, 14(5), 541–566.

    Article  Google Scholar 

  • Höttecke, D., Henke, A., & Rieß, F. (2010). Implementing history and philosophy in science teaching: Strategies, methods, results and experiences from the European HIPST project. Science & Education. doi:10.1007/s11191-010-9330-3.

  • Jammer, M. (1997 [1961]). Concepts of mass: In classical and modern physics. Mineola, NY: Dover Publications.

  • Jammer, M. (1999 [1957]). Concepts of force: A study in the foundations of dynamics. Mineola, NY: Dover Publications.

  • Jammer, M. (2001). Concepts of mass in contemporary physics and philosophy. Princeton: Princeton University Press.

    Google Scholar 

  • Kalman, C. (2002). Developing critical thinking in undergraduate courses: A philosophical approach. Science & Education, 11, 83–94.

    Article  Google Scholar 

  • Kalman, C. (2011a). On the concept of force: A comment on lopes Coelho. Science & Education, 20, 67–69.

    Article  Google Scholar 

  • Kalman, C. (2011b). Enhancing students’ conceptual understanding by engaging science text with reflective writing as a hermeneutical circle. Science & Education, 20, 159–172.

    Article  Google Scholar 

  • Kater, H., & Lardner, D. (1830). Treatise on mechanics. London: Longman, Rees, Orme, Brown, and Green.

    Google Scholar 

  • Kleppner, D., & Kolenkow, R. J. (1976). An introduction to mechanics. Boston: McGraw Hill.

    Google Scholar 

  • Knudsen, J. M., & Hjorth, P. G. (1996). Elements of Newtonian mechanics (2nd ed.). Berlin: Springer.

    Book  Google Scholar 

  • Kuypers, F. (2010). Klassische Mechanik (9th ed.). Weinheim: Wiley-VCH.

    Google Scholar 

  • Lodge, O. (1885). Elementary mechanics, including hydrostatic and pneumatics (revised ed.). London and Edinburgh: Chambers.

  • Lommel, E. (1899). Experimental physics (G. W. Myers, Trans.). London: Kegan Paul, Trench, Trübner & Co.

  • Mach, E. (1902). The science of mechanics: A critical and historical account of its development (2nd ed.) (T. J. McCormack, Trans.). Chicago: The Open Court Publishing Company.

  • Malamitsa, K., Kasoutas, M., & Kokkotas, P. (2009). Developing Greek primary school students’ critical thinking through an approach of science teaching which incorporates aspects of history of science. Science & Education, 18, 457–468.

    Article  Google Scholar 

  • Maltese, G. (1992). La Storia di F = ma: la seconda legge del moto nel XVIII secolo. Firenze: Leo S. Olschki.

    Google Scholar 

  • Matthews, M. R. (2009). Teaching the philosophical and worldviews components of science. Science & Education, 18, 697–728.

    Article  Google Scholar 

  • Matthews, M. R., Gauld, C. F., & Stinner, A. (2005). The pendulum: Scientific, historical, philosophical and educational perspectives. Dordrecht: Springer.

    Google Scholar 

  • Newburgh, R. (2004). The pendulum: A paradigm for the linear oscillator. Science & Education, 13, 297–307.

    Article  Google Scholar 

  • Newburgh, R., Peidle, J., & Rueckner, W. (2004). When equal masses don’t balance. Physics Education, 39(3), 289–293.

    Article  Google Scholar 

  • Newton, I. (1972 [1726]). Isaac Newton’s Philosophiae Naturalis Principia Mathematica (3rd ed.). In A. Koyré & I. B. Cohen (Eds.). Harvard: Harvard University Press.

  • Nolting, W. (2005). Grundkurs: Theoretische Physik 1: Klassische Mechanik (7th ed.). Braunschweig, Wiesbaden: Vieweg.

    Google Scholar 

  • Ohanian, H. C. (1994). Principles of physics. New York, London: W. W. Norton and Company.

    Google Scholar 

  • Planck, M. (1916). Einführung in die Allgemeine Mechanik. Leipzig: S. Hirzel.

    Google Scholar 

  • Poggendorff, J. C. (1853). Abänderung der Fallmaschine. Monatsberichte der Königlichen Akademie der Wissenschaften zu Berlin (pp. 627–629).

  • Poggendorff, J. C. (1854). Über eine Abänderung der Fallmaschine. Annalen der Physik und Chemie, 168, 179–182.

    Google Scholar 

  • Poincaré, H. (1897). Les Idées de Hertz sur la Mécanique. Revue Générale des Sciences, 8, 734–743.

    Google Scholar 

  • Poincaré, H. (1952 [1905]). Science and hypothesis. New York: Dover.

  • Roche, J. (2005). What is mass? European Journal of Physics, 26, 225–242.

    Article  Google Scholar 

  • Rowlands, S., Graham, T., Berry, J., & McWilliam, P. (2007). Conceptual changes through the lens of Newtonian mechanics. Science & Education, 16, 21–42.

    Article  Google Scholar 

  • Rowning, J. (1779). A compendious system of natural philosophy. London: John, Francis, and Ch. Rivington.

  • Rutherforth, T. (1748). A system of natural philosophy being a course of lectures in mechanics, optics, hydrostatics, and astronomy (Vol. 1). Cambridge: J. Bentham, for W. Thurlbourn.

  • Serway, R., & Jewett, J. W. (2004). Physics for scientists and engineers (6th ed.). Belmont, CA: Thomson.

    Google Scholar 

  • Strauch, D. (2009). Classical mechanics: An introduction. Berlin: Springer.

    Book  Google Scholar 

  • Tipler, P. (1991). Physics for scientists and engineers (3rd ed.). New York: Worth Publishers.

    Google Scholar 

  • Turner, S. C. (2012). Changing images of the inclined plane: A case study of a revolution in American science education. Science & Education, 21, 245–270.

    Google Scholar 

  • Westphall, W. H. (1959). Physik (20th ed.). Berlin, Heidelberg, New York: Springer.

    Google Scholar 

  • Wood, J. (1796). The principles of mechanics: Designed for the use of students in the university. Cambridge: J. Burges.

  • Young, H. D., Freedman, R. A., & Sears, F. (2004). Sears and Zemansky’s University Physics (11th ed.). San Francisco: P. Addison-Wesley.

    Google Scholar 

  • Zemplén, G. (2007). Conflicting agendas: Critical thinking versus science education in the international baccalaureate theory of knowledge course. Science & Education, 16, 167–196.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Sciences, University of Lisbon, Campo Grande C4, 1749-016, Lisbon, Portugal

    Ricardo Lopes Coelho

Authors
  1. Ricardo Lopes Coelho
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ricardo Lopes Coelho.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Coelho, R.L. Could HPS Improve Problem-Solving?. Sci & Educ 22, 1043–1068 (2013). https://doi.org/10.1007/s11191-012-9521-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11191-012-9521-1

Keywords

Search

Navigation